Top PDF A Novel Fractional Order Fuzzy PID Controller and Its Optimal Time Domain Tuning Based on Integral Performance Indices

A Novel Fractional Order Fuzzy PID Controller and Its Optimal Time Domain Tuning Based on Integral Performance Indices

A Novel Fractional Order Fuzzy PID Controller and Its Optimal Time Domain Tuning Based on Integral Performance Indices

Genetic algorithm based optimal time domain tuning of a novel fractional order fuzzy PID controller is attempted in this paper while minimizing a weighted sum of various integral performance indices and the control signal. Small magnitude of control signal is a necessity in some typical safety critical process control applications like [49] where the chance of actuator saturation and its undesirable results like integral wind-up is highly detrimental and also increases the cost involved for large actuator size as a preventive measure. In the present study four different integral performance indices [43], [47] have been studied while designing the proposed fuzzy FOPID along with its simpler versions like fuzzy PID, PI D λ μ , fuzzy PID and PID satisfying the same set of optimality criteria. It is observed that the controller performance depends on the type of process to be controlled and also on the choice of integral performance indices. More degrees of freedom in the controller parameters do not necessarily imply better performance in all cases if the performance index is not chosen judiciously. Also for fuzzy enhanced PID controllers it is well known [4] that change in output scaling factor for example has more effect on the controller performance than changes in the membership functions or fuzzification-inferencing-defuzzification mechanism. Thus all the tuning parameters of fuzzy PID controller are not equally potent in affecting the overall performance of the control loop. Our present approach gives additional design parameters viz. the differ- integral orders of a nominal FLC-PID to the designer which can have significant effect on the performance and hence make the applicability of these types of controllers to meet various control objectives.
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Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time

Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time

error signal does not resemble the integer order calculus or conventional differentiation and integration in a pure mathematical sense. Rather it reflects an operator’s experience which gives extra freedom for tuning of control loops. Thus, the control signal generated as a result of his actions may be approximated by appropriate mathematical operations which have the required compensation characteristics. The rationale behind incorporating fractional order operators in the conventional hybrid fuzzy PID input and output can be visualized like a heuristic reasoning for an observation of a particular rate of change in error (not in mathematical sense) by a human operator and the corresponding actions he takes over time which is not static in nature since the fractional differ-integration involves the past history of the integrand and as if the integrand is continuously changing over time [2]. Since, human brain does not observe the rate of change of a variable and its time evolution as classical integer order numerical differentiation and integration, the fractional order of differ-integration perhaps puts some extra flexibility to map information in a more easily decipherable form. Considering these flexibilities incorporated in the fuzzy inference input and output, the present study extends the idea with different hybrid structures of the FLC based FOPID controller and their comparative merits in closed loop control with fixed MF type and rule base and fuzzy inferencing.
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Optimal design and tuning of novel fractional order PID power system stabilizer using a new metaheuristic Bat algorithm

Optimal design and tuning of novel fractional order PID power system stabilizer using a new metaheuristic Bat algorithm

the first time, using a new metaheuristic optimization Bat algorithm (BA) inspired by the echoloca- tion behavior to improve power system stability. The problem of FOPID-PSS design is transformed as an optimization problem based on performance indices (PI), including Integral Absolute Error (IAE), Integral Squared Error (ISE), Integral of the Time-Weighted Absolute Error (ITAE) and Integral of Time multiplied by the Squared Error (ITSE), where, BA is employed to obtain the opti- mal stabilizer parameters. In order to examine the robustness of FOPID-PSS, it has been tested on a Single Machine Infinite Bus (SMIB) power system under different disturbances and operating con- ditions. The performance of the system with FOPID-PSS controller is compared with a PID-PSS and PSS. Further, the simulation results obtained with the proposed BA based FOPID-PSS are compared with those obtained with FireFly algorithm (FFA) based FOPID-PSS. Simulation results show the effectiveness of BA for FOPID-PSS design, and superior robust performance for enhance- ment power system stability compared to other with different cases.
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LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.
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Evolutionary algorithms based tuning of PID controller  for an AVR system

