This paper presents a novel method for tuning PID controllers based on process step response and a damping optimum criterion. The method identifies parameters of an nth order lag (PTn) process model from the step response. This facilitates algebraic rules for adjusting closed-loop response speed and damping. The effectiveness of the proposed PTn parameter estimation and PID tuning is verified through simulations. The method provides a straightforward way to tune both closed-loop response damping and speed in relation to process dynamics for higher-order aperiodic processes.
This document proposes a new one-step method for tuning PI/PID controllers based on closed-loop experiments. It derives simple correlations between data from a proportional-only closed-loop step response experiment and PI/PID settings that provide good performance and robustness. Specifically:
1) A proportional-only controller is used to generate a step response with 10-60% overshoot. The gain, overshoot, peak time, and steady-state change are recorded.
2) Simulations show the proposed controller gain is proportional to the proportional gain used in the experiment, with the ratio dependent only on overshoot. Simple equations are derived relating overshoot and peak time to the PI/PID settings.
3
Design of a new PID controller using predictive functional control optimizati...ISA Interchange
An improved proportional integral derivative (PID) controller based on predictive functional control (PFC) is proposed and tested on the chamber pressure in an industrial coke furnace. The proposed design is motivated by the fact that PID controllers for industrial processes with time delay may not achieve the desired control performance because of the unavoidable model/plant mismatches, while model predictive control (MPC) is suitable for such situations. In this paper, PID control and PFC algorithm are combined to form a new PID controller that has the basic characteristic of PFC algorithm and at the same time, the simple structure of traditional PID controller. The proposed controller was tested in terms of set-point tracking and disturbance rejection, where the obtained results showed that the proposed controller had the better ensemble performance compared with traditional PID controllers.
The document describes a new closed-loop PID tuning method developed by M. Shamssuzzoha. The method overcomes limitations of existing tuning approaches like Ziegler-Nichols. It involves performing a closed-loop step test using a proportional controller, and derives simple correlations to determine PI/PID settings based on overshoot and time to first peak observed. Simulation results show the method gives consistently better performance and robustness for a variety of stable and integrating processes compared to other published methods.
Controller Tuning for Integrator Plus Delay Processes.theijes
A design method for PID controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. Analytical expressions for PID controllers are derived for several common types of process models, including first order and second-order plus time delay models and an integrator plus time delay model. Here in this paper, a simple controller design rule and tuning procedure for unstable processes with delay time is discussed. Simulation examples are included to show the effectiveness of the proposed method
A novel auto-tuning method for fractional order PID controllersISA Interchange
Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.
MODEL BASED ANALYSIS OF TEMPERATURE PROCESS UNDER VARIOUS CONTROL STRATEGIES ...Journal For Research
This paper analyze the temperature process in an empirical model. From the empirical model the system behavior is determined by transfer function and the basic controller strategies Ziegler-Nichols & Cohen-Coon method are implemented in it. With these tuning methods the best control strategies are obtained at the final stage by interfacing the system with NI-myRIO kit.
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...IOSR Journals
The document summarizes a study on model-based controller design for a first-order plus time delay (FOPTD) system. The study identifies the process model of a level control system using process reaction curve methods. Various tuning rules for internal model control-proportional integral derivative (IMC-PID) controllers from literature are applied to the system, including rules from Rivera, Chien, Lee, Skogestad, and Panda. The performance of each controller is evaluated based on rise time, settling time, percentage overshoot, integral absolute error, and integral of time multiplied absolute error. The study finds that the Panda tuning rule has the smallest percentage overshoot and integral absolute error, while the Chien rule has
This document proposes a two-level optimization method for tuning PID controllers to account for nonlinear system behavior. The first level uses classical tuning guidelines to determine bounds on PID parameters. The second level solves an optimization problem to determine PID parameters that minimize the difference between the closed-loop response of a designed nonlinear controller and the PID controller, subject to constraints based on the first level bounds. The method is demonstrated on a nonlinear chemical reactor example. In summary, the method tunes PID controllers to better emulate the performance of a designed nonlinear controller while respecting constraints from classical linear tuning methods.
This document proposes a new one-step method for tuning PI/PID controllers based on closed-loop experiments. It derives simple correlations between data from a proportional-only closed-loop step response experiment and PI/PID settings that provide good performance and robustness. Specifically:
1) A proportional-only controller is used to generate a step response with 10-60% overshoot. The gain, overshoot, peak time, and steady-state change are recorded.
2) Simulations show the proposed controller gain is proportional to the proportional gain used in the experiment, with the ratio dependent only on overshoot. Simple equations are derived relating overshoot and peak time to the PI/PID settings.
3
Design of a new PID controller using predictive functional control optimizati...ISA Interchange
An improved proportional integral derivative (PID) controller based on predictive functional control (PFC) is proposed and tested on the chamber pressure in an industrial coke furnace. The proposed design is motivated by the fact that PID controllers for industrial processes with time delay may not achieve the desired control performance because of the unavoidable model/plant mismatches, while model predictive control (MPC) is suitable for such situations. In this paper, PID control and PFC algorithm are combined to form a new PID controller that has the basic characteristic of PFC algorithm and at the same time, the simple structure of traditional PID controller. The proposed controller was tested in terms of set-point tracking and disturbance rejection, where the obtained results showed that the proposed controller had the better ensemble performance compared with traditional PID controllers.
The document describes a new closed-loop PID tuning method developed by M. Shamssuzzoha. The method overcomes limitations of existing tuning approaches like Ziegler-Nichols. It involves performing a closed-loop step test using a proportional controller, and derives simple correlations to determine PI/PID settings based on overshoot and time to first peak observed. Simulation results show the method gives consistently better performance and robustness for a variety of stable and integrating processes compared to other published methods.
Controller Tuning for Integrator Plus Delay Processes.theijes
A design method for PID controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. Analytical expressions for PID controllers are derived for several common types of process models, including first order and second-order plus time delay models and an integrator plus time delay model. Here in this paper, a simple controller design rule and tuning procedure for unstable processes with delay time is discussed. Simulation examples are included to show the effectiveness of the proposed method
A novel auto-tuning method for fractional order PID controllersISA Interchange
Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.
MODEL BASED ANALYSIS OF TEMPERATURE PROCESS UNDER VARIOUS CONTROL STRATEGIES ...Journal For Research
This paper analyze the temperature process in an empirical model. From the empirical model the system behavior is determined by transfer function and the basic controller strategies Ziegler-Nichols & Cohen-Coon method are implemented in it. With these tuning methods the best control strategies are obtained at the final stage by interfacing the system with NI-myRIO kit.
Model-based Approach of Controller Design for a FOPTD System and its Real Tim...IOSR Journals
The document summarizes a study on model-based controller design for a first-order plus time delay (FOPTD) system. The study identifies the process model of a level control system using process reaction curve methods. Various tuning rules for internal model control-proportional integral derivative (IMC-PID) controllers from literature are applied to the system, including rules from Rivera, Chien, Lee, Skogestad, and Panda. The performance of each controller is evaluated based on rise time, settling time, percentage overshoot, integral absolute error, and integral of time multiplied absolute error. The study finds that the Panda tuning rule has the smallest percentage overshoot and integral absolute error, while the Chien rule has
This document proposes a two-level optimization method for tuning PID controllers to account for nonlinear system behavior. The first level uses classical tuning guidelines to determine bounds on PID parameters. The second level solves an optimization problem to determine PID parameters that minimize the difference between the closed-loop response of a designed nonlinear controller and the PID controller, subject to constraints based on the first level bounds. The method is demonstrated on a nonlinear chemical reactor example. In summary, the method tunes PID controllers to better emulate the performance of a designed nonlinear controller while respecting constraints from classical linear tuning methods.
Tuning of IMC-based PID controllers for integrating systems with time delayISA Interchange
Design of Proportional Integral and Derivative (PID) controllers based on IMC principles for various types of integrating systems with time delay is proposed. PID parameters are given in terms of process model parameters and a tuning parameter. The tuning parameter is IMC filter time constant. In the present work, the IMC filter (Q) is chosen in such a manner that the order of the denominator of IMC controller is one less than the order of the numerator. The IMC filter time constant (λ) is tuned in such a way that a good compromise is made between performance and robustness for both servo and regulatory problems. To improve servo response of the controller a set point filter is designed such that the closed loop response is similar to that of first order plus time delay system. The proposed controller design method is applied to various transfer function models and to the non-linear model equations of jacketed CSTR to demonstrate its applicability and effectiveness. The performance of the proposed controller is compared with the recently reported methods in terms of IAE and ITAE. The smooth functioning of the controller is determined in terms of total variation and compared with recently reported methods. Simulation studies are carried out on various integrating systems with time delay to show the effectiveness and superiority of the proposed controllers.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijics
In this paper first we investigate optimal PID control of a double integrating plus delay process and compare with the SIMC rules. What makes the double integrating process special is that derivative action is actually necessary for stabilization. In control, there is generally a trade-off between performance and
robustness, so there does not exist a single optimal controller. However, for a given robustness level (here defined in terms of the Ms-value) we can find the optimal controller which minimizes the performance J (here defined as the integrated absolute error (IAE)-value for disturbances). Interestingly, the SIMC PID controller is almost identical to the optimal pid controller. This can be seen by comparing the paretooptimal
curve for J as a function of Ms, with the curve found by varying the SIMC tuning parameter Tc.
Second, design of Proportional Integral and Derivative (PID) controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. The performances of the proposed controllers are compared with the
controllers designed by recently reported methods. The robustness of the proposed controllers for the uncertainty in model parameters is evaluated considering one parameter at a time using Kharitonov’s theorem. The proposed controllers are applied to various transfer function models and to non linear model of isothermal continuous copolymerization of styrene-acrylonitrile in CSTR. An experimental set up of tank
with the outlet connected to a pump is considered for implementation of the PID controllers designed by
the three proposed methods to show the effectiveness of the methods.
Tuning of PID controllers for integrating systems using direct synthesis methodISA Interchange
A PID controller is designed for various forms of integrating systems with time delay using direct synthesis method. The method is based on comparing the characteristic equation of the integrating system and PID controller with a filter with the desired characteristic equation. The desired characteristic equation comprises of multiple poles which are placed at the same desired location. The tuning parameter is adjusted so as to achieve the desired robustness. Tuning rules in terms of process parameters are given for various forms of integrating systems. The tuning parameter can be selected for the desired robustness by specifying Ms value. The proposed controller design method is applied to various transfer function models and to the nonlinear model equations of jacketed CSTR to show its effectiveness and applicability.
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...ISA Interchange
In this paper we present a new method for tuning PI controllers with symmetric send-on-delta (SSOD) sampling strategy. First we analyze the conditions that produce oscillations in event based systems considering SSOD sampling strategy. The Describing Function is the tool used to address the problem. Once the conditions for oscillations are established, a new robustness to oscillation performance measure is introduced which entails with the concept of phase margin, one of the most traditional measures of relative stability in closed-loop control systems. Therefore, the application of the proposed robustness measure is easy and intuitive. The method is tested by both simulations and experiments. Additionally, a Java application has been developed to aid in the design according to the results presented in the paper.
PSO based NNIMC for a Conical Tank Level ProcessIRJET Journal
1) The document presents a study on modeling and control of a conical tank level process, which is a non-linear, time-varying system.
2) A mathematical model is developed for the conical tank and the process is divided into three linear regions. A conventional PI controller is designed for each region using Ziegler-Nichols tuning.
3) To overcome the limitations of the PI controller for the non-linear system, a PSO-based neural network internal model controller (NNIMC) is designed. Simulation results show that the PSO-based NNIMC provides better performance than the NNIMC and PI controller in terms of errors and settling time.
A simple nonlinear PD controller for integrating processesISA Interchange
Many industrial processes are found to be integrating in nature, for which widely used Ziegler–Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (eN) and change of error (ΔeN) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.
An optimal PID controller via LQR for standard second order plus time delay s...ISA Interchange
An improved tuning methodology of PID controller for standard second order plus time delay systems (SOPTD) is developed using the approach of Linear Quadratic Regulator (LQR) and pole placement technique to obtain the desired performance measures. The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation. The effectiveness of the proposed methodology has been demonstrated via simulation of stable open loop oscillatory, over damped, critical damped and unstable open loop systems. Results show improved closed loop time response over the existing LQR based PI/PID tuning methods with less control effort. The effect of non-dominant pole on the stability and robustness of the controller has also been discussed.
Closed-loop step response for tuning PID fractional-order filter controllersISA Interchange
Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the frac- tional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled.
Disturbance Rejection with a Highly Oscillating Second-Order Process, Part I...Scientific Review SR
This research paper aims at investigating disturbance rejection associated with a highly oscillating
second-order process. The PD-PI controller having three parameters are tuned to provide efficient rejection of a
step input disturbance input. Controller tuning based on using MATLAB control and optimization toolboxes.
Using the suggested tuning technique, it is possible to reduce the maximum time response of the closed loop
control system to as low as 0.0095 and obtain time response to the disturbance input having zero settling time.
The effect of the proportional gain of the PD-PI controller on the control system dynamics is investigated for a
gain ≤ 100. The performance of the control system during disturbance rejection using the PD -PI controller is
compared with that using a second-order compensator. The PD-PI controller is superior in dealing with the
disturbance rejection associated with the highly oscillating second-order process
This document provides summaries of several appendices related to PID tuning and control. Appendix A offers a short cut tuning method that can identify process dynamics and tune a controller in about five dead times. It reduces open loop test time by over 80% for processes with large time constants. Appendix B provides a PID checklist to help utilize full PID capabilities and ensure parameters are correctly set. Appendix C derives equations to understand the effects of dynamics and tuning on performance. It provides a guide to change plant dynamics and tuning to achieve objectives.
This document proposes a fuzzy logic and neural network-based method for identifying the temperature condition of aircraft gas turbine engines. At early stages of operation when data is limited and uncertain, fuzzy logic and neural networks can be used to create an initial model of the engine's condition. As more normal distribution data is collected over 60-120 measurements, mathematical statistics methods are applied, including analyzing parameters within calculated fuzzy admissible and possible ranges. The method also identifies linear regression models for the engine's initial and actual conditions and compares them to monitor changes using fuzzy correlation and regression analysis. This combined fuzzy-statistical approach allows improved gas turbine engine condition monitoring and diagnostics.
Design of a model reference adaptive PID control algorithm for a tank system IJECEIAES
This paper describes the design of an adaptive controller based on model reference adaptive PID control (MRAPIDC) to stabilize a two-tank process when large variations of parameters and external disturbances affect the closed-loop system. To achieve that, an innovative structure of the adaptive PID controller is defined, an additional PI is designed to make sure that the reference model produces stable output signals and three adaptive gains are included to guarantee stability and robustness of the closed-loop system. Then, the performance of the model reference adaptive PID controller on the behaviour of the closed-loop system is compared to a PI controller designed on MATLAB when both closed-loop systems are under various conditions. The results demonstrate that the MRAPIDC performs significantly better than the conventional PI controller.
Optimised control using Proportional-Integral-Derivative controller tuned usi...IJECEIAES
Time delays are generally unavoidable in the designing frameworks for mechanical and electrical systems and so on. In both continuous and discrete schemes, the existence of delay creates undesirable impacts on the underthought which forces exacting constraints on attainable execution. The presence of delay confounds the design structure procedure also. It makes continuous systems boundless dimensional and also extends the readings in discrete systems fundamentally. As the Proportional-IntegralDerivative (PID) controller based on internal model control is essential and strong to address the vulnerabilities and aggravations of the model. But for an real industry process, they are less susceptible to noise than the PID controller.It results in just one tuning parameter which is the time constant of the closed-loop system λ, the internal model control filter factor. It additionally gives a decent answer for the procedure with huge time delays. The design of the PID controller based on the internal model control, with approximation of time delay using Pade’ and Taylor’s series is depicted in this paper. The first order filter used in the design provides good set-point tracking along with disturbance rejection.
