Fractional Order Fuzzy PID Controller Research Articles

A Novel Augmented Fractional-Order Fuzzy Controller for Enhanced Robustness in Nonlinear and Uncertain Systems with Optimal Actuator Exertion

An appropriate balance between the controller’s performance and its robustness is a complex design challenge. In order to enhance the control system performance, vigorous and rapid variations in controller output are often employed; however, this poses a critical challenge for practical implementations of the control schemes, as it may affect the actuator badly and may reduce its lifetime. To handle this issue, the current work presents an innovative control structure that aims to strike an apt balance between the control output variability while maintaining the desired control performance. The proposed control scheme exploits the abilities of fuzzy logic to cope with uncertainties in the system and along with the use of fractional calculus to enhance the control performance. Further, to evaluate the performance of the proposed improved fractional-order fuzzy controller (IFOFC), extensive simulation studies have been carried out on a multi-input–multi-output nonlinear system for a wide variety of test scenarios. An exhaustive comparative study with an inline state-of-art controller, i.e., fractional-order fuzzy PID (FOFPID) controller has also been carried out on two interesting performance measures. These performance measures include integral of time-weighted absolute error (ITAE) and another measure which corresponds to undesirable variations in the controller output, i.e., integral of the absolute change of torque (IACT). Based on the detailed simulation studies, it was found that the proposed control structure provides a fair balance between controller output aggression and control performance and also completely outperformed the FOFPID controller, even under large parametric variations.

Activity-Based Tracking and Stabilization of Human Heart Rate Using Fuzzy FO-PID Controller

In this article, the unwanted fluctuations ofhuman heart rate are mitigated while regulating it based on the sensed activity. A control system is designed and analyzed for controlling the heart rate of a patient in real time. The fuzzy fractional order-proportional-integral-derivative (fuzzy FO-PID) controller generates electric pulses to maintain the desired heart rate during a particular activity while minimizing unprecedented fluctuations of beats. A comparison of the proposed control model is carried out with the pacemakers using fractional order-PID (FO-PID), fuzzy-PID (F-PID), and PID controllers. The experimental results show the superiority of the fuzzy FO-PID controller over the state-of-the-art controllers in terms of overshoot and transient mitigation.

Tuning of Novel Fractional Order Fuzzy PID Controller for Automatic Voltage Regulator using Grasshopper Optimization Algorithm

One of the most important equipment in the power system is the Automatic Voltage Regulator (AVR) or synchronous generator excitation. The goal of the system is to maintain the terminal voltage of the synchronous generator in the desired level. AVR is inherently uncertain. Hence, the proposed controller should be able to handle the problem. In this paper, Fractional Order Fuzzy PID (FOFPID) controller has been employed to control the system. In order to enhance the performance of the controller, Grasshopper Optimization Algorithm (GOA) is used to tune the parameters of the controller. Unlike other methods, the gains of FOFPID controller are not constant and alter in different operating conditions. The robustness of the controller has been investigated and the comparative results show that the proposed controller has a better performance against other methods.Automatic Voltage Regulator (AVR), Synchronous generator excitation, Fractional-order fuzzy PID (FOFPID) controller, Grasshopper Optimization Algorithm (GOA), Uncertainty

Fractional Order Fuzzy PID Controller for Automatic Generation Control of Power Systems

In this study, a Hybrid Adaptive Differential Evolution and Pattern Search (hADE-PS) tuned Fractional Order Fuzzy PID (FOFPID) structure is suggested for AGC of power systems. At first, a non-reheat type two-area thermal system is considered and the improvement of the proposed approach over Bacteria Foraging Optimization Algorithm (BFOA), Teaching Learning Based Optimization (TLBO), Jaya Algorithm (JA), Genetic Algorithm (GA) and Hybrid BFOA and Particle Swarm Optimization Algorithm (hBFOA-PSO) for the identical test systems has been demonstrated. The analysis was then extended to interconnected thermal power system of reheat type and two-area six-unit system. The results are compared with Firefly Algorithm (FA), Symbiotic Organism Search Algorithm (SOSA) and Artificial Bee colony (ABC) for second test system and TLBO, Hybrid Stochastic Fractal Search and Local Unimodal Sampling (hSFS-LUS), ADE and hADE-PS tuned PID for third test system. Finally, robustness of the suggested controller is examined under varied conditions.

