Fractional Order Fuzzy PID Research Articles

A mMSA-FOFPID controller for AGC of multi-area power system with multi-type generations

The exceptional growth in the penetration of renewable sources as well as complex and variable operating conditions of load demand in power system may jeopardize its operation without an appropriate automatic generation control (AGC) methodology. Hence, an intelligent resilient fractional order fuzzy PID (FOFPID) controlled AGC system is presented in this study. The parameters of controller are tuned utilizing a modified moth swarm algorithm (mMSA) inspired by the movement of moth towards moon light. At first, the effectiveness of the controller is verified on a nonlinear 5-area thermal power system. The simulation outcomes bring out that the suggested controller provides the best performance over the lately published strategies. In the subsequent step, the methodology is extended to a 5-area system having 10-units of power generations, namely thermal, hydro, wind, diesel, gas turbine with 2-units in each area. It is observed that mMSA based FOFPID is more effective related to other approaches. In order to establish the robustness of the controller, a sensitivity examination is executed. Then, experiments are conducted on OPAL-RT based real-time simulation to confirm the feasibility of the method. Finally, mMSA based FOFPID controller is observed superior than the recently published approaches for standard 2-area thermal and IEEE 10 generator 39 bus systems.

Active vibration control of metal foam reinforced agglomerated graphene nanoplatelets nanocomposite truncated conical shells with piezoelectric layers

This study examines active vibration control (AVC) in a truncated conical shell composed of metal foam reinforced with agglomerated graphene nanoplatelets and integrated with piezoelectric layers functioning as sensors and actuators. Both complete and partial agglomeration states are considered based on the Eshelby–Mori–Tanaka approach, and the mechanical properties of the porous core are characterized using a closed-cell metal foam model. The governing equations of motion are derived using Hamilton’s principle, based on the two-dimensional axisymmetric elasticity theory, and solved through the finite element method coupled with the Newmark method. Vibration mitigation is achieved using a fractional-order fuzzy proportional–integral–derivative (PID) controller. A comprehensive parametric study is conducted, examining the effects of geometric dimensions, various boundary conditions, reinforcement parameters (including weight fraction, distribution patterns, and agglomeration parameters), and porosity parameters (including pore size, and porosity pattern) on the vibration properties of the shell. Numerical simulations are performed to assess the effectiveness of the proposed AVC system in reducing structural vibrations compared to a constant velocity feedback control approach. The velocity feedback controller reduced central deflection from 12.65 to 5.089 μ m , while a fractional-order fuzzy PID controller further improved it to 2.348 μ m , representing a 53.86% enhancement over the velocity feedback controller.

Modeling of genetic algorithm tuned adaptive fuzzy fractional order PID speed control of permanent magnet synchronous motor for electric vehicle

This study presents a novel Genetic Algorithm-optimized Adaptive Fuzzy Fractional Order Proportional Integral Derivative (GA-AFFFOPID) controller for enhancing the speed control performance of permanent magnet synchronous motor (PMSM) drives in Electric Vehicles. The proposed GA-AFFFOPID controller, which combines the advantages of genetic algorithm optimization and adaptive fuzzy fractional-order PID control, represents a unique and innovative approach to address the control challenges associated with PMSM drives. Permanent magnet synchronous motor technology, known for its efficiency, compactness, reliability, and versatility in motion control applications, is increasingly adopted in electric vehicle drive systems. However, the inherent non-linearity, dynamics, and uncertainties of permanent magnet synchronous motors pose significant control challenges. The exceptional performance of the GA-AFFFOPID controller, demonstrated through its superior system dynamics, precise speed tracking, and robustness against parameter variations and sudden load disturbances, underscores the significant advancements enabled by the genetic algorithm optimization technique in improving the control performance of PMSM drives for electric vehicle applications. Comparative analysis with traditional control methods demonstrates the exceptional performance of the Genetic Algorithm-optimized Adaptive Fuzzy Fractional Order Proportional Integral Derivative controller. These findings highlight the significant performance improvements facilitated by the genetic algorithm optimization technique in enhancing the control performance of the adaptive fuzzy fractional order PID controller in PMSM drives for electric vehicle applications.

