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.
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.
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
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.
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.
Objective functions modification of GA optimized PID controller for brushed D...IJECEIAES
PID Optimization by Genetic Algorithm or any intelligent optimization method is widely being used recently. The main issue is to select a suitable objective function based on error criteria. Original error criteria that is widely being used such as ITAE, ISE, ITSE and IAE is insufficient in enhancing some of the performance parameter. Parameter such as settling time, rise time, percentage of overshoot, and steady state error is included in the objective function. Weightage is added into these parameters based on users’ performance requirement. Based on the results, modified error criteria show improvement in all performance parameter after being modified. All of the error criteria produce 0% overshoot, 29.51%-39.44% shorter rise time, 21.11%-42.98% better settling time, 10% to 53.76% reduction in steady state error. The performance of modified objective function in minimizing the error signal is reduced. It can be concluded that modification of objective function by adding performance parameter into consideration could improve the performance of rise time, settling time, overshoot percentage, and steady state error.
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.
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.
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
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.
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.
Objective functions modification of GA optimized PID controller for brushed D...IJECEIAES
PID Optimization by Genetic Algorithm or any intelligent optimization method is widely being used recently. The main issue is to select a suitable objective function based on error criteria. Original error criteria that is widely being used such as ITAE, ISE, ITSE and IAE is insufficient in enhancing some of the performance parameter. Parameter such as settling time, rise time, percentage of overshoot, and steady state error is included in the objective function. Weightage is added into these parameters based on users’ performance requirement. Based on the results, modified error criteria show improvement in all performance parameter after being modified. All of the error criteria produce 0% overshoot, 29.51%-39.44% shorter rise time, 21.11%-42.98% better settling time, 10% to 53.76% reduction in steady state error. The performance of modified objective function in minimizing the error signal is reduced. It can be concluded that modification of objective function by adding performance parameter into consideration could improve the performance of rise time, settling time, overshoot percentage, and steady state error.
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.
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.
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.
Enhanced self-regulation nonlinear PID for industrial pneumatic actuatorIJECEIAES
The present article describes the improvement of Self-regulation Nonlinear PID (SN-PID) controller. A new function is introduced to improve the system performance in terms of transient without affecting the steady state performance. It is used to optimize the nonlinear function available on this controller. The signal error is reprocessed through this function, and the result is used to tune the nonlinear function of the controller. Furthermore, the presence of the dead zone on the proportional valve is solved using Dead Zone Compensator (DZC). Simulations and experiments were carried out on the pneumatic positioning system. Comparisons between the existing methods were examined and successfully demonstrated.
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.
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.
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.
FRACTIONAL ORDER PID CONTROLLER TUNING BASED ON IMC IJITCA Journal
In this work, a class of fractional order controller (FOPID) is tuned based on internal model control
(IMC). This tuning rule has been obtained without any approximation of time delay. Moreover to show
usefulness of fractional order controller in comparison with classical integer order controllers, an
industrial PID controller tuned in a similar way, is compared with FOPID and then robust stability of both
controllers is investigated. Robust stability analysis has been done to find maximum delayed time
uncertainty interval which results in a stable closed loop control system. For a typical system, robust
stability has been done to find maximum time constant uncertainty interval of system. Two clarify the
proposed control system design procedure, three examples have been given.
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.
PID Control of Runaway Processes - Greg McMillan DeminarJim Cahill
On-line demo / seminar presented by ModelingAndControl.com's Greg McMillan on August 25, 2010.
Recorded version of presentation will be available post live session at: http://www.screencast.com/users/JimCahill/folders/Deminars
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.
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
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.
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.
Enhanced self-regulation nonlinear PID for industrial pneumatic actuatorIJECEIAES
The present article describes the improvement of Self-regulation Nonlinear PID (SN-PID) controller. A new function is introduced to improve the system performance in terms of transient without affecting the steady state performance. It is used to optimize the nonlinear function available on this controller. The signal error is reprocessed through this function, and the result is used to tune the nonlinear function of the controller. Furthermore, the presence of the dead zone on the proportional valve is solved using Dead Zone Compensator (DZC). Simulations and experiments were carried out on the pneumatic positioning system. Comparisons between the existing methods were examined and successfully demonstrated.
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.
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.
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.
FRACTIONAL ORDER PID CONTROLLER TUNING BASED ON IMC IJITCA Journal
In this work, a class of fractional order controller (FOPID) is tuned based on internal model control
(IMC). This tuning rule has been obtained without any approximation of time delay. Moreover to show
usefulness of fractional order controller in comparison with classical integer order controllers, an
industrial PID controller tuned in a similar way, is compared with FOPID and then robust stability of both
controllers is investigated. Robust stability analysis has been done to find maximum delayed time
uncertainty interval which results in a stable closed loop control system. For a typical system, robust
stability has been done to find maximum time constant uncertainty interval of system. Two clarify the
proposed control system design procedure, three examples have been given.
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.
PID Control of Runaway Processes - Greg McMillan DeminarJim Cahill
On-line demo / seminar presented by ModelingAndControl.com's Greg McMillan on August 25, 2010.
Recorded version of presentation will be available post live session at: http://www.screencast.com/users/JimCahill/folders/Deminars
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.
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
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.
DESIGN OF PID CONTROLLERS INTEGRATOR SYSTEM WITH TIME DELAY AND DOUBLE INTEGR...ijcisjournal
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.
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
Experimental evaluation of control performance of MPC as a regulatory controllerISA Interchange
Proportional integral derivative (PID) control is widely practiced as the base layer controller in the industry due to its robustness and design simplicity. However, a supervisory control layer over the base layer, namely a model predictive controller (MPC), is becoming increasingly popular with the advent of computer process control. The use of a supervisory layer has led to different control structures. In this study, we perform an objective investigation of several commonly used control structures such as “Cascaded PI controller,” “DMC cascaded to PI” and “Direct DMC.” Performance of these control structures are compared on a pilot-scale continuous stirred tank heater (CSTH) system. We used dynamic matrix control (DMC) algorithm as a representative of MPC. In the DMC cascaded to PI structure, the flow-loops are regulated by the PI controller. On top of that a DMC manipulates the set-points of the flow-loops to control the temperature and the level of water in the tank. The “Direct DMC” structure, as its name suggests, uses DMC to manipulate the valves directly. Performance of all control structures were evaluated based on the integrated squared error (ISE) values. In this empirical study, the “Direct DMC” structure showed a promise to act as regulatory controller. The selection of control frequency is critical for this structure. The effect of control frequency on controller performance of the “Direct DMC” structure was also studied.
In this paper, the closed loop speed controller parameters are optimized for the permanent magnet synchronous motor (PMSM) drive on the basis of the indirect field-oriented control (IFOC) technique. In this derive system under study, the speed and current controllers are implemented using the fractional order proportional, integral, and derivative (FOPID) controlling technique. FOPID is considered as efficient techniques for ripple minimization. The hybrid grey wolf optimizer (HGWO) is applied to obtain the optimal controllers in case of implementing conventional PID as well as FOPID controllers in the derive system. The optimal controller parameters tend to enhance the drive response as ripple content in speed and current, either during steady state time or transient time. The drive system is modeled and tested under various operating condition of load torque and speed. Finally, the performance for PID and FOPID are evaluated and compared within MATLAB/Simulink environment. The results attain the efficacy of the operating performance with the FOPID controller. The result shows a fast response and reduction of ripples in the torque and the current.
