Fractional Order PID Controller Research Articles

Fractional-Order PID Control of Permanent Magnet Synchronous Motors Based on Based on Improved Squirrel Algorithm

An adaptive differential squirrel algorithm fractional order PID controller is proposed to address the problems of instability and poor accuracy of Permanent Magnet Synchronous Motor PID control systems. In order to improve the global optimisation of the squirrel search algorithm, the crossover operation of the difference algorithm was combined, adaptive predation probability factor, dynamic crossover probability and Gaussian distribution perturbation operation are added to the squirrel search algorithm to improve its exploration and exploitation capability. In the comparative experiment of PMSM speed control, ADESA fractional-order PID was contrasted with conventional PID and other intelligent optimization algorithms. The results indicate that the PMSM control utilizing fractional-order PID through ADESA demonstrated minimal overshoot, the fastest response time, and superior anti-disturbance capabilities compared to PID and other intelligent optimization algorithms. This significantly enhanced the control performance of the permanent magnet synchronous motor.

Optimal design of time‐varying parameter fractional order controller using ameliorated gazelle optimization algorithm

AbstractThe model parameter uncertainty and controller gain disturbance of the factory servo system are challenges that affect the robustness and control performance of the system. In this paper, a class of factory servo systems with non‐integer order is studied. The stable boundary trajectory method of the fractional order system is used to determine the parameter stability domain that makes the control system stable. An optimal gain trade‐off design method for time‐varying parameter fractional order PID controller () is proposed. The time function is introduced as the adjustment formula to realize the adaptive adjustment of the controller gain. The Lyapunov theorem analyzes the stability of the method. At the same time, an ameliorated gazelle optimization algorithm (AGOA) is proposed to optimize the parameters of the controller, and the weight relationship is changed to set the objective function to obtain the optimal performance combination after optimization. The benchmark function optimization test is completed. Statistical analysis shows that AGOA can enhance the global search ability, prevent the acquisition of local optimum, and have faster convergence speed. The final simulation results show that the proposed scheme is a promising alternative to improve the system control performance.

Time delay recurrent neural networks via PID control law to complex dynamic systems

This paper presents an extension to the theory on the analysis of stability of complex systems with time delay of fractional order; the previous study is based on the theory of functions of Lyapunov–Krasovskii and the fractional-order PID control law. The analytical results are illustrated by the simulation of fractional nonlinear systems interconnected with time delay which are forced to follow complex trajectories as chaotic systems.

Adaptive cruise control system with fractional order ANFIS PD+I controller: optimization and validation

Designing the control structures of fractional order PID controllers has proven to be effective in providing adaptability in set point tracing the performance of a nonlinear cruise control system. Wheel rolling resistance, wind drag force, and road gradient are incorporated into the design to better describe the system under consideration and to show how the nonlinear cruise control system behaves. This study presents a comparative investigation using simulation between control structures such as fractional order proportional–integral–derivative, fractional order integral minus proportional derivative, and fractional order proportional integral minus derivative. By preserving integral error indices as the goal function, a genetic algorithm is used to improve the controller gain parameters and fractional scaling values. To prevent integral windup conflicts and derivative boost issues, both traditional fractional order structures and adaptive neuro-fuzzy-based fractional order structures were used to create the adaptive cruise control system. The FO ANFIS PD plus I controller for the cruise control system exceeds the competition in servo and regulatory difficulties.

Advanced tree‐seed optimization based fractional‐order PID controller design for simplified decoupled industrial tank systems

AbstractControlling coupled tank systems is challenging due to interactions between tanks, nonlinear dynamics, time delays, uncertainties, and cross‐coupling effects. The design of effective control strategies to address these complexities while ensuring stability and robust performance is difficult. Hence, this study focuses on presenting an innovative approach to enhance level control in coupled tank systems by employing a fractional‐order proportional‐integral‐derivative (FOPID) controller. The FOPID controller is designed by imposing constraints on the performance metric and closed‐loop gain. Besides, the defined optimization problem is solved by employing a tree seed algorithm. Further, the stability is analyzed graphically using the singular value analysis. The inherent complexities of coupled tank systems are effectively addressed by designing decouplers. The unique characteristics of the tree seed algorithm to navigate complex solution spaces and its effective handling of constraints offer a robust optimization framework. The validity and efficiency of the proposed method are analyzed in a range of simulation experiments conducted on distinct interconnected tank systems. Besides, the stability is verified graphically. The analysis highlights the effectiveness of the control law in handling uncertainties and disturbances. Besides, the proposed method reduces the settling time to around . Through a systematic integration of optimization and comprehensive stability analysis, the study provides a holistic solution for optimizing level control in coupled tank systems.