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.

An adaptive neuro-fuzzy with nonlinear PID controller design for electric vehicles

In this work, an adaptive neuro-fuzzy (ANF) with a nonlinear proportional integral derivative (NLPID) controller (ANF-NLPID) has been proposed to solve the speed-tracking problem in electric vehicles (EVs) with brushless DC motor (BLDC). The ANF-NLPID controller eliminates the external disturbances caused by environmental or internal issues and uncertainties caused by parameter variations that lead to insufficient speed-tracking performance and increased energy consumption in EVs. An improved particle swarm optimization based on the chaos theory (IPSO-CT) algorithm is introduced to obtain the parameters of the fuzzy logic controller membership function and nonlinear PID controller and present the optimal performance for the EV. Employing the chaos technique with PSO helps to prevent the system from being trapped in the local minimum or optimum problem. The performance of the IPSO-CT algorithm is tested using a numerical comparison with other existing works. The outstanding performance of the ANF-NLPID controller has been evaluated by measuring the speed-tracking performance for the new European driving cycle (NEDC) and circular trajectories. Three case studies have been presented based on measuring the ANF-NLPID controller performance without disturbances, with disturbances, with disturbances, and uncertainties effects, respectively. Furthermore, the ANF-NLPID controller has been employed in different EV models to study the performance of this type of controller. Each of the three cases includes other existing works along with the ANF-NLPID controller to provide an insightful comparison using statistical functions to obtain each controller’s overall objective function value. The other existing works are fuzzy fractional order PID (Fuzzy FOPID), fuzzy integer order PID (Fuzzy IOPID), and integer order PID (IOPID) controllers. A sensitivity analysis has been conducted to test the proposed controller’s ability to present high speed-tracking performance while changing the disturbances and uncertainty rates. The results demonstrate that the ANF-NLPID controller is superior in speed-tracking control regulation for the new European cycle drive (NEDC) and circular speed trajectories and overcomes the external disturbances and uncertainties problem with low error results. In the end, the results reveal that the ANF-NLPID controller is more efficient than the fuzzy FOPID, fuzzy IOPID, and IOPID controllers in each case.

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.

Optimal Fuzzy-FOPID, Fuzzy-PID Control Schemes for Trajectory Tracking of 3DOF Robot Manipulator

The present study explores the guidance of a robotic arm along a predefined path by implementing an optimal fuzzy fractional order PID controller-based control strategy. This method serves as a means to address the nonlinearity and unpredictability of the robotic manipulator, contingent upon the fuzzy logic controller's specifications and the employment of a clonal selection algorithm. The dynamic equation of the manipulator was considered as an initial point, followed by designing a fuzzy controller for this purpose. To validate the effectiveness of this approach, it was compared to other techniques, such as Fuzzy, Fuzzy-PID, and fuzzy-FOPID controllers, with PID and FOPID controller parameters optimized using clonal selection algorithms. Simulation results reveal that the fuzzy-FOPID variant outperformed other methods under varying load conditions and model uncertainties, using SIMULINK/MATLAB 2014a.

A Robust Fuzzy Fractional Order PID Design Based On Multi-Objective Optimization For Rehabilitation Device Control

In this context, Fuzzy Fractional Order Proportional Integral Derivative (FOPID-FLC) controllers are emerged as efficient approaches due to their flexibility and ability to handle nonlinearities and uncertainties. This paper proposes the use of a FOPID-FLC controller for a two-degree-of-freedom (2-DOF) lower limb exoskeleton. Our proposal is based on an enhanced control approach that combines fuzzy logic advantages and fractional calculus benefits. Contrary to popular existing methods, that use the FLC to tune the FOPID parameters, the FLC in this work is used to generate the system torque depending on patient morphology. Indeed, our fundamental contribution is to design and implement an enhanced FOPID-FLC that achieves an adequate optimal control based on system rules composed of optimal torques and input data. The fractional calculus is approximated using successive first order filters. Next, a multi-objective optimization is established for the tuning of each FOPID parameters. Finally, the FLC is used to adjust the torque depending on the kid's age. The effectiveness of the proposed controller in various scenarios is validated based on numerical simulations. Extensive analyses prove that the FOPID-FLC outperforms the FOPID with a 90\% of improvement in terms of error performance indices and 20\% of improvement for the control action. Moreover, the controller exhibits improved robustness against uncertainties and disturbances encountered in rehabilitation environments.

