The document describes the design of various fractional order controllers including T-PID, FO-PID, FO-PI, and FO-PD controllers. It proposes a reference tracking method using constrained optimization to tune the parameters of these fractional order controllers. The method is tested on a first order with dead time system to demonstrate the feasibility of tuning fractional order controllers. Simulation results comparing PID, T-PID, and FO-PID controllers are presented.
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.
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.
Data-based PID control of flexible joint robot using adaptive safe experiment...journalBEEI
This paper proposes the data-based PID controller of flexible joint robot based on adaptive safe experimentation dynamics (ASED) algorithm. The ASED algorithm is an enhanced version of SED algorithm where the updated tuning variable is modified to adapt to the change of the objective function. By adopting the adaptive term to the updated equation of SED, it is expected that the convergence accuracy can be further improved. The effectiveness of the ASED algorithm is verified to tune the PID controller of flexible joint robot. In this flexible joint control problem, two PID controllers are utilized to control both rotary angle tracking and vibration of flexible joint robot. The performance of the proposed data-based PID controller is assessed in terms of trajectory tracking of angular motion, vibration reduction and statistical analysis of the pre-defined control objective function. The simulation results showed that the data-based PID controller based on ASED is able to produce better control accuracy than the conventional SED based method.
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.
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.
Data-based PID control of flexible joint robot using adaptive safe experiment...journalBEEI
This paper proposes the data-based PID controller of flexible joint robot based on adaptive safe experimentation dynamics (ASED) algorithm. The ASED algorithm is an enhanced version of SED algorithm where the updated tuning variable is modified to adapt to the change of the objective function. By adopting the adaptive term to the updated equation of SED, it is expected that the convergence accuracy can be further improved. The effectiveness of the ASED algorithm is verified to tune the PID controller of flexible joint robot. In this flexible joint control problem, two PID controllers are utilized to control both rotary angle tracking and vibration of flexible joint robot. The performance of the proposed data-based PID controller is assessed in terms of trajectory tracking of angular motion, vibration reduction and statistical analysis of the pre-defined control objective function. The simulation results showed that the data-based PID controller based on ASED is able to produce better control accuracy than the conventional SED based method.
Meta-heuristic optimization techniques are important tools to define the optimal solutions for many problems. In this paper, a new advanced artificial intelligence (AI) based direct torque control (DTC) speed drives are optimally designed and implemented in real time to achieve a high performance permanent-magnet synchronous-motor (PMSM) drive. Grey wolf (GW) algorithms are used with the standard PID-based DTC (PIDDTC) and with the DTC with fuzzy logic (FDTC) based speed controllers. DSPACE DS1202 is utilized in the real-time implementation. MATLAB SIMULINK is used to simulate the steady-state (S.S.) and dynamic responses. The overall system is tested at different operating conditions for both simulation and practical work and all results are presented. A comparison between experimental and simulation results is performed and also a comparison between different applied intelligent techniques is introduced.
A comparative analysis for stabilize the temperature variation of a water bod...eSAT Journals
Abstract
Minimization of performance indices is very effective criteria for real time system. The process basically indicates a stable system.
Now, fixing the temperature in a water body is an important method for practical life where fuzzy logic is appl ied naturally. Here
in this paper we will try to show the method of minimization of error parameter using optimal regulator have equally effects the
fuzzy system for that the system runs towards the stable system.
Keywords - Crisp Set, Fuzzy Set, FLC, Cost Function, HJB Method
An Optimal LFC in Two-Area Power Systems Using a Meta-heuristic Optimization...IJECEIAES
In this study, an optimal meta-heuristic optimization algorithm for load frequency control (LFC) is utilized in two-area power systems. This metaheuristic algorithm is called harmony search (HS), it is used to tune PI controller parameters (퐾 ) automatically. The developed controller (HSPI) with LFC loop is very important to minimize the system frequency and 푝 , 퐾 푖 keep the system power is maintained at scheduled values under sudden loads changes. Integral absolute error (IAE) is used as an objective function to enhance the overall system performance in terms of settling time, maximum deviation, and peak time. The two-area power systems and developed controller are modelled using MATLAB software (Simulink/Code). As a result, the developed control algorithm (HS-PI) is more robustness and efficient as compared to PSO-PI control algorithm under same operation conditions.
Design of predictive controller for smooth set point tracking for fast dynami...eSAT Journals
Abstract Model Predictive Control is generally used for slow dynamic system. Here efforts are made to implement MPC controller for Fast dynamic System. Speed control of DC motor is taken as fast dynamic system for which the MPC controller would be implemented. To control the speed of the DC motor Generalized Predictive Control (GPC) algorithm is used. In this paper, ARIX model based GPC control is implemented in 2-DOF structure. Transfer function of the DC motor is derived using LABVIEW and system identification tool of MATLAB. From the response of the system, it can be seen that the GPC has improved the performance of the system rather than PID control algorithm from disturbance rejection point of view. Keywords: MPC (Model Predictive Controller), GPC (Generalized Predictive Controller), ARIX Model (Auto Regressive Integrated Exogenous Model).
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 GAINS IN BASIS WEIGHT USING FUZZY CONTROLLERSpaperpublications3
Abstract: new generation fuzzy logic controllers are based on the integration of conventional and fuzzy controllers. India being the fastest growing market for paper globally presents an exciting industry scenario. The main requirement concerns measured and controlled variable for paper including basis weight and moisture. This research is an effort to achieve better performance with nonlinear processes in servo applications. Three different structures on fuzzy-p, fuzzy-pd and fuzzy-pd+i are studied for variable inputusing simulink and fuzzy logic toolbox. Analysis of four scaling gainsge, gce, gie and gu is done to obtain most appropriate output.
Keywords:fuzzy controllers, fuzzy-p, fuzzy-pd, fuzzy-pd+i, basis weight, simulink.
OPTIMAL PID CONTROLLER DESIGN FOR SPEED CONTROL OF A SEPARATELY EXCITED DC MO...ijscmcjournal
This paper presents a new approach to determine the optimal proportional-integral-derivative controller
parameters for the speed control of a separately excited DC motor using firefly optimization technique.
Firefly algorithm is one of the recent evolutionary methods which are inspired by the Firefly’s behavior in
nature. The firefly optimization technique is successfully implemented using MATLAB software. A
comparison is drawn from the results obtained between the linear quadratic regulator and firefly
optimization techniques. Simulation results are presented to illustrate the performance and validity of the
design method.
Non-integer IMC Based PID Design for Load Frequency Control of Power System t...IJECEIAES
This paper deals with non-integer internal model control (FIMC) based proportional- integral-derivative(PID) design for load frequency control (LFC) of single area nonreheated thermal power system under parameter divergence and random load disturbance. Firstly, a fractional second order plus dead time(SOPDT) reduced system model is obtained using genetic algorithm through step error minimization. Secondly, a FIMC based PID controller is designed for single area power system based on reduced system model. Proposed controller is equipped with single area non-reheated thermal power system. The resulting controller is tested using MATLAB/SIMULINK under various conditions. The simulation results show that the controller can accommodate system parameter uncertainty and load disturbance. Further, simulation shows that it maintains robust performance as well as minimizes the effect of load fluctuations on frequency deviation. Finally, the proposed method applied to two area power system to show the effectiveness.