Comparative performance analysis of fractional-order nonlinear PID controller for complex surge tank system: tuning through machine learning control approach

Comparative performance analysis of fractional-order nonlinear PID controller for complex surge tank system: tuning through machine learning control approach

Load frequency control in Island micro-grid with electric vehicles and renewable energy sources using modified fractional order PID controller

This paper presents a modified fractional-order proportional-integral-differential (MFOPID) controller for load frequency control in an Island microgrid based on an electric vehicle (EV) and renewable energy source. It tackles the intermittent energy sources and the dynamic of the load change with reduced speed and the quality of response generated on the microgrid. The MFOPID controller gains are well turned using a metaheuristic grasshopper optimization algorithm (GOA) technique to determine its robustness and optimal system performance. The controller gains are evaluated with three different searching agent populations. The proposed MFOPID with GOA improved system performance frequency by 19.485 Hz compared to 14.1151 Hz of the benchmark model. It takes 6.9068 s of the proposed model to settle compared to 16.6796 s of FOPID.

Fractional-order PID controller tuned by particle swarm optimization algorithm for a planar CDPR control

The use of cable-driven parallel robots (CDPRs) has been steadily increasing across various sectors due to their expansive workspaces, impressive payload-to-mass ratios, and cost-effective designs. Controlling these robots, particularly those with substantial actuation redundancy, can present challenges. This research paper proposes the implementation of a fractionalorder proportional-integral-derivative (FOPID) controller to effectively regulate the end-effector of a planar CDPR with four actuation cables. The parameters of the controller are fine-tuned using the particle swarm optimization (PSO) algorithm to ensure optimal performance. The proposed controller's performance is evaluated through two numerical experiments: target tracking and trajectory tracking using a point-to-point approach. Furthermore, a comparative study is conducted to highlight the controller's performance, comparing the proposed FOPID controller with both the classical PID controller and an optimized PID controller. The achieved results demonstrate that the proposed controller exhibits superior performance in terms of tracking accuracy and smoothness of control signals when compared to the other controllers under investigation. As a result, the proposed controller design represents a substantial advancement in control performance and can be regarded as a promising control strategy for CDPRs.

Power Quality Conditioners-Based Fractional-Order PID Controllers Using Hybrid Jellyfish Search and Particle Swarm Algorithm for Power Quality Enhancement

Power quality (PQ) is a major issue in today’s electrical system that affects both utilities and customers. The proliferation of power electronics devices, smart grid technology, and renewable energy sources (RES) have all contributed to the emergence of PQ concerns in today’s power system. The Unified Power Quality Conditioner (UPQC) is a versatile tool that can be used to fix distribution grid issues caused by irregular voltage, current, or frequency. Several tuning parameters, however, restrict the effectiveness of the Fractional-Order Proportional Integral Derivative (FOPID) control technique, which is proposed to improve UPQC performance. To move beyond these restrictions and find the optimal solution for the FOPID controller problem, a hybrid optimization strategy called the Hybrid Jellyfish Search Optimizer and Particle Swarm Optimizer (HJSPSO) is employed. To meet the load requirement during PQ issue periods, the suggested model incorporates a renewable energy source into the grid system. Whether the load is linear or non-linear, the design maintains PQ problems to a minimum. Furthermore, the FOPID control technique is compared with other controllers. Results show that grid-connected RES systems using the proposed FOPID control approach for UPQC have fewer PQ problems. The presented UPQC with HJSPSO strategy significantly outperformed, with the shortest computing time of 127.474 s and an objective function value of 1.423.

