A fuzzy logic method is developed for gain scheduling of PID controllers to improve performance. The method uses a single fuzzy input variable based on the rate of change of the PID manipulated variable. Gain scheduling is implemented through a differential equation relating the fuzzy and PID manipulated variables. Only two parameters need to be tuned to improve PID control while retaining the original PID parameters. The method is demonstrated on a physical temperature control model, where a well-tuned PID controller is substantially improved to the level of model predictive control through fuzzy gain scheduling with minimal tuning.
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.
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.
Presentation give by Terry Blevins at the IFAC PID'12 conference in Brescia, Italy on March 28th, 2012. Presentation based on paper by Willy Wojsznis, Terry Blevins, John Caldwell, and Mark Nixon
Design of Controllers for Continuous Stirred Tank ReactorIAES-IJPEDS
The objective of the project is to design various controllers for temperature control in Continuous Stirred Tank Reactor (CSTR) systems. Initially Zeigler-Nichols, modified Zeigler-Nichols, Tyreus-Luyben, Shen-Yu and IMC based method of tuned Proportional Integral (PI) controller is designed and comparisons are made with Fuzzy Logic Controller. Simulations are carried out and responses are obtained for the above controllers. Maximum peak overshoot, Settling time, Rise time, ISE, IAE are chosen as performance index. From the analysis it is found that the Fuzzy Logic Controller is a promising controller than the conventional controllers.
Addressing control applications using wireless hart devicesEmerson Exchange
Many WirelessHART transmitter applications require that the measurement valve be used in closed loop Control. The PIDPlus capability introduced in DeltaV v11.3 enables robust control using WirelessHART measurements. A PIDPlus enhancement in DeltaV v12.3 further improves the response for setpoint changes. Details of the PIDPlus and field results using WirelessHART transmitters and PIDPlus are presented in the workshop.
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.
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.
Presentation give by Terry Blevins at the IFAC PID'12 conference in Brescia, Italy on March 28th, 2012. Presentation based on paper by Willy Wojsznis, Terry Blevins, John Caldwell, and Mark Nixon
Design of Controllers for Continuous Stirred Tank ReactorIAES-IJPEDS
The objective of the project is to design various controllers for temperature control in Continuous Stirred Tank Reactor (CSTR) systems. Initially Zeigler-Nichols, modified Zeigler-Nichols, Tyreus-Luyben, Shen-Yu and IMC based method of tuned Proportional Integral (PI) controller is designed and comparisons are made with Fuzzy Logic Controller. Simulations are carried out and responses are obtained for the above controllers. Maximum peak overshoot, Settling time, Rise time, ISE, IAE are chosen as performance index. From the analysis it is found that the Fuzzy Logic Controller is a promising controller than the conventional controllers.
Addressing control applications using wireless hart devicesEmerson Exchange
Many WirelessHART transmitter applications require that the measurement valve be used in closed loop Control. The PIDPlus capability introduced in DeltaV v11.3 enables robust control using WirelessHART measurements. A PIDPlus enhancement in DeltaV v12.3 further improves the response for setpoint changes. Details of the PIDPlus and field results using WirelessHART transmitters and PIDPlus are presented in the workshop.
Improving Structural Limitations of Pid Controller For Unstable ProcessesIJERA Editor
PID controllers have structural limitations which make it impossible for a good closed-loop performance to be achieved. A step response with high overshoot and oscillations always results. In controlling processes with resonances, integrators and unstable transfer functions, the PI-PD controller provides a satisfactory closed-loop performance. In this paper, a simple approach to extracting parameters of a PI-PD controller from parameters of the conventional PID controller is presented so that a good closed-loop system performance is achieved. Simulated results from this formation are carried out to show the efficacy of the technique proposed.
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.
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.
Design and optimization of pid controller using genetic algorithmeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Design and optimization of pid controller using genetic algorithmeSAT Journals
Abstract Natural evolution is mimicked by Genetic Algorithms (GAs) which is a stochastic global search method used for optimization. . In missile control systems Proportional Integral Derivative (PID) control is widely used, but due to empirically selected parameters Kp, Ki, Kd it is difficult to achieve parameter optimization. Genetic algorithm is a search algorithm that is based on natural selection and genetics principles.GA is a computational algorithm which deals with genetics of the human body. It evolves with the number of iterations. After ever iteration a better result is expected. These results are checked for the error. The fittest roots or solution are considered for the next generation based on the selection criterion. GA randomly generates the initial population of the PID control parameters according to the calculation of selection (Normalized Geometric Selection), crossover (Arithmetic Crossover) and mutation (Uniform Mutation), thus optimizing the control parameters. Mean Square Error (MSE) value is chosen as the performance assessment index. For a missile altitude control Proportional Integral Derivative (PID) controller using genetic algorithm is implemented & compared with the classical method Zeigler-Nichols (Z-N) in the paper. Z-N method is classical method which tunes the parameters of PID. The parameters of PID are difficult to tune. Tuned parameters give the optimum solution. Optimum solution generally converges to a solution having minimum error. Minimum error gives a response of the system in terms of maximum over shoot, Settling time, Rise time & Steady State Error. The designed PID with the Genetic Algorithm has much faster response than the classical method.
In recent times, fractional order controllers are gaining more interest. There are several fractional order controllers are available in literature. Still, tuning of these controllers is one of the main issues which the control community is facing. In this paper, online tuning of five dierent fractional order controllers is discussed viz. tilted proportional-integral-derivative (T-PID) controller, fractional order proportional-integral (FO-PI) controller, fractional order proportional-derivative (FO-PD) controller, fractional order proportional-integral-derivative (FO-PID) controller. A reference tracking method is proposed for tuning of fractional order controllers. First order with dead time (FOWDT) system is used to check feasibility of the control strategy.
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.