Adaptive differential evolution and pattern search tuned fractional order fuzzy PID for frequency control of power systems

ABSTRACT In the fast-growing dimension and difficulty of the electricity network, frequency regulation (FR) is considered to be the major significant choice for presenting superior quality electric power supply to the customers. Load-frequency control (LFC) scheme involves greatly vital, capable and intelligent control method to carry a strong power under the erratic nature of consumers’ demand. Thus, in this study proposes a hybrid Adaptive Differential Evolution and Pattern Search (hADE-PS) tuned Fractional Order Fuzzy PID (FOFPID) structure for FR of power systems (PSs). Firstly, a three unequal area system is taken and results of hADE-PS tuned FOFPID is compared with Teaching Learning-Based Optimization (TLBO) and Firefly Algorithm (FA) based controllers for the identical test systems. Then, the robustness of FOFPID is examined under varied conditions. In the next step, a power system with thermal and solar power is considered. The results of hADE-PS tuned FOFPID are evaluated with Genetic Algorithm (GA), FA, Whale Optimization Algorithm (WOA) and modified WOA for the same test system. It is demonstrated that hADE-PS-based FOFPID controller is more effective compared to some lately proposed methods. To substantiate the practicability of the projected method, experimental justification utilizing OPAL-RT-based real-time simulation has been carried out.

Electronically Tunable ACO Based Fuzzy FOPID Controller for Effective Speed Control of Electric Vehicle

The phenomenal growth of the Electric Vehicle (EV) technology demands efficient and intelligent control strategies for the propulsion system. In this work, a novel fuzzy fractional order PID (FOPID) controller using Ant Colony Optimization (ACO) algorithm has been proposed to control EV speed effectively. The controller parameters and the fuzzy logic controller's membership functions are tuned and updated in real-time using the multi-objective ACO technique. The proposed controller's speed tracking performance is verified using the new European driving cycle (NEDC) test in the MATLAB-Simulink platform. The proposed controller outperforms the ACO-based fuzzy integer-order PID (IOPID), FOPID, and traditional IOPID controllers. The sensitivity analysis confirms the robustness of the proposed controller for varying parameters of the EV model. The stabilization of EV speed in the presence of external disturbance is also confirmed. In the proposed work, an attempt is made to analyze the system's stability using Matignon's theorem, considering the linearized EV model. The proposed controller gives optimum speed tracking performance compared to the Genetic Algorithm (GA) and the Particle Swarm Optimization (PSO) based fuzzy FOPID controllers. Additionally, the optimized fuzzy FOPID controller is realized using a second-generation current conveyor with extra inputs (EX-CCII) and fractional-order capacitors with electronic tunability. The controller circuit's performance evaluation is carried out in the Cadence Analog Design Environment using GPDK 180 nm CMOS process.

Chaotic Harris Hawks Optimization based type-2 Fractional Order Fuzzy PID controller for frequency regulation of power systems

ABSTRACT For the dependable, safe, and stable operation of electric systems, frequency should be regulated continuously employing appropriate intelligent controllers. Hence, this paper proposes a Chaotic Harris Hawks Optimization-based type-2 Fuzzy Fractional Order (FO) PID structure for frequency regulation of Power Systems (PSs). The objective of this paper is to examine the efficacy of the proposed approach in standard PSs and equate its characteristic with some approaches available in the literature. Firstly, a non-reheat type two-area PS is taken and the improvement of the suggested methodology over BFOA, TLBO, JA, GA and hybrid BFOA and PSO for the identical test systems has been demonstrated. The analysis was then extended to reheat type and two-area six-unit system. The outcomes are equated with FA, SOSA and ABC for the second test system and TLBO, hybrid SFS-LUS, Adaptive DE and hybrid ADE and PS tuned PID for the third test system.