Validation of Design Parameters of Radiator using Computational ToolIRJET Journal
This document discusses the validation of design parameters for automobile radiators using computational tools. It presents two case studies where the thermal performance of radiators is analyzed using the log mean temperature difference (LMTD) and number of transfer units (NTU) methods and the results are compared to those from a computational software tool (HXCombine). The results show good agreement between the manual calculations and software outputs, validating the use of computational tools for radiator design. Parameters like heat transfer rate, outlet temperatures, effectiveness and heat transfer area are compared for both case studies. This research demonstrates that computational tools can accurately analyze and design radiator performance.
This document summarizes research on tuning an I-PD controller to control a highly oscillating second-order industrial process. The process has an 85.45% maximum overshoot and 8 second settling time. An I-PD controller is tuned using MATLAB optimization to minimize the integral of the squared error. The tuned controller completely cancels the overshoot and decreases the settling time to 1.46 seconds without undershoot, demonstrating improved performance over standard tuning techniques for controlling highly oscillating processes.
Distributed Control System Applied in Temperatur Control by Coordinating Mult...TELKOMNIKA JOURNAL
In Distributed Control System (DCS), multitasking management has been important issues
continuously researched and developed. In this paper, DCS was applied in global temperature control
system by coordinating three Local Control Units (LCUs). To design LCU’s controller parameters, both
analytical and experimental method were employed. In analytical method, the plants were firstly identified
to get their transfer functions which were then used to derive control parameters based on desired
response qualities. The experimental method (Ziegler-Nichols) was also applied due to practicable reason
in real industrial plant (less mathematical analysis). To manage set-points distributed to all LCUs, master
controller was subsequently designed based on zone of both error and set-point of global temperature
controller. Confirmation experiments showed that when using control parameters from analytical method,
the global temperature response could successfully follow the distributed set-points with 0% overshoot,
193.92 second rise time, and 266.88 second settling time. While using control parameters from
experimental method, it could also follow the distributed set-points with presence of overshoot (16.9%), but
has less rise time and settling time (111.36 and 138.72 second). In this research, the overshoot could be
successfully decreased from 16.9 to 9.39 % by changing master control rule. This proposed method can
be potentially applied in real industrial plant due to its simplicity in master control algorithm and presence
of PID controller which has been generally included in today industrial equipments.
The document discusses using the PIDE instruction in RSLogix 5000 to implement common process control algorithms like adaptive gains, cascade control, ratio control, and multiloop selection. It explains that the PIDE instruction uses a velocity-form PID algorithm, which makes it easier to implement advanced applications compared to traditional positional-form algorithms. The velocity-form algorithm works on the change in error rather than the error directly, allowing features like adaptive gains to be changed without impacting the control output. The document provides details on how to use the PIDE instruction, including the independent and dependent gains forms.
Optimisation problems and methods in Chemical Engineering: a personal surveyEric Fraga
The document is a personal survey by Eric S Fraga of optimisation problems and methods used in chemical engineering over the past 20 years. It covers topics such as process synthesis, heat integration, carbon capture, and power generation. For each topic, it discusses mathematical models used to represent the systems, optimisation approaches applied, and examples of applications and results. The presentation aims to provide an overview of the wide range of problems addressed and methods developed and implemented, from off-the-shelf software to custom programs for specific applications.
Jest wiele wewnętrznych i zewnętrznych sił, które kształtują twoich pracowników. Jeśli pozostawisz grupę pracowników o wysokim potencjale rozwojowym bez nadzoru jej skład i jakość zmienią się samoczynnie i staną się niespójne z potrzebami organizacji.
Modeling supply and return line dynamics for an electrohydraulic actuation sy...ISA Interchange
This document presents a model of an electrohydraulic fatigue testing system that focuses on components upstream of the servovalve and actuator, including the supply and return lines. The model allows prediction of pressure fluctuations in these lines in the time domain using a modular approach. Experiments showed significant pressure fluctuations at the servovalve ports due to supply and return line dynamics. The model was then used to evaluate potential design changes to improve system bandwidth by reducing pressure dynamics from flexible hoses.
11.7 yrs of exp in testing (manual and automation)Vijaya Kumar R
Vijaya Kumar has over 10 years of experience in manual testing and 1.5 years of experience in automation testing using Selenium. He has worked as a Senior Quality Lead, Consultant, QA Engineer, and QA System Analyst for various companies in roles involving manual testing of web, mobile, and desktop applications. His technical skills include Java, Selenium, SoapUI, SQL, and defect tracking tools like JIRA and Quality Center. He aims to use his technology expertise to align IT goals with business objectives.
El documento propone incrementar la jornada laboral de los profesores de educación secundaria de 28 a 30 horas semanales. Esto se basa en una ley de reforma magisterial que permite incrementar la jornada en dos horas cada dos años hasta un máximo de 30 horas. El incremento se usará para actividades de refuerzo educativo, atención a familias y otras tareas determinadas por los directores para mejorar los aprendizajes de los estudiantes.
Tuning of IMC-based PID controllers for integrating systems with time delayISA Interchange
Design of Proportional Integral and Derivative (PID) controllers based on IMC principles for various types of integrating systems with time delay is proposed. PID parameters are given in terms of process model parameters and a tuning parameter. The tuning parameter is IMC filter time constant. In the present work, the IMC filter (Q) is chosen in such a manner that the order of the denominator of IMC controller is one less than the order of the numerator. The IMC filter time constant (λ) is tuned in such a way that a good compromise is made between performance and robustness for both servo and regulatory problems. To improve servo response of the controller a set point filter is designed such that the closed loop response is similar to that of first order plus time delay system. The proposed controller design method is applied to various transfer function models and to the non-linear model equations of jacketed CSTR to demonstrate its applicability and effectiveness. The performance of the proposed controller is compared with the recently reported methods in terms of IAE and ITAE. The smooth functioning of the controller is determined in terms of total variation and compared with recently reported methods. Simulation studies are carried out on various integrating systems with time delay to show the effectiveness and superiority of the proposed controllers.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijics
In this paper first we investigate optimal PID control of a double integrating plus delay process and compare with the SIMC rules. What makes the double integrating process special is that derivative action is actually necessary for stabilization. In control, there is generally a trade-off between performance and
robustness, so there does not exist a single optimal controller. However, for a given robustness level (here defined in terms of the Ms-value) we can find the optimal controller which minimizes the performance J (here defined as the integrated absolute error (IAE)-value for disturbances). Interestingly, the SIMC PID controller is almost identical to the optimal pid controller. This can be seen by comparing the paretooptimal
curve for J as a function of Ms, with the curve found by varying the SIMC tuning parameter Tc.
Second, design of Proportional Integral and Derivative (PID) controllers based on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) method for pure integrating process with time delay is proposed. The performances of the proposed controllers are compared with the
controllers designed by recently reported methods. The robustness of the proposed controllers for the uncertainty in model parameters is evaluated considering one parameter at a time using Kharitonov’s theorem. The proposed controllers are applied to various transfer function models and to non linear model of isothermal continuous copolymerization of styrene-acrylonitrile in CSTR. An experimental set up of tank
with the outlet connected to a pump is considered for implementation of the PID controllers designed by
the three proposed methods to show the effectiveness of the methods.
Tuning of PID controllers for integrating systems using direct synthesis methodISA Interchange
A PID controller is designed for various forms of integrating systems with time delay using direct synthesis method. The method is based on comparing the characteristic equation of the integrating system and PID controller with a filter with the desired characteristic equation. The desired characteristic equation comprises of multiple poles which are placed at the same desired location. The tuning parameter is adjusted so as to achieve the desired robustness. Tuning rules in terms of process parameters are given for various forms of integrating systems. The tuning parameter can be selected for the desired robustness by specifying Ms value. The proposed controller design method is applied to various transfer function models and to the nonlinear model equations of jacketed CSTR to show its effectiveness and applicability.
New Method for Tuning PID Controllers Using a Symmetric Send-On-Delta Samplin...ISA Interchange
In this paper we present a new method for tuning PI controllers with symmetric send-on-delta (SSOD) sampling strategy. First we analyze the conditions that produce oscillations in event based systems considering SSOD sampling strategy. The Describing Function is the tool used to address the problem. Once the conditions for oscillations are established, a new robustness to oscillation performance measure is introduced which entails with the concept of phase margin, one of the most traditional measures of relative stability in closed-loop control systems. Therefore, the application of the proposed robustness measure is easy and intuitive. The method is tested by both simulations and experiments. Additionally, a Java application has been developed to aid in the design according to the results presented in the paper.
PSO based NNIMC for a Conical Tank Level ProcessIRJET Journal
1) The document presents a study on modeling and control of a conical tank level process, which is a non-linear, time-varying system.
2) A mathematical model is developed for the conical tank and the process is divided into three linear regions. A conventional PI controller is designed for each region using Ziegler-Nichols tuning.
3) To overcome the limitations of the PI controller for the non-linear system, a PSO-based neural network internal model controller (NNIMC) is designed. Simulation results show that the PSO-based NNIMC provides better performance than the NNIMC and PI controller in terms of errors and settling time.
A simple nonlinear PD controller for integrating processesISA Interchange
Many industrial processes are found to be integrating in nature, for which widely used Ziegler–Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (eN) and change of error (ΔeN) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.
An optimal PID controller via LQR for standard second order plus time delay s...ISA Interchange
An improved tuning methodology of PID controller for standard second order plus time delay systems (SOPTD) is developed using the approach of Linear Quadratic Regulator (LQR) and pole placement technique to obtain the desired performance measures. The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation. The effectiveness of the proposed methodology has been demonstrated via simulation of stable open loop oscillatory, over damped, critical damped and unstable open loop systems. Results show improved closed loop time response over the existing LQR based PI/PID tuning methods with less control effort. The effect of non-dominant pole on the stability and robustness of the controller has also been discussed.
Closed-loop step response for tuning PID fractional-order filter controllersISA Interchange
Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the frac- tional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled.
Disturbance Rejection with a Highly Oscillating Second-Order Process, Part I...Scientific Review SR
This research paper aims at investigating disturbance rejection associated with a highly oscillating
second-order process. The PD-PI controller having three parameters are tuned to provide efficient rejection of a
step input disturbance input. Controller tuning based on using MATLAB control and optimization toolboxes.
Using the suggested tuning technique, it is possible to reduce the maximum time response of the closed loop
control system to as low as 0.0095 and obtain time response to the disturbance input having zero settling time.
The effect of the proportional gain of the PD-PI controller on the control system dynamics is investigated for a
gain ≤ 100. The performance of the control system during disturbance rejection using the PD -PI controller is
compared with that using a second-order compensator. The PD-PI controller is superior in dealing with the
disturbance rejection associated with the highly oscillating second-order process
This document provides summaries of several appendices related to PID tuning and control. Appendix A offers a short cut tuning method that can identify process dynamics and tune a controller in about five dead times. It reduces open loop test time by over 80% for processes with large time constants. Appendix B provides a PID checklist to help utilize full PID capabilities and ensure parameters are correctly set. Appendix C derives equations to understand the effects of dynamics and tuning on performance. It provides a guide to change plant dynamics and tuning to achieve objectives.
This document proposes a fuzzy logic and neural network-based method for identifying the temperature condition of aircraft gas turbine engines. At early stages of operation when data is limited and uncertain, fuzzy logic and neural networks can be used to create an initial model of the engine's condition. As more normal distribution data is collected over 60-120 measurements, mathematical statistics methods are applied, including analyzing parameters within calculated fuzzy admissible and possible ranges. The method also identifies linear regression models for the engine's initial and actual conditions and compares them to monitor changes using fuzzy correlation and regression analysis. This combined fuzzy-statistical approach allows improved gas turbine engine condition monitoring and diagnostics.
Design of a model reference adaptive PID control algorithm for a tank system IJECEIAES
This paper describes the design of an adaptive controller based on model reference adaptive PID control (MRAPIDC) to stabilize a two-tank process when large variations of parameters and external disturbances affect the closed-loop system. To achieve that, an innovative structure of the adaptive PID controller is defined, an additional PI is designed to make sure that the reference model produces stable output signals and three adaptive gains are included to guarantee stability and robustness of the closed-loop system. Then, the performance of the model reference adaptive PID controller on the behaviour of the closed-loop system is compared to a PI controller designed on MATLAB when both closed-loop systems are under various conditions. The results demonstrate that the MRAPIDC performs significantly better than the conventional PI controller.
Optimised control using Proportional-Integral-Derivative controller tuned usi...IJECEIAES
Time delays are generally unavoidable in the designing frameworks for mechanical and electrical systems and so on. In both continuous and discrete schemes, the existence of delay creates undesirable impacts on the underthought which forces exacting constraints on attainable execution. The presence of delay confounds the design structure procedure also. It makes continuous systems boundless dimensional and also extends the readings in discrete systems fundamentally. As the Proportional-IntegralDerivative (PID) controller based on internal model control is essential and strong to address the vulnerabilities and aggravations of the model. But for an real industry process, they are less susceptible to noise than the PID controller.It results in just one tuning parameter which is the time constant of the closed-loop system λ, the internal model control filter factor. It additionally gives a decent answer for the procedure with huge time delays. The design of the PID controller based on the internal model control, with approximation of time delay using Pade’ and Taylor’s series is depicted in this paper. The first order filter used in the design provides good set-point tracking along with disturbance rejection.
Validation of Design Parameters of Radiator using Computational ToolIRJET Journal
This document discusses the validation of design parameters for automobile radiators using computational tools. It presents two case studies where the thermal performance of radiators is analyzed using the log mean temperature difference (LMTD) and number of transfer units (NTU) methods and the results are compared to those from a computational software tool (HXCombine). The results show good agreement between the manual calculations and software outputs, validating the use of computational tools for radiator design. Parameters like heat transfer rate, outlet temperatures, effectiveness and heat transfer area are compared for both case studies. This research demonstrates that computational tools can accurately analyze and design radiator performance.
This document summarizes research on tuning an I-PD controller to control a highly oscillating second-order industrial process. The process has an 85.45% maximum overshoot and 8 second settling time. An I-PD controller is tuned using MATLAB optimization to minimize the integral of the squared error. The tuned controller completely cancels the overshoot and decreases the settling time to 1.46 seconds without undershoot, demonstrating improved performance over standard tuning techniques for controlling highly oscillating processes.
Distributed Control System Applied in Temperatur Control by Coordinating Mult...TELKOMNIKA JOURNAL
In Distributed Control System (DCS), multitasking management has been important issues
continuously researched and developed. In this paper, DCS was applied in global temperature control
system by coordinating three Local Control Units (LCUs). To design LCU’s controller parameters, both
analytical and experimental method were employed. In analytical method, the plants were firstly identified
to get their transfer functions which were then used to derive control parameters based on desired
response qualities. The experimental method (Ziegler-Nichols) was also applied due to practicable reason
in real industrial plant (less mathematical analysis). To manage set-points distributed to all LCUs, master
controller was subsequently designed based on zone of both error and set-point of global temperature
controller. Confirmation experiments showed that when using control parameters from analytical method,
the global temperature response could successfully follow the distributed set-points with 0% overshoot,
193.92 second rise time, and 266.88 second settling time. While using control parameters from
experimental method, it could also follow the distributed set-points with presence of overshoot (16.9%), but
has less rise time and settling time (111.36 and 138.72 second). In this research, the overshoot could be
successfully decreased from 16.9 to 9.39 % by changing master control rule. This proposed method can
be potentially applied in real industrial plant due to its simplicity in master control algorithm and presence
of PID controller which has been generally included in today industrial equipments.
The document discusses using the PIDE instruction in RSLogix 5000 to implement common process control algorithms like adaptive gains, cascade control, ratio control, and multiloop selection. It explains that the PIDE instruction uses a velocity-form PID algorithm, which makes it easier to implement advanced applications compared to traditional positional-form algorithms. The velocity-form algorithm works on the change in error rather than the error directly, allowing features like adaptive gains to be changed without impacting the control output. The document provides details on how to use the PIDE instruction, including the independent and dependent gains forms.