Design of PID Controller with Inadequate Determination Dependent on Different...ijtsrd
To decide the ideal or close to ideal boundaries of PID regulator with fragmented determination, an original plan strategy dependent on differential advancement calculation is introduced. The regulator is called DE PID controller. To beat the impediments of the necessary exhibition rules in the recurrence space like IAE, ISE, and ITSE, another presentation measure in the time area is proposed. The streamlining methods utilizing the DE calculation to look through the ideal or close to ideal PID controller boundaries of a control framework are shown exhaustively. Three common control frameworks are picked to test and assess the variation and vigor of the proposed DE PID controller. The reproduction results show that the proposed approach has unrivalled provisions of simple execution, stable combination trademark, and great computational efficiency. Contrasted and the ZN, GA, and ASA, the proposed plan technique is without a doubt more efficient and strong in further developing the progression reaction of a control framework. N. Abinaya | V. Gomathi | V. Sudha "Design of PID Controller with Inadequate Determination Dependent on Differential Development Calculation" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-2 , February 2022, URL: https://www.ijtsrd.com/papers/ijtsrd49270.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/49270/design-of-pid-controller-with-inadequate-determination-dependent-on-differential-development-calculation/n-abinaya
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.
An optimal general type-2 fuzzy controller for Urban Traffic NetworkISA Interchange
Urban traffic network model is illustrated by state-charts and object-diagram. However, they have limitations to show the behavioral perspective of the traffic information flow. Consequently, a state space model is used to calculate the half-value waiting time of vehicles. In this study, a combination of the general type-2 fuzzy logic sets and the modified backtracking search algorithm (MBSA) techniques are used in order to control the traffic signal scheduling and phase succession so as to guarantee a smooth flow of traffic with the least wait times and average queue length. The parameters of input and output membership functions are optimized simultaneously by the novel heuristic algorithm MBSA. A comparison is made between the achieved results with those of optimal and conventional type-1 fuzzy logic controllers.
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
Abstract: In this work we have developed a novel, robust practical control structure to regulate an industrial methanol distillation column. This proposed control scheme is based on a override control framework and can manage a non-key trace ethanol product impurity specification while maintaining high product recovery. For comparison purposes, an MPC with a discrete process model (based on step tests) was also developed and tested. The results from process disturbance testing shows that, both the MPC and the proposed controller were capable of maintaining both the trace level ethanol specification in the distillate (XD) and high product recovery (β). Closer analysis revealed that the MPC controller has a tighter XD control, while the proposed controller was tighter in β control. The tight XD control allowed the MPC to operate at a higher XD set point (closer to the 10 ppm AA grade methanol standard), allowing for savings in energy usage. Despite the energy savings of the MPC, the proposed control scheme has lower installation and running costs. An economic analysis revealed a multitude of other external economic and plant design factors, that should be considered when making a decision between the two controllers. In general, we found relatively high energy costs favor MPC.
Fault detection of feed water treatment process using PCA-WD with parameter o...ISA Interchange
Feed water treatment process (FWTP) is an essential part of utility boilers; and fault detection is expected for its reliability improvement. Classical principal component analysis (PCA) has been applied to FWTPs in our previous work; however, the noises of T2 and SPE statistics result in false detections and missed detections. In this paper, Wavelet denoise (WD) is combined with PCA to form a new algorithm, (PCA- WD), where WD is intentionally employed to deal with the noises. The parameter selection of PCA-WD is further formulated as an optimization problem; and PSO is employed for optimization solution. A FWTP, sustaining two 1000 MW generation units in a coal-fired power plant, is taken as a study case. Its operation data is collected for following verification study. The results show that the optimized WD is effective to restrain the noises of T2 and SPE statistics, so as to improve the performance of PCA-WD algorithm. And, the parameter optimization enables PCA-WD to get its optimal parameters in an auto- matic way rather than on individual experience. The optimized PCA-WD is further compared with classical PCA and sliding window PCA (SWPCA), in terms of four cases as bias fault, drift fault, broken line fault and normal condition, respectively. The advantages of the optimized PCA-WD, against classical PCA and SWPCA, is finally convinced with the results.
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.
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.
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.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
A simple nonlinear PD controller for integrating processes
1. Research Article
A simple nonlinear PD controller for integrating processes
Chanchal Dey a
, Rajani K. Mudi b,n
, Dharmana Simhachalam b
a
Department of of Applied Physics, University of Calcutta, 92, A.P.C. Road, Calcutta 700009, West Bengal, India
b
Department of Instrumentation & Electronics Engineering, Jadavpur University, Sector III, Block LB/8, Salt-lake, Calcutta 700098, West Bengal, India
a r t i c l e i n f o
Article history:
Received 2 September 2012
Received in revised form
3 September 2013
Accepted 4 September 2013
Available online 2 October 2013
This paper was recommended for
publication by Prof. A.B. Rad
Keywords:
PID control
Nonlinear PD control
Integrating process
a b s t r a c t
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 con-
tinuously 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.
& 2013 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Proportional-integral-derivative (PID) controllers are widely
used in various industrial process control applications due to their
simplicity and effectiveness [1–6]. But, performances of model free
PID controllers are not usually satisfactory due to their oscillatory
responses and large settling time for integrating processes with
time delay [7–9]. For example, Fig. 1 shows such poor perfor-
mances of the well known Ziegler–Nichols tuned PID (ZNPID) [10]
controllers for IPD and FOIPD processes. In Fig. 1, initially a step set
point change is applied and when the process reaches its steady
state, an impulse load disturbance is introduced at the process
input. Here, overshoots are found to be more than 60%, which is
not acceptable in most of the applications [6]. On the other than
hand, model based PID control techniques, like IMC can provide
lower overshoot with faster settling on proper selection of tuning
parameters (close-loop time constant) [11–15]. Fig. 2 shows the
responses of model based IMC-PID controllers [11] for IPD and
FOIPD processes. It is found that lower overshoot with faster
settling is achieved in the set point response for IMC-PID com-
pared to ZNPID but no significant improvement is observed during
load rejection.
Due to the presence of integral action, PID controllers are likely
to produce oscillations for integrating plus dead time processes [1].
In general, proportional-derivative (PD) controllers, if properly
designed [6], are capable of providing reasonable performances
compared to PID controllers for integrating or zero-load processes
with delay [16]. Robots and manipulators are extensively used in
automation based manufacturing processes where any type of
overshoot and/or undershoot is highly undesirable [17] in position-
ing their arms. In spite of noise sensitivity, PD controllers help to
reduce the overshoot by introducing higher damping [18]. So, there
is a scope for designing improved PD controllers to achieve desired
performance for integrating processes with dead time. But, till
today, unlike PID controllers, probably there are less running
schemes for PD controllers [19].
For IPD processes, Chidambaram and Padma Sree [16] used
equating coefficient method to find the parameters of a PD
controller, which will be denoted here as CPPD. Kristiansson and
Lennartson [20] reported that the derivative action can signifi-
cantly improve the control performance compared to PI control
with equal stability margin for most of the plants including those
with noticeably large time delay. Authors in [21] proposed a
Lyapunov based approach to obtain PD parameters. Xu et al. [22]
designed a nonlinear PD controller with increased damping
corresponding to its linear counterpart. Its proportional and
derivative gains are modulated nonlinearly based on the instanta-
neous value of error (e) and the sign of change of error (Δe), and its
various tunable parameters are chosen heuristically maintaining
the stability of the system. Visioli [23] used genetic algorithm
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.2013.09.011
n
Corresponding author. Tel.: þ91 33 23352587; fax: þ91 33 23357254.
E-mail addresses: chanchaldey@yahoo.co.in, cdaphy@caluniv.ac.in (C. Dey),
rkmudi@yahoo.com, rkmudi@iee.jusl.ac.in (R.K. Mudi), chalamju10@gmail.com
(D. Simhachalam).
ISA Transactions 53 (2014) 162–172
2. based optimization scheme to minimize various integral errors
like ISE and ITSE and finally got PD settings (here termed as VPD)
for set point tracking. For FOIPD processes, Vítečková et al. [24]
and O'Dwyer [25] suggested PD controllers towards achieving
improved responses. There is a possibility to enhance the perfor-
mance of a PD controller by extending its integer order of the
derivative element to fractional order [26].