Robust design of a 2 dof gmv controller a direct self-tuning and fuzzy schedu...ISA Interchange
This paper presents a study on self-tuning control strategies with generalized minimum variance control in a fixed two degree of freedom structure–or simply GMV2DOF–within two adaptive perspectives. One, from the process model point of view, using a recursive least squares estimator algorithm for direct self-tuning design, and another, using a Mamdani fuzzy GMV2DOF parameters scheduling technique based on analytical and physical interpretations from robustness analysis of the system. Both strategies are assessed by simulation and real plants experimentation environments composed of a damped pendulum and an under development wind tunnel from the Department of Automation and Systems of the Federal University of Santa Catarina.
The DeltaV PIDPlus is based on a modification of the PID reset and rate calculation to account for non-periodic measurement updates. An alternate approach is to use PID with a modified Kalman filter or modified Smith Predictor. Test results are presented that compare the PIDPlus to these alternate approaches.
Modified smith predictor based cascade control of unstable time delay processesISA Interchange
An improved cascade control structure with a modified Smith predictor is proposed for controlling open-loop unstable time delay processes. The proposed structure has three controllers of which one is meant for servo response and the other two are for regulatory responses. An analytical design method is derived for the two disturbance rejection controllers by proposing the desired closed-loop complementary sensitivity functions. These two closed-loop controllers are considered in the form of proportional–integral-derivative (PID) controller cascaded with a second order lead/lag filter. The direct synthesis method is used to design the setpoint tracking controller. By virtue of the enhanced structure, the proposed control scheme decouples the servo response from the regulatory response in case of nominal systems i.e., the setpoint tracking controller and the disturbance rejection controller can be tuned independently. Internal stability of the proposed cascade structure is analyzed. Kharitonov’s theorem is used for the robustness analysis. The disturbance rejection capability of the proposed scheme is superior as compared to existing methods. Examples are also included to illustrate the simplicity and usefulness of the proposed method.
Improving Structural Limitations of Pid Controller For Unstable ProcessesIJERA Editor
PID controllers have structural limitations which make it impossible for a good closed-loop performance to be achieved. A step response with high overshoot and oscillations always results. In controlling processes with resonances, integrators and unstable transfer functions, the PI-PD controller provides a satisfactory closed-loop performance. In this paper, a simple approach to extracting parameters of a PI-PD controller from parameters of the conventional PID controller is presented so that a good closed-loop system performance is achieved. Simulated results from this formation are carried out to show the efficacy of the technique proposed.
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.
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.
Design and optimization of pid controller using genetic algorithmeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Design and optimization of pid controller using genetic algorithmeSAT Journals
Abstract Natural evolution is mimicked by Genetic Algorithms (GAs) which is a stochastic global search method used for optimization. . In missile control systems Proportional Integral Derivative (PID) control is widely used, but due to empirically selected parameters Kp, Ki, Kd it is difficult to achieve parameter optimization. Genetic algorithm is a search algorithm that is based on natural selection and genetics principles.GA is a computational algorithm which deals with genetics of the human body. It evolves with the number of iterations. After ever iteration a better result is expected. These results are checked for the error. The fittest roots or solution are considered for the next generation based on the selection criterion. GA randomly generates the initial population of the PID control parameters according to the calculation of selection (Normalized Geometric Selection), crossover (Arithmetic Crossover) and mutation (Uniform Mutation), thus optimizing the control parameters. Mean Square Error (MSE) value is chosen as the performance assessment index. For a missile altitude control Proportional Integral Derivative (PID) controller using genetic algorithm is implemented & compared with the classical method Zeigler-Nichols (Z-N) in the paper. Z-N method is classical method which tunes the parameters of PID. The parameters of PID are difficult to tune. Tuned parameters give the optimum solution. Optimum solution generally converges to a solution having minimum error. Minimum error gives a response of the system in terms of maximum over shoot, Settling time, Rise time & Steady State Error. The designed PID with the Genetic Algorithm has much faster response than the classical method.
In recent times, fractional order controllers are gaining more interest. There are several fractional order controllers are available in literature. Still, tuning of these controllers is one of the main issues which the control community is facing. In this paper, online tuning of five dierent fractional order controllers is discussed viz. tilted proportional-integral-derivative (T-PID) controller, fractional order proportional-integral (FO-PI) controller, fractional order proportional-derivative (FO-PD) controller, fractional order proportional-integral-derivative (FO-PID) controller. A reference tracking method is proposed for tuning of fractional order controllers. First order with dead time (FOWDT) system is used to check feasibility of the control strategy.
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.
Robust design of a 2 dof gmv controller a direct self-tuning and fuzzy schedu...ISA Interchange
This paper presents a study on self-tuning control strategies with generalized minimum variance control in a fixed two degree of freedom structure–or simply GMV2DOF–within two adaptive perspectives. One, from the process model point of view, using a recursive least squares estimator algorithm for direct self-tuning design, and another, using a Mamdani fuzzy GMV2DOF parameters scheduling technique based on analytical and physical interpretations from robustness analysis of the system. Both strategies are assessed by simulation and real plants experimentation environments composed of a damped pendulum and an under development wind tunnel from the Department of Automation and Systems of the Federal University of Santa Catarina.
The DeltaV PIDPlus is based on a modification of the PID reset and rate calculation to account for non-periodic measurement updates. An alternate approach is to use PID with a modified Kalman filter or modified Smith Predictor. Test results are presented that compare the PIDPlus to these alternate approaches.
Modified smith predictor based cascade control of unstable time delay processesISA Interchange
An improved cascade control structure with a modified Smith predictor is proposed for controlling open-loop unstable time delay processes. The proposed structure has three controllers of which one is meant for servo response and the other two are for regulatory responses. An analytical design method is derived for the two disturbance rejection controllers by proposing the desired closed-loop complementary sensitivity functions. These two closed-loop controllers are considered in the form of proportional–integral-derivative (PID) controller cascaded with a second order lead/lag filter. The direct synthesis method is used to design the setpoint tracking controller. By virtue of the enhanced structure, the proposed control scheme decouples the servo response from the regulatory response in case of nominal systems i.e., the setpoint tracking controller and the disturbance rejection controller can be tuned independently. Internal stability of the proposed cascade structure is analyzed. Kharitonov’s theorem is used for the robustness analysis. The disturbance rejection capability of the proposed scheme is superior as compared to existing methods. Examples are also included to illustrate the simplicity and usefulness of the proposed method.