Optimisation problems and methods in Chemical Engineering: a personal surveyEric Fraga
The document is a personal survey by Eric S Fraga of optimisation problems and methods used in chemical engineering over the past 20 years. It covers topics such as process synthesis, heat integration, carbon capture, and power generation. For each topic, it discusses mathematical models used to represent the systems, optimisation approaches applied, and examples of applications and results. The presentation aims to provide an overview of the wide range of problems addressed and methods developed and implemented, from off-the-shelf software to custom programs for specific applications.
Jest wiele wewnętrznych i zewnętrznych sił, które kształtują twoich pracowników. Jeśli pozostawisz grupę pracowników o wysokim potencjale rozwojowym bez nadzoru jej skład i jakość zmienią się samoczynnie i staną się niespójne z potrzebami organizacji.
Modeling supply and return line dynamics for an electrohydraulic actuation sy...ISA Interchange
This document presents a model of an electrohydraulic fatigue testing system that focuses on components upstream of the servovalve and actuator, including the supply and return lines. The model allows prediction of pressure fluctuations in these lines in the time domain using a modular approach. Experiments showed significant pressure fluctuations at the servovalve ports due to supply and return line dynamics. The model was then used to evaluate potential design changes to improve system bandwidth by reducing pressure dynamics from flexible hoses.
11.7 yrs of exp in testing (manual and automation)Vijaya Kumar R
Vijaya Kumar has over 10 years of experience in manual testing and 1.5 years of experience in automation testing using Selenium. He has worked as a Senior Quality Lead, Consultant, QA Engineer, and QA System Analyst for various companies in roles involving manual testing of web, mobile, and desktop applications. His technical skills include Java, Selenium, SoapUI, SQL, and defect tracking tools like JIRA and Quality Center. He aims to use his technology expertise to align IT goals with business objectives.
El documento propone incrementar la jornada laboral de los profesores de educación secundaria de 28 a 30 horas semanales. Esto se basa en una ley de reforma magisterial que permite incrementar la jornada en dos horas cada dos años hasta un máximo de 30 horas. El incremento se usará para actividades de refuerzo educativo, atención a familias y otras tareas determinadas por los directores para mejorar los aprendizajes de los estudiantes.
Internet Rzeczy? W polskich firmach to wciąż fikcjaBPSC
Internet Rzeczy to w polskich przedsiębiorstwach raczej puste hasło niż realna potrzeba – wynika z danych Urzędu Komunikacji Elektronicznej. Zaledwie 3% firm korzysta z Internetu Rzeczy. Niewiele więcej, bo 6% przedsiębiorstw zamierza w przyszłości wprowadzić rozwiązania M2M.
“Artículo 208.- Contratación de profesores
208.1 La contratación de profesores en las
Instituciones Educativas Públicas de Educación Básica
y Técnico Productiva se realiza mediante concurso
público convocado cada dos (2) años, bajo los principios
de calidad, capacidad profesional y oportunidad. Este
concurso determina los cuadros de méritos vigentes para
los procesos de contratación anuales que se realicen en
dicho periodo.
208.2 En las Instituciones Educativas Públicas de
Educación Básica, la contratación de profesores se lleva
a cabo a través de la aplicación de una Prueba Única
Nacional, a cargo del MINEDU. Los cuadros de mérito
se determinan considerando el puntaje fi nal obtenido por
cada postulante en la citada prueba y la elección de UGEL
que realizó
Este documento describe el proceso de contratación de un profesor de química para un colegio de alto rendimiento en Lambayeque. Se especifican los requisitos académicos, experiencia, funciones y cronograma del proceso de selección. El contrato será de 3 meses con un salario de 4500 soles.
This document discusses elements of process control systems including sensors, controllers, and control elements. It provides definitions of these elements and describes how they relate and interact in a process control loop based on a block diagram approach. The key elements are the process being controlled, sensors that measure process variables, a controller that determines necessary control actions, and control elements that implement adjustments to the process. The document also discusses criteria for evaluating how well a control system is performing including stability, steady-state regulation, and transient response.
The KING-GAGE 780XD Purge Control is an extremely rugged unit designed specifically for hazardous areas requiring flameproof or ATEX (Ex d) rating. A proprietary wet check assembly ensures positive seal of fluids to ensure containment integrity. Loop powered transmitter provides 4-20mAdc output while components are isolated from the process media by a continuous air purge. Total consumption rate is less than 0.083 scfm for energy saving operation with external air/gas supply.The only internal element is a simple length of pipe extending into the tank.
Steam traps are the hardest working components in the steam system. Maintenance or replacement of steam traps must be as quick and efficient as possible to avoid unnecessary disruption to related processes.
Traditional steam trapping assemblies often require the plant to be shut down for traps to be maintained or replaced taking significant time and reducing production output.
The PC3000 and PC4000 incorporate isolation valves, strainer, two-bolt steam trap connection and blowdown valves, all in a single unit for quick and easy installation and operation.
Insertion turbine flow meters measure flow of liquid, gas, and
steam by detecting the frequency of rotation of the turbine blades. The frequency of turbine rotation is directly proportional to the flow velocity. Insertion turbine flow meters measure flow by detecting the local velocity within the pipe. The fluid velocity is combined with other parameters to calculate the average pipe velocity and volumetric flow rate.
2016-03-17 Structural Value EngineeringPiet Lambert
Presentatie van Piet Lambert (Lambert Engineering) tijdens 5-jarig verjaardagsevent op 17 maart 2016.
Structural Value Engineering is de methode om als stabiliteitsingenieur ruwbouwkosten in de uitvoering reeds in ontwerp te verlagen. Zo worddt extra (architecturale) waarde gecreëerd
This document describes the open-loop transient response method for tuning controllers. It involves disconnecting the controller, making a small manual disturbance to the process, and recording the response of the controlled variable over time. The lag time and process reaction time are determined from the response curve. These values along with the disturbance size are used with Ziegler-Nichols tuning formulas to calculate controller settings for proportional, PI, and PID control modes. The document provides details on applying this tuning technique and references for further information.
This document discusses performance criteria for tuning controllers. It describes three main performance criteria - integral of the square error (ISE), integral of the absolute error (IAE), and integral of the time-weighted absolute error (ITAE). These criteria are used to minimize the error in a system's response by selecting the appropriate controller (P, PI, or PID) and tuning its parameters. The document provides guidelines for selecting a criterion based on the system characteristics and explains the tuning process involves computing the criterion value for different controllers and selecting the best one.
This document compares several classical tuning methods for PID controllers, including both closed-loop and open-loop approaches. It describes the Ziegler-Nichols, Tyreus-Luyben, Damped Oscillation, C-H-R, Cohen-Coon, Ciancone-Marlin, and Minimum Error Integral tuning methods. The document aims to compare the performance and robustness of these tuning methods through simulation of first, second, and third-order processes. It also describes developing a GUI to automatically compare the tuning methods for a given process model.
A fluid coupling is a hydrodynamic device that transmits rotational mechanical power using a hydraulic fluid. It was invented by German engineer Hermann Föttinger and is used in industrial applications involving machine drives. A fluid coupling consists of a housing containing hydraulic fluid and two turbines - one connected to the input shaft and one to the output shaft. It has advantages like gradually accelerating driven machines and limiting torque, but disadvantages like being unable to develop output torque when input and output speeds are identical.
1. Heme is synthesized through a series of enzymatic reactions beginning with the condensation of glycine and succinyl-CoA to form delta-aminolevulinic acid (ALA).
2. The liver and bone marrow are the major sites of heme synthesis. In the liver, heme is used to synthesize cytochromes while in bone marrow it is used in hemoglobin synthesis.
3. Defects in heme synthesis can cause porphyrias, characterized by accumulation of heme precursors and acute attacks triggered by certain drugs and chemicals.
The document discusses the five main human sense organs - eyes, nose, ears, tongue, and skin. It provides details on the structure and function of each organ, noting that eyes are for seeing, nose is for smelling, ears are for hearing, tongue is for tasting, and skin is for touch. The conclusion states that these sense organs allow us to perform vital functions and that without them, we could not live.
Marketing strategy for ice-cream companyShamim Hasan
Cold Berg is an Irish ice cream company that has acquired a license to operate in Bangladesh. It aims to grab market share and satisfy customers through high quality products while earning maximum profits. A S.W.A.T. analysis identified strengths in Irish equipment/technology and product variety, while weaknesses included high costs and seasonal demand fluctuations. Existing research found high competition targeting premium customers, so Cold Berg plans to promote new flavors, family packages, and advertise to attract upper middle class customers through retail channels, events, and ice cream parlors.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijcisjournal
This document discusses PID controller design methods for integrating processes with time delay. It proposes designing PID controllers using three methods: internal model control (IMC), direct synthesis, and stability analysis. It evaluates the performance of controllers designed with these methods by applying them to models of various chemical processes that can be represented by integrating processes with time delay. These include level control systems, distillation columns, and continuous stirred-tank reactors. The robustness of the proposed controllers is analyzed considering parameter uncertainty using Kharitonov's theorem. Simulation results show the proposed IMC method provides superior performance over other existing tuning methods. An experimental setup is used to validate the effectiveness of the proposed design methods.
PID controller auto-tuning based on process step response and damping optimum...ISA Interchange
This paper presents a novel method for tuning PID controllers based on identifying higher-order process models from step response data and applying a damping optimum criterion. The method estimates parameters for an nth-order lag (PTn) process model from a single integration of the process step response. This allows deriving algebraic rules for adjusting closed-loop response speed and damping. Simulations show the effectiveness of the proposed PTn model parameter estimation and damping optimum-based PID auto-tuning for achieving a well-damped closed-loop response.
This document discusses using particle swarm optimization (PSO) to tune the parameters of proportional-integral-derivative (PID) and fractional-order PID (FOPID) controllers for speed control of a DC motor. PSO is a bio-inspired optimization technique that can automatically tune controller parameters online. The document presents the mathematical model of a DC motor and compares tuning PID and FOPID controllers with PSO. PSO is shown to find optimal controller parameters that improve the dynamic and static performance of the closed-loop speed control system.
Robust pole placement using firefly algorithmIJECEIAES
In this paper, the new automatic tool that is based on the firefly algorithm whose purpose is optimization of pole location in the control of state feedback has been presented. The aim is satisfying specifications of performance like settling and rise time, steady state as well as overshoot error. Utilization of Firefly algorithm has demonstrated the benefits of controllers based on this kind of time domain over controllers based on the frequency domain like Proportional-Integral Derivative (PID). The presented method is more particular for the multi-input multi-output (MIMO) systems that have substantial state numbers. The simulation results indicated that the proposed method had superior performance in providing solution to the problems that involved stabilization of helicopter under the Rationalized Model of helicopter/ Moreover, it demonstrates the Firefly algorithm effectiveness with regards to, the state observer design and feedback controller and auto-tuning.
This document compares the performance of PID, PI, and MPC controllers for controlling water level in a tank process. It describes modeling the first-order plus dead time process in MATLAB and tuning the PID controller using Ziegler-Nichols method. Simulation results show that the MPC controller achieved better performance than the PID and PI controllers in terms of rise time, settling time, and overshoot. Specifically, the MPC controller had the shortest rise time and settling time, as well as the lowest overshoot of the three controllers evaluated.
Robustness enhancement study of augmented positive identification controller ...IAESIJAI
The dissolved oxygen concentration in the wastewater treatment process
(WWTP) must remain in a specific range while the factory operates. The
augmented positive identification (PID) controller with a nonlinear element
(sigmoid function) is proposed to assure stability and reduce uncertainties in
the wastewater direct reuse/recycling model. The nonlinear controller gains
(PID controller with sigmoid function) for uncertain wastewater treatment
processes are tuned using the particle swarm optimization (PSO) technique.
The proposed robust method for controlling wastewater treatment processes
has good robustness during model mismatching, reduces treatment time
compared to traditional positive identification (PID) controllers tuned by
PSO, is easy to apply, and has good performance, according to simulation
results.
Comparison Analysis of Indirect FOC Induction Motor Drive using PI, Anti-Wind...IAES-IJPEDS
This paper presents the speed performance analysis of indirect Field Oriented Control (FOC) induction motor drive by applying Proportional Integral (PI) controller, PI with Anti-Windup (PIAW) and Pre- Filter (PF). The objective of this experiment is to have quantitative comparison between the controller strategies towards the performance of the motor in term of speed tracking and load rejection capability in low, medium and rated speed operation. In the first part, PI controller is applied to the FOC induction motor drive which the gain is obtained based on determined Induction Motor (IM) motor parameters. Secondly an AWPI strategy is added to the outer loop and finally, PF is added to the system. The Space Vector Pulse Width Modulation (SVPWM) technique is used to control the voltage source inverter and complete vector control scheme of the IM drive is tested by using a DSpace 1103 controller board. The analysis of the results shows that, the PI and AWPI controller schemes produce similar performance at low speed operation. However, for the medium and rated speed operation the AWPI scheme shown significant improvement in reducing the overshoot problem and improving the setting time. The PF scheme on the other hand, produces a slower speed and torque response for all tested speed operation. All schemes show similar performance for load disturbance rejection capability.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document discusses optimizing the parameters of fractional order PID (FOPID) controllers for a permanent magnet synchronous motor (PMSM) drive system using a hybrid grey wolf optimizer (HGWO). The PMSM drive utilizes indirect field-oriented control (IFOC) with both conventional PID and FOPID controllers for speed and current control. HGWO is used to determine optimal parameters for both controller types to minimize speed error and current/torque ripples. Simulation results show the FOPID controller achieves faster response and less ripple compared to the PID controller.
Data-based PID control of flexible joint robot using adaptive safe experiment...journalBEEI
This paper proposes the data-based PID controller of flexible joint robot based on adaptive safe experimentation dynamics (ASED) algorithm. The ASED algorithm is an enhanced version of SED algorithm where the updated tuning variable is modified to adapt to the change of the objective function. By adopting the adaptive term to the updated equation of SED, it is expected that the convergence accuracy can be further improved. The effectiveness of the ASED algorithm is verified to tune the PID controller of flexible joint robot. In this flexible joint control problem, two PID controllers are utilized to control both rotary angle tracking and vibration of flexible joint robot. The performance of the proposed data-based PID controller is assessed in terms of trajectory tracking of angular motion, vibration reduction and statistical analysis of the pre-defined control objective function. The simulation results showed that the data-based PID controller based on ASED is able to produce better control accuracy than the conventional SED based method.
A fuzzy model based adaptive pid controller design for nonlinear and uncertai...ISA Interchange
We develop a novel adaptive tuning method for classical proportional–integral–derivative (PID)
controller to control nonlinear processes to adjust PID gains, a problem which is very difficult to
overcome in the classical PID controllers. By incorporating classical PID control, which is well-known in
industry, to the control of nonlinear processes, we introduce a method which can readily be used by the
industry. In this method, controller design does not require a first principal model of the process which is
usually very difficult to obtain. Instead, it depends on a fuzzy process model which is constructed from
the measured input–output data of the process. A soft limiter is used to impose industrial limits on the
control input. The performance of the system is successfully tested on the bioreactor, a highly nonlinear
process involving instabilities. Several tests showed the method's success in tracking, robustness to noise,
and adaptation properties. We as well compared our system's performance to those of a plant with
altered parameters with measurement noise, and obtained less ringing and better tracking. To conclude,
we present a novel adaptive control method that is built upon the well-known PID architecture that
successfully controls highly nonlinear industrial processes, even under conditions such as strong
parameter variations, noise, and instabilities
IRJET- Analysis of 3-Phase Induction Motor with High Step-Up PWM DC-DC Conver...IRJET Journal
This document discusses control methods for STATCOMs using fuzzy logic controllers and genetic algorithm-tuned PID controllers. STATCOMs are shunt FACTS devices that help solve power quality issues through fast reactive power control. Conventionally, PID controllers are used but require trial and error to tune parameters. The document proposes using fuzzy logic controllers and genetic algorithms to optimize PID parameters to improve STATCOM current control response. It describes STATCOM modeling, fuzzy logic controller design including fuzzification, inference, and defuzzification. Genetic algorithms are used to find optimal PID parameters. Simulation results in MATLAB show the proposed methods improve current control response over conventional PID control.