Fuzzy controllers have been successfully designed with
improved performances compared to their conventional counter-
parts [27–33]. In [28], the nonlinear gain modification scheme
following an operator's strategy continuously adjusts the output
scaling factor (considered to be the close-loop gain) of a fuzzy PD
controller with the help of 49 fuzzy If-Then rules, defined on the
current process states, i.e., e and Δe. Su et al. [29] developed a
hybrid fuzzy PD controller by combining two nonlinear tracking
differentiators to a conventional fuzzy PD controller. In spite of a
number of merits, there are many limitations while designing a
fuzzy controller, since, till now there is no standard methodology
for its various design steps. Moreover, no clear guidelines are
available for selecting appropriate values of its large number of
design parameters.
The above discussion and our literature survey reveal that
compared to the well established PI and PID control techniques,
less importance/attention has been given for the development of
conventional PD control. Hence, there is a good prospect for
further development of PD controllers with enhanced perfor-
mance. With this perspective in mind, and encouraging results
of [22,28], in this study, we are motivated to introduce a real time
nonlinear gain modification scheme for a PD controller. Due to lack
of a suitable auto-tuning scheme, here, we consider the most
widely accepted Ziegler–Nichols ultimate cycle based PID (i.e.,
ZNPID) tuning rules [10] by ignoring its integral part for the initial
setting of the proposed PD controller (APD). Note that, Ziegler–
Nichols rules were originally developed for the tuning of P, PI, and
PID controllers, but not for a PD controller. In the proposed APD,
the proportional and derivative gains are continuously adjusted
depending on the instantaneous process trend by introducing
a nonlinear gain updating parameter α. The basic idea behind this
real time gain adjustment mechanism is that when the process is
moving towards the set point, control action will be conservative
to avoid possible large overshoots and/or undershoots in the
subsequent operating phases, and when the process is moving
away from the set point, control action will be aggressive to bring
it back quickly to its desired value. It is to be mentioned that, our
proposed scheme is different from others [22,28] as far as its
design simplicity and practical implementation are concerned.
Nonlinear gain variation in [22] involves a number of heuristically
chosen tunable parameters along with an exponential function in
its gain update rules, whereas, in [28] the output scaling factor is
adjusted through a number of fuzzy conditional rules derived from
experts’ knowledge.
The performance of the proposed PD controller is tested and
compared with a large number of PID and PD tuning rules
reported over the last decade for IPD and FOIPD processes. In
addition, real time experimentation is also performed on a
laboratory scale DC servo position control system. Performance
analysis with respect to a number of performance indices reveals
that APD is capable of providing an overall improved performance
in comparison with PID settings given by AHPID [2], DMPID [3],
ZNPID [10], SLPPID [11], CPPID [16], VPID [23], PCPID [34], ACPID
[35], RRCPID [36], AMPID [37], HXCPID [38], RPID [50], and PD
settings by CPPD [16], VPD [23], and LLPPD [39] for the IPD process
under both set point change and load disturbance. Similarly,
enhanced performance is also observed for the FOIPD process in
comparison with PID tuning rules of DMPID [3], ZNPID [10], SPID
[12], AMPID [37], HXCPID [38], YPID [40], WCPID [41], RRCPID [42],
SLPID [44], KLPID [47], RPID [50] and PD settings of VVSPD [24],
DPD [25], EOMPD [45], and SJLPD [46]. Performance robustness
of the proposed APD is studied with þ25% perturbations in
process dead time and also in presence of measurement noise.
Its stability robustness is established from the gain margin (GM)
and phase margin (PM) values as well as through Kharitonov
polynomials [48]. The rest of the paper is divided into three sections.
In Section 2, we describe the various steps of the controller
design, its nonlinear gain variation mechanism for different operat-
ing points during transient phase, and its stability and robustness
issues. Section 3 presents simulation study with detailed perfor-
mance analysis as well as real time experimentation on a DC servo
position control system modeled as a FOIPD process. There is
a conclusion in Section 4.
2. The proposed controller
A simplified block diagram of the proposed APD is shown in
Fig. 3. In order to achieving a faster convergence of the system
with smaller overshoot and undershoot, both the proportional and
derivative gains are modified at each sampling instant based on
the instantaneous values of normalized error eN and change of
0 20 40 60 80 100 120 140 160 180 200
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Time(sec)
Response
IPD
FOIPD
Fig. 1. Responses for IPD ½GpðsÞ ¼ 0:0506eÀ 6s
=sŠ and FOIPD ½GpðsÞ ¼ eÀ 4s
=sð4sþ1ÞŠ
processes under ZNPID [10].
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
IPD
FOIPD
Fig. 2. Responses for IPD ½GpðsÞ ¼ 0:0506eÀ6s
=sŠ and FOIPD ½GpðsÞ ¼ eÀ 4s
=sð4sþ1ÞŠ
processes under IMC-PID [11].
-
r
Process
+
+
Normalization
Ne
-
y
Z
−1
+
e
e
(1 + )αpK
+
+NeΔ
-
×
Load
disturbance
+
+
+
+
Noise
Kd(1+γ )α
Z
−1
Fig. 3. Block diagram of the proposed auto-tuning PD controller (APD).
C. Dey et al. / ISA Transactions 53 (2014) 162–172 163
3. error ΔeN of the controlled variable. In this study, load disturbance
is applied at the process input and white noise is introduced at the
process output as shown in Fig. 3.
2.1. Design of the proposed controller APD
Discrete form of a PD controller at kth sampling instant can be
described as:
uðkÞ ¼ Kp eðkÞþ
Td
Δt
ΔeðkÞ
ð1Þ
or
uðkÞ ¼ KpeðkÞþKdΔeðkÞ; ð2Þ
when
Kd ¼ Kp
Td
Δt
Here, Kp is the proportional gain, Td is the derivative time, Kd is
the derivative gain, and Δt is the sampling interval. Error e(k) and
change of error Δe(k) at kth sampling instant are defined by
eðkÞ ¼ rÀyðkÞ; and ΔeðkÞ ¼ eðkÞÀeðkÀ1Þ: ð3Þ
In Eq. (3), r is the set point and y(k) is the process output at kth
instant. It has already been mentioned that, due to absence of any
simple auto-tuning scheme for the initial setting of the propor-
tional and derivative gains of a PD controller, we have chosen the
widely practiced Ziegler–Nichols PID tuning rules [10] by dropping
its integral term. Therefore, the values of Kp and Td of the initial PD
controller are obtained by the following relations:
Kp ¼ 0:6Ku; ð4Þ
and
Td ¼ 0:125Tu: ð5Þ
where Ku is the ultimate gain and Tu is the ultimate period
obtained by relay-feedback test [51]. These initial values of Kp
and Kd (Eq. (2)) get modified continuously by the nonlinear gain
updating factor α, which is defined by
αðkÞ ¼ eNðkÞ Â ΔeNðkÞ; ð6Þ
where eNðkÞ ¼ eðkÞ=jrj and ΔeNðkÞ ¼ eNðkÞÀeNðkÀ1Þ.
In Eq. (6), eN(k) and ΔeN(k) are considered as the normalized
values of e(k) and Δe(k), respectively. Eq. (6) indicates that the
instantaneous value of α(k) may vary between À1 and þ1, since
the usual range of eN(k) or ΔeN(k) is [À1, 1] for an acceptable close-
loop performance where the peak overshoot remains within 100%.