특별법안을 만들 수 있는 힘은 오직 희생자 실종자 가족과 국민으로부터, 특별법 제정의 ‘골든 타임’을 놓쳐서는 안돼
새누리당과 박근혜 정부는 이후에도 지속적으로 진상규명과 안전사회를 위한 특별법 제정을 회피하려 할 것이다. 국민과 유가족들의 힘으로 특별법을 제정해야 한다.
70일만에 350만명의 국민서명을 받고 그 서명을 평일 날 2000여명이 모여 국회 본청 까지 행진해 국회의장을 직접 만나 접수했다. 끊임없이 밀려들어온 국민의 물결. 세월호 유족들은 그 모습을 보며 특별법 제정의 가능성을 보았다고 얘기 한다.
살아오면서 데모 한번 구호 한번 외치지 않았다던 가족들이 국회 본청앞에서 8일째 농성을 진행하고 있고 벌써 6일째 단식을 진행 중이다.
단식은 체력 저하와 오랜 스트레스로 극도의 심리 불안 상태에서 자칫 위험 할 수 있다는 의사의 만류도 가족들의 의지를 꺽지 못했다. 그리고 가족 스스로 자신의 아이들의 마지막 장면을, 동영상을 국민들께 공개할 것을 결정했다. 너무 아픈 결정이었다. 그 결정까지 너무나 많은 시간이 필요했다. 가족분들의 이러한 결정은 특별법 제정의 [골든 타임] 을 더 이상 놓쳐서는 안된다고 생각했기 때문이다. 그제부터 서울 전역을 돌며 동영상을 틀고, 국민께 호소한다. 특별법을 위해 7월 19일 서울광장을 모여달라고.
왜 우리의 아이들이, 가족들이 스러져 갔는지 그리고 왜 단 한명도 구하지 못했는지 그 진실을 밝혀야 한다.
세월호 특별법이 제정되지 못한다면 누구든 2014년 4월 15일 인천항을 떠나는 또 다른 세월호를 타게 될 수 도 있다. 그래서 세월호 참사 전과 후는 달라야 하는 것이다.
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
Performance based Comparison between Various Z-N Tuninng PID and Fuzzy Logic ...ijsc
The objective of this paper is to compare the time specification performance between conventional controller and Fuzzy Logic controller in position control system of a DC motor. The scope of this research is to apply direct control technique in position control system. Two types of controller namely PID and fuzzy logic PID controller will be used to control the output response. This paper was written to reflect on the work done on the implementation of a fuzzy logic PID controller. The fuzzy controller was used to control the position of a motor which can be considered for a general basis in any project design containing logic control. Motor parameters were taken from a datasheet with respect to a real motor and a simulated model was developed using Matlab Simulink Toolbox. The fuzzy control was also designed using the Fuzzy Control Toolbox provided within Matlab, with each rule consisting of fuzzy sets conditioned to provide appropriate response times with regards to the limitations of our chosen motor. The Fuzzy Inference Engine chosen for our control was the Mamdani Minimum Inference engine. The results of the control provided response times suitable for our application.
Performance Based Comparison Between Various Z-N Tuninng PID And Fuzzy Logic ...ijsc
The objective of this paper is to compare the time specification performance between conventional
controller and Fuzzy Logic controller in position control system of a DC motor. The scope of this research
is to apply direct control technique in position control system. Two types of controller namely PID and
fuzzy logic PID controller will be used to control the output response. This paper was written to reflect on
the work done on the implementation of a fuzzy logic PID controller. The fuzzy controller was used to
control the position of a motor which can be considered for a general basis in any project design
containing logic control. Motor parameters were taken from a datasheet with respect to a real motor and a
simulated model was developed using Matlab Simulink Toolbox. The fuzzy control was also designed using
the Fuzzy Control Toolbox provided within Matlab, with each rule consisting of fuzzy sets conditioned to
provide appropriate response times with regards to the limitations of our chosen motor. The Fuzzy
Inference Engine chosen for our control was the Mamdani Minimum Inference engine. The results of the
control provided response times suitable for our application.
A simple nonlinear PD controller for integrating processesISA Interchange
Many industrial processes are found to be integrating in nature, for which widely used Ziegler–Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (eN) and change of error (ΔeN) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.
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
The application of Self-adaptive Fuzzy PID control the evaporator superheatIJRES Journal
In view of the characteristics of the cold storage refrigeration system, such as nonlinear, time-varying and coupling, the traditional PID control accuracy is low, this study adopted the method of adaptive Fuzzy PID to control the superheat of the evaporator outlet. Fuzzy PID controller can adjust the parameters according to the deviation and deviation rat. It can avoid the disadvantages of traditional PID controller that it cannot adjust control parameters according to operating conditions.
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.
Fuzzy gain scheduling control apply to an RC Hovercraft IJECEIAES
The Fuzzy Gain Scheduling (FGS) methodology for tuning the ProportionalIntegral-Derivative (PID) traditional controller parameters by scheduling controlled gains in different phases, is a simple and effective application both in industries and real-time complex models while assuring the high achievements over pass decades, is proposed in this article. The Fuzzy logic rules of the triangular membership functions are exploited on-line to verify the Gain Scheduling of the Proportional-Integral-Derivative controller gains in different stages because it can minimize the tracking control error and utilize the Integral of Time Absolute Error (ITAE) minima criterion of the controller design process. For that reason, the controller design could tune the system model in the whole operation time to display the efficiency in tracking error. It is then implemented in a novel Remote Controlled (RC) Hovercraft motion models to demonstrate better control performance in comparison with the PID conventional controller.