IRJET- Design and Analysis of Fuzzy and GA-PID Controllers for Optimized Perf...IRJET Journal
This document describes research into using different controller types, including fuzzy logic controllers and genetic algorithm optimized PID controllers, to control a STATCOM device for improved reactive power compensation performance. A STATCOM is a shunt Flexible AC Transmission System device that can help solve power quality issues. Conventionally, PID controllers are used but require trial and error to tune parameters. The document models a STATCOM system and explores using fuzzy logic control or genetic algorithms to automatically determine optimal PID parameters to achieve faster response compared to conventional PID control. Simulation results in MATLAB show that both fuzzy logic control and genetic algorithm optimized PID control improve the STATCOM current control response compared to manually tuned PID controllers.
Comparison Analysis of Model Predictive Controller with Classical PID Control...ijeei-iaes
pH control plays a important role in any chemical plant and process industries. For the past four decades the classical PID controller has been occupied by the industries. Due to the faster computing technology in the industry demands a tighter advanced control strategy. To fulfill the needs and requirements Model Predictive Control (MPC) is the best among all the advanced control algorithms available in the present scenario. The study and analysis has been done for First Order plus Delay Time (FOPDT) model controlled by Proportional Integral Derivative (PID) and MPC using the Matlab software. This paper explores the capability of the MPC strategy, analyze and compare the control effects with conventional control strategy in pH control. A comparison results between the PID and MPC is plotted using the software. The results clearly show that MPC provide better performance than the classical controller.
IRJET- Optimum Design of PSO based Tuning using PID Controller for an Automat...IRJET Journal
This document discusses using particle swarm optimization (PSO) to tune the parameters of a PID controller for an automatic voltage regulator (AVR) system. The goal is to improve the system's transient performance by minimizing overshoot and steady state error. PSO is applied to optimize the proportional, integral, and derivative parameters of the PID controller. Simulation results show the PSO-tuned PID controller provides significantly better control of the AVR system compared to a traditionally tuned PID controller. The tuned controller gives faster response, lower overshoot, and improved stability when subjected to disturbances and parameter variations.
The document presents a genetic algorithm tuned PID controller for temperature control in a shell and tube heat exchanger. It models the heat exchanger and develops a GA based PID control scheme to regulate the temperature of the output fluid. Simulation results show that the proposed controller achieves less settling time (65 sec) and peak overshoot (3.22%) compared to a conventional PID controller (74 sec and 3.54% overshoot).
Control Loop Foundation - Batch And Continous ProcessesEmerson Exchange
This presentation, by Emerson's Terry Blevins and Mark Nixon, is a guide for engineers, managers, technicians, and others that are new to process control or experienced control engineers who are unfamiliar with multi-loop control techniques.
Their book is available in the ISA Bookstore at: http://emrsn.co/1E
PID Tuning for Near Integrating Processes - Greg McMillan DeminarJim Cahill
Greg McMillan shares how to reduce tuning time for near integrating processes.
Recorded video version available for viewing at: http://www.screencast.com/t/NmUxZTBiNTg
On the fragility of fractional-order PID controllers for FOPDT processesISA Interchange
This paper analyzes the fragility issue of fractional-order proportional-integral-derivative controllers applied to integer first-order plus-dead-time processes. In particular, the effects of the variations of the controller parameters on the achieved control system robustness and performance are investigated. Results show that this kind of controllers is more fragile with respect to the standard proportional-integral-derivative controllers and therefore a significant attention should be paid by the user in their tuning.
Ascc04 334 Comparative Study of Unstable Process ControlF15TV
This document compares several existing control methods for unstable time-delayed processes. It summarizes 6 control methods (A through F) and evaluates their performance based on simulations of processes with small, medium, and large normalized time delays. For small delays, Methods E and F showed excellent setpoint tracking and disturbance rejection. For medium delays, Methods G, E, and F performed best. For large delays, only Methods E and F were applicable, with Method E showing slightly better setpoint tracking and Method F better disturbance rejection. Based on overall performance, robustness, and applicability, the document ranks Method F as the best existing control method.
Similar to PID controller auto tuning based on process step response and damping optimum criterion (20)
An optimal general type-2 fuzzy controller for Urban Traffic NetworkISA Interchange
This document presents an optimal general type-2 fuzzy controller (OGT2FC) for controlling traffic signal scheduling and phase succession to minimize wait times and average queue length. The OGT2FC uses a combination of general type-2 fuzzy logic sets and the Modified Backtracking Search Algorithm (MBSA) to optimize the membership function parameters. Simulation results show the OGT2FC performs better than conventional type-1 fuzzy controllers in regulating urban traffic flow.
Embedded intelligent adaptive PI controller for an electromechanical systemISA Interchange
In this study, an intelligent adaptive controller approach using the interval type-2 fuzzy neural network (IT2FNN) is presented. The proposed controller consists of a lower level proportional - integral (PI) controller, which is the main controller and an upper level IT2FNN which tuning on-line the parameters of a PI controller. The proposed adaptive PI controller based on IT2FNN (API-IT2FNN) is implemented practically using the Arduino DUE kit for controlling the speed of a nonlinear DC motor-generator system. The parameters of the IT2FNN are tuned on-line using back-propagation algorithm. The Lyapunov theorem is used to derive the stability and convergence of the IT2FNN. The obtained experimental results, which are compared with other controllers, demonstrate that the proposed API-IT2FNN is able to improve the system response over a wide range of system uncertainties.
State of charge estimation of lithium-ion batteries using fractional order sl...ISA Interchange
This paper presents a state of charge (SOC) estimation method based on fractional order sliding mode observer (SMO) for lithium-ion batteries. A fractional order RC equivalent circuit model (FORCECM) is firstly constructed to describe the charging and discharging dynamic characteristics of the battery. Then, based on the differential equations of the FORCECM, fractional order SMOs for SOC, polarization voltage and terminal voltage estimation are designed. After that, convergence of the proposed observers is analyzed by Lyapunov’s stability theory method. The framework of the designed observer system is simple and easy to implement. The SMOs can overcome the uncertainties of parameters, modeling and measurement errors, and present good robustness. Simulation results show that the presented estima- tion method is effective, and the designed observers have good performance.
Fractional order PID for tracking control of a parallel robotic manipulator t...ISA Interchange
This paper presents the tracking control for a robotic manipulator type delta employing fractional order PID controllers with computed torque control strategy. It is contrasted with an integer order PID controller with computed torque control strategy. The mechanical structure, kinematics and dynamic models of the delta robot are descripted. A SOLIDWORKS/MSC-ADAMS/MATLAB co-simulation model of the delta robot is built and employed for the stages of identification, design, and validation of control strategies. Identification of the dynamic model of the robot is performed using the least squares algorithm. A linearized model of the robotic system is obtained employing the computed torque control strategy resulting in a decoupled double integrating system. From the linearized model of the delta robot, fractional order PID and integer order PID controllers are designed, analyzing the dynamical behavior for many evaluation trajectories. Controllers robustness is evaluated against external disturbances employing performance indexes for the joint and spatial error, applied torque in the joints and trajectory tracking. Results show that fractional order PID with the computed torque control strategy has a robust performance and active disturbance rejection when it is applied to parallel robotic manipulators on tracking tasks.
Fuzzy logic for plant-wide control of biological wastewater treatment process...ISA Interchange
The application of control strategies is increasingly used in wastewater treatment plants with the aim of improving effluent quality and reducing operating costs. Due to concerns about the progressive growth of greenhouse gas emissions (GHG), these are also currently being evaluated in wastewater treatment plants. The present article proposes a fuzzy controller for plant-wide control of the biological wastewater treatment process. Its design is based on 14 inputs and 6 outputs in order to reduce GHG emissions, nutrient concentration in the effluent and operational costs. The article explains and shows the effect of each one of the inputs and outputs of the fuzzy controller, as well as the relationship between them. Benchmark Simulation Model no 2 Gas is used for testing the proposed control strategy. The results of simulation results show that the fuzzy controller is able to reduce GHG emissions while improving, at the same time, the common criteria of effluent quality and operational costs.
Design and implementation of a control structure for quality products in a cr...ISA Interchange
In recent years, interest for petrochemical processes has been increasing, especially in refinement area. However, the high variability in the dynamic characteristics present in the atmospheric distillation column poses a challenge to obtain quality products. To improve distillates quality in spite of the changes in the input crude oil composition, this paper details a new design of a control strategy in a conventional crude oil distillation plant defined using formal interaction analysis tools. The process dynamic and its control are simulated on Aspen HYSYS dynamic environment under real operating conditions. The simulation results are compared against a typical control strategy commonly used in crude oil atmospheric distillation columns.
Model based PI power system stabilizer design for damping low frequency oscil...ISA Interchange
This paper explores a two-level control strategy by blending a local controller with a centralized controller for the low frequency oscillations in a power system. The proposed control scheme provides stabilization of local modes using a local controller and minimizes the effect of inter-connection of sub-systems performance through a centralized control. For designing the local controllers in the form of proportional-integral power system stabilizer (PI-PSS), a simple and straight forward frequency domain direct synthesis method is considered that works on use of a suitable reference model which is based on the desired requirements. Several examples both on one machine infinite bus and multi-machine systems taken from the literature are illustrated to show the efficacy of the proposed PI-PSS. The effective damping of the systems is found to be increased remarkably which is reflected in the time-responses; even unstable operation has been stabilized with improved damping after applying the proposed controller. The proposed controllers give remarkable improvement in damping the oscillations in all the illustrations considered here and as for example, the value of damping factor has been increased from 0.0217 to 0.666 in Example 1. The simulation results obtained by the proposed control strategy are favorably compared with some controllers prevalent in the literature.
A comparison of a novel robust decentralized control strategy and MPC for ind...ISA Interchange
This document summarizes a research article that compares a novel decentralized control strategy based on override control to a model predictive controller (MPC) for controlling an industrial high purity methanol distillation column. Both controllers were able to maintain tight product purity and high recovery specifications under disturbances. The MPC provided tighter control of product purity but used more energy, while the proposed override control provided tighter recovery control and had lower costs. An economic analysis showed the optimal choice depends on factors like energy costs.
Fault detection of feed water treatment process using PCA-WD with parameter o...ISA Interchange
This research article proposes a new fault detection algorithm called PCA-WD that combines wavelet denoising (WD) with principal component analysis (PCA) to improve fault detection performance for feed water treatment processes (FWTP). The algorithm is applied to operational data from a FWTP sustaining two 1000 MW coal-fired power plants. Parameter selection for the PCA-WD algorithm is formulated as an optimization problem solved using particle swarm optimization to determine optimal parameters automatically rather than relying on individual experience. Results show that WD effectively reduces noise in PCA statistics, improving fault detection. The optimized PCA-WD algorithm outperforms classical PCA and a related method in detecting various faults in the FWTP data.
Model-based adaptive sliding mode control of the subcritical boiler-turbine s...ISA Interchange
As higher requirements are proposed for the load regulation and efficiency enhancement, the control performance of boiler-turbine systems has become much more important. In this paper, a novel robust control approach is proposed to improve the coordinated control performance for subcritical boiler-turbine units. To capture the key features of the boiler-turbine system, a nonlinear control-oriented model is established and validated with the history operation data of a 300 MW unit. To achieve system linearization and decoupling, an adaptive feedback linearization strategy is proposed, which could asymptotically eliminate the linearization error caused by the model uncertainties. Based on the linearized boiler-turbine system, a second-order sliding mode controller is designed with the super-twisting algorithm. Moreover, the closed-loop system is proved robustly stable with respect to uncertainties and disturbances. Simulation results are presented to illustrate the effectiveness of the proposed control scheme, which achieves excellent tracking performance, strong robustness and chattering reduction.
A Proportional Integral Estimator-Based Clock Synchronization Protocol for Wi...ISA Interchange
Clock synchronization is an issue of vital importance in applications of wireless sensor networks (WSNs). This paper proposes a proportional integral estimator-based protocol (EBP) to achieve clock synchronization for wireless sensor networks. As each local clock skew gradually drifts, synchronization accuracy will decline over time. Compared with existing consensus-based approaches, the proposed synchronization protocol improves synchronization accuracy under time-varying clock skews. Moreover, by restricting synchronization error of clock skew into a relative small quantity, it could reduce periodic re-synchronization frequencies. At last, a pseudo-synchronous implementation for skew compensation is introduced as synchronous protocol is unrealistic in practice. Numerical simulations are shown to illustrate the performance of the proposed protocol.
An artificial intelligence based improved classification of two-phase flow patte...ISA Interchange
Flow pattern recognition is necessary to select design equations for finding operating details of the process and to perform computational simulations. Visual image processing can be used to automate the interpretation of patterns in two-phase flow. In this paper, an attempt has been made to improve the classification accuracy of the flow pattern of gas/ liquid two- phase flow using fuzzy logic and Support Vector Machine (SVM) with Principal Component Analysis (PCA). The videos of six different types of flow patterns namely, annular flow, bubble flow, churn flow, plug flow, slug flow and stratified flow are re- corded for a period and converted to 2D images for processing. The textural and shape features extracted using image processing are applied as inputs to various classification schemes namely fuzzy logic, SVM and SVM with PCA in order to identify the type of flow pattern. The results obtained are compared and it is observed that SVM with features reduced using PCA gives the better classification accuracy and computationally less intensive than other two existing schemes. This study results cover industrial application needs including oil and gas and any other gas-liquid two-phase flows.
Load estimator-based hybrid controller design for two-interleaved boost conve...ISA Interchange
This paper is devoted to the development of a hybrid controller for a two-interleaved boost converter dedicated to renewable energy and automotive applications. The control requirements, resumed in fast transient and low input current ripple, are formulated as a problem of fast stabilization of a predefined optimal limit cycle, and solved using hybrid automaton formalism. In addition, a real time estimation of the load is developed using an algebraic approach for online adjustment of the hybrid controller. Mathematical proofs are provided with simulations to illustrate the effectiveness and the robustness of the proposed controller despite different disturbances. Furthermore, a fuel cell system supplying a resistive load through a two-interleaved boost converter is also highlighted.
Effects of Wireless Packet Loss in Industrial Process Control SystemsISA Interchange
Timely and reliable sensing and actuation control are essential in networked control. This depends on not only the precision/quality of the sensors and actuators used but also on how well the communications links between the field instruments and the controller have been designed. Wireless networking offers simple deployment, reconfigurability, scalability, and reduced operational expenditure, and is easier to upgrade than wired solutions. However, the adoption of wireless networking has been slow in industrial process control due to the stochastic and less than 100% reliable nature of wireless communications and lack of a model to evaluate the effects of such communications imperfections on the overall control performance. In this paper, we study how control performance is affected by wireless link quality, which in turn is adversely affected by severe propagation loss in harsh industrial environments, co-channel interference, and unintended interference from other devices. We select the Tennessee Eastman Challenge Model (TE) for our study. A decentralized process control system, first proposed by N. Ricker, is adopted that employs 41 sensors and 12 actuators to manage the production process in the TE plant. We consider the scenario where wireless links are used to periodically transmit essential sensor measurement data, such as pressure, temperature and chemical composition to the controller as well as control commands to manipulate the actuators according to predetermined setpoints. We consider two models for packet loss in the wireless links, namely, an independent and identically distributed (IID) packet loss model and the two-state Gilbert-Elliot (GE) channel model. While the former is a random loss model, the latter can model bursty losses. With each channel model, the performance of the simulated decentralized controller using wireless links is compared with the one using wired links providing instant and 100% reliable communications. The sensitivity of the controller to the burstiness of packet loss is also characterized in different process stages. The performance results indicate that wireless links with redundant bandwidth reservation can meet the requirements of the TE process model under normal operational conditions. When disturbances are introduced in the TE plant model, wireless packet loss during transitions between process stages need further protection in severely impaired links. Techniques such as re-transmission scheduling, multi-path routing and enhanced physical layer design are discussed and the latest industrial wireless protocols are compared.