Research on Fuzzy Fractional Order PID Control of Liquid Temperature in Displacement Digester

Research on Fuzzy Fractional Order PID Control of Liquid Temperature in Displacement Digester

Intelligent frequency control in microgrid: Fractional order fuzzy PID controller

Intelligent frequency control in microgrid: Fractional order fuzzy PID controller

MVO optimized hybrid FOFPID-LQG controller for load frequency control of an AC micro-grid system

Purpose This paper aims to implement a maiden methodology for load frequency control of an AC multi micro-grid (MG) by using hybrid fractional order fuzzy PID (FOFPID) controller and linear quadratic Gaussian (LQG). Design/methodology/approach The multi MG system considered is consisting of photovoltaic, wind turbine and a synchronous generator. Different energy storage devices i.e. battery energy storage system and flywheel energy storage system are also integrated to the system. The renewable energy sources suffer from uncertainty and fluctuation from their nominal values, which results in fluctuation of system frequency. Inspired by this difficulty in MG control, this research paper proposes a hybridized FOFPID and LQG controller under random and stochastic environments. Again to confer viability of proposed controller its performances are compared with PID, fuzzy PID and fuzzy PID-LQG controllers. A comparative study among all implemented techniques i.e. proposed multi-verse optimization (MVO) algorithm, particle swarm optimization and genetic algorithm has been done to justify the supremacy of MVO algorithm. To check the robustness of the controller sensitivity analysis is done. Findings The merged concept of fractional calculus and state feedback theory is found to be efficient. The designed controller is found to be capable of rejecting the effect of disturbances present in the system. Originality/value From the study, the authors observed that the proposed hybrid FOPID and LQG controller is robust hence, there is no need to reset the controller parameters with a large change in network parameters.

Tracking Control for an Electro-Hydraulic Rotary Actuator Using Fractional Order Fuzzy PID Controller

This paper presents a strategy for a fractional order fuzzy proportional integral derivative controller (FOFPID) controller for trajectory-tracking control of an electro-hydraulic rotary actuator (EHRA) under variant working requirements. The proposed controller is based on a combination of a fractional order PID (FOPID) controller and a fuzzy logic system. In detail, the FOPID with extension from the integer order to non-integer order of integral and derivative functions helps to improve tracking, robustness and stability of the control system. A fuzzy logic control system is designed to adjust the FOPID parameters according to time-variant working conditions. To evaluate the proposed controller, co-simulations (using AMESim and MATLAB) and real-time experiments have been conducted. The results show the effectiveness of the proposed approach compared to other typical controllers.

Hybrid fractional fuzzy PID design for MPPT-pitch control of wind turbine-based bat algorithm

The power quality and protection enhancement of wind turbine becomes an important paramount. This requires a competitive controller with high performances. For this purpose, the paper presents a novel hybrid controller named fractional fuzzy PID (FFPID) strategy tunning with an efficient metaheuristic optimization bat algorithm (BA) for controlling the wind turbine equipped with permanent magnet synchronous generator (WT-PMSG). The main control objectives are to drive WT-PMSG for extracting the maximum power point (MPPT) in the low range of weather conditions and further to protect the wind turbine in high-wind region using pitch angle control. The performance of proposed strategy is analysed for all regions low–high wind speed disturbances. The obtained results are obviously proved that the optimal hybrid fractional-order fuzzy PID controller is highly better than the optimal classical PID, fuzzy PID (FPID) and fractional-order PID (FOPID) controllers in terms of response, overshoot and indices performances. Further, the WT-PMSG is effectively controlled at different conditions of wind velocities by the proposed scheme.