Observe that the gain updating parameter α changes with the
instantaneous values of eN and ΔeN, hence, it contains the
information regarding the current position and direction of move-
ment of the process in the response trajectory. We utilize this
intelligence property of α to realize the desired gain variation
strategy mentioned earlier, i.e., control action will be made
conservative or aggressive depending on the movement of the
process towards or away from its set point, respectively. Keeping
in mind such a real time gain adjustment in APD, we propose the
following update rules:
Ka
pðkÞ ¼ Kpð1þαðkÞÞ; ð7Þ
Ka
dðkÞ ¼ Kdð1þγjαðkÞjÞ: ð8Þ
Here, Ka
p and Ka
d are the time varying nonlinear proportional
and derivative gains. γ is a positive constant for providing an
appropriate variation of damping to get the desired close-loop
response. In steady state condition αðkÞ ¼ 0, hence Ka
pðkÞ ¼ Kp and
Ka
dðkÞ ¼ Kd. During transient phases, Ka
p may be higher or lower
than Kp depending on the sign of α but Ka
d will always be higher
than Kd. Such nonlinear gain variations are expected to provide
necessary damping required for achieving an enhanced control
performance. Detailed discussion about this online gain modifica-
tion mechanism at different operating points and its influence on
the close-loop performance is provided in the following Section 2.2.
Thus, the proposed APD can be expressed as:
ua
ðkÞ ¼ Ka
pðkÞ eðkÞþKa
dðkÞ ΔeðkÞ: ð9Þ
For proper tuning of the controller, suitable value of γ is to be
selected, which may be done either using operator's knowledge or
by trial depending on the process dynamics. In addition, for
specific performance based applications where some constraints
are imposed on the system behavior, the value of γ may be
obtained through some optimization technique, so that the result-
ing system response meets those specified performance indices.
Through an extensive simulation study on a large number of
integrating (IPD and FOIPD) processes, we suggest the following
simple empirical relation for γ, which gives an overall satisfactory
performance for all such cases.
γ ¼ 2  Ku  Tu  K: ð10Þ
In Eq. (10), K is the open-loop gain of the related process.
Observe that γ depends on the dynamics of the process under
control, which may be characterized by its critical point (Ku, Tu).
Moreover, γ does not increase the design complexity as all the
parameters, i.e., Ku, Tu, and K are obtained from the relay-feedback
test [51], which is also used for setting the initial parameters of the
proposed APD. We use the same relation of γ, i.e., Eq. (10), for both
the IPD and FOIPD processes in our simulation as well as in
experimental study on a DC servo system. In (Section 3) to come,
we will observe that considerable deviations of γ from its respec-
tive nominal values bring only a little change in the close-loop
performance of IPD as well as FOIPD processes.
2.2. Online gain modification
From the dynamic proportional and derivative gain expres-
sions, as given by Eqs. (7) and (8), it is evident that α makes real
time variations in Ka
p and Ka
d. The gain update rules (Eqs. (7) and
(8)) are chosen in such a way that the proposed APD will be able to
provide an improved performance under both set point change
and load disturbance. Note that, unlike the linear control surface of
PD controller with static gains, control surface of APD as shown in
Fig. 4 is highly nonlinear in nature. Now, we explain how the
proportional and derivative gains of APD are modified by the
proposed scheme for providing appropriate control action under
different operating conditions for achieving the desired perfor-
mance. For a better understanding, we refer Fig. 5, which represents
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
u
a
ΔeN
eN
Fig. 4. Control surface of APD.
C. Dey et al. / ISA Transactions 53 (2014) 162–172164
4. a typical close-loop response of an under-damped second-order
process due to set point change and load disturbance.
(i) During the operating stage, when the process is moving fast
towards the set point (e.g., point like A or C in Fig. 5), there is a
possibility of larger overshoot or undershoot in the subsequent
operating phase. To avoid such situations, a considerable amount
of damping should be present in the control action. This may be
possible either by increasing the derivative action or by decreas-
ing the proportional action separately, or by making such
changes simultaneously. In this case, since e and Δe are of
opposite sign, α will be negative, as a result, Ka
p oKp (Eq. (7)).
At the same time Eq. (8) indicates that Ka
d 4Kd. A combined
effect of the increased damping and reduced proportional gain
will make the speed of response slow, which is expected to
reduce the overshoot or undershoot. Thus, the proposed gain
variation mechanism fulfills the requirement of appropriate
control action for achieving an improved transient response.
(ii) Opposite to the previous operating stage, when the process is
far from the set point and moving away very fast from it (e.g.,
point B in Fig. 5), both the proportional and derivative gains
should be large enough to restore the controlled variable
quickly to its desired value. Under such situations, both
e and Δe have large values with the same sign, thereby making
α large and positive according to Eq. (6). Such a large positive
value of α makes Ka
p 4Kp and Ka
d 4Kd respectively according to
Eqs. (7) and (8). Therefore, ua
4u (i.e., control action becomes
more aggressive) according to Eqs. (2) and (9). Similar situa-
tion is also observed during load disturbance. Immediately
after a load disturbance, e may be small, but Δe will be
sufficiently large (e.g., point D in Fig. 5) and they are of the
same sign, as a result α becomes positive. Therefore, according
to Eqs. (7) and (8) both the proportional and derivative gains
of APD will be higher than those of conventional PD controller.
These higher gains will make APD to generate the required
strong control action for restoring the process quickly to its
desired value. Thus, APD is capable of providing the required
variation in control action to improve the process recovery.
From the above discussion, it appears that our simple gain
modification scheme always attempts to generate an appropriate
control action towards achieving an enhanced performance both
under set point change and load disturbance. Next, we mention
how the proposed scheme is tested for good stability margins as
well as robustness against parametric variations.
2.3. Stability and robustness
The proposed APD reduces to a simple nonlinear controller due
to nonlinear gain variation through α. We know that the stability
analysis for nonlinear control systems is not straight forward.
Here, we study the relative stability for APD by calculating the
stability margins along with their corner frequencies for two
boundary values of α, i.e., at its maximum (αmax) and minimum
(αmin) values. Under close-loop operation of the process, gain
margin (GM) and phase margin (PM) values are calculated at
αmax and αmin. For both the IPD and FOIPD processes, APD will be
found to provide good stability margins in terms of GM and PM,
which will be justified in the result section. In addition to the
relative stability margins, stability robustness of the close-loop
system for a given process is tested by Kharitonov's interval
polynomials [48] at the boundary values of α (αmax and αmin) along
with 725% simultaneous perturbations in process parameters.
Stability robustness is ensured as all the roots of Kharitonov's
polynomials will be found to be negative.
3. Results
In this section, we present the detailed performance analysis of
our proposed APD through simulation as well as real time
implementation. For simulation study, we consider two well
known integrating process models—pure integrating process with
delay (IPD) [12,23,49] and first-order integrating process with
delay (FOIPD) [43,44]. For the IPD process, performance of the
proposed APD is compared with the reported PID tuning relations
of AHPID [2], DMPID [3], ZNPID [10], SLPPID [11], CPPID [16], VPID
[23], PCPID [34], ACPID [35], RRCPID [36], AMPID [37], HXCPID
[38], and RPID [50], and PD settings of CPPD [16], VPD [23], and
LLPPD [39]. Similarly, for the FOIPD process, performance of APD is
compared with PID tuning rules reported in DMPID [3], ZNPID
[10], SPID [12], AMPID [37], HXCPID [38], YPID [40], WCPID [41],
RRCPID [42], SLPID [44], KLPID [47], and RPID [50], and PD settings
in VVSPD [24], DPD [25], EOMPD [45], and SJLPD [46]. For an in-
depth comparison, in addition to the response characteristics,
several performance indices, such as percentage overshoot (%OS),
rise time (tr), settling time (ts), integral absolute error (IAE) and
integral time absolute error (ITAE) are calculated for each setting.
Here, ts is calculated following 2% criterion. To verify the robust-
ness of the proposed APD, performance indices are also evaluated
at the nominal as well as 25% increased value of process dead time.
Experimental verification of the proposed APD along with all the
above reported PID and PD settings is made on a laboratory scale
DC servo position control system [52] identified to be a FOIPD
model under both set point change and load disturbance. To verify
the noise sensitivity of the proposed controller, white noise (with
mean¼0 and variance¼0.1) is added to the measured controlled
variable during simulation as well as experimental verification. For
all the simulation and experimental studies, the only additional
tuning parameter γ is estimated using Eq. (10). During perfor-
mance study, first we apply a step set point change followed by an
impulse load disturbance as shown in Fig. 3.