Fault Detection in the Distillation Column ProcessISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
Neural Network-Based Actuator Fault Diagnosis for a Non-Linear Multi-Tank SystemISA Interchange
The paper is devoted to the problem of the robust actuator fault diagnosis of the dynamic non-linear systems. In the proposed method, it is assumed that the diagnosed system can be modelled by the recurrent neural network, which can be transformed into the linear parameter varying form. Such a system description allows developing the designing scheme of the robust unknown input observer within H1 framework for a class of non-linear systems. The proposed approach is designed in such a way that a prescribed disturbance attenuation level is achieved with respect to the actuator fault estimation error, while guaranteeing the convergence of the observer. The application of the robust unknown input observer enables actuator fault estimation, which allows applying the developed approach to the fault tolerant control tasks.
A KPI-based process monitoring and fault detection framework for large-scale ...ISA Interchange
Large-scale processes, consisting of multiple interconnected sub-processes, are commonly encountered in industrial systems, whose performance needs to be determined. A common approach to this problem is to use a key performance indicator (KPI)-based approach. However, the different KPI-based approaches are not developed with a coherent and consistent framework. Thus, this paper proposes a framework for KPI-based process monitoring and fault detection (PM-FD) for large-scale industrial processes, which considers the static and dynamic relationships between process and KPI variables. For the static case, a least squares-based approach is developed that provides an explicit link with least-squares regression, which gives better performance than partial least squares. For the dynamic case, using the kernel re- presentation of each sub-process, an instrument variable is used to reduce the dynamic case to the static case. This framework is applied to the TE benchmark process and the hot strip mill rolling process. The results show that the proposed method can detect faults better than previous methods.
An adaptive PID like controller using mix locally recurrent neural network fo...ISA Interchange
Being complex, non-linear and coupled system, the robotic manipulator cannot be effectively controlled using classical proportional integral derivative (PID) controller. To enhance the effectiveness of the conventional PID controller for the nonlinear and uncertain systems, gains of the PID controller should be conservatively tuned and should adapt to the process parameter variations. In this work, a mix locally recurrent neural network (MLRNN) architecture is investigated to mimic a conventional PID controller which consists of at most three hidden nodes which act as proportional, integral and derivative node. The gains of the mix locally recurrent neural network based PID (MLRNNPID) controller scheme are initi- alized with a newly developed cuckoo search algorithm (CSA) based optimization method rather than assuming randomly. A sequential learning based least square algorithm is then investigated for the on- line adaptation of the gains of MLRNNPID controller. The performance of the proposed controller scheme is tested against the plant parameters uncertainties and external disturbances for both links of the two link robotic manipulator with variable payload (TL-RMWVP). The stability of the proposed controller is analyzed using Lyapunov stability criteria. A performance comparison is carried out among MLRNNPID controller, CSA optimized NNPID (OPTNNPID) controller and CSA optimized conventional PID (OPTPID) controller in order to establish the effectiveness of the MLRNNPID controller.
A method to remove chattering alarms using median filtersISA Interchange
Chattering alarms are the most found nuisance alarms that will probably reduce the usability and result in a confidence crisis of alarm systems for industrial plants. This paper addresses the chattering alarm reduction using median filters. Two rules are formulated to design the window size of median filters. If the alarm probability is estimated using process data, one rule is based on the probability of alarms to satisfy some requirements on the false alarm rate, or missed alarm rate. If there are only historical alarm data available, the other rule is based on percentage reduction of chattering alarms using alarm duration distribution. Experimental results for industrial cases testify that the proposed method is effective.
Distillation Column Process Fault Detection in the Chemical IndustriesISA Interchange
Chemical plants are complex large-scale systems which need designing robust fault detection schemes to ensure high product quality, reliability and safety under different operating conditions. The present paper is concerned with a feasibility study of the application of the black-box modeling method and Kullback Leibler divergence (KLD) to the fault detection in a distillation column process. A Nonlinear Auto-Regressive Moving Average with eXogenous input (NARMAX) polynomial model is firstly developed to estimate the nonlinear behavior of the plant. Furthermore, the KLD is applied to detect abnormal modes. The proposed FD method is implemented and validated experimentally using realistic faults of a distillation plant of laboratory scale. The experimental results clearly demonstrate the fact that proposed method is effective and gives early alarm to operators.
3 Simple Steps To Buy Verified Payoneer Account In 2024SEOSMMEARTH
Buy Verified Payoneer Account: Quick and Secure Way to Receive Payments
Buy Verified Payoneer Account With 100% secure documents, [ USA, UK, CA ]. Are you looking for a reliable and safe way to receive payments online? Then you need buy verified Payoneer account ! Payoneer is a global payment platform that allows businesses and individuals to send and receive money in over 200 countries.
If You Want To More Information just Contact Now:
Skype: SEOSMMEARTH
Telegram: @seosmmearth
Gmail: seosmmearth@gmail.com
Unveiling the Dynamic Personalities, Key Dates, and Horoscope Insights: Gemin...my Pandit
Explore the fascinating world of the Gemini Zodiac Sign. Discover the unique personality traits, key dates, and horoscope insights of Gemini individuals. Learn how their sociable, communicative nature and boundless curiosity make them the dynamic explorers of the zodiac. Dive into the duality of the Gemini sign and understand their intellectual and adventurous spirit.
Industrial Tech SW: Category Renewal and CreationChristian Dahlen
Every industrial revolution has created a new set of categories and a new set of players.
Multiple new technologies have emerged, but Samsara and C3.ai are only two companies which have gone public so far.
Manufacturing startups constitute the largest pipeline share of unicorns and IPO candidates in the SF Bay Area, and software startups dominate in Germany.
buy old yahoo accounts buy yahoo accountsSusan Laney
As a business owner, I understand the importance of having a strong online presence and leveraging various digital platforms to reach and engage with your target audience. One often overlooked yet highly valuable asset in this regard is the humble Yahoo account. While many may perceive Yahoo as a relic of the past, the truth is that these accounts still hold immense potential for businesses of all sizes.
Digital Transformation and IT Strategy Toolkit and TemplatesAurelien Domont, MBA
This Digital Transformation and IT Strategy Toolkit was created by ex-McKinsey, Deloitte and BCG Management Consultants, after more than 5,000 hours of work. It is considered the world's best & most comprehensive Digital Transformation and IT Strategy Toolkit. It includes all the Frameworks, Best Practices & Templates required to successfully undertake the Digital Transformation of your organization and define a robust IT Strategy.
Editable Toolkit to help you reuse our content: 700 Powerpoint slides | 35 Excel sheets | 84 minutes of Video training
This PowerPoint presentation is only a small preview of our Toolkits. For more details, visit www.domontconsulting.com
Navigating the world of forex trading can be challenging, especially for beginners. To help you make an informed decision, we have comprehensively compared the best forex brokers in India for 2024. This article, reviewed by Top Forex Brokers Review, will cover featured award winners, the best forex brokers, featured offers, the best copy trading platforms, the best forex brokers for beginners, the best MetaTrader brokers, and recently updated reviews. We will focus on FP Markets, Black Bull, EightCap, IC Markets, and Octa.
How to Implement a Real Estate CRM SoftwareSalesTown
To implement a CRM for real estate, set clear goals, choose a CRM with key real estate features, and customize it to your needs. Migrate your data, train your team, and use automation to save time. Monitor performance, ensure data security, and use the CRM to enhance marketing. Regularly check its effectiveness to improve your business.
Event Report - SAP Sapphire 2024 Orlando - lots of innovation and old challengesHolger Mueller
Holger Mueller of Constellation Research shares his key takeaways from SAP's Sapphire confernece, held in Orlando, June 3rd till 5th 2024, in the Orange Convention Center.
An introduction to the cryptocurrency investment platform Binance Savings.Any kyc Account
Learn how to use Binance Savings to expand your bitcoin holdings. Discover how to maximize your earnings on one of the most reliable cryptocurrency exchange platforms, as well as how to earn interest on your cryptocurrency holdings and the various savings choices available.
Zodiac Signs and Food Preferences_ What Your Sign Says About Your Tastemy Pandit
Know what your zodiac sign says about your taste in food! Explore how the 12 zodiac signs influence your culinary preferences with insights from MyPandit. Dive into astrology and flavors!
Best practices for project execution and deliveryCLIVE MINCHIN
A select set of project management best practices to keep your project on-track, on-cost and aligned to scope. Many firms have don't have the necessary skills, diligence, methods and oversight of their projects; this leads to slippage, higher costs and longer timeframes. Often firms have a history of projects that simply failed to move the needle. These best practices will help your firm avoid these pitfalls but they require fortitude to apply.
Part 2 Deep Dive: Navigating the 2024 Slowdownjeffkluth1
Introduction
The global retail industry has weathered numerous storms, with the financial crisis of 2008 serving as a poignant reminder of the sector's resilience and adaptability. However, as we navigate the complex landscape of 2024, retailers face a unique set of challenges that demand innovative strategies and a fundamental shift in mindset. This white paper contrasts the impact of the 2008 recession on the retail sector with the current headwinds retailers are grappling with, while offering a comprehensive roadmap for success in this new paradigm.
PID controller auto tuning based on process step response and damping optimum criterion
1. Research Article
PID controller auto-tuning based on process step response
and damping optimum criterion
Danijel Pavković a,n
, Siniša Polak b
, Davor Zorc a,1
a
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, I. Lučića 5, HR-10000 Zagreb, Croatia
b
INA-Oil Industry d.d. – Sisak Oil Refinery, Ante Kovačića 1, HR-44000 Sisak, Croatia
a r t i c l e i n f o
Article history:
Received 2 November 2012
Received in revised form
12 March 2013
Accepted 19 August 2013
Available online 12 September 2013
This paper was recommended for
publication by Dr. K.A. Hoo
Keywords:
PID controller
PTn process model
Damping optimum criterion
Identification
Auto-tuning control
a b s t r a c t
This paper presents a novel method of PID controller tuning suitable for higher-order aperiodic processes
and aimed at step response-based auto-tuning applications. The PID controller tuning is based on the
identification of so-called n-th order lag (PTn) process model and application of damping optimum
criterion, thus facilitating straightforward algebraic rules for the adjustment of both the closed-loop
response speed and damping. The PTn model identification is based on the process step response,
wherein the PTn model parameters are evaluated in a novel manner from the process step response
equivalent dead-time and lag time constant. The effectiveness of the proposed PTn model parameter
estimation procedure and the related damping optimum-based PID controller auto-tuning have been
verified by means of extensive computer simulations.
& 2013 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Many industrial processes such as heat and fluid flow processes
are characterized by slow aperiodic dynamics (lag behavior)
and dead-time (transport delay), which are frequently modeled by
a control-oriented first-order plus dead-time (FOPDT) process model
[1,2], and are in a majority of cases still controlled by Proportional-
Integral-Derivative (PID) controllers [3–5]. Accordingly, the PID con-
troller auto-tuning still remains an interesting and propulsive R&D
field (see [6] and references therein), which has resulted in numerous
PID controller auto-tuning patents and commercial controller units
over the last several decades [7]. Among the patented and imple-
mented PID adaptation approaches the so-called analytical formula
methods, typically based on process open-loop (input step) or
closed-loop (limit-cycle) excitation test are usually preferred over
more complex tuning methods, such as those based on heuristic
rules, artificial intelligence and numerical optimization approaches.
In latter cases the closed-loop behavior is typically monitored with
the PID controller turned on, and PID controller adaptation is
performed in real-time without applying a dedicated test signal [8].
The conventional formula-based tuning methods, such as the
Ziegler–Nichols (ZN) tuning rules, even though still used in practical
applications due to their simplicity, may result in a relatively large
closed-loop step response overshoot and related weak response
damping [9,10]. The closed-loop damping issues have been tradi-
tionally addressed by using the Chien–Hrones–Reswick (CHR) ZN
rule modification based on the time-domain FOPDT process model
identification, while the so-called Kappa-Tau method has been
used for frequency response-based (i.e. ultimate point finding)
auto-tuning [11,12]. Some of the more recent efforts at ZN-rule
improvement have included controller parameters numerical opti-
mization for a wide range of FOPDT process model parameters
variations [5], and on-line adaptation of the PID controller propor-
tional gain [10].
In order to further improve the PID controller performance com-
pared to the above traditional tuning formulas, a wide range of process
excitation-based auto-tuning approaches has been proposed in the
literature over the last decade or so, which may be categorized as
Frequency response-based approaches aimed at (i) improved
gain and phase margin estimation [13–15], (ii) process model
identification based on closed-loop relay experiment in combi-
nation with internal model control (IMC) based controller
tuning for improved control-loop load disturbance rejection
[16], (iii) using a more general case of binary noise signal for
the process model frequency characteristic identification and
loop-shaping-based controller tuning for robust behavior [17],
(iv) use of Bode's integrals for improved closed-loop system
robustness [18], and (v) relay experiment with cascaded
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/isatrans
ISA Transactions
0019-0578/$ - see front matter 2013 ISA. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.isatra.2013.08.011
n
Corresponding author. Tel.: þ385 1 6168 325; fax: þ385 1 6168 351.
E-mail addresses: danijel.pavkovic@fsb.hr (D. Pavković),
Sinisa.Polak@ina.hr (S. Polak), davor.zorc@fsb.hr (D. Zorc).
1
Tel.: þ385 1 6168 436; fax: þ385 1 6168 351.
ISA Transactions 53 (2014) 85–96
2. PI controller for load disturbance compensation and filtering
effect during process model identification [19]. For a rather
comprehensive review of relay-feedback frequency-domain
auto-tuning methods the reader is also referred to [20].
Time response approaches based on (i) process output multiple
integration and regression analysis in order to find the para-
meters of a second-order plus dead-time (SOPDT) process
model [21], (ii) multiple process step response integration to
find a general linear process model [22–24] combined with
the utilization of the so-called magnitude optimum criterion
in order to achieve well-damped closed-loop response, and
(iii) step-response identification of FOPDT model combined with
IMC tuning approach [25,26], or a robust loop-shaping controller
design (the so-called AMIGO method) [26,27].
Combined approaches wherein the time-domain and frequency-
domain process model identification is used, such as the
combined relay experimentþstep response identification of a
FOPDT process model [28], or a random signal-based process
excitation and SOPDT process model parameters estimation
and controller tuning based on zero-pole conditioning (cancel-
ing) [29].
However, in most of the above cases the PID controller tuning
was based on the relatively simple FOPDT (or SOPDT) process
model approximation with first-order Taylor or Padé dead-time
approximations used for the purpose of PID controller design,
which may not be accurate in the presence of more pronounced
higher-order process dynamics. In order to capture the higher-
order dynamics, while simultaneously having a relatively simple
dead-time-free process model formulation, an n-th order lag
process model (the so-called PTn model) can conveniently be
used, wherein analytical relationships between the PTn model and
FOPDT model parameters are typically given through the equiva-
lence of the process model step response flexion tangent (the so-
called Strejc method) [30,31]. By utilizing the PTn process model
as the basis for the control system design in [32], straightforward
analytical expressions have been derived for the PID controller
parameters based on the magnitude optimum criterion (see e.g.
[33] and references therein). The PTn model parameters have been
identified in [32] by using the so-called moment method (see e.g.