Evolutionary algorithms based tuning of PID controller for an AVR system

In recent literature many evolutionary optimization algorithms are proposed for tuning PID controller in the AVR system such as Anarchic Society Optimization [16], reinforcement learning automata optimization approach [17], real coded GA with fuzzy logic technique [18], Choatic ant swarm algorithm [19], Artificial Bee Colony algorithm [20], Hybrid GA-Bacterial Foraging (BF) algorithm [21] and local unimodal sampling algorithm [22]. GA and Ant Colony Optimization techniques are proposed to tune the parameters of FOPID controller in controlling of AVR system. In some of the research papers novel performance criteria has been proposed for optimal tuning of PID and FOPID controller in AVR control system. A novel performance criterion comprises of overshoot, settling time, steady state error and mean of time weighted integral absolute error has been proposed for optimal tuning of PID controller in AVR system using cuckoo search algorithm [23]. A. Sikander et. al, 2018 has proposed a cuckoo search algorithm based fractional order PID controller for AVR system with performance criterion which was proposed by Gaing et. al in 2004 [24]. In this research work, Cuckoo search (CS) and particle swarm optimization (PSO) algorithms are proposed to find the optimal parameters of PID controller in the control of automatic voltage regulator (AVR) system with new performance criterion comprises of Integral absolute error, rise time, settling time and peak overshoot. The performance of this new proposed performance criterion is compared with performance of other performance criterion such as ITAE, ITSE, ISE, MSE and IAE. The paper is mainly organized such that section two describes about the Automatic Voltage Regulator (AVR) system; section three examines the Cuckoo search (CS) algorithm and particle swarm optimization (PSO) algorithms; section four and five concentrate on the application of CS-PID, PSO-PID and conventional tuning method (Ziegler-Nichols) in optimal tuning PID controller for both servo and regulatory control of AVR system. Additionally, section six describes conclusions of the study.
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Regression model for tuning the PID controller with fractional order time delay system

Regression model for tuning the PID controller with fractional order time delay system

A particle swarm optimized I-PD controller of Second Order Time Delayed System has been suggested by Suji Prasad et al. [24] . Optimization was based on the presentation indices like settling time, rise time, peak overshoot, ISE (integral square error) and IAE (integral absolute error). PID control- lers and its alternatives are most commonly used, although there are important improvements in the control systems in industrial processes. If the parameter of controller was not appropriately planned, next needed control output may not succeed. Compared with Ziegler Nichols and Arvanitis tuning, they have confirmed that their simulation results with opti- mized I-PD controller to be specified enhanced presentations. A PID controller for time delay systems has been explained by Rama Reddy et al. [25] . Their suggested technique pre´cised the stable areas of PID and a novel PID with cycle leading cor- rection (SLC) for network control systems with time delay. The latest PID controller has a modification parameter ‘b’. They have obtained that relation of the parameters of the sys- tem. The outcome of plant parameters on constancy areas of PID controllers and SLC-PID controllers in first-order and second-order systems with time delay is moreover pre´cised. Finally, an open-loop zero was introduced into the plant- unstable second order system with time delay so that the con- stancy areas of PID and SLC-PID controllers get competently made bigger.
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Performance Analysis of Fuzzy PID Controller Response

Performance Analysis of Fuzzy PID Controller Response

As discussed previously, the most common shapes of membership functions used are triangular, trapezoidal, Gaussian and bell curves, but the shape is generally less important than the number of curves and their placement. The major components to strategy the fuzzy logic control are Fuzzification, knowledge base, decision making logic and Defuzzification

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Continuous firefly algorithm for optimal tuning of PID controller in AVR system

Continuous firefly algorithm for optimal tuning of PID controller in AVR system

This paper presents a tuning approach based on Continuous firefly algorithm (CFA) to obtain the proportional-integral- derivative (PID) controller parameters in Automatic Voltage Regulator system (AVR). In the tuning processes the CFA is iterated to reach the optimal or the near optimal of PID controller parameters when the main goal is to improve the AVR step response characteristics. Conducted simulations show the effectiveness and the efficiency of the proposed approach. Furthermore the proposed approach can improve the dynamic of the AVR system. Compared with particle swarm optimization (PSO), the new CFA tuning method has better control system performance in terms of time domain specifications and set-point tracking.
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Design of PID, Fuzzy PD/PID and Single Input Fuzzy Logic Controller for Higher Order System

Design of PID, Fuzzy PD/PID and Single Input Fuzzy Logic Controller for Higher Order System

Conventional PID controllers have been a wide range of use in industry because of its simple structure and acceptable performance. This controller deals with both time response and frequency response improvements if they are properly tuned. But as the demands increases to control the different systems in industries, performance of conventional controllers are tend to degrade. Now systems are getting complicated day by day introducing higher order plants. There is drastic change in the performance of controllers with the introduction of Fuzzy systems and so the Fuzzy controllers (PD and PID) has been designed and tuned for third order system which is difficult to control by the use of conventional controllers. FLC has been widely used for nonlinear, high order & high dead time plants. This paper has three main considerations. Firstly, a PID controller has been designed for nonlinear unstable third order plant using Zeigler Nichols tuning method I & its performance is analyzed. Secondly, for the same system a FLC has been proposed with simple approach and smaller number of rules(four rules) as it gives the same performance by the larger set rule II . Even though modern control methods are very promising for non-linear control applications, they require substantial computational power because of complex decision making processes. For example FLC has to deal with fuzzification, rule base storage, inference mechanism and defuzzification operations. Larger set of rules yields more accurate control at the expense of longer computational time. Therefore it may not be practical because there are many implementation aspects that must be addressed, namely real-time response, communication bandwidth, computational capacity and onboard battery. The use of NN is also thought to be impractical due to its unpredictability, particularly when real time self-tuning is considered. Despite these issues, it is known that FLC requires simpler mathematics and offers higher degree of freedom in tuning its control parameters compared to other nonlinear controllers. In this paper, the Single Input Fuzzy Controller
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Bounded solutions for fuzzy integral equations of fractional order