3.1. Integrating process with delay (IPD)
Integrating processes are frequently encountered in process
industries. Chien and Freuhauf [49] suggested that a number of
chemical processes can be approximated by a pure integral plus
time delay (IPD) model, defined by
Gp ¼
KeÀ θs
s
: ð11Þ
Here, we consider the well known IPD process model with open
loop gain K¼0.0506 and dead time θ¼6 s [12,23,49]. Performance
of APD for this IPD process is investigated along with other
model based PID tuning rules proposed in AHPID [2], SLPPID [11],
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Time(sec)
Response
A C D
e
Δe
A
B
C
D
B
Fig. 5. Typical close-loop response of an under-damped second-order process.
C. Dey et al. / ISA Transactions 53 (2014) 162–172 165
5. CPPID [16], VPID [23], PCPID [34], ACPID [35], RRCPID [36], AMPID
[37], HXCPID [38], and RPID [50], and PD settings in CPPD [16], VPD
[23], and LLPPD [39]. In addition, model free PID tuning rules of
DMPID [3] and ZNPID [10] are also considered for performance
comparison. Close-loop responses with the nominal value of dead
time (i.e., θ¼6 s) are shown in Fig. 6 for different controllers. The
related performance indices are given in Table 1a. It is found that
most of the model based and model free PID controllers fail to
provide satisfactory performance under set point change and load
variation simultaneously. In case of VPID [23], the process shows
highly oscillatory response and for AHPID [2] it completely diverges.
In comparison with VPD [23] and CPPD [16], APD offers lower
overshoot with faster settling during set point change and at the
same time process recovery is found to be improved under load
variation as shown in Fig. 7(a). In case of LLPPD [39] due to over
damped response no overshoot is found but load rejection is quite
poor compared to APD.
Performance robustness of the proposed APD is tested with
25% increased process dead time, i.e., θ¼7.5 s, and the respective
performance indices are listed in Table 1b. From Table 1b it is
found that under VPID [23], CPPID [16], and SLPPID [11] the
process fails to settle within the simulation period and AMPID
[37] shows a large overshoot in the set point response as well as
poor load regulation. On the other hand, our proposed APD shows
consistently improved performance compared to VPD [23] and
CPPD [16]. Thus, from the process responses as shown in
Figs. 6 and 7 and performance indices of Tables 1a and 1b it is
found that the proposed APD shows an overall improved perfor-
mance compared to others tuning relations. Moreover, response
characteristics of APD shown in Fig. 7(c) reveal that the proposed
scheme can overcome the effects of measurement noise.
Fig. 7(b) shows the variation of proportional and derivative
gains of the proposed APD with the gain updating factor α for
θ¼6 s, which shows a considerable change in the derivative gain
Ka
d during transient phases of the close-loop operation. To check
the sensitivity of the tuning parameter γ, performance indices are
evaluated with 725% perturbations in its initial value (γ¼12.49)
for both the nominal (i.e., θ¼6 s) and increased (i.e., θ¼7.5 s)
values of dead time (Tables 1a and 1b). No considerable deviation
is observed in the performance of APD due to such variations of γ,
which justifies the robustness of our proposed scheme. Stability
analysis of APD is provided in Table 1c in terms of GM and PM
values with their corner frequencies. Stability robustness is
observed (Table 1c) from the Kharitonov polynomials for two
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
2
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
-100
-50
0
50
100
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.2
0.4
0.6
0.8
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.2
0.4
0.6
0.8
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
CPPID [16]
PCPID [34] SLPPID [11]
RRCPID [36]
HXCPID [38]
VPD [23]
RPID [50]
ZNPID [10] VPID [23]
AHPID [2]
ACPID [35] DMPID [3]
AMPID [37]
CPPD [16] LLPPD [39]
Fig. 6. Responses for the IPD process GpðsÞ ¼ 0:0506eÀ 6s
=s.
C. Dey et al. / ISA Transactions 53 (2014) 162–172166
6. extreme values of α (αmax and αmin) along with 725% simulta-
neous perturbations in process parameters (K and θ).
3.2. First-order integrating process with delay (FOIPD)
First-order integrating process with delay can be described by
Gp ¼
KeÀ θs
sðτ sþ1Þ
: ð12Þ
Here, we consider K¼1, θ¼4 s, and τ¼4 s [43,44]. Performance
of APD is compared with a number of model free and model based
PID tuning relations given by DMPID [3], ZNPID [10], SPID [12],
AMPID [37], HXCPID [38], YPID [40], WCPID [41], RRCPID [42],
SLPID [44], KLPID [47], and RPID [50], and model based PD settings
of VVSPD [24], DPD [25], EOMPD [45], and SJLPD [46]. Responses
of (12) with θ¼4 s are shown in Fig. 8 and the performance indices
for θ¼4 s and 5 s (with þ25% perturbation) are given in Tables 2a
and 2b respectively. Fig. 8 shows that the process either goes to
the verge of instability for RRCPID [42] or completely diverges
under HXCPID [38], SLPID [44], and RPID [50]. In comparison with
VVSPD [24] and DPD [25], our proposed APD exhibits lower
overshoot with faster recovery as depicted in Fig. 9(a). Fig. 9
(c) justifies the robustness of APD against measurement noise.
Fig. 9(b) shows the variations of proportional and derivative gains
of APD with gain updating factor α. Under both set point change
Table 1a
Performance indices for the IPD process GpðsÞ ¼ 0:0506eÀ 6s
=s.
Controller %OS tr ts IAE ITAE
Model based PID tuning methods
VPID [23] (2001) 118.20 9.81 143.75 37.36 2899.0
CPPID [16] (2003) 61.26 10.54 88.75 24.14 1545.0
AHPID [2] (2004) Diverges completely
PCPID [34] (2005) 34.47 12.27 83.56 25.6 1597.0
ACPID [35] (2007) 27.51 21.99 144.21 39.45 3020.0
SLPPID [11] (2008) 2.85 18.29 59.03 14.67 1508.0
RPID [50] (2008) 40.46 19.56 133.27 39.73 3053.0
RRCPID [36] (2009) 0.00 64.12 64.12 29.33 1963.0
AMPID [37] (2010) 56.96 11.34 62.70 24.92 1478.0
HXCPID [38] (2011) 7.05 63.08 148.34 41.40 2749.0
Model free PID tuning methods
ZNPID [10] (1942) 67.63 11.23 90.15 30.8 1919.0
DMPID [3] (2009) 20.96 11.80 107.64 24.71 1642.0
Model based PD tuning methods
VPD [23] (2001) 16.67 11.64 61.48 16.41 988.4
CPPD [16] (2003) 13.77 12.05 58.62 15.99 946.4
LLPPD [39] (2006) 0.00 53.72 53.72 23.80 1440.0
Proposed auto-tuning PD method
APD γ ¼ 12:49 4.01 12.86 41.87 15.06 859.6
γþ25% ¼ 15:61 3.28 13.27 41.87 15.09 863.1
γÀ25% ¼ 9:37 4.73 12.86 41.87 15.04 856.5
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
-2
0
2
4
Time(sec)
Controlaction
0 50 100 150 200 250
-0.03
-0.02
-0.01
0
0.01
0 50 100 150 200 250
3
3.05
3.1
0 50 100 150 200 250
9
10
11
12
13
Time(sec)
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
-15
-10
-5
0
5
10
15
Time(sec)
Controlaction
APD
APD
α
Kd
a
Kp
a
APD
APD
Fig. 7. (a) Response and the corresponding control action for the IPD process GpðsÞ ¼ 0:0506eÀ 6s
=s. (b) Variation of α, Ka
p, and Ka
d under APD for the IPD process
GpðsÞ ¼ 0:0506eÀ 6s
=s. (c) Response and the corresponding control action with measurement noise for the IPD process GpðsÞ ¼ 0:0506eÀ 6s
=s.