Signature PSO: A novel inertia weight adjustment using fuzzy signature for LQ...journalBEEI
Particle swarm optimization (PSO) is an optimization algorithm that is simple and reliable to complete optimization. The balance between exploration and exploitation of PSO searching characteristics is maintained by inertia weight. Since this parameter has been introduced, there have been several different strategies to determine the inertia weight during a train of the run. This paper describes the method of adjusting the inertia weights using fuzzy signatures called signature PSO. Some parameters were used as a fuzzy signature variable to represent the particle situation in a run. The implementation to solve the tuning problem of linear quadratic regulator (LQR) control parameters is also presented in this paper. Another weight adjustment strategy is also used as a comparison in performance evaluation using an integral time absolute error (ITAE). Experimental results show that signature PSO was able to give a good approximation to the optimum control parameters of LQR in this case.
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.
Hybrid fuzzy-PID like optimal control to reduce energy consumptionTELKOMNIKA JOURNAL
The electric motor is one of the appliances that consume considerable energy. Therefore, the control method which can reduce energy consumption with better performance is needed. The purpose of this research is to minimize the energy consumption of the DC motor with maintaining the performance using Hybrid Fuzzy-PID. The input of the Fuzzy system is the error and power of the system. Where error is correlated with matric Q and power is correlated with matric R. Therefore, adjusting the fuzzy rule on error and power is like adjust matrices Q and R in LQR method. The proposed algorithm can reduce energy consumption. However, system response is slightly decrease shown from ISE (Integral Square Error). The energy reduction average is up to 5.58% while the average of ISE increment is up to 1.89%. The more speed variation in the system, the more energy can be saved by the proposed algorithm. While in terms of settling time, the proposed algorithm has the longest time due to higher computation time in the fuzzy system. This performance can be increased by tuning fuzzy rules. This algorithm offers a solution for a complex system which difficult to be modeled.
A new scaled fuzzy method using PSO segmentation (SePSO) applied for two area...IJECEIAES
The balance of the power supply and demand (frequency control) is one of the most ancient approaches for the power systems, which is considered as a highly complex system.The power systems frequency response is a perfect indicator of the resilience to the multi-disturbances. In this work, the fuzzy logichas been scaledusing PSO segmentation (SePSO) and suggested to get high performance of frequency stability. PSO has participated into multi-segments for calculating the scald-fuzzy membership with basic rules. Two identical interconnectedpower areas wereselected to exam the new scaled fuzzy method. The time response of the results has undertaken the effectiveness of the controller reactionusing the MATLAB Simulink. The work feed back proved that the proposed SePSO optimization for the controlhas significantly faster with low undershot concerningthe classical controllers in differenttime schedules and disturbance values.
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.
Modeling and Control of MIMO Headbox System Using Fuzzy LogicIJERA Editor
The Headbox plays an important role in pulp supply system with sheet forming in paper making process. The air cushion headbox is a nonlinear & strong coupling system. In the air cushion headbox system there were two important parameters which include total head and the stock level for improving pulp product quality. These two parameters make this system MIMO output system so for this a decoupling controls strategy was required for interaction between these two control loops. In this paper fuzzy tuned PID control scheme is proposed for controlling the nonlinear control problem in air cushion headbox after the system being decoupled. An attempt has been made for comparison between classical (PID) and fuzzy tuned PID controller. It concludes that the fuzzy tuned PID controller is found most suitable for MIMO system in terms of obtaining steady state properties. The effects of disturbances are studied through computer simulation using Matlab/Simulink toolbox.
Meta-heuristic optimization techniques are important tools to define the optimal solutions for many problems. In this paper, a new advanced artificial intelligence (AI) based direct torque control (DTC) speed drives are optimally designed and implemented in real time to achieve a high performance permanent-magnet synchronous-motor (PMSM) drive. Grey wolf (GW) algorithms are used with the standard PID-based DTC (PIDDTC) and with the DTC with fuzzy logic (FDTC) based speed controllers. DSPACE DS1202 is utilized in the real-time implementation. MATLAB SIMULINK is used to simulate the steady-state (S.S.) and dynamic responses. The overall system is tested at different operating conditions for both simulation and practical work and all results are presented. A comparison between experimental and simulation results is performed and also a comparison between different applied intelligent techniques is introduced.
A comparative analysis for stabilize the temperature variation of a water bod...eSAT Journals
Abstract
Minimization of performance indices is very effective criteria for real time system. The process basically indicates a stable system.
Now, fixing the temperature in a water body is an important method for practical life where fuzzy logic is appl ied naturally. Here
in this paper we will try to show the method of minimization of error parameter using optimal regulator have equally effects the
fuzzy system for that the system runs towards the stable system.
Keywords - Crisp Set, Fuzzy Set, FLC, Cost Function, HJB Method
An Optimal LFC in Two-Area Power Systems Using a Meta-heuristic Optimization...IJECEIAES
In this study, an optimal meta-heuristic optimization algorithm for load frequency control (LFC) is utilized in two-area power systems. This metaheuristic algorithm is called harmony search (HS), it is used to tune PI controller parameters (퐾 ) automatically. The developed controller (HSPI) with LFC loop is very important to minimize the system frequency and 푝 , 퐾 푖 keep the system power is maintained at scheduled values under sudden loads changes. Integral absolute error (IAE) is used as an objective function to enhance the overall system performance in terms of settling time, maximum deviation, and peak time. The two-area power systems and developed controller are modelled using MATLAB software (Simulink/Code). As a result, the developed control algorithm (HS-PI) is more robustness and efficient as compared to PSO-PI control algorithm under same operation conditions.
Design of predictive controller for smooth set point tracking for fast dynami...eSAT Journals
Abstract Model Predictive Control is generally used for slow dynamic system. Here efforts are made to implement MPC controller for Fast dynamic System. Speed control of DC motor is taken as fast dynamic system for which the MPC controller would be implemented. To control the speed of the DC motor Generalized Predictive Control (GPC) algorithm is used. In this paper, ARIX model based GPC control is implemented in 2-DOF structure. Transfer function of the DC motor is derived using LABVIEW and system identification tool of MATLAB. From the response of the system, it can be seen that the GPC has improved the performance of the system rather than PID control algorithm from disturbance rejection point of view. Keywords: MPC (Model Predictive Controller), GPC (Generalized Predictive Controller), ARIX Model (Auto Regressive Integrated Exogenous Model).
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 GAINS IN BASIS WEIGHT USING FUZZY CONTROLLERSpaperpublications3
Abstract: new generation fuzzy logic controllers are based on the integration of conventional and fuzzy controllers. India being the fastest growing market for paper globally presents an exciting industry scenario. The main requirement concerns measured and controlled variable for paper including basis weight and moisture. This research is an effort to achieve better performance with nonlinear processes in servo applications. Three different structures on fuzzy-p, fuzzy-pd and fuzzy-pd+i are studied for variable inputusing simulink and fuzzy logic toolbox. Analysis of four scaling gainsge, gce, gie and gu is done to obtain most appropriate output.
Keywords:fuzzy controllers, fuzzy-p, fuzzy-pd, fuzzy-pd+i, basis weight, simulink.