Optimised control using Proportional-Integral-Derivative controller tuned usi...IJECEIAES
Time delays are generally unavoidable in the designing frameworks for mechanical and electrical systems and so on. In both continuous and discrete schemes, the existence of delay creates undesirable impacts on the underthought which forces exacting constraints on attainable execution. The presence of delay confounds the design structure procedure also. It makes continuous systems boundless dimensional and also extends the readings in discrete systems fundamentally. As the Proportional-IntegralDerivative (PID) controller based on internal model control is essential and strong to address the vulnerabilities and aggravations of the model. But for an real industry process, they are less susceptible to noise than the PID controller.It results in just one tuning parameter which is the time constant of the closed-loop system λ, the internal model control filter factor. It additionally gives a decent answer for the procedure with huge time delays. The design of the PID controller based on the internal model control, with approximation of time delay using Pade’ and Taylor’s series is depicted in this paper. The first order filter used in the design provides good set-point tracking along with disturbance rejection.
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.
Similar to PID gain scheduling using fuzzy logic (20)
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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
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PID gain scheduling using fuzzy logic
1. ISA Transactions 39 (2000) 317±325
www.elsevier.com/locate/isatrans
PID gain scheduling using fuzzy logic
T.P. Blanchett a, G.C. Kember a,*, R. Dubay b
a
Department of Engineering Mathematics, DalTech, Dalhousie University, PO Box 1000, Halifax, NS, Canada B3J 2X4
b
Department of Mechanical Engineering, University of New Brunswick, Federicton, NB, Canada E3B 5A3
Abstract
A simple, yet robust and stable alternative to proportional, integral, derivative (PID) gain scheduling is developed
using fuzzy logic. This fuzzy gain scheduling allows simple online duplication of PID control and the online improvement
of PID control performance. The method is demonstrated with a physical model where PID control performance is
improved to levels comparable to model predictive control. The fuzzy formulation is uniquely characterized by; (i) one
fuzzy input variable involving the PID manipulated variable, (ii) two parameters to be tuned, while previously tuned
PID parameters are retained, and (iii) a gain scheduling di€erential equation which relates the fuzzy and conventional
PID manipulated variables and enables fuzzy gain scheduling. # 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Gain scheduling; Fuzzy control; Model predictive control; PID control
1. Introduction desired and predicted responses. However, chan-
ging to MPC is not justi®ed for the majority of
Most industrial process control continues to rely industrial PID controllers since its control struc-
upon `classical', or `conventional' proportional, tures are very di€erent from PID, are much more
integral, derivative (PID) control. Gain scheduling complicated, and have an increased computational
is the most common PID advancement used in cost.
industry to overcome nonlinear process character- Fuzzy logic approaches have been shown in
istics through the tailoring of controller gains over numerous studies to be a simpler alternative to
local operating bands. This scheduling is compli- improve conventional PID control performance
cated by the need for detailed process knowledge (for example, [1±5] for a recent overview). The pro-
to de®ne operating bands and open loop tests which blem of interest here, is the control of a manipulated
must be performed to locally calibrate the controller variable to a constant set point. Performance
gain within each band. An alternative method is improvements for such a problem are usually
predictive control which uses a `black box' model to demonstrated by reductions in the amplitude of
remove the need for detailed knowledge of process undesirable oscillations in the manipulated vari-
characteristics. For example, in model predictive able around the set point, shorter times to converge
control (MPC), controller moves are determined by to the set point, and the maintenance of control
continuously minimizing the di€erence between the stability seen in conventional PID control. Since
substantial, but similar improvements are found
* Corresponding author. Tel.: +1-902-494-3262; fax: +1- from a wide variety of fuzzy logic schemes, the
902-494-1801. main feature which delineates these approaches is
E-mail address: guy.kember@dal.ca (G.C. Kember). their relative complexity. For those fuzzy logic
0019-0578/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0019-0578(00)00024-0
2. 318 T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325
controllers intended to replace existing conven- Note that a fuzzy logic scheme incorporating
tional PID controllers in the industrial setting, the these features is a true gain scheduler Ð a `fuzzy
drive to simplify fuzzy logic controllers is impor- gain scheduler'. Fuzzy gain scheduling is com-
tant to reduce the costs of their implementation pactly and generally formulated in terms of a `gain
[3]. Two features shared by most of these fuzzy scheduling' di€erential equation: the rate of
logic setups are: each error component (taken change of the fuzzy manipulated variable is equa-
from the proportional error and its derivatives) is ted to a function of the rate of change of the con-
de®ned as a separate input, and the fuzzy rule- ventional PID manipulated variable. The form of
bases are redundant, that is, the rulebases show a this function is globally determined by details of
linear dependence upon the error components. the fuzzy formulation and the defuzzi®cation
Such `fuzzy redundancy' together with appro- strategy. The existence of a limiting linear form is
priate input and output bounds has been shown to used to preserve conventional PID control and
lead to stable control in a large class of nonlinear allow the desired online replacement. Then, mod-
control problems [6]. However, a practical obser- i®cation of this linear form, to a nonlinear sig-
vation [6,7] is that fuzzy input variables taken moidal form, yields fuzzy gain scheduling. The use
from linear combinations of the error components of a di€erential equation also makes this approach
(termed here `summed fuzzy input variables') should equally convenient for continuous and discrete
be used to reduce the number of input variables control situations.
where separated inputs would lead to a more The layout of the paper is as follows. The con-
redundant rulebase. Such designs are simpler and trol of a temperature process by conventional PID
thus provide more ecient control than the more is used for illustration (Section 2). The fuzzy gain
redundant fuzzy formulations, yet do not sacri®ce scheduling method and approach to independent
stability [6]. In addition, control robustness with tuning of parameters is developed (Section 3) and
respect to parameter ¯uctuations, seen in most demonstrated with a physical model (Section 4). A
fuzzy designs is related to widespread use of error well-tuned PID controller is substantially improved
components involving the proportional error and to performance levels of the benchmark MPC
its derivatives [6], i.e. there is no integral term of after tuning the fuzzy gain scheduling method with
the error, and such control has been coined `slid- a few tests (Section 5). Excellent control robust-
ing mode control' in [6]. ness and stability to large disturbances and large
Therefore, the aim of this study is to provide a set point modi®cations is also demonstrated.