Fuzzy Fractional Order PID Tuned via PSO for a Pneumatic Actuator with Ball Beam (PABB) System

This study aims to improve the performance of a pneumatic positioning system by designing a control system based on Fuzzy Fractional Order Proportional Integral Derivative (Fuzzy FOPID) controllers. The pneumatic system’s mathematical model was obtained using a system identification approach, and the Fuzzy FOPID controller was optimized using a PSO algorithm to achieve a balance between performance and robustness. The control system’s performance was compared to that of a Fuzzy PID controller through real-time experimental results, which showed that the former provided better rapidity, stability, and precision. The proposed control system was applied to a pneumatically actuated ball and beam (PABB) system, where a Fuzzy FOPID controller was used for the inner loop and another Fuzzy FOPID controller was used for the outer loop. The results demonstrated that the intelligent pneumatic actuator, when coupled with a Fuzzy FOPID controller, can accurately and robustly control the positioning of the ball and beam system.

Squirrel search algorithm based intelligent controller for interconnected power system

ABSTRACT In this paper, a novel controller, namely fractional order fuzzy proportional-integral-derivative (FOFPID) has been proposed for the dual area power system of hydro-thermal-gas units (DAHTG). The squirrel search algorithm (SSA) is implemented to achieve the optimal values of the controller tuning parameters. Further, various non-linearity constraints, such as governor dead band (GDB), generation rate constraint (GRC) and communication time delays (CTDs) have also been considered to test the effectiveness of the proposed controller in a real-time environment. The step load of 10% is provided as the disturbance under the regulation. In addition, the coordinated strategy of a static synchronous series compensator (SSSC) device and superconducting magnetic energy storage (SMES) is employed in the proposed system to enhance the system’s performance. Further, the accuracy, effectiveness and robustness of the proposed controller are revealed through the comparative analysis with classical PID and traditional fuzzy PID controllers. Furthermore, presented controller efficacy is revealed with the other recently reported control techniques by implementing it on the two-area thermal system with GDB. The comparative analysis shows the better performance of the proposed controller than these two. Finally, the sensitivity analysis is performed to check the controller robustness.

Satellite Tracking Control System Using Optimal Variable Coefficients Controllers Based on Evolutionary Optimization Techniques

Satellite tracking control system is mechanism that redirects the parabolic antenna to the chosen satellite automatically. It perfectly tracks the satellite as it spins across the sky in its orbit. To maintain a continuous communication signal throughout multiple satellite tracking missions, the tracking process must be fast and smooth, with minimal deviations from the target position. Various controller models have been presented over time to address the problem of antenna positioning in satellite systems and to track moveable targets using servomechanism. The purpose of this study is to describe and debate a satellite tracking control system based on a DC servo motor. For optimal tuning of Proportional-Integral-Derivative (PID), Fractional Order PID (FOPID) and Variable Coefficient Fractional Order PID (V-FOPID) controllers that were used in satellite control system, Particle Swarm Optimization (PSO), Gravitational Search Algorithm with Particle Swarm Optimization (GSA-PSO) and Eagle Strategy with Particle Swarm Optimization (ES-PSO) techniques were proposed. Dynamic Performance Indices Based Objective Functions is used to compute the Performance Index. Furthermore, Self-Tuning Fuzzy FOPID (STF-FOPID) is proposed for satellite tracking control system. The system's response is analyzed, and the outcomes of various control strategies are measured and compared to others. The obtained results implies that Variable Coefficient Fractional Order PID controller tuned using Eagle Strategy with Particle Swarm Optimization can precisely trace the desired position with the fastest settling time and free overshoot when compared to other control strategies.