OPTIMAL PID CONTROLLER DESIGN FOR SPEED CONTROL OF A SEPARATELY EXCITED DC MO...ijscmcjournal
This paper presents a new approach to determine the optimal proportional-integral-derivative controller
parameters for the speed control of a separately excited DC motor using firefly optimization technique.
Firefly algorithm is one of the recent evolutionary methods which are inspired by the Firefly’s behavior in
nature. The firefly optimization technique is successfully implemented using MATLAB software. A
comparison is drawn from the results obtained between the linear quadratic regulator and firefly
optimization techniques. Simulation results are presented to illustrate the performance and validity of the
design method.
Non-integer IMC Based PID Design for Load Frequency Control of Power System t...IJECEIAES
This paper deals with non-integer internal model control (FIMC) based proportional- integral-derivative(PID) design for load frequency control (LFC) of single area nonreheated thermal power system under parameter divergence and random load disturbance. Firstly, a fractional second order plus dead time(SOPDT) reduced system model is obtained using genetic algorithm through step error minimization. Secondly, a FIMC based PID controller is designed for single area power system based on reduced system model. Proposed controller is equipped with single area non-reheated thermal power system. The resulting controller is tested using MATLAB/SIMULINK under various conditions. The simulation results show that the controller can accommodate system parameter uncertainty and load disturbance. Further, simulation shows that it maintains robust performance as well as minimizes the effect of load fluctuations on frequency deviation. Finally, the proposed method applied to two area power system to show the effectiveness.
Signature PSO: A novel inertia weight adjustment using fuzzy signature for LQ...journalBEEI
Particle swarm optimization (PSO) is an optimization algorithm that is simple and reliable to complete optimization. The balance between exploration and exploitation of PSO searching characteristics is maintained by inertia weight. Since this parameter has been introduced, there have been several different strategies to determine the inertia weight during a train of the run. This paper describes the method of adjusting the inertia weights using fuzzy signatures called signature PSO. Some parameters were used as a fuzzy signature variable to represent the particle situation in a run. The implementation to solve the tuning problem of linear quadratic regulator (LQR) control parameters is also presented in this paper. Another weight adjustment strategy is also used as a comparison in performance evaluation using an integral time absolute error (ITAE). Experimental results show that signature PSO was able to give a good approximation to the optimum control parameters of LQR in this case.
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.
Hybrid fuzzy-PID like optimal control to reduce energy consumptionTELKOMNIKA JOURNAL
The electric motor is one of the appliances that consume considerable energy. Therefore, the control method which can reduce energy consumption with better performance is needed. The purpose of this research is to minimize the energy consumption of the DC motor with maintaining the performance using Hybrid Fuzzy-PID. The input of the Fuzzy system is the error and power of the system. Where error is correlated with matric Q and power is correlated with matric R. Therefore, adjusting the fuzzy rule on error and power is like adjust matrices Q and R in LQR method. The proposed algorithm can reduce energy consumption. However, system response is slightly decrease shown from ISE (Integral Square Error). The energy reduction average is up to 5.58% while the average of ISE increment is up to 1.89%. The more speed variation in the system, the more energy can be saved by the proposed algorithm. While in terms of settling time, the proposed algorithm has the longest time due to higher computation time in the fuzzy system. This performance can be increased by tuning fuzzy rules. This algorithm offers a solution for a complex system which difficult to be modeled.
A new scaled fuzzy method using PSO segmentation (SePSO) applied for two area...IJECEIAES
The balance of the power supply and demand (frequency control) is one of the most ancient approaches for the power systems, which is considered as a highly complex system.The power systems frequency response is a perfect indicator of the resilience to the multi-disturbances. In this work, the fuzzy logichas been scaledusing PSO segmentation (SePSO) and suggested to get high performance of frequency stability. PSO has participated into multi-segments for calculating the scald-fuzzy membership with basic rules. Two identical interconnectedpower areas wereselected to exam the new scaled fuzzy method. The time response of the results has undertaken the effectiveness of the controller reactionusing the MATLAB Simulink. The work feed back proved that the proposed SePSO optimization for the controlhas significantly faster with low undershot concerningthe classical controllers in differenttime schedules and disturbance values.
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.
Modeling and Control of MIMO Headbox System Using Fuzzy LogicIJERA Editor
The Headbox plays an important role in pulp supply system with sheet forming in paper making process. The air cushion headbox is a nonlinear & strong coupling system. In the air cushion headbox system there were two important parameters which include total head and the stock level for improving pulp product quality. These two parameters make this system MIMO output system so for this a decoupling controls strategy was required for interaction between these two control loops. In this paper fuzzy tuned PID control scheme is proposed for controlling the nonlinear control problem in air cushion headbox after the system being decoupled. An attempt has been made for comparison between classical (PID) and fuzzy tuned PID controller. It concludes that the fuzzy tuned PID controller is found most suitable for MIMO system in terms of obtaining steady state properties. The effects of disturbances are studied through computer simulation using Matlab/Simulink toolbox.
Comparison of Tuning Methods of PID Controllers for Non-Linear Systempaperpublications3
Abstract: Modern days have seen vast developments in the field of controller’s .There are various controllers developed these days with various different specifications. But the only drawback is that, there is no fixed method for the tuning of these controllers, which is necessary for controlling of the system based on the variation of the input or for the changes in the system. In order to overcome this drawback, in this paper we have compared various tuning methods of PID controller for non-linear system. As a non-linear system we have taken the dc motor as a system. For the particular DC motor controller transfer function has been determined and control parameters such as Proportional Gain, Integral Time and Derivative time are identified. They are numerous methods of developing a Proportional Integral and Derivative (PID) Controller, amongst them some methods are adopted in this paper and Comparisons of Time Domain specifications of those controllers has been carried out.
COMPARATIVE ANALYSIS OF CONVENTIONAL PID CONTROLLER AND FUZZY CONTROLLER WIT...IJITCA Journal
All the real systems exhibits non-linear nature,conventional controllers are not always able to provide good and accurate results. Fuzzy Logic Control is used to obtain better response. A model for simulation is designed and all the assumptions are made before the development of the model. An attempt has been made to analyze the efficiency of a fuzzy controller over a conventional PID controller for a three tank level control system using fuzzification & defuzzification methods and their responses are compared. Analysis is done through computer simulation using Matlab/Simulink toolbox. This study shows that the application of Fuzzy Logic Controller (FLC) gives the best response with triangular membership function and centroid defuzzification 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.
On the fragility of fractional-order PID controllers for FOPDT processesISA Interchange
This paper analyzes the fragility issue of fractional-order proportional-integral-derivative controllers applied to integer first-order plus-dead-time processes. In particular, the effects of the variations of the controller parameters on the achieved control system robustness and performance are investigated. Results show that this kind of controllers is more fragile with respect to the standard proportional-integral-derivative controllers and therefore a significant attention should be paid by the user in their tuning.
Numerical Optimization of Fractional Order PID Controller inventionjournals
: The fractional order PID controller is the generalization of classical PID controller, many Researchers interest in tuning FOPID controller here we use the Pareto Optimum technique to estimate the controller parameter and compare our result with the classical model and with other Researchers result .we used both mathematica package and matlab for tuning and simulation
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.