Table 1b
Performance indices for the IPD process with 25% increased dead time
GpðsÞ ¼ 0:0506eÀ 7:5s
=s.
Controller %OS tr ts IAE ITAE
Model based PID tuning methods
VPID [23] (2001) Unstable
CPPID [16] (2003) 103.80 11.83 Not settled 52.37 4445.0
AHPID [2] (2004) Completely diverges
PCPID [34] (2005) 67.14 13.55 80.25 30.11 1889.0
ACPID [35] (2007) 35.08 21.73 145.65 43.23 3296.0
SLPPID [11] (2008) 36.12 17.43 Not settled 52.51 6895.0
RPID [50] (2008) 50.22 23.19 121.98 44.94 3489
RRCPID [36] (2009) 0.00 74.66 74.66 30.81 2226.0
AMPID [37] (2010) 97.96 12.69 107.36 36.05 2560.0
HXCPID [38] (2011) 7.46 60.77 147.75 42.04 2853.0
Model free PID tuning methods
ZNPID [10] (1942) 115.28 12.69 98.32 43.51 2943.0
DMPID [3] (2009) 49.15 13.54 110.80 29.58 2001.0
Model based PD tuning methods
VPD [23] (2001) 42.35 13.12 109.08 28.07 2056.0
CPPD [16] (2003) 38.94 13.55 107.36 26.36 1877.0
LLPPD [39] (2006) 0.00 37.65 37.65 23.93 1432.0
Proposed auto-tuning PD method
APD γ ¼ 12:49 27.14 13.55 66.48 22.68 1534.0
γþ25% ¼ 15:61 26.19 13.98 66.48 22.62 1537.0
γÀ25% ¼ 9:37 28.10 13.98 66.48 22.74 1531.0
Table 1c
Stability and robustness analysis for the IPD process GpðsÞ ¼ 0:0506eÀ 6s
=s.
APD (αmax) APD (αmin) Kharitonov's Polynomials
with αmax and αmin and
725% variation in K and θ
GM (dB) 4.68 (Inf rad/s) 3.83 (Inf rad/s) s2
þ0.51sþ0.15¼0
s2
þ1.49sþ0.14¼0
PM (deg) 64.9 (0.19 rad/s) 68.7 (0.20 rad/s) s2
þ1.28sþ0.14¼0
s2
þ0.59sþ0.15¼0
C. Dey et al. / ISA Transactions 53 (2014) 162–172 167
7. and load disturbance, APD shows an overall improved perfor-
mance than other PID and PD settings as revealed by Tables 2a and
2b. Its robustness is observed with þ25% perturbation in dead
time as well as 725% variation in γ from its nominal value 16.51
(Tables 2a and 2b). GM and PM along with their corner frequencies
are listed in Table 2c, which represents good stability margins.
Kharitonov's polynomials of Table 2c also confirm its stability
robustness under maximum and minimum values of α as well as
725% simultaneous variations in K, τ, and θ.
3.3. Real time implementation
Servo position control system is a typical example of integrat-
ing process. Here, performance of the proposed APD is verified on
a DC servo position control system. The schematic block diagram
of the position control system is shown in Fig. 10(a) and its
experimental setup is shown in Fig. 10(b). The hardware setup is
a Quanser make DC Motor Control Trainer (DCMCT) [52] and it has
been identified as a FOIPD model. A small delay of 0.01 s is
introduced by the Simulink delay block in the forward path of
the process loop. This DC servo motor is a high quality 18-Watt
motor of Maxon brand. This is a graphite brush DC motor with low
inertia rotor. It has zero cogging and very low unloaded running
friction. The transfer function of this servo motor (as provided by
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
-1000
-500
0
500
1000
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
1.5
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
-1000
-500
0
500
1000
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
0
0.5
1
Time(sec)
Response
0 50 100 150 200 250
-50
0
50
Time(sec)
Response
WCPID [41]
KLPID [47] RRCPID [42]
AMPID [37]
DPD [25]
RPID [50]
ZNPID [10] YPID [40]
SPID [12]
SLPID [44] DMPID [3]
HXCPID [38]VVSPD [24]
EOMPD [45] SJLPD [46]
1.5
Fig. 8. Responses for the FOIPD process GpðsÞ ¼ eÀ 4s
=sð4sþ1Þ.
Table 2a
Performance indices for the FOIPD process GpðsÞ ¼ eÀ 4s
=sð4sþ1Þ.
Controller %OS tr ts IAE ITAE
Model based PID tuning methods
WCPID [41] (2002) 22.19 17.56 57.89 29.70 2561.0
SPID [12] (2003) 34.47 15.27 101.09 35.32 3017.0
KLPID [47] (2006) 34.88 17.57 87.27 39.64 3390.0
RRCPID [42] (2007) 30.26 12.96 Not settled 56.03 6836.0
SLPID [44] (2008) Completely diverges
RPID [50] (2008) Completely diverges
AMPID [37] (2010) 58.83 11.81 69.41 28.51 2122.0
HXCPID [38] (2011) Completely diverges
Model free tuning PID tuning methods
ZNPID [10] (1942) 69.74 12.96 87.27 38.0 3083.0
YPID [40] (1999) 67.63 17.57 Not settled 62.78 6304.0
DMPID [3] (2009) 25.06 14.11 127.59 31.30 2654.0
Model based PD tuning methods
VVSPD [24] (2000) 16.46 12.96 49.83 18.01 1263.0
DPD [25] (2001) 26.29 11.81 67.68 20.52 1564.0
SJLPD [46] (2006) 0.00 36.0 36.0 14.94 1164.0
EOMPD [45] (2009) 1.73 28.51 41.76 24.74 1882.0
Proposed auto-tuning PD method
APD γ ¼ 16:51 6.64 15.84 37.73 17.91 1237.0
γ þ25% ¼ 20:64 5.82 15.84 38.31 17.80 1226.0
γÀ25% ¼ 12:39 7.05 15.84 38.31 18.03 1248.0
C. Dey et al. / ISA Transactions 53 (2014) 162–172168
8. Quanser [52]) is
GpðsÞ ¼
19:9eÀ0:01s
sð0:09sþ1Þ
: ð13Þ
Quanser-Q8 DAQ board interfaces the DCMCT with the PC
through USB port. With the help of QuaRC soft-ware based on
Matlab–Simulink we implement the proposed auto-tuning PD con-
troller. Similarly, other reported PID and PD controllers are also
implemented for their performance evaluation on DCMCT. Real Time
Workshop (RTW) and Real Time Windows Target (RTWT) generate C
code using Microsoft Cþ þ
Professional from the QuaRC block
diagram, and the Quanser-Q8 board acts as the intermediary for
two way data flow from the physical servo system to and from the
QuaRC model. A high resolution encoder is used for position sensing
of the DC motor. Performances of the proposed APD and other PID/
PD tuning rules (DMPID [3], ZNPID [10], SPID [12], VVSPD [24], DPD
[25], AMPID [37], HXCPID [38], YPID [40], WCPID [41], RRCPID [42],
SLPID [44], EOMPD [45], SJLPD [46], KLPID [47], and RPID [50]) are
tested on the DCMCT. Responses of the DC servo motor for different
controllers other than APD during set-point tracking and load
variation for the nominal value of dead time (θ¼0.01 s) are shown
in Fig. 11. We observe that even with this nominal value of dead time
VVSPD [24], AMPID [37], HXCPID [38], RRCPID [42], SLPID [44], SJLPD
[46], and RPID [50] provide unstable performances. The close-loop
response and its corresponding control action for the proposed APD
is shown in Fig. 12(a). Performance of APD has also been tested with
measurement noise as shown in Fig. 12(b). Fig. 13 shows only stable
performances of different controllers with 25% higher value of
dead time, i.e., θ¼0.0125 s. Fig. 14(a) and (b), respectively, shows
the responses of APD without and with measurement noise. Thus,
results obtained from both nominal and increased values of dead
time (Figs. 11–14) reveal that the proposed APD exhibits an overall
improved performance compared to other PID and PD tuning rules as
well as robustness against measurement noise.