Grid Mode Selection Scheme based on a Novel Fractional Order Proportional Resonant Controller for Hybrid Renewable Energy Resources

The operation of Renewable Energy Sources (RES) on grid-connected and islanded operations is challenging due to the unstable generation of power. This challenge is due to the unregulated power supply. To mitigate this effect, several controllers were proposed, but they rely on smooth transition by controlling the power supply. The studies have not considered the regulation during switching between the grid connections. Hence this article investigates the novel Fractional-Order Proportional Resonant controller (FOPR) for the regulated supply to the grid connections. The controller aimed to achieve faster stabilization even with the intermittent power supply. The modified grid connection changes fetch the data of fault, unregulated supply. The Modified particle swarm optimization (MPSO) will test the data and send the signal for switching based on the available voltage to the switch and the controller. The controller’s stability is evaluated in both simulation and experimentation, and the employed method’s robustness is compared with other fractional order controllers. The experimentation result shows that the proposed controller has improved its performance to 35% with the intelligent-based control design and 81.25% over the Fuzzy fractional order proportional integral derivative (FFOPID) controller.

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 PMSG Based Wind Energy Conversion System with Sparse Matrix Converter Topology

Sparse matrix converter (SMC) is an indirect AC-to-AC power electronic converter that has a fictitious DC link between rectification and inversion stages in which neither a capacitor nor an inductor, as the storage element, is utilized. Due to this advantage, SMC is used in AC drives, marine thrust systems, aerospace industry, as well as in wind energy applications. On the other hand, permanent magnet synchronous generator (PMSG) is competitive in wind turbine applications due to their prominent features. In this work, a fuzzy fractional-order PID (FFOPID) controller is designed for a PMSG based wind energy conversion system (WECS) which employs a three-phase three-level SMC. The FFOPID controller is chosen to combine the salient features of the fractional-order calculus and fuzzy logic operations to enhance the dynamic response of classical PID controller with fixed gains. The simulation results taken under different case studies are analyzed in detail, which demonstrate the superiority of the designed FFOPID controller over classical PID control approach in tracking d- and q-axis current references of the SMC at the output. With the designed control approach, the smooth control of the real and reactive power injections into the grid from the WECS are ensured with acceptable transient response.

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.

Tidal turbine support in microgrid frequency regulation through novel cascade Fuzzy-FOPID droop in de-loaded region

The goal of this study is to introduce an effective load frequency control scheme with the integration of tidal turbines in a standalone microgrid (μG) system. As standalone μG experiences lower inertia and lacks primary frequency control, the use of variable tidal turbines in the de-loaded region may be accepted as one of the feasible solutions for managing frequency regulation issues. In this condition, the de-load region alludes to an area where tidal turbines liberate their accumulated kinetic energy in rotational parts pursuing frequency fluctuations. An effectual cascade fractional order fuzzy PID-integral double derivative (CFOFPID-IDD) controller suggested for efficient utilization of tidal turbines, whose design variables are tuned through a recently appeared Jaya algorithm. An investigation is made between the acquired outcomes of the studied CFOFPID-IDD droop controller with fractional order fuzzy PID droop control to analyze the proposed strategy performance in various load conditions, with different physical constraints like time delay, dead zone, and generation rate constraints. Moreover, the sensitivity test reveals that the Jaya-optimized CFOFPID-IDD controller can undergo ± (10–25) % variation in various coefficients without retuning the design variable values. The simulation outcomes validate the effectiveness and adequacy of the proposed regulator.

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.

Construction and Evaluation of a Control Mechanism for Fuzzy Fractional-Order PID

In this research, a control mechanism for fuzzy fractional-order proportional integral derivatives was suggested (FFOPID). The fractional calculus application has been used in different fields of engineering and science and showed to be improved in the past few years. However, there are few studies on the implementation of the fuzzy fractional-order controller for control in real time. Therefore, for an experimental pressure control model, a fractional order PID controller with intelligent fuzzy tuning was constructed and its results were calculated through simulation. To highlight proposed control scheme advantages, the performances of the controller were inspected under load disturbances and variations in set-point conditions. Furthermore, with classical PID control schemes and fractional order proportional integral derivative (FOPID), a comparative study was made. It is revealed from the results that the suggested control scheme outclasses other categories of the control schemes.

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.