Balance Adjustment of Power-Line Inspection Robot Using General Type-2 Fractional Order Fuzzy PID Controller

In this study, a general type-2 fractional order fuzzy PID (GT2FO-FPID) controller is proposed to fulfil the balance adjustment of the Power-line Inspection (PLI) robot system. It is a combination of Mamdani general type-2 fuzzy logic controller (GT2-FLC) and fractional PID controller. Since the PLI robot system is an under-actuated system, it’s necessary to get complete information of the system. However, when all state variables are treated as input to the controller, there is a problem with the rule explosion. Because of this, the information fusion method is adopt to solve the problem and simplify the controller design. At the same time, fractional-order integral-differential operators and input-output scaling factors, which are taken as design variables and optimized by genetic algorithm (GA). To assess the performance of proposed controller based on symmetry criterion, we compared it against existing controllers, i.e., interval type-2 fractional order fuzzy PID (IT2FO-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), and conventional fractional order (FOPID) controllers. Furthermore, to show the anti-inference ability of the proposed controller, three common perturbed process are tested. Finally, simulation results show that the GT2FO-FPID controller outperforms other controllers in the presence of external perturbations on the PLI robot system.

Fractional-order modeling and control of pneumatic-hydraulic upper limb rehabilitation training system1

In this paper, by replacing the integral mass flow equation to fractional-order mass flow equation, the fractional-order mathematical model of 2DOF pneumatic-hydraulic upper limb rehabilitation training system is established. A new 2DOF fractional-order fuzzy PID (FOFPID) controller is designed, to provides a new reference for improving the control accuracy of the pneumatic system. In the design of the controller, the weight parameters of the input terms are transformed into the weight parameters of the error, and the input, which are analyzed to improve the accuracy of the controller design. The parameters of the control system are determined by multi-objective particle swarm optimization. To prove the effectiveness of the proposed control method, the experimental research was carried out by building the experimental platform of pneumatic-hydraulic upper limb rehabilitation training system. The results show that the 2DOF FOFPID controller has better performance than other designed controllers under different working conditions.

Optimal design of fractional order fuzzy PID controller using an intelligent hybrid algorithm for nonlinear power system

Optimal design of fractional order fuzzy PID controller using an intelligent hybrid algorithm for nonlinear power system

Novel fuzzy fractional order PID controller for non linear interacting coupled spherical tank system for level process

In this paper, a novel Fuzzy Fractional Order Proportional Integral Derivative (FFOPID) controller is proposed to control the liquid level of Two Tank Spherical Interacting System (TTSIS). Spherical tanks are widely used in process industries due to its high storage capacity. These are non-linear due to its varying surface area with respect to its height and hence the level control of a spherical tank system is a challenging task. Fractional Order Proportional Integral Derivative (FOPID) controller is designed for a liquid level control of a spherical tank which is modelled as a fractional Order System. The performance indices such as rise time, settling time, peak time and peak overshoot are analysed for the proposed control scheme and compared to conventional controllers such as PI, PID, PID-SMC, FOPID. Moreover the time integral performance measures such as ITAE, IAE and ISE are analysed. Experimental results are shown to validate the obtained results with those of simulations. It has been proven that FFOPID outperforms all other existing techniques in terms of various time domain specifications and time integral performance measures.

Precision Displacement Control of a Diamond-shaped Amplifying Mechanism Driven by Piezoelectric Actuator Based on Fuzzy Fractionalorder PIλDμ Controller