Hybrid controller design using gain scheduling approach for compressor systemsIJECEIAES
The automatic control system plays a crucial role in industries for controlling the process operations. The automatic control system provides a safe and proper controlling mechanism to avoid environmental and quality problems. The control system controls pressure flow, mass flow, speed control, and other process metrics and solves robustness and stability issues. In this manuscript, The Hybrid controller approach like proportional integral (PI) and proportional derivative (PD) based fuzzy logic controller (FLC) using with and without gain scheduling approach is modeled for the compressor to improve the robustness and error response control mechanism. The PI/PD-based FLC system includes step input function, the PI/PD controller, FLC with a closed-loop mechanism, and gain scheduler. The error signals and control response outputs are analyzed in detail for PI/PD-based FLC’s and compared with conventional PD/PID controllers. The PD-based FLC with the Gain scheduling approach consumes less overshoot time of 74% than the PD-based FLC without gain scheduling approach. The PD-based FLC with the gain scheduling approach produces less error response in terms of 7.9% in integral time absolute error (ITAE), 7.4% in integral absolute error (IAE), and 16% in integral square error (ISE) than PD based FLC without gain scheduling approach.
This paper presents a developed application for using Fraction Order PID controller (FOPID) in controlling of DC motors installed incelestron telescope, this is done through controlling the angles of two DC motors driven the telescope. The model of celestron telescope is mathematically represented by highly non linear differential equations, this types of nonlinear model is recommended to be controlled using Artificial Intelligent based controller. In this paper, optimal fuzzy FOPID is implemented instead of conventional PID controllers. Genetic Algorithm, fuzzy logic are used for tuning the FOPID parameters.FOPID controller is based on position error and its rate of change as an input vector, the proposed controller set presents a complete precision in forcing the telescope motors to satisfy the predefined position. The simulation results show the dynamic response of the system and the enhancement achieved in rising time and settling time when using FOPID. The response of FOPID is compared with the conventional PID with the same input position reference.
Similar to Design of fractional order controllers using constrained optimization and reference tracking method (20)
The aim of this research is the speed tracking of the permanent magnet synchronous motor (PMSM) using an intelligent Neural-Network based adapative backstepping control. First, the model of PMSM in the Park synchronous frame is derived. Then, the PMSM speed regulation is investigated using the classical method utilizing the field oriented control theory. Thereafter, a robust nonlinear controller employing an adaptive backstepping strategy is investigated in order to achieve a good performance tracking objective under motor parameters changing and external load torque application. In the final step, a neural network estimator is integrated with the adaptive controller to estimate the motor parameters values and the load disturbance value for enhancing the effectiveness of the adaptive backstepping controller. The robsutness of the presented control algorithm is demonstrated using simulation tests. The obtained results clearly demonstrate that the presented NN-adaptive control algorithm can provide good trackingperformances for the speed trackingin the presence of motor parameter variation and load application.
This paper presents a fast and accurate fault detection, classification and direction discrimination algorithm of transmission lines using one-dimensional convolutional neural networks (1D-CNNs) that have ingrained adaptive model to avoid the feature extraction difficulties and fault classification into one learning algorithm. A proposed algorithm is directly usable with raw data and this deletes the need of a discrete feature extraction method resulting in more effective protective system. The proposed approach based on the three-phase voltages and currents signals of one end at the relay location in the transmission line system are taken as input to the proposed 1D-CNN algorithm. A 132kV power transmission line is simulated by Matlab simulink to prepare the training and testing data for the proposed 1D- CNN algorithm. The testing accuracy of the proposed algorithm is compared with other two conventional methods which are neural network and fuzzy neural network. The results of test explain that the new proposed detection system is efficient and fast for classifying and direction discrimination of fault in transmission line with high accuracy as compared with other conventional methods under various conditions of faults.
Among the most widespread renewable energy sources is solar energy; Solar panels offer a green, clean, and environmentally friendly source of energy. In the presence of several advantages of the use of photovoltaic systems, the random operation of the photovoltaic generator presents a great challenge, in the presence of a critical load. Among the most used solutions to overcome this problem is the combination of solar panels with generators or with the public grid or both. In this paper, an energy management strategy is proposed with a safety aspect by using artificial neural networks (ANNs), in order to ensure a continuous supply of electricity to consumers with a maximum solicitation of renewable energy.
In this paper, the artificial neural network (ANN) has been utilized for rotating machinery faults detection and classification. First, experiments were performed to measure the lateral vibration signals of laboratory test rigs for rotor-disk-blade when the blades are defective. A rotor-disk-blade system with 6 regular blades and 5 blades with various defects was constructed. Second, the ANN was applied to classify the different x- and y-axis lateral vibrations due to different blade faults. The results based on training and testing with different data samples of the fault types indicate that the ANN is robust and can effectively identify and distinguish different blade faults caused by lateral vibrations in a rotor. As compared to the literature, the present paper presents a novel work of identifying and classifying various rotating blade faults commonly encountered in rotating machines using ANN. Experimental data of lateral vibrations of the rotor-disk-blade system in both x- and y-directions are used for the training and testing of the network.
This paper focuses on the artificial bee colony (ABC) algorithm, which is a nonlinear optimization problem. is proposed to find the optimal power flow (OPF). To solve this problem, we will apply the ABC algorithm to a power system incorporating wind power. The proposed approach is applied on a standard IEEE-30 system with wind farms located on different buses and with different penetration levels to show the impact of wind farms on the system in order to obtain the optimal settings of control variables of the OPF problem. Based on technical results obtained, the ABC algorithm is shown to achieve a lower cost and losses than the other methods applied, while incorporating wind power into the system, high performance would be gained.
The significance of the solar energy is to intensify the effectiveness of the Solar Panel with the use of a primordial solar tracking system. Here we propounded a solar positioning system with the use of the global positioning system (GPS) , artificial neural network (ANN) and image processing (IP) . The azimuth angle of the sun is evaluated using GPS which provide latitude, date, longitude and time. The image processing used to find sun image through which centroid of sun is calculated and finally by comparing the centroid of sun with GPS quadrate to achieve optimum tracking point. Weather conditions and situation observed through AI decision making with the help of IP algorithms. The presented advance adaptation is analyzed and established via experimental effects which might be made available on the memory of the cloud carrier for systematization. The proposed system improve power gain by 59.21% and 10.32% compare to stable system (SS) and two-axis solar following system (TASF) respectively. The reduced tracking error of IoT based Two-axis solar following system (IoT-TASF) reduces their azimuth angle error by 0.20 degree.
Kosovo has limited renewable energy resources and its power generation sector is based on fossil fuels. Such a situation emphasizes the importance of active research and efficient use of renewable energy potential. According to the analysis of meteorological data for Kosovo, it can be concluded that among the most attractive potential wind power sites are the locations known as Kitka (42° 29' 41" N and 21° 36' 45" E) and Koznica (42° 39′ 32″ N, 21° 22′30″E). The two terrains in which the analysis was carried out are mountain areas, with altitudes of 1142 m (Kitka) and 1230 m (Koznica). the same measuring height, about 84 m above the ground, is obtained for these average wind speeds: Kitka 6,667 m/s and Koznica 6,16 m/s. Since the difference in wind speed is quite large versus a difference in altitude that is not being very large, analyses are made regarding the terrain characteristics including the terrain relief features. In this paper it will be studied how much the roughness of the terrain influences the output energy. Also, that the assumption to be taken the same as to how much they will affect the annual energy produced.