new fuzzy formulation which provides a signi®cant
simpli®cation over existing fuzzy-PID schemes
intended to improve conventional PID controllers. 2. PID control
The larger simplicity of the method stems from
three features: The control of a temperature process to a set
point temperature is used to illustrate the fuzzy
1. Fuzzy redundancy is eliminated by using gain scheduling developed here. For the control of
only one fuzzy input variable proportional to a temperature process by varying heater power,
the derivative of the conventional PID the heater power is determined in conventional
manipulated variable. PID control by manipulating
2. Online replacement and subsequent improve- … !
ment of PID control is simpli®ed through the 1 t d
À…t† ˆ Kp e…t† ‡ e…u†du ‡ Td e…t† Y …I†
introduction of a di€erential equation relat- Ti 0 dt
ing the fuzzy input and output variables.
3. Online control improvement is achieved by the where the error at time t is e ˆ Ts À T; T is the
independent tuning of only two parameters, process temperature, and Ts is the process set
while the previously tuned conventional PID point temperature. The three PID control para-
parameters Ti and Td are retained. meters are: the proportional gain Kp , the integral
3. T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325 319
time constant Ti , and the derivative time constant with initial condition g…0† ˆ 2…0†. Hence, gain
Td . The heater power, P is equal to À, but P is set scheduling of the input, d2ad(, is modelled in (3)
to 0 or the maximum heater power Pm—x , when À is as a nonlinear dependence of the output dgad(
respectively less than 0, or is greater than Pm—x . upon d2ad(. The positive scaling constants and
The temperature T is conveniently rescaled with are necessary to scale the fuzzy input and output
respect to the set point temperature and the ambient respectively (this is further detailed in Section 3.3),
temperature TI , using 0 ˆ …T À TI †a …Ts À TI †, ”
and the dimensionless heater power, P, equals g
so that TI 4T4Ts corresponds to 04041. The truncated to the range (0,1), i.e. P” ˆ 1 when g b 1,
time is also rescaled, using a timescale ts , as ( ˆ tats . ”
and P ˆ 0 when g ` 0. Conventional PID control
With these de®nitions, the dimensionless error is is generally recovered (`fuzzy logic equivalent')
E ˆ 1 À 0, and if 2 ˆ ÀaPm—x , then the dimen- when g ˆ 2; if f… d2ad( † ˆ d2ad( and ˆ ,
sionless form of the manipulated variable (1) is then integration and application of the initial
… ! condition, g…0† ˆ 2…0†, yields g ˆ 2. Note that,
à 1 ( à d although fuzzy gain scheduling could also be
2…( † ˆ Kp E…( † ‡ Ã E…u†du ‡ Td E…( † X …P†
Ti 0 d( based upon 2 instead of d2ad(, and this may seem
attractive for 2 perturbed by noise, the tradeo€ is
”
Now, P, the dimensionless heater power, is equal that it introduces an increased sensitivity to para-
”
to 2 truncated to the range [0,1], i.e. P ˆ 1 when metric ¯uctuations. Hence, the approach taken
2 b 1, and P ” ˆ 0 when 2 ` 0. The dimensionless here is to utilize the robustness associated with
PID control parameters are KÃ ˆ Kp …Ts À TI †a
p sliding mode control [6], and to supplement this
Pm—x Y TÃ ˆ Ti ats , and TÃ ˆ Td ats .
i d with explicit signal processing for noise suppres-
sion (Section 5).
A discrete equivalence to PID is also important
3. Fuzzy gain scheduling for discrete control applications, such as pulse
width modulation (Section 4). Assume that the
Fuzzy gain scheduling is in three steps: a fuzzy process is sampled at intervals of ts seconds so
logic system is built that incorporates the features that the dimensionless sampling interval is unity.
listed in the Introduction while preserving con- If d2ad( in (3) is approximated, at ( ˆ n, as
ventional PID control (Section 3.1), gain schedul- 2n À 2nÀ1 [note, any di€erencing scheme produces
ing is then implemented by modifying this system a fuzzy logic equivalent if it is applied to both
(Section 3.2), and two parameters are indepen- sides of (3)], and g at ( ˆ n is gn , then
dently tuned (Section 3.3) to improve PID control
performance. 1
gn ˆ gnÀ1 ‡ f…‰2n À 2nÀ1 Š†X …R†
3.1. Fuzzy logic system
The fuzzy input variable is taken to be equal to ” ” ”
At ( ˆ n, the power P is Pn , and Pn is equal to
the rate of change of the PID manipulated vari- gn truncated to the range (0,1). The fuzzy logic
able 2 in (2). Gain scheduling of d2ad( ensures equivalent now follows the continuous case.