To summarize, from the simulation as well as real time experi-
mentation, it is observed that for both IPD and FOIPD processes, the
proposed APD shows consistently improved overall performance
under set point change and load disturbance. APD is also found to
provide good stability margins and performance robustness. Stability
robustness of the proposed scheme is also verified at the boundary
values of the gain modifying parameter α (i.e., αmax and αmin) along
with 725% simultaneous perturbations in process parameters.
4. Conclusion
We proposed a real time gain modification scheme through
nonlinear parameterization of a PD auto-tuner. The proportional
and derivative gains of the proposed auto-tuning PD controller
(APD) have been modified in each instant by a nonlinear gain
updating factor α defined on the instantaneous process states.
Fig. 9. (a) Response and the corresponding control action for the FOIPD process GpðsÞ ¼ eÀ4s
=sð4sþ1Þ. (b) Variation of α, Ka
p, and Ka
d under APD for the FOIPD process
GpðsÞ ¼ eÀ 4s
=sð4sþ1Þ. (c) Response and the corresponding control action with measurement noise for the FOIPD process GpðsÞ ¼ eÀ 4s
=sð4sþ1Þ.
Table 2c
Stability and robustness analysis for the FOIPD process GpðsÞ ¼ eÀ 4s
=sð4sþ1Þ.
APD (αmax) APD (αmin) Kharitonov's polynomials
with αmax and αmin and
725% variation in K, τ, and θ
GM (dB) 9.07 (0.51 rad/s) 9.17 (0.52 rad/s) s3
þ0.61s2
þ0.57sþ0.04¼0
s3
þ0.52s2
þ0.17sþ0.01¼0
PM (deg) 53.1 (0.18 rad/s) 54.2 (0.17 rad/s) s3
þ0.52s2
þ0.57sþ0.01¼0
s3
þ0.61s2
þ0.17sþ0.04¼0
Table 2b
Performance indices for the FOIPD process with 25% increased dead time
GpðsÞ ¼ eÀ 5s
=sð4sþ1Þ.
Controller %OS tr ts IAE ITAE
Model based PID tuning methods
WCPID [41] (2002) 33.11 17.57 48.68 32.61 2834.0
SPID [12] (2003) 46.27 15.84 106.28 38.56 3307.0
KLPID [47] (2006) 42.32 17.57 83.81 42.78 3674.0
RRCPID [42] (2007) Completely diverges
SLPID [44] (2008) Completely diverges
RPID [50] (2008) Completely diverges
AMPID [37] (2010) 87.43 12.38 125.29 43.10 3908.0
HXCPID [38] (2011) Completely diverges
Model free tuning PID tuning methods
ZNPID [10] (1942) 91.52 13.54 97.06 47.14 4025.0
YPID [40] (1999) 78.68 18.15 Not settled 73.18 7531.0
DMPID [3] (2009) 39.39 14.69 127.02 34.65 2957.0
Model based PD tuning methods
VVSPD [24] (2000) 34.47 13.54 100.52 27.88 2341.0
DPD [25] (2001) 49.47 12.38 Not settled 43.83 4378.0
SJLPD [46] (2006) 10.32 11.81 42.34 15.74 1170.0
EOMPD [45] (2009) 4.59 24.48 45.22 26.41 2049.0
Proposed auto-tuning PD method
APD γ ¼ 16:51 18.92 15.26 52.71 23.14 1782.0
γ þ25% ¼ 20:64 18.51 15.26 52.13 22.98 1769.0
γÀ25% ¼ 12:39γ 19.74 15.26 52.71 23.31 1796.0
C. Dey et al. / ISA Transactions 53 (2014) 162–172 169
9. DCMCT
Hardware
Quanser DAQ
Board (Q8)
PC with Maltab and RTW
and RTWT
PC Inertial Load
Encoder DAQ D/A Converter Amplifier DC Motor
PCI Link
Motor
Load
Encoder
Fig. 10. (a) Schematic diagram of DCMCT. (b) Experimental setup of DC servo rig (Quanser DCMCT).
0 1 2 3 4 5
0
5
10
Time(sec)
Response
0 1 2 3 4 5
0
5
10
Time(sec)
Response
0 1 2 3 4 5
0
2
4
6
8
Time(sec)
Response
0 1 2 3 4 5
0
2
4
6
8
Time(sec)
Response
0 1 2 3 4 5
0
2
4
6
8
Time(sec)
Response
0 1 2 3 4 5
0
5
10
Time(sec)
Response
0 1 2 3 4 5
-10
-5
0
5
10
Time(sec)
Response
0 1 2 3 4 5
0
5
10
Time(sec)
Response
ZNPID [10] YPID [40]
WCPID [41] SPID [12]
KLPID [47] DMPID [3]
DPD [25] EOMPD [45]
Fig. 11. Responses with nominal value of dead time for DCMCT.
Fig. 12. (a) Response and the corresponding control action for the proposed APD with nominal value of dead time for DCMCT. (b) Response and the corresponding control
action for the proposed APD under measurement noise with nominal value of dead time for DCMCT.
C. Dey et al. / ISA Transactions 53 (2014) 162–172170
10. An empirical relation has also been suggested for the selection of
the single additional tuning parameter γ. The proposed gain
modification scheme can be easily incorporated in conventional
control loops. Performance analysis for integrating processes with
varying dead time under both set point change and load distur-
bance has revealed that the proposed APD is capable of providing
an improved overall performance compared to other tuning rules
reported in the literature. Performance robustness of the close-
loop system under APD has been observed with considerable
variations in process dead time as well as with measurement
noise. Stability robustness has also been established by applying
725% simultaneous perturbations in process parameters.
Further works may be done for setting more appropriate
parameters of the initial PD controller, and finding more suitable
value of γ for a given process. Similar gain adjustment schemes
may be tried for other real world problems, which exhibit inverse
response. All these possibilities are under investigation.
References
[1] Åström KJ, Hägglund T. The future of PID control. Control Engineering Practice
2001;9(11):1163–75.
[2] Åström KJ, Hägglund T. Revisiting the Ziegler–Nichols step response method
for PID control. Journal of Process Control 2004;14(6):635–50.
[3] Dey C, Mudi RK. An improved auto-tuning scheme for PID controllers. ISA
Transactions 2009;48(4):396–409.
[4] Tang KM, Lo WL, Rad AB. Adaptive delay compensated PID controller by phase
margin design. ISA Transactions 1998;37(3):177–87.
[5] Lo HL, Rad AB, Chan CC, Wong YK. Comparative studies of three adaptive
controllers. ISA Transactions 1999;38(1):43–53.
[6] Ang KH, Chong GCY, Li Y. PID control system analysis, design, and technology.
IEEE Transactions on Control Systems Technology 2005;13(4):559–76.
[7] Lo WL, Rad AB, Li CK. Self-tuning control of systems with unknown time delay
via extended polynomial identification. ISA Transactions 2003;42(2):259–72.
[8] Vijayan V, Panda RC. Design of simple set point filter for minimizing overshoot
for low order processes. ISA Transactions 2012;51(2):271–6.
[9] Vijayan V, Panda RC. Design of PID controllers in double feedback loops for
SISO systems with set-point filters. ISA Transactions 2012;51(4):514–21.
[10] Ziegler JG, Nichols NB. Optimum setting for automatic controllers. ASME
Transactions 1942;64(11):759–68.
[11] Shamsuzzoha Md, Lee M. PID controller design for integrating processes with
time delay. Korean Journal of Chemical Engineering 2008;25(4):637–45.
[12] Skogestad S. Simple analytic rules for model reduction and PID controller
tuning. Journal of Process Control 2003;13(4):291–309.