Large-scale grid-tied photovoltaic (PV) station are increasing rapidly. However, this large penetration of PV system creates frequency fluctuation in the grid due to the intermittency of solar irradiance. Therefore, in this paper, a robust droop control mechanism of the battery energy storage system (BESS) is developed in order to damp the frequency fluctuation of the multi-machine grid system due to variable active power injected from the PV panel. The proposed droop control strategy incorporates frequency error signal and dead-band for effective minimization of frequency fluctuation. The BESS system is used to consume/inject an effective amount of active power based upon the frequency oscillation of the grid system. The simulation analysis is carried out using PSCAD/EMTDC software to prove the effectiveness of the proposed droop control-based BESS system. The simulation result implies that the proposed scheme can efficiently curtail the frequency oscillation.
This study investigates experimentally the performance of two-dimensional solar tracking systems with reflector using commercial silicon based photovoltaic module, with open and closed loop control systems. Different reflector materials were also investigated. The experiments were performed at the Hashemite University campus in Zarqa at a latitude of 32⁰, in February and March. Photovoltaic output power and performance were analyzed. It was found that the modified photovoltaic module with mirror reflector generated the highest value of power, while the temperature reached a maximum value of 53 ̊ C. The modified module suggested in this study produced 5% more PV power than the two-dimensional solar tracking systems without reflector and produced 12.5% more PV power than the fixed PV module with 26⁰ tilt angle.
This paper focuses on the modeling and control of a wind energy conversion chain using a permanent magnet synchronous machine. This system behaves a turbine, a generator, DC/DC and DC/AC power converters. These are connected on both sides to the DC bus, where the inverter is followed by a filter which is connected to the grid. In this paper, we have been used two types of controllers. For the stator side converter, we consider the Takagi-Sugeno approach where the parameters of controller have been computed by the theory of linear matrix inequalities. The stability synthesis has been checked using the Lyapunov theory. According to the grid side converter, the proportional integral controller is exploited to keep a constant voltage on the DC bus and control both types of powers. The simulation results demonstrate the robustness of the approach used.
The development of modeling wind speed plays a very important in helping to obtain the actual wind speed data for the benefit of the power plant planning in the future. The wind speed in this paper is obtained from a PCE-FWS 20 type measuring instrument with a duration of 30 minutes which is accumulated into monthly data for one year (2019). Despite the many wind speed modeling that has been done by researchers. Modeling wind speeds proposed in this study were obtained from the modified Rayleigh distribution. In this study, the Rayleigh scale factor (Cr) and modified Rayleigh scale factor (Cm) were calculated. The observed wind speed is compared with the predicted wind characteristics. The data fit test used correlation coefficient (R2), root means square error (RMSE), and mean absolute percentage error (MAPE). The results of the proposed modified Rayleigh model provide very good results for users.
This paper deals with an advanced design for a pump powered by solar energyto supply agricultural lands with water and also the maximum power point is used to extract the maximum value of the energy available inside the solar panels and comparing between techniques MPPT such as Incremental conductance, perturb & observe, fractional short current circuit, and fractional open voltage circuit to find the best technique among these. The solar system is designed with main parts: photovoltaic (PV) panel, direct current/direct current (DC/DC) converter, inverter, filter, and in addition, the battery is used to save energy in the event that there is an increased demand for energy and not to provide solar radiation, as well as saving energy in the case of generation more than demand. This work was done using the matrix laboratory (MATLAB) simulink program.
The objective of this paper is to provide an overview of the current state of renewable energy resources in Bangladesh, as well as to examine various forms of renewable energies in order to gain a comprehensive understanding of how to address Bangladesh's power crisis issues in a sustainable manner. Electricity is currently the most useful kind of energy in Bangladesh. It has a substantial influence on a country's socioeconomic standing and living standards. Maintaining a stable source of energy at a cost that is affordable to everyone has been a constant battle for decades. Bangladesh is blessed with a wealth of natural resources. Bangladesh has a huge opportunity to accelerate its economic development while increasing energy access, livelihoods, and health for millions of people in a sustainable way due to the renewable energy system.
When the irradiance distribution over the photovoltaic panels is uniform, the pursuit of the maximum power point is not reached, which has allowed several researchers to use traditional MPPT techniques to solve this problem Among these techniques a PSO algorithm is used to have the maximum global power point (GMPPT) under partial shading. On the other hand, this one is not reliable vis-à-vis the pursuit of the MPPT. Therefore, in this paper we have treated another technique based on a new modified PSO algorithm so that the power can reach its maximum point. The PSO algorithm is based on the heuristic method which guarantees not only the obtaining of MPPT but also the simplicity of control and less expensive of the system. The results are obtained using MATLAB show that the proposed modified PSO algorithm performs better than conventional PSO and is robust to different partial shading models.
A stable operation of wind turbines connected to the grid is an essential requirement to ensure the reliability and stability of the power system. To achieve such operational objective, installing static synchronous compensator static synchronous compensator (STATCOM) as a main compensation device guarantees the voltage stability enhancement of the wind farm connected to distribution network at different operating scenarios. STATCOM either supplies or absorbs reactive power in order to ensure the voltage profile within the standard-margins and to avoid turbine tripping, accordingly. This paper present new study that investigates the most suitable-location to install STATCOM in a distribution system connected wind farm to maintain the voltage-levels within the stability margins. For a large-scale squirrel cage induction generator squirrel-cage induction generator (SCIG-based) wind turbine system, the impact of STATCOM installation was tested in different places and voltage-levels in the distribution system. The proposed method effectiveness in enhancing the voltage profile and balancing the reactive power is validated, the results were repeated for different scenarios of expected contingencies. The voltage profile, power flow, and reactive power balance of the distribution system are observed using MATLAB/Simulink software.
The electrical and environmental parameters of polymer solar cells (PSC) provide important information on their performance. In the present article we study the influence of temperature on the voltage-current (I-V) characteristic at different temperatures from 10 °C to 90 °C, and important parameters like bandgap energy Eg, and the energy conversion efficiency η. The one-diode electrical model, normally used for semiconductor cells, has been tested and validated for the polemeral junction. The PSC used in our study are formed by the poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61-butyric acid methyl ester (PCBM). Our technique is based on the combination of two steps; the first use the Least Mean Squares (LMS) method while the second use the Newton-Raphson algorithm. The found results are compared to other recently published works, they show that the developed approach is very accurate. This precision is proved by the minimal values of statistical errors (RMSE) and the good agreement between both the experimental data and the I-V simulated curves. The obtained results show a clear and a monotonic dependence of the cell efficiency on the studied parameters.
The inverter is the principal part of the photovoltaic (PV) systems that assures the direct current/alternating current (DC/AC) conversion (PV array is connected directly to an inverter that converts the DC energy produced by the PV array into AC energy that is directly connected to the electric utility). In this paper, we present a simple method for detecting faults that occurred during the operation of the inverter. These types of faults or faults affect the efficiency and cost-effectiveness of the photovoltaic system, especially the inverter, which is the main component responsible for the conversion. Hence, we have shown first the faults obtained in the case of the short circuit. Second, the open circuit failure is studied. The results demonstrate the efficacy of the proposed method. Good monitoring and detection of faults in the inverter can increase the system's reliability and decrease the undesirable faults that appeared in the PV system. The system behavior is tested under variable parameters and conditions using MATLAB/Simulink.