that control is less susceptible to parameter ¯uc- The parameter [(3) and (4)], is necessary to
tuations [6] since control near the set point always scale the input ˆ d2ad( to ˆ O…1† (`O'
corresponds to d2ad( ˆ 0 (sliding mode control means `the order of'). Therefore, the function f,
[6]). Gain scheduling of d2ad( is formulated using that the fuzzy logic system must reproduce to
a di€erential equation where the rate of change of obtain a fuzzy logic equivalent is; f… † ˆ Y 41,
the fuzzy output (manipulated) variable satis®es and it is further assumed that f ˆ 1, 51,
and f ˆ À1Y 4 À 1. Given that f ˆ over 41,
dg 1 d2 it is also clear that the fuzzy logic equivalence
ˆ f Y …Q†
d( d( relating to (3) and (4), requires such
4. 320 T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325
that d2ad( 41. Note that, in practice 2 has increase f, which are respectively denoted as Yd ,
superimposed noisy perturbations and conditions Yn , and Yi and these sets are all unity respectively
 à  à  Ã
do change between control runs. Hence, a peak
in f P À 3 Y À 1 Y f P À 1 Y 1 , and f P 1 Y 3 , and are
2 2 2 2 2 2
value of d2ad( is normally estimated from pre- 0 otherwise. The consequence of each rule is
vious control runs, and this value is used to deter- represented as a fuzzy set following [7]. For
mine . A fuzzy logic system that reproduces this example, the consequent for Rule 1, labelled as
f… † is developed now. To implement fuzzy gain the set Y1 , is equated to the fuzzy set Yd , where
scheduling it is necessary to at least resolve the the maximum value of Y1 is Xn … †. Following the
scalar inputs into three domains: negative, near same procedure for the three rules gives the
zero and positive (this point is further examined in  Ã
three consequence sets: (i) Y1 ˆ Xn … †Y f P À 3 Y À 1 ,
Section 3.2 where the generalization to more than  à 2 2
(ii) Y2 ˆ Xz … †Y f P À 1 Y 1 , and (iii) Y3 ˆ Xp … †Y
three domains is also outlined). Therefore, three Â1 3Ã 2 2
rules, relating the scalar input , and the scalar f P 2 Y 2 . It remains to evaluate the scalar output
output f, are introduced: Rule 1; IF is negative f. Adopting an additive centroidal defuzzi®cation
THEN decrease f, Rule 2; IF is zero THEN do strategy [8]
nothing to f, Rule 3; IF is positive THEN
increase f. The three input fuzzy sets are negative, €
3
Aj … †cj
zero, and positive, and the three output fuzzy sets jˆ1
are, decrease f, do nothing to f, and increase f. It is f… † ˆ X …S†
€
3
necessary to convert these three rules into a com- A j … †
jˆ1
putational framework. This requires a means; (i)
to compute the degree of membership of the scalar
input in the input fuzzy sets, or the IF portion of Aj Y j ˆ 1Y 2Y 3, are the areas respectively corre-
each rule, (ii) to evaluate the consequence of sponding to the consequent fuzzy sets Yj Y
membership in each set, or the THEN portion of j ˆ 1Y 2Y 3; A1 ˆ Xn … †, A2 ˆ Xz … †, A3 ˆ Xp … †.
each rule, and (iii) to estimate the scalar output f The values c1 ˆ À1, c2 ˆ 0, c3 ˆ 1 are the respec-
from the three consequences of membership eval- tive centroids of these consequent sets. The sum of
uated in (ii). the areas in the denominator of (5) is always unity
The input fuzzy sets, negative, zero, and posi- since the components x sum to unity. The
tive, are respectively denoted as Xn Y Xz Y Xp . The numerator evaluates to for 41, and is 1 for
typical linear sets are used, i.e. Xn ˆ ÀY and À 1 for 4 À 1. Hence f… † ˆ for
51
À1440 …Xn 1Y 4 À 1, and 0 otherwise), 41, while f… † ˆ 1Y 51, and f… † ˆ À1Y
ˆ
Xz ˆ 1 À Y 41 (0 otherwise), Xp ˆ Y 04
À 4 À 1, that is, f preserves conventional PID.
41 Xp ˆ 151, and 0 otherwise). The degree of
membership of the scalar input in the input 3.2. Gain scheduling
fuzzy sets, is evaluated as the three scalars:
Xn … †Y Xz … †, and Xp … †, and these are stored in
 à Global PID control performance can be
the vector x ˆ Xn … †Y Xz … †Y Xp … † . When 41, improved by scheduling the gain KÃ as a function
p
the control is not truncated, and x ˆ ‰ÀY 1‡ of the derivative of the PID manipulated variable
Y 0ŠY À1440, and x ˆ ‰0Y 1 À Y ŠY 0441. d2ad(. More speci®cally, the sensitivity to small
Similarly, when 51, the control is truncated, and deviations from the set point is increased, and
x ˆ ‰1Y 0Y 0ŠY 4 À 1, and x ˆ ‰0Y 0Y 1ŠY 51. The the reverse is applied to larger deviations, i.e.
locations where the control is truncated are chosen dfad is increased near ˆ 0, and decreased near
without loss of generality as ˆ 1 and ˆ À1, ˆ 1, so that f is sigmoidal. This is achieved
since the inputs are scaled to ensure is order 1. here by applying variable weights to the con-
To evaluate the consequence of membership, it sequent fuzzy sets ([8] does so for an unrelated
is necessary ®rst to de®ne the output fuzzy sets, i.e. problem) so that the defuzzi®cation strategy in (5)
the three fuzzy sets decrease f, do nothing to f, becomes
5. T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325 321
€
3 right-hand side of (8) is a monotone function of
wj Aj … †cj the derivative of the PID manipulated variable,
jˆ1
f… † ˆ X …T† absolutely bounded by 1a (this is analogous to
€
3
wj Aj … † the statement regarding stability made in [6] noted
jˆ1 in the Introduction). Note, for control problems
where the gain scheduling requires ®ner control of
The weights are positive, and conventional PID the sigmoidal shape of f… †, the number of sets
is recovered in the same fashion as in Section 3.1 may be increased and this simply adds extra
with the additional requirement w1 ˆ w2 ˆ w3 . weights to the defuzzi®cation strategy.