[30]), implemented through multiple time-weighted integrations
of the process output, thus avoiding the estimation of the process
step response flexion tangent slope (and related measurement
noise issues). Since the main advantage of the magnitude opti-
mum criterion is that it can assure a well-damped (over-damped)
closed-loop system response, this approach has also been pursued
for a wider class of linear process models in [22]. Further refine-
ments of the tuning method from [22] have included a filtering
term added to the PID controller transfer function to facilitate
relatively straightforward closed-loop response speed (response
time) tuning [23], and extending the PID controller with a
reference pre-filtering or weighting action to facilitate separate
closed-loop system tuning with respect to reference and external
disturbance [24].
Still, the aforementioned magnitude optimum-based PID con-
troller auto-tuning does not provide a straightforward way of closed-
loop damping adjustment, while the repetitive integration of process
output may result in an increased computational burden of the
PID controller auto-tuning algorithm, especially if application on a
relatively low-cost industrial controller is considered. Hence, a more
flexible pole-placement-like tuning method, as well as a simpler
process step response-based auto-tuning experiment (e.g. based on a
single integration of process step response) would result in a more
accommodating and less-demanding PID auto-tuner realization. To
this end, this paper proposes a PID controller tuning approach based
on the so-called damping optimum criterion [34,35] in combination
with the PTn process model formulation, which facilitates an
analytical and straightforward way of adjusting both the closed-
loop response damping and response speed with respect to process
dynamics. The estimation of PTn process model parameters is based
herein on the single integration of the process step response in
order to find the parameters of the basic FOPDT process model.
The simpler FOPDT model is then related to the equivalent dead-
time-free PTn model by using a higher-order Taylor expansion of the
dead-time (pure delay) dynamic term via simple analytical expres-
sions. The proposed PID controller tuning, the FOPDT and PTn
process model identification procedures and the resulting PID con-
troller auto-tuning algorithm is verified by means of extensive
computer simulations.
The paper is organized as follows. Section 2 presents the
analytical control system design procedure based on the damping
optimum criterion and the compact PTn aperiodic process model,
and illustrates the effectiveness of resulting closed-loop damping
and response speed tuning method. These results are also accom-
panied by the analysis of the closed-loop robustness with respect
to modeling uncertainties. The identification of PTn process model,
based on a single integration of the process output is described in
Section 3. The proposed identification procedure and the related
PID controller auto-tuning are thoroughly tested in Section 4 by
means of simulations. Concluding remarks are given in Section 5.
2. Control system design
This section presents the damping optimum criterion-based
tuning of the PID controller for the process model with aperiodic
step response dynamics, including the compact-form PTn process
model. The effectiveness of the proposed PID controller tuning
procedure, including the closed-loop damping tuning is illustrated
by means of simulations.
2.1. Control system structure
The structure of the linear control system comprising a mod-
ified PID feedback controller (the so-called IþPD controller, [41])
is shown in Fig. 1. In comparison with the traditional PID controller
where the proportional (P), integral (I), and derivative (D) terms
are placed into the path of the control error e, the proportional
and derivative terms of the modified PID controller act upon
the measured process output y only (Fig. 1). By opting to use the
modified PID controller structure which does not introduce addi-
tional controller zeros in the closed-loop transfer function, the
desired closed-loop system behavior can be achieved with respect
to the external disturbance w, while also avoiding the potentially
excessive control effort related to sudden reference yR changes or
“noisy” reference. Since the proposed control system design does
not introduce additional closed-loop zeros due to controller PþD
action, the proposed approach also results in relatively simple
Fig. 1. Block diagram of control system with modified PID controller.
D. Pavković et al. / ISA Transactions 53 (2014) 85–9686
3. and straightforward PID controller tuning rules (see Section 2.2).
Should the traditional PID controller structure be preferred, or the
reference and disturbance behavior of the closed-loop system be
tuned independently, somewhat more complex (two-step) tuning
approaches may be required, such as those presented in Refs. [24,36],
wherein the magnitude optimum-based tuning has been proposed to
separately tune the closed-loop system response with respect to
reference.
Note that in order to avoid relatively large step response
overshoots in the large-signal operating mode (so-called integra-
tor windup problem), the controller integral term should be
saturated when controller output saturation is performed
(Fig. 1), e.g. by using the so-called reset-integrator method [37].
It is assumed that the process is characterized by relatively
slow aperiodic dynamics (no step response overshoot or tran-
sient oscillations), which can be approximated by the n-th order
aperiodic process model with a single time constant Tp (the
so-called PTn model) [30–32], given in the following compact
transfer function form:
GpðsÞ ¼
yðsÞ
uðsÞ
¼
Kp
ð1þTpsÞn ¼
Kp
1þa1sþa2s2 þ⋯ansn
; ð1Þ
where Kp is the PTn model gain, nZ2 is the process order, and
the parameters of the process model characteristic polynomial am
(m¼1… n) are given by
am ¼
n
m
Tm
p ¼
n!
m!ðnÀmÞ!
Tm
p : ð2Þ
2.2. PID controller tuning
The PID controller tuning procedure is based on the damping
optimum (or double ratios) criterion [34,35]. This is a pole-
placement-like analytical method of design of linear continuous-
time closed-loop systems with a full or reduced-order controller,
which results in straightforward analytical relations between
the controller parameters, the parameters of the process model,
and desired level of response damping via characteristic design-
specific parameters. Even though somewhat less well known than
the magnitude optimum criterion [33], the damping optimum
criterion has found application in those control systems where the
closed-loop damping needs to be tuned in a precise and straight-
forward manner (e.g. in electrical servodrives with emphasized
transmission compliance effects, see [38–40]).
The tuning procedure starts with the transfer function of
the closed-loop control system in Fig. 1 assuming idealized PID
controller (typically, the derivative filter time constant Tν5TD, so it
may be neglected):
GcðsÞ ¼
yðsÞ
yRðsÞ
¼ 1= 1þ
ð1þKRKpÞTIs
KRKp
þ
ðKRKpTD þa1ÞTIs2
KRKp
þ
a2TIs3
KRKp
þ
a3TIs4
KRKp
þ⋯þ
anTIsn þ1
KRKp
: ð3Þ
The characteristic polynomial of the closed-loop system (3) can
be rewritten in terms of the damping optimum criterion in the
following form:
GcðsÞ ¼
1
AcðsÞ
¼
1
1þTesþD2T2
e s2 þD3D2
2T3
e s3⋯þDlD2
lÀ1 U U UDlÀ1
2 Tl
esl
;
ð4Þ
where Te is the equivalent time constant of the overall closed-loop
system, D2, D3, …, Dl are the so-called damping optimum char-
acteristic ratios, and l is the closed-loop system order (l¼nþ1 in
the case of PID controller, cf. (3)).
When all characteristic ratios are set to the so-called “optimal”
values D2¼D3¼…¼Dl¼0.5 (e.g. by applying a full-order controller),
the closed-loop system of any order l has a quasi-aperiodic step
response characterized by an overshoot of approximately 6% (thus
resembling a second-order system with damping ratio ζ¼0.707)
and the approximate settling time of 1.8–2.1Te, as illustrated in
Fig. 3a. This particular closed-loop tuning may be regarded as
optimal in those cases where small overshoot and related well-
damped behavior are critical, such as in controlled electrical drives
and related servodrive control applications. By choosing larger Te
value, the control system robustness is improved and the noise
sensitivity is decreased (i.e. bandwidth ΩBW$1/Te), but, in turn,
a slower response and less efficient disturbance rejection are
obtained. For a reduced-order controller with the number of free
parameters equal to r, only the dominant characteristic ratios
D2,…, Dr þ1 should be set to desired values. In this case, however,
the non-dominant characteristic ratios (corresponding to non-
dominant high-frequency closed-loop poles) cannot be adjusted
arbitrarily, so their effect to closed-loop damping should be
analyzed separately. In general, the response damping is adjusted
through varying the characteristic ratios D2, D3, … Dl, wherein the
damping of dominant closed-loop dynamics (i.e. the dominant
closed-loop poles damping ratio) is primarily influenced by the
most dominant characteristic ratio D2. By reducing the character-
istic ratio D2 to approximately 0.35 the fastest (boundary) aper-
iodic step response without overshoot is obtained. On the other
hand, if D2 is increased above 0.5 the closed-loop system response
damping decreases (see Fig. 3b).
The PID controller (r¼3) can arbitrarily adjust only the closed-
loop characteristic ratios D2, D3 and D4. Hence, the analytical
expressions for PID controller proportional gain KR, integral
time constant TI, and derivative time constant TD are obtained by
equating lower-order coefficients of the characteristic polynomial
in (3) with the coefficients of the characteristic polynomial (4) up
to s4
, which after some manipulation and rearranging yields the
following relatively simple analytical expressions:
KR ¼
1
Kp
nðnÀ1ÞT2
p
2D2
2D3T2
e
À1
!
; ð5Þ
TI ¼ 1À
2D2
2D3T2
e
nðnÀ1ÞT2
p
!
Te; ð6Þ
TD ¼ D2TeTpn
ðnÀ1ÞTpÀ2D2D3Te
nðnÀ1ÞT2
pÀ2D2
2D3T2
e
; ð7Þ
with the closed-loop equivalent time constant Te given as follows
(valid for n42):
Te ¼
ðnÀ2ÞTp
3D2D3D4
ð8Þ
Fig. 2. Block diagram of discrete-time PID controller with zero-order-hold element
at controller output.
D. Pavković et al. / ISA Transactions 53 (2014) 85–96 87
4. Similarly, in the case of PI controller (TD¼0), only the closed-
loop characteristic ratios D2, D3 can be tuned, so the design is
based on the coefficients of the characteristic polynomial (4)
up to s3
:
KR ¼
1
Kp
nTp
D2Te
À1
; ð9Þ
TI ¼ 1À
D2Te
nTp
Te; ð10Þ
while the equivalent time constant Te is now given by (valid for
n41):
Te ¼
ðnÀ1ÞTp
2D2D3
ð11Þ
The above expressions indicate that the PID controller para-
meters KR, TI and TD are directly influenced by the dominant
characteristic ratios D2 and D3, while the non-dominant character-
istic ratio D4 only affects the closed-loop equivalent time constant
Te. Similarly, the simpler PI controller tuning is directly affected by
the most dominant characteristic ratio D2, while the closed-loop
equivalent time constant Te directly depends on the less-dominant
characteristic ratio D3 value. Thus, it appears that the closed-
loop response speed and dominant-mode damping tuning can be
effectively decoupled, because the damping of the dominant
closed-loop system modes is primarily determined by the choice
of the most dominant characteristic ratio D2, while the response
speed primarily depends on the closed-loop equivalent time
constant Te.
It should be noted, however, that for the cases of first-order lag
model (n¼1) or a second-order model (n¼2), the above expressions
for PI and PID controller parameters (5)–(11) are characterized by a
singularity. Namely, in those particular cases the PI and PID con-
trollers may be considered as respective full-order controllers, which
results in an arbitrary choice for the equivalent time constant Te
(see discussion above). For those particular cases, the expressions
for controller parameters are listed in Table 1. Note, however, that
a too small Te choice would result in significant control efforts
and controller output saturation during reference or disturbance
response transients. Moreover, the closed-loop system noise
sensitivity (i.e. bandwidth ΩBW) is directly related to the Te value
(ΩBW$1/Te), so the closed-loop equivalent time constant should also
have to be chosen such as to achieve favorable suppression of the
measurement noise and related chattering effects in the controller
output (manipulated variable) u.
Since PI and PID controller are of a relatively low order, they
cannot arbitrarily set the higher, non-dominant characteristic
ratios in the case of a high-order closed-loop system, so the effect
of high-order closed-loop modes is analyzed herein in terms of
damping optimum criterion and closed-loop system root-locus
plots. By combining Eqs. (3) and (4), and using the expression (2)
for the process parameters am, the higher-order characteristic
ratios Dm (where m43 for PI controller, and m44 for PID
controller) can be expressed by the following simple relation:
Dm ¼
ðnÀmþ1ÞðmÀ1Þ
ðnÀmþ2Þm
¼ 1À
1
nÀmþ2
1À
1
m
: ð12Þ
These characteristic ratios should be close to 0.5 for higher-order
characteristic ratios (i.e. higher m):
lim
m-n
Dm ¼
1
2
1À
1
n
; ð13Þ
which points out to well-damped nature of high-frequency modes.
Fig. 4 shows the root-locus plots of closed-loop systems with
PI and PID controller (normalized with respect to the PTn model
time constant Tp), for a wide range of process model orders n. The
root-locus plots confirm that the higher-order closed-loop modes
are indeed well-damped, i.e. the less-dominant closed-loop poles
(corresponding to higher-frequency modes) are all characterized
by damping ratio ζE0.707.
2.3. Discrete-time PID controller implementation
In the case when the PID controller is implemented as a discrete-
time controller (Fig. 2), the design procedure can still be carried out in
the continuous-time domain if the influence of the time-discretization
(sampling) is adequately taken into account. The series connection of
the sampler and the zero-order hold (ZOH):
GsEðsÞ ¼
1
T
GEðsÞ ¼
1ÀeÀsT
Ts
; ð14Þ
corresponds to a T/2 delay (T is the sampling time) cascaded to the
process [41].
The time-differentiation effective delay T/2 of the PID controller
derivative term (z–1)/(Tz) [42] can be added to the T/2 time delay
due to the sampler and time-discretization, thus resulting in the
overall parasitic time delay Tpar ¼T. This equivalent parasitic time
delay can then be lumped with the process equivalent dead-time
Td (see e.g. [41]), obtained by the FOPDT model identification
procedure described in Section 3.
Fig. 3. Step response of prototype system tuned according to damping optimum (a) and illustration of closed-loop damping variation through dominant characteristic ratio
D2 (b).
Table 1
PI and PID controller parameters for first-order and
second-order process model formulations.
Controller (process model order)
PI (n¼1) PID (n¼2)
KR ¼
1
Kp
Tp
D2Te
À1
KR ¼
1
Kp
T2
p
D3D2
2T2
e
À1
!
TI ¼ Te 1À
D2Te
Tp
TI ¼ Te 1À
D3D2
2T2
e
T2
p
!
–
TD ¼ Tp
Tp
D3D2Te
À2
D. Pavković et al. / ISA Transactions 53 (2014) 85–9688
5. The sampling time choice (where possible) represents a trade-off
between the controller performance and its computational burden
and measurement noise issues. For processes with notable response
pure delay, the sampling time T is typically chosen with respect to
the equivalent process dead-time Td and lag time constant Ta of the
process step response (see Section 3) as follows [41]
T %
ð0:35À1:2ÞTd; 0:1rTd=Ta r1;
ð0:22À0:35ÞTd; 1rTd=Ta r10:
(
ð15Þ
Note, however, that in the case of commercial PID controller
modules (see e.g. [12]), or PLC control hardware configuration
utilizing intelligent sensors (with internal signal processing fea-
tures and typically fixed data transfer rate), the controller sam-
pling rate may be pre-determined by the control hardware
internal design. Therefore, in those cases the sampling time may
not be regarded as the controller design parameter chosen
relatively freely according to Eq. (15), but rather as a fixed
parameter which needs to be taken into account during the
controller design (tuning), as explained earlier.
2.4. Simulation verification of controller tuning
The properties of the proposed PI and PID controller tuning
approach are illustrated in Figs. 5 and 6 by simulation results.
Fig. 5 shows the comparative simulation responses of continuous-
time closed-loop systems with PI and PID controllers tuned for a
damping-wise conservative, quasi-aperiodic response (D2¼D3¼
D4¼0.5) and PTn process models characterized by Kp¼1, Tp¼10 s
and model orders in the range n¼3–5. The results show that the
proposed controller tuning with all dominant characteristic ratios
set to 0.5 indeed results in well-damped control system responses
with respect to both the reference yR and input disturbance w
step changes, characterized by approximately 6% response overshoot.
As expected, the closed-loop equivalent time constant Te, and, hence,
the control system response time increases with the process order n
(cf. Eqs. (8) and (11)). Note also that for low process model order
n¼3, the PID controller results in a much faster step reference
response and notably improved disturbance rejection compared to PI
controller, because in that particular case the PID controller design
yields a notably smaller value of the closed-loop equivalent time
constant (Te¼26.7 s) compared to PI controller (Te¼40 s). However,
as the process model order increases, the aforementioned discre-
pancy becomes smaller, and the PID controller yields control system
performance similar to simpler PI controller.
