Fractional Order Fuzzy PID Controller Research Articles

Fractional-Order Fuzzy PID Controller with Evolutionary Computation for an Effective Synchronized Gantry System

Gantry-type dual-axis platforms can be used to move heavy loads or perform precision CNC work. Such gantry systems drive a single axis with two linear motors, and under heavy loads, a high driving force is required. This can generate a pulling force between the drive shafts in the coupling mechanism. In these situations, when a synchronization error becomes too large, mechanisms can become deformed or damaged, leading to damaged equipment, or in industrial settings, an additional power consumption. Effectively and accurately acquiring the synchronized movement of the platform is important to reduce energy consumption and optimize the system. In this study, a fractional-order fuzzy PID controller (FOFPID) using Oustaloup’s recursive filter is used to control a synchronous X–Y gantry-type platform. The optimized controller parameters are obtained by the measurement of control errors in a simulated environment. Four optimization methods are tested and compared: particle swarm optimization, invasive weed optimization, a gray wolf optimizer, and biogeography-based optimization. The systems were tested and compared in order to optimize the control parameters. Each of the four algorithms is simulated on four contour shapes: a circle, bow, heart, and star. The simulations and control scheme of the experiments are implemented using MATLAB, and the reference paths were planned using non-uniform rational B-splines (NURBS). After running the simulations to determine the optimal control parameters, each set of acquired control parameters is also tested and compared in the experiments and the results are recorded. Both the simulations and experiments show good results, and the tracking of the X–Y platform showed improved performance. Two performance indices are used to determine and validate the relative performance of the models and results.

RED FOX-BASED FRACTIONAL ORDER FUZZY PID CONTROLLER FOR SMART LED DRIVER CIRCUIT

Recently, traditional lighting has been replaced by high-power LED (HPLED) due to its significant developments, prolonged lifetime, high brightness, high reliability, and high energy efficiency. Even though conventional converters can precisely match each LED's current, they have some limitations when driving a long string of LEDs. To solve this issue, this paper presents a novel red fox optimized fractional order fuzzy PID Controller (RF-FOFPID) based high gain improved transformerless dc-dc (ITDC) boost converter for a smart LED driver circuit with optimal voltage regulation capability. The error bias is increased to zero by applying FOPID to the fuzzy logic-based compensation steps. The Red Fox optimization algorithm is used to adjust the control parameters of the fractional-level fuzzy PID controller with higher precision to solve limited problems with diverse search spaces. The Simulink model of the proposed converter was created using the MATLAB software tool Simulink and compared with controllers using fractional order PID, fuzzy PID, and conventional proportional integral derivative (PID). The results demonstrated that in terms of minimum overshoot, settling time, rise time, and steady-state error, the proposed converter based on RF-FOFPID outperforms current converters in voltage regulation.

Optimum of fractional order fuzzy logic controller with several evolutionary optimization algorithms for inverted pendulum

AbstractThis paper compared the performance between Integer Order Fuzzy PID (IOFPID) and Fractional Order Fuzzy PID (FOFPID) controllers for inverted pendulum system as a controlling plant. The parameters of each controller were tuned with four evolutionary optimization algorithms (Social Spider Optimization (SSO), Swarm Optimization (PSO), Genetic Algorithm (GA), and Particle Ant Colony Optimization (ACO)). The comparisons were carried out between the two controllers IOFPID and FOFPID, as well as among the four optimization algorithms for the two controllers. The results of comparisons proved that the FOFPID controller with SSO has achieved the best time response characteristics and the least tuning time.

Modified Harris Hawks Optimization-Based Fractional-Order Fuzzy PID Controller for Frequency Regulation of Multi-Micro-Grid

Modified Harris Hawks Optimization-Based Fractional-Order Fuzzy PID Controller for Frequency Regulation of Multi-Micro-Grid

Fuzzy fractional-order PID control for heat exchanger

Fractions have recently become widespread in technology and science. The current research looked at a fractional-order fuzzy PID controller. Furthermore, the tubular heat exchanger procedure aids in the investigation of controller behavior. The advantages of the recommended control strategy are highlighted to examine controller reactions under variations in variation and loads within the reference environment. There are additional comparisons with the conventional PID control scheme. The findings showed that the control approach performs better than a traditional PID control framework.