Bounded solutions for fuzzy integral equations of fractional order

The concept of fuzzy derivative was first introduced by Chang and Zadeh [1]. Kaleva [2], Puri and Ralescu [3] introduced the notion of fuzzy derivative as an extension of the Hukuhara derivative and the fuzzy integral, which was the same as that proposed by Dubois and Prade [4]. There has been a significant development in the study of fuzzy dif- ferential and integral equations (see, for example, [5–8], and the references therein). Under suitable conditions, it was proved in [9] that the boundedness of solutions of the following fuzzy integral equation:
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Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization

Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization

Traditionally the PID controller has been used in the AVR loop due to its simplicity and ease of implementation [5]. However, recently the fractional order PID (FOPID) controller have been used in the design of AVR systems and have been shown to outperform the PID in many cases [6], [7]. In Zamani et al. [8], the FOPID has been tuned for an AVR system using the Particle Swarm Optimisation (PSO) algorithm employing time domain criterion like the Integral of Absolute Error (IAE), percentage overshoot, rise time, settling time, steady state error, controller effort etc. In Tang et al. [6], the optimal parameters of the FOPID controller for the AVR system, has been found using a chaotic ant swarm algorithm. In [6] a customised objective function has been designed using the peak overshoot, steady state error, rise time and the settling time. The above mentioned literatures perform optimisation considering only a single objective. But in a practical control system design multiple objectives need to be addressed. In the study by Pan and Das [9], the AVR design problem has been cast as a multi- objective problem and the efficacy of the PID and the FOPID controllers are compared with respect to different contradictory objective functions like the Integral of Time Multiplied Squared Error (ITSE) and the controller effort etc. However, the optimisation is done in the time domain and the obtained controller values are checked for robustness against gain variation by varying different parameters of the control loop. All these above mentioned literatures which employ time domain optimisation techniques cannot guarantee a certain degree of gain or phase margins which are important for the plant operator. These margins are useful from a control practitioner’s view point as they can give an estimate of how much uncertainty the system can tolerate before
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Introduction of fractional elements for improvising the performance of PID controller for heating furnace using AMIGO tuning technique

Introduction of fractional elements for improvising the performance of PID controller for heating furnace using AMIGO tuning technique

Summary The paper demonstrates about melioration of integer order and fractional order model of heating furnace. Both models are being placed in closed loop along with the propor- tional integral derivative (PID) controller and fractional order proportional integral derivative (FOPID) controller so that the various time domain performance characteristics of the heating furnace can be meliorated. The tuning parameters (K p , Ki and Kd ) of the controllers has been found using the Astrom-Hagglund tuning technique and the differ-integrals ( and ) are found using the Nelder-Mead optimisation technique.
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Analysis of Fractional order PID controller for Ceramic Infrared Heater

Analysis of Fractional order PID controller for Ceramic Infrared Heater

By using Equation (20, 21, 22, 25, 28) five unknown parameter K K K p , i , d ,  and  can be solved by using FMINCON optimization toolbox of Mat Lab. Equation (21) is considered as a main equation and other equations are taken as non-linear constraints for optimization. Value of the all five unknown parameters are calculated to obtain the PI D   controller to control the ceramic IR heater as Kp=0.6073 , Ki=6.1194,Kd=0.2045,  =0.7815,  =0.4454 and transfer function of fractional order PID controller given as
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Speed Control of Brushless DC Motor based on Fractional Order PID Controller

Speed Control of Brushless DC Motor based on Fractional Order PID Controller

The BLDC motor has been widely used in many applications such as, industrial automation, medical, electric traction, consumer, aerospace, road vehicles, aircraft, military equipment, hard disk, etc. It has the advantages of high reliability, good efficiency, high power density, lower weight, low maintenance requirements, and wide speed range. On the other hand, the developments in power semiconductor technology, power electronic technology and microprocessors/logic ICs make the BLDC motor gaining popularity[1,2]. BLDC motors do not have brushes for commutation, Instead they are electronically commutated using three phase bridge inverter with feedback rotor position. The rotor position feedback is necessary for starting and providing proper commutation to turn on the inverter. The BLDC motor consists of permanent magnet rotor and distributed stator winding which are wound such that the back emf's is trapezoidal. The phase current, typically quisi - squar shape, is synchronized with the back emf to produce constant torque at constant speed. The BLDC motor is operated when two phases are ON at any time while the third phase is floating.
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A Robust Fractional Order PID Controller for Liquid Level system