Since the form of (6) is unchanged when the
weights are multiplied by a constant, the weight w2 3.3. Parameter tuning
is set to unity without loss of generality, and
attention is further restricted to symmetric weights There are three parameters in the fuzzy gain
w1 ˆ w3 w. Applying both of these to (6) gives
scheduling in (8): , , and w. The parameter is
for 41 used to scale d2ad( to order 1, so that control
far from the set point is d2ad( ˆ O…1†, and
w near to the set point is d2ad( ( 1. More pre-
f… † ˆ Y …U†
…w À 1† ‡ 1 cisely, the necessity of preserving conventional
PID control is used to ®x ; if is such that
where f ˆ 1 for b 1, and f ˆ À1 for ` À1. The d2ad( 41, where d2ad( is taken from the
end point values of f…Æ1† ˆ Æ1, and f…0† ˆ 0 are existing PID manipulated variable, then the fuzzy
independent of w, in contrast to the slopes
logic equivalent follows from ˆ , and w ˆ 1.
dfad ˆ0 ˆ w, and dfad ˆÆ1 ˆ 1awY f… † is sig- Therefore, it is only necessary to tune two para-
moidal when w b 1 and this is the desired gain meters, and w to globally improve the existing
scheduling described above. The derivative of f… † PID control performance. A key observation
is also continuous at ˆ 0 so that special treat- leading to independent tuning of and w is that
ment of control near, and across ˆ 0 [6] is avoi- for improvement of well-tuned PID, ˆ O…†.
ded and this justi®es the restriction to symmetric Then dgad( ˆ O…wd2ad( † near the set point and
weights. Furthermore, the parameter 3 de®nes the control sensitivity near there is O…w†. Therefore,
extent to which inputs near 0 in¯uence the output control sensitivity near the set point is increased by
relative to those further away from 0 and thus it is setting equal to and independently tuning w b
necessary to de®ne at least three sets (as in Section 1 to reduce maximum set point overshoot. Next,
3.1) since inputs can at least be, near zero, large is independently modi®ed to b to reduce
and positive, or large and negative. control sensitivity far from the set point and fur-
Substituting f… † (3) gives explicitly for
ther reduce maximum set point overshoot. Whilst,
d2ad( 41 is varied, the sensitivity near the set point is
maintained at the previously tuned w, by modifying
dg 1 w d2ad( w such that wa is unchanged. A physical model
ˆ Y …V† (Section 4) is now used to demonstrate (Section 5)
d( …w À 1†d2ad( ‡ 1
improvement of well-tuned PID control.
where dgad( ˆ 1a for d2ad( b 1, and dgad( ˆ
À1a for d2ad( ` À1. To recover conventional 4. Physical model
PID control; 3 ˆ 1, ˆ , and is chosen such
that d2ad( 41, whereupon (8) reduces to The control of a temperature process, depicted
dgad( ˆ d2ad(, and then integration and appli- in the schematic in Fig. 1, is conducted on a solid
cation of g…0† ˆ 2…0† yields the desired g ˆ 2. cylindrical block of aluminum, 5 cm diameter and
Control based upon (8) is stable, since the 12.5 cm in length. The block is externally heated
6. 322 T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325
Fig. 1. Experimental setup for control of temperature process by pulse width modulation.
by a 300 watt electrical heater band wrapped power setting, a continuous variable, it is easily
around the block circumference. A type E, modi®ed to the discrete pulse width modulation.
ungrounded thermocouple, measures the object's To avoid confusion, the nomenclature in Sections
temperature at its center, and these analog mea- 2 and 3.1 is adopted. During the nth duty cycle,
surements are converted to digital readings using a the on time of the heater, or pulse width Pn s, is
12 bit analog-to-digital converter. Process control determined by the control algorithm, while the
is over contiguous duty cycles of constant dura- heater power setting is held ®xed between duty
tion. The heater is on for a portion of a duty cycle, cycles. The maximum pulse width, Pm—x s, is equal
starting at the beginning, and then o€ for the to the duty cycle duration. The average error
remainder; the heater on time during a duty cycle within a duty cycle is en ˆ Ts À Tn where Tn is the
is termed the pulse width. A pulse is implemented average temperature over a duty cycle. The time
using a 16 bit digital timing board, and an opti- scale, for the dimensionless form, is taken to be
cally isolated solid state SSR-20 electronic relay. the duty cycle duration (the sampling interval of
Two logic states, on and o€, corresponding to the the average temperature), and the nth duty cycle is
heater being on or o€, are generated by the digital then over n À 14(4n. The average dimensionless
counter and are inputted to the relay. The process error within the nth duty cycle, is En ˆ 1 À 0n ,
control algorithm determines the duration of the ”
where 0n ˆ …Tn À TI †a…Ts À TI †. Finally, Pn Y 2n ,
on logic state for each duty cycle, or modulates the and gn , follow the description in Section 3.1.
pulse width between duty cycles Ð hence pulse The general approach followed here to ®lter
width modulation. The duty cycle duration is noisy ¯uctuations from the error components (i.e.