The electrical distribution network is undergoing tremendous modifications with the introduction of distributed generation technologies which have led to an increase in fault current levels in the distribution network. Fault current limiters have been developed as a promising technology to limit fault current levels in power systems. Though, quite a number of fault current limiters have been developed; the most common are the superconducting fault current limiters, solid-state fault current limiters, and saturated core fault current limiters. These fault current limiters present potential fault current limiting solutions in power systems. Nevertheless, they encounter various challenges hindering their deployment and commercialization. This research aimed at designing a bridge-type nonsuperconducting fault current limiter with a novel topology for distribution network applications. The proposed bridge-type nonsuperconducting fault current limiter was designed and simulated using PSCAD/EMTDC. Simulation results showed the effectiveness of the proposed design in fault current limiting, voltage sag compensation during fault conditions, and its ability not to affect the load voltage and current during normal conditions as well as in suppressing the source powers during fault conditions. Simulation results also showed very minimal power loss by the fault current limiter during normal conditions.
This paper provides a new approach to reducing high-order harmonics in 400 Hz inverter using a three-level neutral-point clamped (NPC) converter. A voltage control loop using the harmonic compensation combined with NPC clamping diode control technology. The capacitor voltage imbalance also causes harmonics in the output voltage. For 400 Hz inverter, maintain a balanced voltage between the two input (direct current) (DC) capacitors is difficult because the pulse width modulation (PWM) modulation frequency ratio is low compared to the frequency of the output voltage. A method of determining the current flowing into the capacitor to control the voltage on the two balanced capacitors to ensure fast response reversal is also given in this paper. The combination of a high-harmonic resonator controller and a neutral-point voltage controller working together on the 400 Hz NPC inverter structure is given in this paper.
Direct current (DC) electronic load is a useful equipment for testing the electrical system. It can emulate various load at a high rating. The electronic load requires a power converter to operate and a linear regulator is a common option. Nonetheless, it is hard to control due to the temperature variation. This paper proposed a DC electronic load using the boost converter. The proposed electronic load operates in the continuous current mode and control using the integral controller. The electronic load using the boost converter is compared with the electronic load using the linear regulator. The results show that the boost converter able to operate as an electronic load with an error lower than 0.5% and response time lower than 13 ms.
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The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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Design of fractional order controllers using constrained optimization and reference tracking method
1. International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 11, No. 1, March 2020, pp. 291∼301
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v11.i1.pp291-301 r 291
Design of fractional order controllers using constrained
optimization and reference tracking method
Manoj D. Patil1
, K. Vadirajacharya2
, Swapnil Khubalkar3
1
Department of Electrical Engineering, Annasaheb Dange College of Engineering and Technology, Ashta, India
2
Department of Electrical Engineering, Dr. Babasaheb Ambedkar Technological University, Lonere, Raigad, India
3
Department of Electrical Engineering, G. H. Raisoni College of Engineering, Nagpur, India
Article Info
Article history:
Received Jun 7, 2019
Revised Jul 8, 2019
Accepted Nov 12, 2019
Keywords:
Constrained optimization
Controller
Fractional order control
Tuning
ABSTRACT
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 different 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.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Manoj D. Patil,
Assistant Professor, ADCET, Ashta, Maharashtra,
Tel: +91 9763530440
Email: mdpatileps@gmail.com
1. INTRODUCTION
The proportional-integral-derivative (PID) controllers are broadly used in many industrial
applications [1]. The simplicity of structure and easily implementable tuning strategies are behind their
success. Many industrial systems can be presented by first order with dead time (FOWDT) models and design of
controllers for such systems is important [2]. Ziegler-Nichols tuning, some nature inspired optimization
technique like genetic algorithm, particle swarm optimization, ant colony algorithm have widely used
techniques for PID controllers [3, 4]. Now-a-days, generalized form of PID controller is getting very
popular which is known as fractional order PID (FO-PID) controller [6]. In these controller strategies,
integral and differentiators are of fractional order. To use the fractional order is a step closure to real life
because the natural processes are mostly fractional [7, 8]. However, the fractional nature may be very small.
Clearly, the use of integer order in place of fractional order will differ significantly to the actual situation.
However, the integer order models are welcomed due to the absence of solutions to the fractional models.
Recently, the fractional order models are analyzed and implemented successfully in [9, 10]. It is shown that the
performance of conventional PID controllers can be improved using the extra degree of freedom from the use
of fractional integrator and differentiator [12, 13]. Fractional order controllers are being increasingly used for
controlling FOWDT systems [14].
Unlike traditional PID controller, the order of integration and/or differentiation in fractional
controllers are real and unknown parameters to be tuned. This leads to solving nonlinear equations to
design fractional controller. There are different optimization methods are tried to find the parameters of these
Journal homepage: http://ijpeds.iaescore.com
2. 292 r ISSN: 2088-8694
controllers [15]. The conventional tuning rules are not applicable here. A genetic algorithm is proposed for
tuning in [16]. Particle swarm optimization is proposed in [17]. In [18], artificial bee colony algorithm is
proposed. Some other literature for tuning is reported in [19, 20]. Still, the area of tuning the fractional order
controllers is opened.
In [21], iterative feedback tuning algorithm is employed to tune a type of FO-PID controller.
The paper [22] deals with an optimal design of a new type variable coefficient FO-PID controller by using
heuristic optimization algorithms. Although many studies have tried to correct the performance of the system’s
transient and steady state responses. It is obvious that handling the step response and reference tracing together
will bring out a better control response. However, there are no studies using different controller parameters of
the system with uncertain plant structure. The major contribution of the paper is to fill this gap by presenting a
novel approach. In present paper, a reference tracking optimization method is proposed for tuning the fractional
controllers. Tuning of different fractional controllers is shown using this method. In the proposed method, even
though the controller has changed the optimization algorithm remains same. Only, the controller structure has
to be changed. If the plant gets changed, still the reference tracking optimization method works. Hence, the
proposed method can provide the solution for tuning of all other fractional controllers.
The organization of the paper is as: some preliminary information is given in Section II. Section III
introduces the different controller structures. In Section IV, the tuning methodology is proposed. In Section V,
simulation results are given. The paper has been concluded in Section VI.
2. PRELIMINARIES
Fractional calculus enables the use of real powers of the integration or differentiation operator.
The basics of fractional calculus are described in [23, 24]. Riemann-Liouville (RL) defined the fractional
operator as,
aDα
t f(t) =
1
Γ(m − α)
d
dt
!m Z t
a
f(τ)
(t − τ)α−m+1
dτ (1)
where, (m − 1) ≤ α < m, α is a real number, m is an integer, and Γ(.) is the Euler’s gamma function.
The Laplace transform of (2) gives,
L{aD±α
t f(t)} = s±α
F(s) (2)
s±α
has to be approximated in integer order for realization. There are several approximation techniques are
available [26].
2.1. Method of Approximation
Any transfer function can be approximated by interlacing real poles and zeros [27]. The integer order
approximation can be obtained within the desired band of frequency by using Oustaloup et al. method [24].