Seismic control of the structures with active tuned mass damper and variable fractional order fuzzy proportional–integral–derivative controller

The structural control of the building is a critical part of mitigating the catastrophic consequences of the earthquakes. The active control of structures has gained popularity in the construction industry because of its ability to adapt to different ground motion characteristics. The active tuned mass damper (ATMD) is one of the most versatile devices used for active structural control. This paper uses the ATMD and variable fractional order fuzzy PID (VFOFPID) controller for improving the performance of building structures subjected to horizontal ground motions. Having obtained the response of an 11-story shear building with this controller, the optimized control forces are determined through the pattern search algorithm and the performance indices of the system subjected to 100 different ground motions are evaluated. The performance indices are compared with those of uncontrolled as well as genetic fuzzy and fuzzy PID controlled structure. The results indicate that the VFOFPID controller proposed here can effectively reduce the drift and the absolute acceleration of the structure.

A Robustness Analysis of a Fuzzy Fractional Order PID Controller Based on Genetic Algorithm for a DC-DC Boost Converter

In this paper, a new topology of a Fractional Order PID (FOPID) controller is proposed to control a boost DC-DC converter with minimum over/undershoot. The fractional controller parameters are tuned using a genetic algorithm (GA) with a combined cost function composed of the Integral of Time-Weighted Absolute Error (ITAE) and the Integral of Time-Weighted Square Error (ITSE). Despite adding moderate complexity to the control structure, the simulation results reveal that the GA-based FOPID controller tuning provided better performance for the setpoint tracking both under load variations and parameters deviation due to the prolonged use. The proposed FOPID shows a wide operational range concerning load disturbances, and capacitance/inductance deviations of ±30% and ±50% from nominal values, achieving functionality and voltage stability even with output power 50% higher than the converter power specification. The assessment was made considering operation in voltage mode and the performance was compared to conventional Proportional-Integral (PI), Type II and current mode controllers. Finally, a fuzzy fractional-order PID (FFOPID) was designed to outperform the FOPID during disturbances in the control variable.

Control for Isokinetic Exercise with External Disturbance

Isokinetic exercise is considered as one of the most effective ways for rehabilitation and muscle strength enhancement. As rehabilitation equipment, the isokinetic exercise device assists isokinetic movement using a single fixed axis and relevant joint adapters, and it requires high stability and safety performances to cooperate with human. In this paper, a brushless DC motor (BLDCM) was adopted to make a study of isokinetic control. Fractional-order fuzzy PID (FOFPID) controller is an effective controller for the nonlinear system to realize isokinetic control according to reference speed and irregular disturbance (load torque). The model of the BLDCM and FOFPID controller system is built in MATLAB/Simulink to simulate the velocity response of the controller, and a comparison between the FOFPID controller and PID controller is made to verify the system stability.

Design of interval type-2 fuzzy fractional order PID controller based on particle swarm optimization

Abstract In this paper, an interval type-2 fuzzy fractional order PID controller (IT2F-FOPIDC) based on particle swarm optimization is proposed. The proposed controller has two adjustable degree of freedom parameters, so the control range of the controller parameters becomes larger and can control the controlled object more flexibly. Aiming at the difficult problem of many controller parameters and tuning, this paper introduces particle swarm optimization algorithm to optimize the controller parameters. In order to avoid the problems of long iteration time and high computational cost caused by Karnik-Mendel reduction algorithm, the enhanced iterative with stop condition algorithm is selected for the proposed controller. Finally, the proposed controller is applied to the second order systems with time delays. Simulation results show that the proposed strategy has faster response time and smaller oscillation amplitude, and its performance is better than fuzzy controller and interval type-2 fuzzy controller.

Fuzzy fractional-order PID control for two-wheeled self-balancing robots on inclined road surface

Two-wheeled self-balancing robots (TWSBR) is a highly nonlinear and inherently unstable under-driving system. When controlling its movement on an inclined surface, it is more difficult than when it is on a level road. This paper proposes a fuzzy fractional-order PID (FFOPID) controller for the motion control of a TWSBR system in an inclined environment. The control goal of TWSBR is to realize the wheel position control and to stabilize the non-vertical direction of intermediate body (IB). Finally, we compare the control effect of the proposed FFOPID controller with that of the integer-order PID controller, the fuzzy PID (FPID) controller, and the fractional-order PID (FOPID) controller when TWSBR moving on the inclined plane. The simulation results show that the FFOPID controller has better control performance and anti-interference ability.