empirically set at 4.25 s, and at steady state this the error variable and its derivatives), does not
corresponds to a maximum error, over a duty rely upon features of the control setup or choice of
cycle, of less than 1% (the thermocouple accuracy sampling period (prone to aliasing errors). Rather,
is about 1%). the error variable is ®rst sampled at a high enough
rate to establish all features relevant for the con-
trol application. Then, each independent error
5. Results component is separately processed for noise sup-
pression. For the experiments conducted here, the
Although the process control described in Sec- average temperature Tn during a duty cycle is the
tion 2 is based on the determination of heater average of 10, equally spaced temperature mea-
7. T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325 323
surements. A least squares regression is also used and the fuzzy logic equivalent corresponds to ˆ
to reduce noise in the error and the numerical ˆ 38 and w ˆ 1. Fuzzy gain scheduling is used
approximation of its derivatives. Speci®cally, the to improve upon the existing PID control perfor-
error value En (essentially Tn ) and its ®rst deriva- mance by tuning the parameters and w away
tive are calculated from a line, and the second from ˆ and w ˆ 1. Firstly, maximum set point
derivative from a quadratic polynomial, all least overshoot is reduced by increasing control sensi-
squares regressed on measurements taken from the tivity near the set point. This is achieved by inde-
most recent 16 duty cycles. The choice of 16 duty pendently tuning 3 (Section 3.3) with four
cycles (about 1 min) is arbitrary, but is chosen to experiments w ˆ 2Y 4Y 6Y 8, where ˆ ˆ 38. The
be much smaller than the process time constant value w ˆ 6 is chosen (see Fig. 2; w ˆ 2Y 4Y 8 are
(about 500 duty cycles or 30 min). The least not shown) since it gives about a ®vefold reduc-
squares regression is eciently implemented as a tion in maximum overshoot and w ˆ 8 provides
convolution using the Savitzky±Golay formula- marginal additional improvement. The maximum
tion [9]. The set point temperature is chosen as overshoot is somewhat reduced again, by decreas-
Ts=100 C and the ambient temperature is ing the control response, dgad(, away from the set
approximately 25 C. The dimensionless PID con- point and this corresponds to b . The pre-
trol parameters Kpà ˆ 1Y Tià ˆ 37X5, and Tdà ˆ 9X4, viously tuned control sensitivity near the set point
and the temperature response 0 is shown in Fig. 2 is maintained at w ˆ 6 by varying w such that wa
[well-tuned PID control ( ˆ ˆ 38, w ˆ 1) in the is constant, while is increased by 20, 30, and
®gure] as a function of the dimensionless time (. 40%. The overshoot for each of these values is
This control (tuned for minimum overshoot) shows about 3, 2, and 10%, respectively. Hence, as is
approximately one quarter amplitude damping increased the maximum overshoot is ®rst reduced
with settling time approximately the process time by the initial reduction in control sensitivity far
constant and is typical of well-tuned PID. This from the set point, but then increases as the control
temperature response can be greatly improved by sensitivity becomes too reduced. A 30% increase over
fuzzy gain scheduling. is chosen to scale
ˆ 38 is chosen and the ®nal results are shown in
d2ad( to order 1. From the existing PID Fig. 2 for ˆ 50 which also corresponds to w ˆ 7X8
manipulated variable (not shown), if % 38, then
(a 30% increase over 3 ˆ 6). The maximum over-
d2ad( 41 for the duration of the PID control, shoot has now been reduced about sixfold to 2.5%
maximum overshoot. Five indices are also used to
assess the overall control performance: the max-
imum overshoot and undershoot of the tempera-
ture expressed as a percentage of the set point, the
rise time, which is the time needed to rise to within
90% of the set point, the settling time, or time the
process requires to fall within Æ2.5% of the set
point, and the steady state error. These ®ve indices
are presented for the conventional PID control
…w ˆ 1Y ˆ ˆ 38† fuzzy gain scheduled control
…w ˆ 6Y ˆ 38Y —nd Y w ˆ 7X8Y ˆ 50†, and MPC
control in Table 1. From Table 1 and Fig. 2, it is
clear that fuzzy gain scheduling ( ˆ 38Y w ˆ 7X8,
and ˆ 50) provides much better control perfor-
mance than the well-tuned PID control …w ˆ 1Y
ˆ ˆ 38†. In particular, the settling time is
Fig. 2. Temperature response for conventional PID control,
reduced to about one half the process time con-
fuzzy gain scheduled PID, and model predictive control stant, and the percentage maximum overshoot is
(MPC). reduced from 15 to 2.5%.
8. 324 T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325
The benchmark experiment is based on MPC. In in 50 cm3 of water at 10 C for 5 s), and large
the MPC approach used here (details are in [10]) a (40 C) changes in the set point (Fig. 4), is clearly
discrete step response of the physical model is demonstrated for the tuned fuzzy gain scheduling
obtained by an open loop test. The method utilizes … ˆ 38Y w ˆ 7X8Y ˆ 50† where the manipulated
two horizons: a `control' horizon equal to the
number of predicted control moves, and a `predic-
tion' horizon equal to the number of sampling
intervals to reach 95% of the open loop steady
state. Predictions of the physical model output are
made within the prediction horizon, and these are
compared to the desired set point pro®le. Least
squares minimization of the di€erence between the
predictions and the set point pro®le, over the pre-
diction horizon, is used to determine the manipu-
lated variable within the control horizon. A
control horizon of length 2 and a prediction horizon
of length 139 was used here for controlling the
temperature. Although MPC control is funda-
mentally di€erent from conventional PID, it pro-
duces control actions similar to PID control, but
shows a very reduced overshoot and settling time to
the set point due to its predictive capability. Thus, Fig. 3. Temperature response of fuzzy gain scheduled PID to a
MPC is practically useful to provide a range of disturbance (applied at ( % 280), and the same for model pre-
comparison to fuzzy gain scheduling. A surprising dictive control (MPC) (applied at ( % 350). The fuzzy gain
scheduled response is almost Identical to that seen for MPC.
result, evident in Fig. 2, is that the fuzzy gain sche-
duling fares very well in comparison to the more
sophisticated benchmark MPC control. Better per-
formance indices were also obtained for gain
scheduling, w ˆ 7X8Y ˆ 50, over MPC control
when only the rise time and settling time are con-
sidered, and marginally worse results for percen-
tage maximum overshoot and undershoot.
Control robustness to a short, cooling disturbance
(Fig. 3) (the cylindrical block was suddenly placed
Table 1
Control performance indices
Performance indices w ˆ 1, w ˆ 6, w ˆ 7X8, MPC
ˆ 38, ˆ 38 ˆ 38
ˆ 38 ˆ 38 ˆ 38
Percentage 15 3.2 2.5 0
maximum overshoot
Percentage 4 1 1 0
maximum undershoot
Rise time (min) 7.7 7.3 6.9 14
Fig. 4. Temperature response (a) and manipulated variable (b)
Setting time (min) 30 15 14 19
for fuzzy gain scheduled PID. Control is depicted for set points
Percentage Æ0.5 Æ0.5 Æ0.5 Æ0.5
40% larger …Ts ˆ 140 g† and smaller …Ts ˆ 60 g† than that
steady state error
used for the parameter tuning …Ts ˆ 100 g†.
9. T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325 325
variable is shown together with the temperature operating grants held by G.C.K. and R.D., and an
response. NSERC postgraduate scholarship held by T.P.B.
The authors would like to thank Dr. Gordon
Fenton, Dr. Adam Bell and thoughtful reviewers
6. Summary and conclusion for comments.
A fuzzy gain scheduling scheme that allows for
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