Here, poles and zeros are obtained as follows,
DN (s) =
ωu
ωh
α
ΠN
k=−N
1 + s/ω0
k
1 + s/ωk
(3)
where, ωk = ωb
ωh
ωb
(k+N+1/2+α/2)
(2N+1)
and ωk0 = ωb
ωh
ωb
k+N+1/2−α/2
(2N+1)
. The number of poles and zeros
are available as 2N+1, the approximation order is considered as N.
3. DESIGN OF FRACTIONAL ORDER CONTROLLERS
Various controller strategies, which are designed based on the fractional calculus, are discussed here.
3.1. Controller 1. T-PID
In [23], a different structure of fractional order controller is given, where the proportional term of
PID controller is changed with a tilted term with a transfer function s1/m
. The new transfer function of
T-PID controller closely approximate an optimal transfer function, hence provides improvement in controller.
The T-PID controller allows smaller effects of plant parameter variation and better disturbance rejection ratio
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3. Int J Pow Elec Dri Syst ISSN: 2088-8694 r 293
as compared to conventional PID controller. The T-PID controller is obtained as,
u(t) = KP D−α
e(t) + KI
Z
e(t) + KDDe(t) (4)
Applying Laplace transform,
u(s) = KP s−α
+ KI/s + KDs (5)
where, KP , KD, KI are proportional, derivative, and integral constant, u(s) is control signal, D is derivative
operator. The structure of T-PID controller is shown in Figure 1. It shows tilted component with proportional
component which is key factor in this controller structure.
Figure 1. Structure of T-PID controller
3.2. Controller 2. FO-PID
FO-PID controller used to minimize the error of the system. The error e(t) is scaled by gain KP in the
proportional control. The steady state error is minimized by integral control. The transients in the system are
taken care by derivative control. In FO-PID, in addition to KP , KD, and KI, two more parameters α - integrator
order, µ - order of differentiator are added to give more degree of freedom due to which improvement can be
seen in the controller’s performance. By adding up all these terms, FO-PID controller is achieved. The FO-PID
controller is given by,
u(t) = KP e(t) + KID−α
e(t) + KDDµ
e(t) (6)
Applying Laplace transform,
u(s) = KP + KIs−α
+ KDsµ
, (α, µ 0) (7)
When α = 1, µ = 1, PID controller is obtained. When α = 1, µ = 0, it becomes PI controller. At α = 0,
µ = 1, the PD controllers is obtained. The generalization of fractional controllers is shown in Figure 2. It shows
the different structures available in the PID domain. FO-PID can be anywhere in the plane. The structure of
FO-PID controller is depicted in Figure 3.
Figure 2. FO-PID generalization Figure 3. FO-PID controller
Design of fractional order controllers using... (Manoj D. Patil)
4. 294 r ISSN: 2088-8694
3.3. Controller 3. FO-PI
When the µ = 0 and 2 α 0, then the FO-PI controller is obtained as,
u(s) = KP + KIs−α
(8)
The FO-PI controller is depicted in Figure 4. The difference is that derivative part is not present, here. If steady
state is key issue the FO-PI controller is the best choice.
3.4. Controller 4. FO-PD
When the α = 0 and 2 µ 0, then the FO-PD controller is obtained as,
u(s) = KP + KDsµ
(9)
Here, integral part is not in the controller structure. If the plant is having transients then this controller is best
choice. The FO-PD controller is depicted in Figure 5.
Figure 4. FO-PI controller
Figure 5. FO-PD controller
4. PROPOSED TUNING OF THE CONTROLLERS
Several techniques are available for optimizing the parameters of controllers. Here, constrained
optimization method with reference tracking is proposed to optimize the controller parameters. Constrained
minimization is the problem of finding a feasible solution that is optimum to a problem subject to constraints.
The aim of constrained optimization is to convert the problem into an smaller subproblems which can then
be solved by iterative methods. The characteristic of these methods is to translate the constrained problem to
unconstrained problem by using an objective function for constraints. In such a way, the solution is found out
for constrained problem using a sequence of unconstrained optimizations. The strategy of the simulated model
is shown in Figure 6. The constraints are kept on the plant response, including maximum overshoot, settling
time, rise time as shown in Figure 7. Also, the reference tracking signal is provided as a goal to be achieved as
shown in Figure 8. The model is simulated and the response is checked with initial parameters. The simulation
produces an un-optimized step response and the initial data for tuning. The plots are updated so that the design
requirements can satisfied.
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Figure 6. Proposed scheme of optimization process of fractional controllers
Figure 7. Step response specifications Figure 8. Reference tracking specifications
The optimization algorithm are divided as large and medium scale. The large scale algorithm
requires linear algebra that does not store full matrices. This can be done by storing sparse matrices internally.
A large-scale algorithm can be used for a small problem. The medium-scale algorithm creates full matrices
internally and requires dense linear algebra. If a problem is significantly large, then full matrices require a large
amount of memory and a long time to execute. Whereas, a medium-scale algorithm provides extra functionality
such as additional constraint types which tends to provide better performance. The guidelines for constrained
optimization with reference tracking is as follows:
Step I: Start the process with the use of the ‘interior − point’ algorithm which is a large-scale
algorithm. ‘interior − point’ not only handles sparse large problems but also a small dense problems.
The algorithm satisfies constraints at all iterations, and can recover from ‘Inf/NaN’ results. After that go
for a different algorithms. The other algorithm may fail, as some algorithms may use more time and memory,
while some algorithms may not accept an initial point [28, 29]. If the problem did not solve then move towards
step II.
Step II: In this step, use sequential programming ‘sqp’ algorithm should be used. A ‘sqp’ algorithm
is one of the nonlinear programming methods. ‘sqp’ can satisfy bounds at all iterations. The algorithm can
recover easily from ‘Inf/NaN’. Here, a quadratic programming subproblem is solved at every major iteration.
This method allows constrained optimization [30]. An overview of ‘sqp’ is found in [31]. If the results are not
as per the requirement then go for Step III.
Step III: The ‘active − set’ algorithm can take large steps that gives speed to the algorithm.
The algorithm is effective for problems with nonsmooth constraints. In this method, active constraints are
included in canceling operation. These three steps will give the required results.
5. RESULTS AND DISCUSSION
Systems with first order plus dead time models have been classified in three categories based on
relative dead time δ which is function of time T and dead time τ as given below [32]:
1. Lag dominated systems - δ 0.1; where δ = τ
τ+T
2. Lag delay balanced systems - 0.1 δ 0.6
3. Delay dominated systems - δ 0.6
Here, the results are shown for lag dominated systems only. Whereas, the methodology is tested
against lag delay balanced and delay dominated system also.
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5.1. Case 1. with PID
The step response specification is shown in Figure 9 and the reference tracking specifications achieved
with PID controller is shown in Figure 10. Optimization progress with PID controller is shown in Table 1.
The obtained PID parameters are KP = 1.659, KI = 0.315, KD = 0.173.