Real-time trajectory tracking control of Stewart platform using fractional order fuzzy PID controller optimized by particle swarm algorithm

PurposeThe purpose of this paper is to address a fractional order fuzzy PID (FOFPID) control approach for solving the problem of enhancing high precision tracking performance and robustness against to different reference trajectories of a 6-DOF Stewart Platform (SP) in joint space.Design/methodology/approachFor the optimal design of the proposed control approach, tuning of the controller parameters including membership functions and input-output scaling factors along with the fractional order rate of error and fractional order integral of control signal is tuned with off-line by using particle swarm optimization (PSO) algorithm. For achieving this off-line optimization in the simulation environment, very accurate dynamic model of SP which has more complicated dynamical characteristics is required. Therefore, the coupling dynamic model of multi-rigid-body system is developed by Lagrange-Euler approach. For completeness, the mathematical model of the actuators is established and integrated with the dynamic model of SP mechanical system to state electromechanical coupling dynamic model. To study the validness of the proposed FOFPID controller, using this accurate dynamic model of the SP, other published control approaches such as the PID control, FOPID control and fuzzy PID control are also optimized with PSO in simulation environment. To compare trajectory tracking performance and effectiveness of the tuned controllers, the real time validation trajectory tracking experiments are conducted using the experimental setup of the SP by applying the optimum parameters of the controllers. The credibility of the results obtained with the controllers tuned in simulation environment is examined using statistical analysis.FindingsThe experimental results clearly demonstrate that the proposed optimal FOFPID controller can improve the control performance and reduce reference trajectory tracking errors of the SP. Also, the proposed PSO optimized FOFPID control strategy outperforms other control schemes in terms of the different difficulty levels of the given trajectories.Originality/valueTo the best of the authors’ knowledge, such a motion controller incorporating the fractional order approach to the fuzzy is first time applied in trajectory tracking control of SP.

Frequency Regulation of Multi Area Renewable Energy Source system with Practical Constraints under Fractional-order Fuzzy Controller

This paper introduces a novel control strategy of fractional order (FO) fuzzy (F) PID (FOFPID) controller optimized with the latest soft computing technique of seagull optimization algorithm (SOA) for power system frequency regulation. Initially, a simple and widely accepted power system of dual area photovoltaic (PV) and reheat thermal (RT) (PVRT) system is perceived and named as test system-1 in this paper. The performance of FOFPID fine-tuned with SOA mechanism is tested on PVRT system for a step load disturbance of 10% (SLD) on area-2 along with other controllers reported in the literature. Dynamical analysis of the PVRT system reveals the potency of the proposed controller over others. Further, the SOA based FOFPID controller is extended to frequency regulation of multi-area system with hybrid generating sources (MAHS) named as test system-2 in this paper for 10% SLD on area-1. MAHS system is constituted with realistic constraints to conduct research close to realistic practice. The potentiality of SOA based FOFPID is demonstrated by comparing it with traditional controllers of PID/FPID/FOPID on MAHS system. Finally, robustness analysis is perpetuated to reveal the presented control scheme robustness.

Sunflower optimization based fractional order fuzzy PID controller for frequency regulation of solar-wind integrated power system with hydrogen aqua equalizer-fuel cell unit

ABSTRACT The rapid advancement of electric consumer demand enforces challenging situations to manage high penetration of Solar PV and Wind Power into the hydrothermal system resulting in load frequency control (LFC) problem. This article introduces an advanced strategy to manage the LFC issue in an integrated power system (PS) with the impact of hydrogen aqua equalizer (HAE)-based Fuel cells (FC). A transformative fractional-order fuzzy-based PID (FOFPID) controller regulated by the Sunflower optimizing (SFO) technique has been proposed for frequency regulation of the proposed integrated PS. The preeminence of the FOFPID controller has been validated over PID, Fuzzy-PID (FPID), and fractional order PID (FOPID) controller. The effectiveness of the SFO technique has been established over teaching learning-based optimization (TLBO) and Genetic Algorithm (GA). The supremacy of the SFO approach authenticated by some recent frequency regulation research outcomes. The influence of HAE-FC for frequency regulation in an integrated PS has been studied with the proposed SFO-tuned FOFPID controller. From the observation, it is perceived that the values of reduction in ITAE with suggested SFO-tuned FOFPID controller as compared to GA & TLBO are 84.61% & 56.04% and further 35.16% is reduced with the occurrence of HAE-FC element. It is also perceived that the improvement in settling time for ∆f1, ∆f2, ∆Ptie12 with SFO approach related to GA are 78.07%, 76%, and 83.87% and compared to TLBO are 9.97%, 38.25%, and 68.23%. Furthermore, 26.45%, 18.64%, and 31.21% are reduced with the presence of HAE-FC unit. Lastly, the sturdiness of the anticipated strategy was authenticated by a sensitivity test and a real-time validation test using OPAL-RT.