A Robust Fractional Order PID Controller for Liquid Level system

ABSTRACT: Many controllers have been implemented in a Liquid Level System by control engineers such as conventional PID controller, fussy logic. But with development of Fractional calculus the control technique are also being improved. The thesis work deals with design of Fractional Order PID [FOPID] and a Robust Fractional order PID controller for the Liquid Level System.

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Self-balancing Robot Control Using Fractional-Order PID Controller

Self-balancing Robot Control Using Fractional-Order PID Controller

literature reviews [4-8] In section II, we will discuss theories related to this paper include of fractional calculus, fractional order PI λ D µ controller, digital IIR filter, and Kalman filter that necessary to eliminate the measurement error from the tilt sensor. Section III discusses in mechanical structure, mathematical model, and state - space of the robot. Section IV demonstrates PID and FOPID controller design and their simulation results. Section V demonstrates to realization implemented both controllers on the real system and result of PID controller on the real system.
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Tuning of a 2DOF PI-PID Controller for use with Second-order-like Processes

Tuning of a 2DOF PI-PID Controller for use with Second-order-like Processes

Abdelaty, Ahmed and Ouda (2018) studied the analysis and design of a set point weighting 2DOF PID controller. They used a 2/2 sub-controller receiving the reference input signal with set point weight on the proportional and derivative terms and a PID sub-controller in the forward path receiving the error signal of the control system with filter on its derivative part [8]. Hassaan (2018) studied the tuning process of a 2DOF PID controller for use with second-order-like processes. He used a 2DOF controller consisting of PD sub-controller receiving a reference input signal and set in a feedforward loop and a PID sub-controller set in the forward path of the control system receiving the error signal of the system. He tuned the controller for use with second order-like processes of damping ratio from 0.05 to 2 and a natural frequency up to 10 rad/s [9].
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Tuning Of Conventional Pid And Fuzzy Logic Controller Using Different Defuzzification Techniques

Tuning Of Conventional Pid And Fuzzy Logic Controller Using Different Defuzzification Techniques

Abstract:- This paper presents a method for tuning of conventional PID controller. Simplicity, robustness, wide range of applicability and near-optimal performance are some of the reasons that have made PID control so popular in the academic and industry sectors. Recently, it has been noticed that PID controllers are often poorly tuned and some efforts have been made to systematically resolve this matter. Thus Fuzzy logi c can be used in context to vary the parameters values during the transient response, in order to improve the step response performances. Simulation analysis has been carried out for the different processes by conventional and different defuzzification techniques and the results indicate that the values of percentage overshoot are reduced by using fuzzy logic mechanism.
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Design of Model Based PID Controller Tuning for Pressure Process

Design of Model Based PID Controller Tuning for Pressure Process

ABSTRACT: Measurement of Pressure is one of the very essential parameter in a process station which needs to be controlled. This paper deals with obtaining the real time response of a pressure process from which the system transfer function is identified using two point method. The identified model is in the form of first order plus dead time (FOPTD). PID controllers are effectively used in controlling liner feedback systems with the suitable tuning methods. Predominantly available tuning methods like Ziegler Nicholas method (Z-N), and Internal Model Control (IMC), are used here to compare the responses using software LabVIEW to get the optimum controller for the pressure process.
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On fractional-order PID controllers

On fractional-order PID controllers

Multivariable system control is known to be more challenging to design when compared to scalar processes. This is primarily due to the presence of interactions and directionality in such systems. This limits the scope of application of most parametric model-based design algorithms to Single Input Single Output (SISO) applications (Huang, et al., 2003). Over the past decades, several methods of solving multivariable control issues have been proposed for conventional PID controllers (Loh, et al., 1993; Luyben, 1986). Niederlinski modified Ziegler-Nichol’s tuning rule for MIMO processes by introducing a detuning factor to meet the stability and performance of the multi-loop control system. Luyben introduced the Biggest Log-modulus Tuning (BLT) method which is a frequency domain PID controller design method. It uses a detuning factor (F) iteratively to decouple an interactive MIMO system (Luyben, 1986). A detailed review of some multivariable PID design methods was published by Shiu and Hwang (Shiu & Hwang, 1998). One common limitation of these design methods is that all the algorithms are limited to conventional PID controllers and do not address fractional- order controllers.
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