The closed-loop step responses in Fig. 6 illustrate the effects of
varying the closed-loop equivalent time constant Te according to
Eqs. (8) and (11), wherein Te adjustment reflects in the change
of the less-dominant characteristic ratios (D3 in the case of
PI controller, and D4 in the case of PID controller). If the closed-
loop equivalent time constant Te is increased above the design
value according to (8) and (11), this results in a slower closed-
loop response. As expected, by decreasing the closed-loop equiva-
lent time constant Te below these values, the response speed
Fig. 4. Normalized root-locus plots of optimally-tuned closed loop-systems with PI controller (a) and PID controller (b) for different PTn process model orders.
Fig. 5. Reference and disturbance step responses of control systems with PI controller (a) and PID controller (b) for different orders of PTn process model.
D. Pavković et al. / ISA Transactions 53 (2014) 85–96 89
6. can indeed be increased. However, this corresponds to effective
increase of less-dominant characteristic ratios (D3 or D4), and
related lower damping of the less-dominant (higher-frequency)
closed-loop modes.
2.5. Robustness analysis
The effects of PTn process model uncertainty to control system
robustness (i.e. damping of dominant closed-loop modes) have
been analyzed by means of root-locus plots and simulations for
two choices of the most dominant characteristic ratio D2 used in
PI/PID controller design (with D3, D4 ¼0.5), and a fourth-order PTn
process model formulation. Note that the results of dominant
mode damping analysis should generally be valid for a wide range
of PTn model orders n, because the damping of higher-order
modes is not affected by controller tuning or by the value of PTn
model time constant Tp (see results in Fig. 4 and the related
discussion in Section 2.2). The modeling uncertainty effects are
examined for the case of relatively large 725% variation of the
PTn model time constant Tp, reflected through its relative
error εTp¼Tp/Tpn À1 (where Tpn is the nominal PTn model time
constant used in PI/PID controller design and Tp is the actual time
constant value).
The normalized root locus plots in Fig. 7 show that for the case
of PI and PID controller tuned for a damping-wise conservative
behavior (D2 ¼0.5), the dominant conjugate-complex closed-loop
pole pair for εTP¼ À25% (Tp oTpn) is shifted towards the area of
higher damping (ζ40.707), while in the case of Tp larger then
nominal (εTP¼ þ25%), the aforementioned pole pair remains fairly
well-damped (ζE0.5). On the other hand, for the case of PI and
PID controller tuned less-conservatively, i.e. with higher D2 value
(D2 ¼0.8) corresponding to weaker damping (and faster response),
the dominant closed-loop poles are shifted towards the area of
somewhat weaker damping (0.5oζo0.25), which may still be
acceptable for process control applications favoring fast response
over closed-loop damping considerations [12].
The root-locus results in Fig. 7 are also corroborated by the
closed-loop system simulation results shown in Fig. 8 (with the
time responses also normalized with respect to time constant Tp).
The results show that for the case of damping-wise conservative
tuning (D2 ¼0.5) the closed-loop responses are indeed rather well-
damped, with notably slower (aperiodic) response without over-
shoot occurring for the case of time constant Tp smaller nominal
(εTp¼ À25%). By tuning the PI or PID controller less conservatively
(D2 ¼0.8), faster closed-loop responses can be obtained, but this
is indeed paid for by somewhat more oscillatory reference step
response.
Based on the above results, the proposed method apparently
ensures a favorable level of closed-loop system robustness in the
presence of rather large process model uncertainty even for the
Fig. 7. Normalized root-locus plots of differently-tuned closed loop-systems with PI controller (a) and PID controller (b) for 725% variations of PTn process model time
constant Tp (n¼4).
Fig. 6. Comparative control systems responses for PI controller (a) and PID controller (b) tuned with D2¼0.5 and different values of closed-loop equivalent time constant Te
(PTn process model, Kp ¼1, Tp ¼10 s, n¼4).
D. Pavković et al. / ISA Transactions 53 (2014) 85–9690
7. case of damping-wise less-conservative controller tuning choice.
Still, the choice of the main PI/PID controller tuning parameter
(i.e. characteristic ratio D2) is obviously a trade-off between the
closed-loop response speed performance, and the prescribed
(desired) lower bound of the dominant closed-loop modes damp-
ing ratio.
3. Process model identification
This section presents the estimation of aperiodic process model
parameters based on the process step response integration and
identification of equivalent FOPDT process model (the so-called area
method). The proposed process model identification approach is
compared to the traditional flexion tangent method of estimation of
FOPDT and PTn process model parameters, and is used as a basis for a
PID controller auto-tuning algorithm.
3.1. Step response flexion tangent approach
Traditionally, processes characterized by aperiodic step response
and notable initial delay (equivalent dead-time) are modeled by using
the equivalent first-order plus dead-time (FOPDT) process model:
GpðsÞ ¼
KpeÀsTd
1þTas
ð16Þ
where the equivalent dead-time Td and the time constant Ta of the
first-order lag term are typically determined by the so-called flexion-
tangent approach [31], as illustrated in Fig. 9. In order to obtain a more
convenient dead-time-free process model (suitable for PI/PID control-
ler tuning described in Section 2), the FOPDT process model can be
directly related to the more accurate PTn process model (1), char-
acterized by the same response slope (time-derivative) at the flexion
point (the so-called Strejc method [30]). The relationships between the
FOPDT model and PTn process model parameters are given by
Td
Ta
¼ eð1ÀnÞ ðnÀ1Þn
ðnÀ1Þ!
þ ∑
nÀ1
m ¼ 0
ðnÀ1Þm
m!
À1; ð17Þ
Tp
Ta
¼
ðnÀ1ÞnÀ1
ðnÀ1Þ!
eð1ÀnÞ
; ð18Þ
with the results of numerical evaluation of above equations for n¼
2–10 shown in Table 2.
Note, however, that the accuracy of thus obtained FOPDT model
is favorable only over the equivalent dead-time interval Td and in
the vicinity of the process response flexion point, while the later
part of the process transient response is captured less accurately
(see Fig. 9).
3.2. FOPDT process model identification based on step
response integration
Since the above flexion tangent identification method may
be sensitive to process measurement noise (when finding the
response time-derivative maximum point), the FOPDT model may
instead be identified based on the step response time-integral
(area) method [43], shown in Fig. 10. In this approach, the pro-
cess step response time integral is related to the FOPDT model
response in the following manner:
I1 ¼
Z Tf in
0
ðyðtÞÀy1Þdt %
Z Tf in
0
ðy2Ày1Þ½1ÀeÀðtÀTdÞ=Ta
Šdt
¼ ðy2Ày1Þ Tf inÀTdÀTa þTaeÀðTf inÀTdÞ=Ta
h i
; ð19Þ
If the identification interval Tfin is larger than 5TaþTd (the
steady-state condition), the exponential term on the rightmost
side of Eq. (19) becomes negligible (i.e. it is less than 0.01), and the
following relationship is valid:
Ta ¼ Tf inÀTdÀ
I1
y2Ày1
; ð20Þ
The process model equivalent dead-time Td can be determined
by means of a simple threshold crossing logic, as illustrated in
Fig. 10, while the process model gain Kp is estimated based on the
Fig. 8. Normalized simulation responses of differently-tuned closed loop-systems with PI controller (a) and PID controller (b) for 725% variations of PTn process model time
constant Tp (n¼4).
Fig. 9. Illustration of identification of FOPDT model based on the step response
flexion tangent approach.
D. Pavković et al. / ISA Transactions 53 (2014) 85–96 91
8. process steady-states y2 and y1 and the input step magnitude Δu
as Kp¼(y2 Ày1)/Δu (see Fig. 9).
In practical applications, the above FOPDT process model
identification procedure (implemented as a discrete-time algo-
rithm) would also need to include the following features:
Process output averaging (low-pass filtering) required to correctly
estimate the process initial state y1 and the step response steady-
state y2 in the presence of process output measurement noise.
This can be facilitated by using a simple first-order low-pass term
(filter):
yf ðkTsÞ ¼ af yf ðkTsÀTsÞþð1Àaf ÞyðkTsÞ; ð21Þ
where Ts is the process response sampling time, and the discrete-
time filter coefficient af is related to the filter equivalent time
constant Tf as af¼exp(ÀTs/Tf). The same filtered output signal
can conveniently be used for the detection of process response
equivalent dead-time. Note that in that case the dead-time value
Tdf obtained from the filtered process output should be adjusted
with respect to the low-pass filter equivalent delay (correspond-
ing to filter time constant Tf):
Td ¼ Tdf ÀTf : ð22Þ
Finally, the low-pass filter can also be used to detect the process
response settling after the step transient by monitoring the time-
difference of the low-pass filtered process output Δyf(kTs)¼
yf(kTs)Àyf(kTs–Ts), where the steady-state could be detected by
simple threshold logic (i.e. the settling would be indicated by
|Δyf(kTs)|rΔythr).
Estimation of process output noise RMS in order to find a proper
threshold value δthr for the detection of process response
equivalent dead-time Td.
Process response numerical integration, wherein a relatively simple
trapezoidal integration formula (Tustin integration method) can
be used to approximate expression (19):
I1ðkTsÞ ¼ I1ðkTsÀTsÞþ
Ts
2
½yðkTsÞþyðkTsÀTsÞÀ2y1Š: ð23Þ
Note that the accuracy of the FOPDT process model para-
meters estimation (primarily reflected through the accuracy of
lag constant Ta estimation) is directly related to the error bound ΔI
of the trapezoidal integration formula given by [44]:
ΔIj jr
Tf inT2
s
12
max
t A ½0;Tf inŠ
€yðtÞ
9.
10.
11.
12.
13.
14.
15.
16. ; ð24Þ
which for the case of FOPDT model (16) step response can be
rewritten as
ΔIj jr
Tf in
12
T2
s
T2
a
jy2Ày1j: ð25Þ
The above result, in combination with Eq. (20) gives the follow-
ing estimate of Ta absolute and relative error upper bounds,
respectively:
Δ^Ta
17.
18.
19.
20.
21.
22. r
Tf in
12
T2
s
T2
a
; ð26Þ
jΔ^Taj
Ta
r
1
12
Tf in
Ta
T2
s
T2
a
: ð27Þ
Since the Ta estimation error upper bound decreases with the Ts
vs. Ta ratio squared, the estimation accuracy should not be an issue
provided that the process response is notably slower (Ta value
much larger) than the integration step size Ts, and that the
response integration interval Tfin is also bounded with respect to
the actual Ta value (which is ensured by the utilization of the
process response steady-state detection logic).
3.3. Evaluation of equivalent PTn model parameters
However, the FOPDT model dead-time Td and the lag time
constant Ta obtained by the above identification procedure cannot
be used to directly calculate the PTn model parameters according
to (17) and (18), because the flexion tangent slope equivalence
no longer holds. In order to find the parameters of the dead-time-
free equivalent higher-order process model, the pure delay can be
approximated by its Taylor expansion [43]:
eÀsTd
¼
1
esTd
%
1
1þTdsþðT2
ds2=2ÞþðT3
ds3=6Þþ⋯
; ð28Þ
which results in the following approximation of the FOPDT
model (16):
GpðsÞ ¼
Kp
1þðTd þTaÞsþððTd=2ÞþTaÞTds2 þððTd=6ÞþðTa=2ÞÞT2
ds3 þððTd=24ÞþðTa=6ÞÞT3
ds4 þ⋯
:
ð29Þ
The above dead-time-free model can be related to the compact
PTn model (1) conveniently used in PID controller design by
equating the first three (dominant) coefficients of the PTn model
characteristic polynomial (1) with those of the process model
approximation (29). After some manipulations and rearranging,
the following expression for the PTn model order n is obtained
(which is then rounded to the nearest integer value):
n ¼
2
1ÀTdðTd þ3TaÞ=ððTd þTaÞðTd þ2TaÞÞ
: ð30Þ
Similarly, the relationship between the PTn model time con-
stant Tp and the FOPDT model dead-time Td and lag time constant
Fig. 10. Illustration of process response integration (area) method for identification
of FOPDT model.
Table 2
Relationships between FOPDT model and equivalent PTn model according to flexion-tangent approach.
n 2 3 4 5 6 7 8 9 10
Td/Ta 0.1036 0.2179 0.3195 0.4098 0.4926 0.5714 0.6410 0.7092 0.7752
Tp/Ta 0.3679 0.2707 0.2240 0.1954 0.1755 0.1606 0.1490 0.1396 0.1318
D. Pavković et al. / ISA Transactions 53 (2014) 85–9692
23. Ta is obtained in the following form (valid for n42):
Tp ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
TdðTd þTaÞðTd þ3TaÞ
nðnÀ2ÞðTd þ2TaÞ
s
ð31Þ
In the special case when the process equivalent dead-time Td is
rather small, n¼2 may be obtained (after rounding). In that case,
the time constant Tp should be calculated by using a simpler
expression:
Tp ¼
TdðTd þ2TaÞ
ðnÀ1ÞðTd þTaÞ
: ð32Þ
which is obtained by equating lower-order coefficients of the
characteristic polynomials (1) and (29).
In the case of discrete-time (digital) controller (Section 2.3),
the equivalent dead-time Td should also include effect of time-
discretization (sampling with controller sampling time T), zero-
order-hold (ZOH) element and time-differentiation (PID controller
only) in order to facilitate straightforward continuous-time
domain controller design (Section 2). This is done by lumping
the parasitic time delay Tpar to the FOPDT model equivalent time
constant Td (with Tpar¼T/2 for PI controller, and Tpar¼T for PID
controller)
Tn
d ¼ Td þTpar; ð33Þ
and using the modified equivalent dead-time Tn
d instead of the
estimated equivalent dead-time Td for the evaluation of parameters
of the controller design-oriented PTn process model (Eqs. (30)–(32)).
4. Simulation results
4.1. Process model identification results
The effectiveness of the proposed PTn model identification
procedure is first illustrated through comparison with the tradi-
tional flexion-tangent method for the case of process model
(taken from [41]) comprising aperiodic dynamics, dead-time and
a relatively non-emphasized transfer function zero:
GpðsÞ ¼
yðsÞ
uðsÞ
¼
ð1þT4sÞeÀTt s
ð1þT1sÞð1þT2sÞð1þT3sÞ
; ð34Þ
with the following values of time constants T1¼3 s, T2¼7 s, T3¼
10 s, T4¼2 s, and the dead-time Tt taking a relatively large range of
values Tt¼{4 s, 8 s, 12 s, 16 s} for the sake of detailed simulation
analysis.
Fig. 11 shows the comparative results of FOPDT and PTn process
model identification with the choice of identification sampling
time Ts ¼0.1 s. The numerical values of the estimated parameters
of the FOPDT and PTn process models, are given in Table 3, along
with the and the model prediction RMS error:
RMSe ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
N
∑
NÀ1
k ¼ 0
ðyðkÞÀ^yðkÞÞ2
s
; ð35Þ
where y(k) is the output of the process model (34), and ^yðkÞ is the
predicted output of the identified FOPDT or PTn process model.
The results in Fig. 11a show that the proposed area-based FOPDT
model identification procedure results in a much better fit of the
process model response compared to the case of flexion-tangent
Fig. 11. Comparative results of identification of FOPDT model (a) and PTn model (b) by means of flexion tangent and area method for different values of pure delay in model
(34).
D. Pavković et al. / ISA Transactions 53 (2014) 85–96 93
24. method, which gives good approximation of the process model
dynamics only in the vicinity of the step response flexion point.