[13] Ali A, Majhi S. PI/PID controller design based on IMC and percentage overshoot
specification to controller setpoint change. ISA Transactions 2009;48(1):10–5.
[14] Selvi JAV, Radhakrishnan TK, Sundaram S. Performance assessment of PID and
IMC tuning methods for a mixing process with time delay. ISA Transactions
2007;46(3):391–7.
[15] Chia TL, Lefkowitz I. Internal model-based control for integrating processes.
ISA Transactions 2010;49(4):519–27.
[16] Chidambaram M, Sree R Padma. A simple method of tuning PID controllers for
integrator/dead time processes. Computers Chemical Engineering 2003;27(2):
211–5.
[17] Atia KR, Cartmell MP. A new methodology for designing PD controllers.
Robotica 2001;19(3):267–73.
[18] Ogata K. Modern control engineering. New Jersey: Prentice-Hall; 2002.
0 1 2 3 4 5
0
5
10
Time(sec)
Response
0 1 2 3 4 5
-5
0
5
10
15
Time(sec)
Response
0 1 2 3 4 5
0
2
4
6
8
Time(sec)
Response
0 1 2 3 4 5
0
2
4
6
8
Time(sec)
Response
0 1 2 3 4 5
-10
-5
0
5
10
Time(sec)
Response
0 1 2 3 4 5
0
5
10
Time(sec)
Response
ZNPID [10] YPID [40]
KLPID [47] DMPID [3]
DPD [25] EOMPD [45]
Fig. 13. Responses with 25% increased value of dead time for DCMCT.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
5
10
Time(sec)
Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-20
0
20
Controlaction
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
5
10
Time(sec)
Response
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-20
0
20
Time(sec)
Controlaction
APD
APDAPD
APD
Time(sec)
Fig. 14. (a) Response and the corresponding control action for the proposed APD with 25% increased value of dead time for DCMCT. (b) Response and the corresponding
control action for the proposed APD under measurement noise with 25% increased value of dead time for DCMCT.
C. Dey et al. / ISA Transactions 53 (2014) 162–172 171
11. [19] Åström KJ, Hägglund T. PID controllers: theory, design, and tuning, instrument
society of America. North Carolina; 1995.
[20] Kristiansson B, Lennartson B. Evaluation and simple tuning of PID controllers with
high-frequency robustness. Journal of Process Control 2006;16(1):91–102.
[21] Aguilar-Ibáñez C, Sira-Ramírez H. PD control for active vibration damping in an
under actuated nonlinear system. Asian Journal of Control 2002;4(4):502–8.
[22] Xu Y, Hollerbach JM, Ma D. A nonlinear PD controller for force and contact
transient control. IEEE Control Systems Magazine 1995;15(1):15–21.
[23] Visioli A. Optimal tuning of PID controllers for integral and unstable processes.
IEE Proceedings, Control Theory and Applications 2001;148(2):180–4.
[24] Vítečková, M, Víteček, A, Smutný, L. Controller tuning for controlled plants
with time delay. In: Proceedings IFAC workshop on digital control, past,
present and future of PID control 2000, Terrassa, Spain; 2000. p. 283–288.
[25] O'Dwyer, A. PI and PID controller tuning rule design for processes with delay,
to achieve constant gain and phase margins for all values of delay. In:
Proceedings of the Irish signals and systems conference 2001, Maynooth,
Ireland; 2001. p. 96–100.
[26] Hamamci SE, Koksal M. Calculation of all stabilizing fractional-order PD
controllers for integrating time delay systems. Computers Mathematics
with Applications 2010;59(5):1621–9.
[27] Malki HA, Li H, Chen G. New design and stability analysis of fuzzy proportional
derivative control systems. IEEE Transactions on Fuzzy Systems 1994;2(4):
245–54.
[28] Mudi RK, Pal NR. A self-tuning fuzzy PD controller. IETE Journal of Research
1998;44(4-5):177–89.
[29] Su YX, Yang SX, Sun D, Duan BY. A simple hybrid fuzzy PD controller.
Mechatronics 2004;14(8):877–90.
[30] Boubertakh H, Tadjine M, Glorennec P-Y, Labiod S. Tuning fuzzy PD and PI
controllers using reinforcement learning. ISA Transactions 2010;49(4):543–51.
[31] Ho HF, Wong YK, Rad AB. Adaptive fuzzy approach for a class of uncertain
nonlinear systems in strict-feedback form. ISA Transactions 2008;47(3):
286–99.
[32] Bhattacharya S, Chatterjee A, Munshi S. A new self-tuned fuzzy controller as a
combination of two-term controllers. ISA Transactions 2004;43(3):413–26.
[33] Pan I, Das S, Gupta A. Tuning of an optimal fuzzy PID controller with stochastic
algorithms for networked control systems with random time delay. ISA
Transactions 2011;50(1):28–36.
[34] Padma Sree R, Chidambaram M. A simple and robust method of tuning PID
controllers for integrator/dead time processes. Journal of Chemical Engineering
of Japan 2005;38(2):113–9.
[35] Arbogast JE, Cooper DJ. Extension of IMC tuning correlations for non-self
regulating (integrating) processes. ISA Transactions 2007;46(3):303–11.
[36] Rao S, Rao VSR, Chidambaram M. Direct synthesis-based controller design for
integrating processes with time delay. Journal of the Franklin Institute
2009;346(1):38–56.
[37] Ali A, Majhi S. PID controller tuning for integrating processes. ISA Transactions
2010;49(1):70–8.
[38] Hu, W, Xiao, G, Cai, WJ. PID controller design based on two-degrees-of-
freedom direct synthesis. In: Proceedings Chinese control and decision
conference CCDC 2011, Mianyang, China; 2011. p. 629–634.
[39] Lee Y, Lee M, Park S. Consider the generalized IMC-PID method for PID
controller tuning of time-delay processes. Hydrocarbon Processing 2006:
87–91 (January).
[40] Yu CC. Auto tuning of PID controllers: a relay feedback approach. Berlin:
Springer-Verlag; 2006.
[41] Wang YG, Cai WJ. Advanced proportional-integral-derivative tuning for
integrating and unstable processes with gain and phase margin specifications.
Industrial Engineering Chemistry Research 2002;41(12):2910–4.
[42] Rao S, Rao VSR, Chidambaram M. Set point weighted modified Smith predictor
for integrating and double integrating processes with time delay. ISA
Transactions 2007;46(1):59–71.
[43] Zhang W, Xu X, Sun Y. Quantitative performance design for integrating
processes with time delay. Automatica 1999;35(4):719–23.
[44] Shamsuzzoha M, Lee M. Design of advanced PID controller for enhanced
disturbance rejection of second-order processes with time delay. AIChE
Journal 2008;54(6):1526–36.
[45] Eriksson L, Oksanen T, Mikkola K. PID controller tuning rules for integrating
processes with varying time-delays. Journal of The Franklin Institute 2009;346:
470–87.
[46] Shamsuzzoha M, Junho P, Lee M. IMC based method for control system design of
PID cascaded filter. Theoretical and Applied Chemical Engineering 2006;12(1):
111–4.
[47] Kristiansson B, Lennartson B. Robust tuning of PI and PID controllers. IEEE
Control Systems Magazine 2006;26(1):55–69.
[48] Grimble MJ. Robust industrial control. New York: Prentice-Hall; 1994.
[49] Chien IL, Freuhauf PS. Consider IMC tuning to improve performance. Chemical
Engineering Progress 1990;10(1):33–41.
[50] Panda RC. Synthesis of PID tuning rules using the desired closed-loop
response. Industrial Engineering Chemistry Research 2008;47(22):8684–92.
[51] Ho WK, Feng EB, Gan OP. A novel relay auto-tuning technique for processes
with integration. Control Engineering Practice 1996;4(7):923–8.
[52] Documentation for the Quanser DCMCT, Quanser, Canada; 2010.
C. Dey et al. / ISA Transactions 53 (2014) 162–172172