Background: As a high-performance functional material, stacked piezoelectric actuator can produce a displacement under the effect of changing voltage. Its advantages of fast response and easy operation make it to be widely applied in the precision structure field. However, its small displacement stroke and hysteresis nonlinearity affect the accuracy of the output. : In the next step, some experiments were undertaken based on the constructed platform. Methods: In order to enlarge the displacement of piezoelectric actuator and reduce the influence of hysteresis, this study designs a diamond-shaped amplifying mechanism to amplify the output of the piezoelectric actuator, and then develops a self-tuning fuzzy fractional-order PIλDμ controller for the high precision displacement control of the proposed amplifying mechanism. After analyzing the working principle and modeling the amplifying mechanism, the fractional-order PIλDμ control model of the proposed mechanism was built and discretized according to the theoretical base of the fractional calculus in the time domain. Moreover, the fuzzy control algorithm was also introduced to achieve self-turning of parameters. Besides, the amplifying mechanism was also adopted for a microdroplet jetting dispenser to verify the practicability of the mechanism and control strategy. In the next step, some experiments were undertaken based on the constructed platform. Results: Experiments show that the displacement overshoots, the times of reaching a steady state of the traditional integer-order controller and the fractional-order controller are 5.08%, 1.17% and 17.25 s, 12.00 s, respectively. However, the fuzzy PIλDμ controller lowers the overshoot and the time of reaching a steady state to 0.95% and 9.00 s, respectively. The control algorithm can not only improve the follow-ability of the output displacement of the proposed mechanism, but also maintain the deviation within the range of 0.4% after the displacement stroke is stable and reduce the entering time of the mechanism up to 47.8%. In actual application, the droplet volume of micro-droplet jetting dispenser under fuzzy fractional-order PID control method is more stable, and its repeatability accuracy can reach up to 1.6475%. Conclusion: Experimental results indicate that the self-tuning fuzzy fractional-order PIλDμ controller can significantly improve the tracking performances of the PID and the integer-order PID with regard to the amplifying mechanism with the advantages of good dynamic character and regulation precision. Furthermore, the diamond-shaped amplification mechanism and control strategy can be applied for some micro-droplet jetting dispensers used in microelectronic packaging, life science and 3D printing fields.

MVO-PS Optimized Hybrid FOFPID Controller for Load Frequency Control of an AC Micro-Grid System

This paper proposes a new approach for load frequency control in a multi micro grid system by using hybrid multi verse with pattern search (hMVO-PS) algorithm based Fractional Order Fuzzy PID controller. A multi micro grid system may be molded by some of the renewable resources (RESs) like photovoltaic (PVs), wind (WTGs), energy storage system (ESSs) and loads. The fractional order fuzzy PID (FOFPID) controller parameters are optimized by novel hybrid Multi verse with pattern search (hMVO-PS) technique. The flexibility and robustness of proposed FOFPID controller is inspected under different disturbance like stochastic variations. The superiority of FOFPID structure over conventional Fuzzy PID/PID and hMVO-PS technique over multi verse optimization (MVO), particle swarm optimization (PSO) and genetic algorithm (GA) has been manifested.

Robotic manipulator control based on an optimal fractional-order fuzzy PID approach: SiL real-time simulation

Robotic manipulator control is a challenging task due to its nonlinear, interacting multi-input–multi-output dynamics. In this paper, we proposed an optimal robust fractional-order fuzzy PID controller based on multi-objective particle swarm optimization (MOPSO) algorithm for a two-link robotic manipulator. In order to minimize position and trajectory-tracking error, MOPSO finds the optimal parameters of fuzzy membership functions and order of the fractional operators. To show the effectiveness of the proposed controller, the software-in-the-loop real-time simulation is executed, and the results are compared to conventional fuzzy PID, fractional-order PID, and linear PID controllers.

Efficient control of a 3-link planar rigid manipulator using self-regulated fractional-order fuzzy PID controller

A self-regulated fractional-order fuzzy proportional–integral–derivative (SRFOFPID) controller is proposed to control a highly non-linear, complex and coupled 3-link planar rigid robotic manipulator in a virtual industrial environment. Industrial environment was simulated by introducing different kind of disturbances in the system and sensor noise. Proposed SRFOFPID controller is a direct non-linear adaptive controller having self-regulating feature and has been realized using fractional-order operators i.e. integrator and differentiator in self-regulated integer-order fuzzy PID (SRIOFPID) controller. Gains of SRFOFPID and SRIOFPID controllers are optimized using Backtracking Search Algorithm by minimizing an amalgamation of integral absolute error signal and integral absolute change in control signal as cost function. Performance of SRFOFPID and SRIOFPID controllers are assessed and compared with reference path under virtually simulated industrial environment. Presented intensive simulation studies revealed that both the controllers offered decent reference trajectory tracking performance under nominal operating conditions while SRFOFPID controller offered exceptionally robust performance under industrial scenario and uncertainties. Finally, the stability analysis of overall closed loop system is performed using small gain theorem and necessary and sufficient bounded-input and bounded-output stability conditions are established.