Figure 9. Step response specifications with PID
controller
Time (seconds)
Amplitude
0 10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Figure 10. Reference tracking specifications
with PID controller
5.2. Case 2. with T-PID
Step response specification is shown in Figure 11 whereas reference tracking specifications achieved
with T-PID controller is depicted in Figure 16. Optimization progress with T-PID controller is shown in
Table 2. The obtained T-PID parameters are KP = 0.2, KI = 0.312, KD = 1.144, α = 0.8.
Table 1. Optimization Progress with PID Controller
Iteration
F-
count
Reference Tracking
Specifications
(minimum)
Step Response
Specification
(Upper) (=0)
Step Response
Specification
(Lower) (=0)
0 8 217.2816 -0.0396 -0.3833
1 32 51.6097 -0.0146 -0.4510
2 49 50.4433 -0.0142 -0.4093
3 57 14.5348 -0.0101 -0.2185
4 65 6.4976 -0.0093 0.0017
5 75 5.0369 -0.0089 0.0028
6 84 3.8441 -0.0090 0.0021
7 92 3.8441 -0.0090 0.0021
Figure 11. Step response specifications with T-PID
controller
Time (seconds)
Amplitude
0 10 20 30 40 50 60 70 80 90 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 12. Reference tracking specifications
with T-PID controller
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5.4. Case 4. with FO-PD
Step response specification is shown in Figure 15 whereas reference tracking specifications achieved
with FO-PD controller is shown in Figure 16. Optimization progress with FO-PD controller is shown in
Table 4. The obtained FO-PD parameters are KP = 107.8, KD = 1.968, µ = 0.63.
Figure 15. Step response specifications with FO-PD
controller
Time (seconds)
Amplitude
0 10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Figure 16. Reference tracking specifications
with FO-PD controller
Table 4. Optimization Progress with FO-PD Controller
Iteration
F-
count
Reference Tracking
Specifications
(minimum)
Step Response
Specification
(Upper) (=0)
Step Response
Specification
(Lower) (=0)
0 8 4.6123e+04 -0.5694 -0.6106
1 37 4.2841e+04 -0.5977 -0.5954
2 90 4.2834e+04 -0.5977 -0.5951
3 98 1.1651e+04 -0.1515 -0.2874
4 106 4.9829e+03 0.0738 -0.1398
5 114 2.3560e+03 0.0450 -0.0682
6 122 2.0831e+03 0.0241 -0.0318
7 130 2.1208e+03 0.0119 -0.0138
8 138 2.2145e+03 0.0049 -0.0051
9 146 2.3234e+03 0.0014 -0.0013
10 154 2.3443e+03 2.4580e-04 -1.3125e-04
11 162 2.3429e+03 2.4999e-05 -3.0894e-06
12 163 2.3429e+03 2.4999e-05 -3.0894e-06
5.5. Case 5. with FO-PID
Step response specification is shown in Figure 17 whereas reference tracking specifications achieved
with FO-PID controller is shown in Figure 18 . Optimization progress with FO-PID controller is shown in
Table 5. The obtained FO-PID parameters are KP = 107.8, KI = 0.05, KD = 73.9, α = 0.51, µ = 0.62.
Figure 17. Step response specifications with FO-PID
controller
Time (seconds)
Amplitude
0 10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Figure 18. Reference tracking specifications
with FO-PID controller
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9. Int J Pow Elec Dri Syst ISSN: 2088-8694 r 299
Table 5. Optimization Progress with FO-PID Controller
Iteration
F-
count
Reference Tracking
Specifications
(minimum)
Step Response
Specification
(Upper) (=0)
Step Response
Specification
(Lower) (=0)
0 8 3.3061e+04 -0.4414 -0.5273
1 16 8.4492e+03 -0.0965 -0.2408
2 24 3.6500e+03 0.0549 -0.1193
3 32 2.1838e+03 -0.0070 -0.0522
4 40 2.0712e+03 -0.0034 -0.0240
5 48 2.1917e+03 -0.0013 -0.0099
6 56 2.3034e+03 -6.4314e-04 -0.0033
7 64 2.3730e+03 -4.5363e-05 -6.6447e-04
8 72 2.3881e+03 1.2499e-06 -4.1323e-05
9 81 2.3873e+03 1.0911e-06 -1.2722e-05
10 90 2.3855e+03 1.2882e-06 -3.8773e-06
11 91 2.3855e+03 -3.8773e-06 1.2882e-06
Hence, all the available controllers can be tuned with the help of method discussed in this paper.
Only the controller structure need to be changed in the simulation and according to constrained and reference
tracking method every type of fractional order controller can be optimized. All the five controllers are compared
with each other and FO-PID controller is found to be superior in all the five cases. Since, the FO-PID controller
is the combination of fractional integrator and differentiator. Fractional differentiator takes care of transient
response while fractional integrator looks after the steady state response.
6. CONCLUSION
In this paper, different structures of FO-PID controllers are designed and applied to FOWDT process.
The tuning methods of fractional controllers involves complex equations. So, it is difficult to find a solution to
the problem. Because of that, the tuning method is simplified so that the controller can be tuned very easily and
effectively. So that, the constrained optimization algorithm with reference tracking specifications is found to
provide solution to tune these controller strategies. The proposed tuning algorithm can be applied to different
control strategies and different plant structures.
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BIOGRAPHIES OF AUTHORS
Mr. Manoj D. Patil was born in Sangli, Maharashtra, India, in 1987. He has received his B.E.
Degree in Electrical Engineering from Shivaji University Kolhapur, Maharashtra, India in 2009, and
the M.E. Degree in Electrical Power Systems from Government College of Engineering Aurangabad
(which is affiliated to Dr. Babasaheb Ambedkar Marathwada University Aurangabad), Maharashtra,
India in 2011. He is working as Assistant Professor at Annasaheb Dange College of Engineering
Technology, Ashta, Sangli, Maharashtra since July 2011. He is currently working toward the
Ph.D. degree with the Division of Electrical Engineering at Dr. Babasaheb Ambedkar Technological
University (BATU), Lonere, Raigad, Maharashtra, India.
Int J Pow Elec Dri Syst, Vol. 11, No. 1, March 2020 : 291 – 301
11. Int J Pow Elec Dri Syst ISSN: 2088-8694 r 301
Dr. K. Vadirajacharya received the B.E. degree in Electrical Engineering from PDA College of Engi-
neering, Gulbarga, India, in 1984, the M.E. degree in Power Electronics from GSITS Indore, India, in
1994, and the Ph.D. degree from the Indian Institute of Technology Roorkee, India, in 2009. He has
more than 25 publications in different national and international conferences and journals of repute.
Currently, he is an Associate Professor in the Department of Electrical Engineering, BATU, Lonere,
India. His areas of interest include power quality conditioning, flexible ac transmission device, energy
audit, and energy conservation.
Dr. Swapnil Khubalkar received the B.E. degree in Electronics Engineering in 2010, the M.Tech.
degree in Industrial Drives and Control in 2012 from Nagpur University. He received the Ph.D.
degree from the Visvesvaraya National Institute of Technology, Nagpur, India, in 2018. He has
more than 15 publications in different national and international conferences and journals of repute.
Currently, he is an Assistant Professor in the Department of Electrical Engineering, G.H. Raisoni
College of Engineering, Nagpur. His areas of interest include Power Electronics, Drives, Fractional
order control, etc.
Design of fractional order controllers using... (Manoj D. Patil)