Namely, according to Table 3, both identification methods yield
similar values of the equivalent FOPDT model dead time, but the
flexion-tangent method overestimates the equivalent lag time con-
stant Ta by approximately 65%. This results in much slower settling
of the flexion tangent-based FOPDT model response (cf. Fig. 11),
and significantly larger model RMS prediction errors compared to the
FOPDT model obtained by area-based identification method. The
responses of the related PTn process models are shown in Fig. 11b.
These responses, along with the prediction error RMS data in Table 3,
also point out to a notably better process step response fit obtained
by the area method, both during the transient phase and in the
response settling stage.
4.2. Auto-tuner simulation verification
The proposed PTn process model identification procedure is also
tested within the framework of PID auto-tuning by means of
simulations. In order to test the robustness of the process model
identification and the related PID controller auto-tuning algorithm,
a Gaussian noise source has been added to the process output. This
mainly concerns the practical aspects of the process PTn model
identification (see Section 3.2): the choice of detection thresholds
δthr and Δythr, and the bandwidth (time constant Tf) of the process
response low-pass filter. The low-pass filter time constant Tf is
chosen such as to facilitate favorable noise attenuation (averaging)
properties. The threshold values δthr and Δythr are adjusted with
respect to the steady-state noise RMS value (RMSss) according to
(35) with replaced with the process steady-state response yss
(obtained from the process response low-pass filter (21)). In order
to ensure robust detection of both the equivalent dead-time Td and
the response settling, the choices δthr¼1.6·RMSss and
Δythr¼0.05 Á RMSe are used herein. Two process model identification
scenarios have been considered:
(i) identification with the same identification sampling time
(integration step size) Ts¼0.1 s as in the noise-free case in
Fig. 11, corresponding to controller with flexible sampling time
choice, and
(ii) identification with larger sampling times in order to illustrate
the effectiveness of the proposed identification algorithm for
the case of controller with fixed sampling rate (i.e. Ts¼T).
Fig. 12 shows the comparative responses of the auto-tuning PID
controller with identification sampling time Ts ¼0.1 s applied to
the process model (34) with process model dead-time Tt ¼8 s, and
for the cases of process noise RMS set to 2% and 5% of the process
output step response magnitude. In the initial phase of auto-
tuning (to40 s), the process initial state and the noise RMS are
estimated, which is then followed by the step response-based
process model identification, and final closed-loop verification of
the PID controller tuned with different values of the dominant
Table 3
Comparative parameters of FOPDT and PTn models obtained by flexion tangent and area method, and related model RMS prediction errors.
Pure delay Method FOPDT model PTn model
Td [s] Ta [s] RMS error n Tp [s] RMS error
Tt¼4 s Flexion tangent 6.94 24.04 32.05 Â 10À4
4 5.13 6.87 Â 10À4
Area 7.50 14.48 7.27 Â 10À4
4 5.37 4.54 Â 10À4
Tt¼8 s Flexion tangent 10.94 24.03 32.07 Â 10À4
6 4.05 7.85 Â 10À4
Area 11.50 14.47 7.29 Â 10À4
5 5.20 4.59 Â 10À4
Tt¼12 s Flexion tangent 14.94 24.04 32.02 Â 10À4
8 3.52 8.13 Â 10À4
Area 15.50 14.45 7.32 Â 10À4
6 5.06 6.61 Â 10À4
Tt¼16 s Flexion tangent 18.94 24.02 31.99 Â 10À4
10 3.20 8.64 Â 10À4
Area 19.50 14.43 7.35 Â 10À4
8 4.23 5.92 Â 10À4
Fig. 12. Simulation results of auto-tuning PID control in presence of measurement noise for identification integration step Ts ¼0.1 s much smaller than controller sampling
time T (process model (34) with Tt¼8 s): noise RMS¼0.02 (a), and noise RMS¼0.05 (b).
Table 4
Results of process model identification during PID controller auto-tuning simula-
tion tests for different measurement noise RMS values.
Noise RMS Ta [s] Td [s] T [s] Tn
d [s] n Tp [s] Kp
0.02 14.27 11.3 4.0 15.3 6 4.98 0.990
0.05 14.04 12.0 4.2 16.2 7 4.30 0.993
D. Pavković et al. / ISA Transactions 53 (2014) 85–9694
25. characteristic ratio D2. The identification results summarized
in Table 4 indicate that the proposed area-based FOPDT model
identification procedure is fairly robust even in the presence of
relatively large-magnitude process noise, and results in highly-
consistent estimation of FOPDT and PTn process model para-
meters. Note, however, that the choice of discrete-time PID
controller sampling time2
T according to recommendation (15)
results in a slower controller sampling rate (see Table 4), and
approximately 30% larger “lumped” dead-time parameter Tn
d used
for the evaluation of the PTn process model parameters. After the
auto tuning phase is finished, the PID controller is turned on, and a
constant reference is applied to the closed-loop system. The auto-
tuned PID controllers are characterized by different levels of closed
loop damping depending on the choice of the dominant charac-
teristic ratios D2 (with D3 ¼D4 ¼0.5). As expected, a well-damped
(quasi-aperiodic) reference step response is obtained when D2 is
set to 0.5. As the dominant characteristic ratio D2 is increased
above 0.5, the closed-loop response time and damping are in turn
decreased in accordance with the damping optimum criterion
tuning properties (cf. Fig. 3b). In all cases, the controller output
(manipulated variable u) is characterized by a relatively small
magnitude of noise due to controller bandwidth being effectively
limited due to a relatively large equivalent closed-loop time
constant Te.
The auto-tuner simulation results for the case of much larger
identification sampling times and auto-tuner/controller fixed sam-
pling rate (Ts¼T) are shown in Fig. 13. The presented results indicate
that the proposed identification approach works well even for
relatively large sampling times Ts (comparable to process model
(34) lag time constants), and ultimately results in anticipated
closed-loop behavior for the particular D2 tuning parameter choices
(cf. results in Fig. 12).
5. Conclusion
The paper has presented a novel analytical method of PID
controller tuning based on the n-th order aperiodic process model
description (PTn model) and the utilization of damping optimum
criterion, which facilitates a rather straightforward adjustment of
both closed-loop system damping and response speed, and whose
main features have been verified by means of simulations. The
effect of modeling errors has been examined by root locus plots
and simulation analysis, which have shown that the proposed
tuning method can facilitate fairly robust closed-loop behavior in
the presence of relatively large process model variations (i.e. PTn
process model time constant).
In order to find the parameters of the controller design-oriented
PTn process model, a relatively computationally-simple auto-tuning
algorithm based on process model step response time integral has
been developed and tested. The auto-tuning algorithm finds the
parameters of the simplified first-order plus dead-time (FOPDT)
process model, which is then related to the dead-time-free PTn
process model used in PID controller design by using a higher-order
Taylor expansion of the process equivalent dead-time term.
The proposed step response-based PTn process model identifi-
cation has been verified on a prototype process model comprising
both the aperiodic (lag) dynamics and emphasized dead-time effect,
and it has resulted in a consistent estimation of key parameters of
the equivalent PTn model for a wide range of the process dead-time
parameter values, while also achieving notably improved model
prediction accuracy compared to the traditional flexion-tangent
identification approach. The overall auto-tuning PID controller
has also been verified by means of simulations. The PTn model
identification procedure has shown favorable robustness in the
presence of emphasized process measurement noise and for a wide
range of sampling time choices. The resulting automatically-tuned
PID controllers have yielded expected (favorable) closed-loop sys-
tem behavior, wherein the closed-loop system dominant mode
damping is easily tuned by means of the damping optimum tuning
method.
Future work may be directed towards the development of auto-
tuning procedures for other process model structures and related
refinement of the damping optimum criterion-based PID control-
ler tuning.
Acknowledgment
The first author would like to express his appreciation to
Prof. Joško Deur from the Faculty of Mechanical Engineering and
Naval Architecture, University of Zagreb for his insights and help-
ful discussions regarding the damping optimum criterion.
References
[1] Bonivento C, Castaldi P, Mirotta D. Predictive control vs. PID control of an
industrial heat exchanger. In: CD ROM Proceedings of 9th Mediterranean
conference on control and automation (MED 2001), Dubrovnik, Croatia; 2001.
[2] Al-Dawery SK, Alrahawi AM, Al-Zobai KM. Dynamic modeling and control of
plate heat exchanger. International Journal of Heat and Mass Transfer 2012;55
(23–24) (6873–5880).
Fig. 13. Simulation results of auto-tuning PID control for fixed integration step Ts equal to controller sampling time T (process model (34) with Tt ¼8 s) with noise RMS¼0.02:
Ts ¼1 s (a), and Ts ¼2 s (b).
2
In order to avoid noise aliasing issues in the case of relatively large controller
sampling time T choice, the high-sampling-rate process output (Ts ¼0.1 s) is
averaged within the controller sampling time window (with the width W¼T/Ts),
thus substituting for the anti-aliasing low-pass filter of the process output signal.
D. Pavković et al. / ISA Transactions 53 (2014) 85–96 95
26. [3] Åström KJ, Hägglund T. The future of PID control. Control Engineering Practice
2001;9(11):1163–75.
[4] Panda RC, Yu C-C, Huang H-P. PID tuning rules for SOPDT systems: review and
some new results. ISA Transactions 2004;43(2):283–95.
[5] Åström KJ, Hägglund T. Revisiting the Ziegler–Nichols step response method
for PID control. Journal of Process Control 2004;14(6):635–50.
[6] Leva A, Negro S, Papadopoulos AV. PI/PID autotuning with contextual model
parametrisation. Journal of Process Control 2010;20(4):452–63.
[7] Li Y, Ang K-H, Chong G. Patents, software and hardware for PID control. IEEE
Control Systems Magazine 2006;26(1):42–54.
[8] Ang K-H, Chong G, Li Y. PID control system analysis, design and technology.
IEEE Transactions on Control Systems Technology 2005;13(4):559–76.
[9] Åström KJ, Hägglund T. Revisiting the Ziegler–Nichols step response method
for PID control. Journal of Process Control 2004;14(6):635–50.
[10] Dey C, Mudi RK. An improved auto-tuning scheme for PID controllers. ISA
Transactions 2009;48(4):396–409.
[11] Hagglund T, Åström KJ. Automatic tuning of PID controllers. In: Levine WS, editor.
The control handbook. Boca Raton, FL, USA: CRC Press; 2000 [chapter 52].
[12] Åström KJ, Hägglund T. PID controllers: theory, design and tuning. 2nd ed..
Research Triangle Park, Durham, NC, USA: Instrument Society of America;
1995.
[13] Wang Q-G, Fung H-W, Zhang Y. PID tuning with exact gain and phase margins.
ISA Transactions 1999;38(3):243–9.
[14] Atherton DP. Relay autotuning: a use of old ideas in a new setting. Transac-
tions of the Institute of Measurement and Control 2000;22(1):103–22.
[15] Preitl S, Precup R-E. An extension of tuning relations after symmetrical
optimum method for PI and PID controllers. Automatica 1999;35(10):1731–6.
[16] Lui T, Gao F. Relay-based autotuning of pid controller for improved load
disturbance rejection. In: Proceedings of the 17th IFAC world congress, Seoul,
South Korea; July 2008. p. 10933–38.
[17] Carnevale C, Piazzi A, Visioli A. A methodology for integrated system identifica-
tion, PID controller tuning and noncausal feedforward control design. In:
Proceedings of the 17th IFAC world congress, Seoul, South Korea; July 2008.
p. 13324–29.
[18] Karimi A, Garcia D, Longchamp R. PID controller tuning using bode's integrals.
IEEE Transactions on Control System Technology 2003;11(6):812–21.
[19] Padhy PK, Majhi S. Improved automatic tuning of PID controller for stable
processes. ISA Transactions 2009;48(4):423–7.
[20] Hang CC, Åström KJ, Wang QG. Relay feedback auto-tuning of process
controllers – a tutorial review. Journal of Process Control 2002;12(1):143–62.
[21] Wang Q-G, Zhang Y. Robust identification of continuous systems with dead-
time from step response. Automatica 2001;37(3):377–90.
[22] Vrančić D, Peng Y, Strmčnik S. A new PID controller tuning method based on
multiple integrations. Control Engineering Practice 1999;7(5):623–33.
[23] Vrančić D, Strmčnik S, Juričić Đ. A magnitude optimum multiple integration
tuning method for filtered PID controller. Automatica 2001;37(9):1473–9.
[24] Vrančić D, Strmčnik S, Kocijan J, de Moura Oliveira PB. Improving disturbance
rejection of PID controllers by means of the magnitude optimum method. ISA
Transactions 2010;49(1):47–56.
[25] Villanova R. IMC based robust PID design: tuning guidelines and automatic
tuning. Journal of Process Control 2008;18(1):61–70.
[26] Leva A. Comparative study of model-based PI(D) autotuning methods. In:
Proceedings of the 2007 American control conference (ACC 2007), New York,
USA; July 2007. p. 5796–801.
[27] Garpinger O, Hägglund T. A software tool for robust PID design. In: Proceedings
of the 17th IFAC world congress, Seoul, South Korea; July 2008. p. 6416–21.
[28] Bi Q, Cai W-B, Wang Q-G, Hang C-C, Lee E-L, Sun Y, et al. Advanced controller
auto-tuning and its application in HVAC systems. Control Engineering Practice
2000;8(6):633–44.
[29] Thomson M, Cassidy PG, Sandoz DJ. Automatic tuning of PID controllers using
a combined time- and frequency-domain method. Transaction of the Institute
of Measurement and Control 1989;11(1):40–7.
[30] Unbehauen H, Rao GP. Identification of continuous systems, North Holland;
1987 [chapter 4].
[31] Mikleš J, Fikar M. Process modelling, identification and control. Berlin-
Heidelberg, Germany: Springer-Verlag; 2007 [chapter 6].
[32] Preuss HP. PTn-modell-identifikation im adaptiven PID-Regelkreis. Automati-
sierungstechnik 1990;38(9):337–43.
[33] Umland JW, Safiuddin M. Magnitude and symmetric optimum criterion for the
design of linear control systems: what is it and how does it compare with the
others. IEEE Transactions on Industry Applications 1990;26(3):489–97.
[34] Naslin P. Essentials of optimal control. London, UK: Iliffe Books; 1968
[chapter 2].
[35] Zäh M, Brandeburg G. Das erweiterte Dämpfungsoptimum. Automatisierung-
stechnik 1987;35(7):275–83.
[36] Deur J, Perić N, Stajić D. Design of reduced-order feedforward controller. In:
Proceedings of the UKACC international conference on CONTROL’98, Swansea,
UK; 1998. p. 207–12.
[37] Åström KJ, Wittenmark B. Computer controlled systems – theory and design.
3rd ed.. New Jersey, USA: Prentice Hall; 1997 [chapter 8].
[38] Schmidt C, Heinzl J, Brandenburg G. Control approaches for high-precision
machine tools with air bearings. IEEE Transactions on Industrial Electronics
1999;46(5):979–89.
[39] Schröder D. ElektrischeAntriebe – Regelung von Antriebssystemen. 3rd ed.
Berlin, Germany: Springer-Verlag; 2007 [chapter 19].
[40] Pavković D, Deur J, Lisac A. A torque estimator-based control strategy for oil-
well drill-string torsional vibrations active damping including an auto-tuning
algorithm. Control Engineering Practice 2011;19(8):836–50.
[41] Isermann R. Digital control systems, vol. 1. Berlin: Springer-Verlag; 1989
[chapter 5].
[42] Saito K, Kamiyama K, Ohmae T, Matsuda T, Microprocessor-Controlled Speed
A. Regulator with instantaneous speed estimation for motor drives. IEEE
Transactions on Industrial Electronics 1988;35(1):95–9.
[43] Normey-Rico JE, Camacho EF. Control of dead-time processes. London, UK:
Springer-Verlag; 2007 [chapters 2 and 3].
[44] Kreyszig E. Advanced engineering mathematics. 8th ed. New York, USA: John
Wiley Sons; 1999 [chapter 17].
D. Pavković et al. / ISA Transactions 53 (2014) 85–9696