Design of optimal fractional order fuzzy PID controller based on cuckoo search algorithm for core power control in molten salt reactors

In case of the adverse effects of unforeseeable or uncertain disturbances on control systems, stability robustness of control performance is crucial for controller design. Accordingly, in this study, an optimal design scheme for Fractional Order Fuzzy Proportional Integral Derivative (FOFPID) controller with adoption of Cuckoo Search (CS) optimization algorithm is presented in order to examine the application of the FOFPID in the core power control of molten salt reactors (MSRs) as an example. By using the proposed scheme, PID, FOPID and fuzzy PID controllers are also designed by the CS for the purpose of showing the superiority of the FOFPID controller. Firstly, a nonlinear dynamic model of the MSR system is introduced by means of point kinetic equations considering the time delay in the fluid's transit connecting the core and the heat exchanger. Then, the nonlinear model is linearized for obtaining a linear model of MSR core system. Also, for the purpose of performing the sensitivity analysis, transit behaviors for both the linear and nonlinear approaches are shown and compared for different reactivity inputs. The core power control of molten salt reactor system is examined for each tuned controller in terms of stability, time domain and the robustness analysis under instantaneous and continuous disturbances. The results showed that the proposed CS based FOFPID controller has better control performance as compared to the PID, FOPID and fuzzy PID controllers tuned by the CS, especially in point of capability of disturbance suppression, improving tracking performance, and robustness against parameter uncertainty.

General type industrial temperature system control based on fuzzy fractional-order PID controller

A fuzzy fractional-order PID control algorithm for a general type industrial temperature control system is proposed in this paper. In order to improve the production quality and controlled model accuracy, a fractional-order elementary system is used to describe the temperature control process. The gain coefficients of the proposed fractional-order PID controller is updated online based on a set of fractional-order fuzzy rules which are defined by Mittag–Leffler functions and follow fat-tailed distributions. Therefore, the proposed controller parameters could be auto-tuned according to model uncertainties, noise disturbance, random delay, and etc. Examples of the studied temperature control systems are shown to verify the effectiveness of the proposed controller. The superiority of fractional calculus is fully explored in the presented control methodology. The controlled temperature profile with the proposed algorithm could realize more satisfactory dynamic performance, better robustness respect to environment changes caused by internal and external disturbance.

Efficiency and robustness of type-2 fractional fuzzy PID design using salps swarm algorithm for a wind turbine control under uncertainty

An accurate and efficient control of the Maximum Power Point Tracking (MPPT) and pitch angle for the Wind Turbine (WT) system can provide more energy while also protecting the material. Thus, considering these economic aspects, many controllers are proposed to guarantees their performances. The most studied strategy is the classical PID controller. However, its performance is limited due to the nonlinear model and the difficult wind speed form, which inflict many uncertainties. To solve these drawbacks, an advanced controller named Type-2 Fractional Order Fuzzy PID (T2-FOPID) controller is suggested in this paper to improve the exigence controls. Meanwhile, an efficient optimization technique named the Salps Swarm Algorithm (SSA) has been introduced in order obtaining the best controller parameters. The efficiency of the proposed controller is tested to the 10 kW-WT under various wind speed scenarios. The derived results explicitly indicate that the proposed strategy outperforms the PID controller and other controllers, in terms. the minimum of error, the overshoot and the settling time.

Enhancing the performance of a deregulated nonlinear integrated power system utilizing a redox flow battery with a self-tuning fractional-order fuzzy controller

Load frequency regulation is one of the most vital and complex ancillary services in a deregulated power system. Increasing penetration from renewable energy sources in an integrated power system (IPS) further escalates the related control complexity due to a considerable decrement in IPS’s effective inertia. This may incur additional costs and can even lead to the destabilization of IPS. To overcome these problems in frequency regulation, this work proposes and investigates the use of an intelligent, direct adaptive control scheme, i.e., self-tuning fractional order fuzzy PID (STFOFPID) controller with and without the presence of a recently devised energy storage unit, i.e., the redox flow battery. The IPS’ efficacy with the STFOFPID controller is validated for various contracts in a deregulated operation mode for considered three area IPS. Extensive simulation studies are carried out, and detailed comparative studies have been drawn with conventional PID and fractional order PID controllers for load frequency regulation in Poolco, bilateral, and contract-violation mode of operation. Robustness analysis in terms of parametric variations in different nonlinearities present in a reheated thermal power plant is also carried out, and the efficacy of the STFOFPID controller is established using a thorough quantitative comparative analysis. The real-time digital simulation validation of the investigated control structure has been carried out on OPAL-RT 4150 based on Xilinx Kintex-7 FPGA board with INTEL multi-core processor.

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