Implementation of FOPID controller with modified harmony search optimization for precise modelling and auto-tuning of nonlinear systems

This research aims to optimize the fractional order proportional integral derivative (FOPID) controller for nonlinear process tests. Instead of relying on the traditional trial-and error method for dynamic parameter selection, this proposes a modified harmony search optimization method to compute the optimal dynamic parameters. Based on the physical parameters, using mathematical modelling techniques system transfer function is determined. Additionally, the delay of the control scheme is determined using the Open Loop Transfer Function (OLTF) response. The dynamic parameters of the FOPID controller are evaluated using the Harmonic Search Algorithm – Fractional Order Proportional Integral Derivative (HAS_FOPID) optimization technique, which aims to minimize the system's Integral Square Error (ISE). Time responses, including rise time, peak time, and peak overshoot, are obtained and optimized through the HAS_FOPID algorithm. To verify systems stability, the output response is analysed using various techniques such as bode plots, pole placement, and Nyquist plots. Furthermore, the HAS_FOPID optimization technique is compared with other natural optimization techniques to assess its effectiveness. The research also evaluates the system's robustness by supply/ load disturbances. The objective is to demonstrate that, the optimized HAS_FOPID technique, has significantly enhanced control performance, stability, and robustness of nonlinear systems compared to natural and alternative optimization approaches.

Optimized fractional order PID controller with sensorless speed estimation for torque control in induction motor

With rising concern on environmental protection, the exploitation of EV has been widely focused. The IM is said to be the best in comparing varied electric motors for EV applications due to its lower price and robustness. In addition, sensor-less controlling schemes like DTC and FOC are found to be appropriate for crucial appliances owing to their energy savings, improved efficiency, and reliability. The “Optimized Fractional Order Proportional Integral Controller (FoPID)” with a sensor-less speed estimate mechanism is proposed in this work. Additionally, the parameters of FoPID are adjusted using a brand-new hybrid method called the Wolf based Elephant Herding method (W-EHA), which combines the ideas of Grey wolf optimization (GWO) model and Elephant herding optimization (EHO). The superiority of the recommended technique is finally shown in terms of controller performance and error. The RMSE obtained by the developed model at speed = 100 is 3.344, which is 53.89 %, 24.22 %, 1.09 %, and 38.96 % superior to existing approaches like P-controller, MFI-DA + FoPID, EHO-FoPID, and GWO-FoPID respectively.

Enhancing Power Generation for Solar-Based Cardiac Pacemakers: A Novel Approach with FOPID and HCMKH-BS2

Biomedical implants, such as implantable cardioverter heart monitors, rely on limited battery life, which necessitates costly replacements and patient discomfort. To address these challenges, a novel solar-based pacemaker model is proposed that is integrated with a fractional-order proportional integral derivative (FOPID) controller and a Hybridized Chaotic multiverse Krill Herd-based Backtracking Search Strategy (HCMKH-BS2) to enhance power generation for pacemaker operation. Our approach considers the impact of partial shading conditions on solar power. To mitigate these conditions, a FOPID controller with an HCMKH-BS2 model is developed which also addresses environmental issues through the adoption of a DC-DC converter. The gain parameters of the FOPID controller are determined using the proposed HCMKH-BS2 algorithm. The proposed technique is implemented to evaluate its performance using various measures in terms of duty cycle, convergence analysis, and power. The performance validation is performed based on the analyses of constant irradiance and changed irradiance. The proposed method achieved a fitness value of 0.01 from the convergence analysis and the duty cycle of 0.48D. These results demonstrate the superiority of our proposed technique over previous methods, highlighting its potential for enhancing the performance of solar-based cardiac pacemakers.

Development of renewable energy fed three-level hybrid active filter for EV charging station load using Jaya grey wolf optimization

This work develops a hybrid active power filter (HAPF) in this article to operate in conjunction with the energy storage system (ESS), wind power generation system (WPGS), and solar energy system (SES). It employs three level shunt voltage source converters (VSC) connected to the DC-bus. Optimization of the gain values of the fractional-order proportional integral derivative controller (FOPIDC) and parameter values of the HAPF is achieved using the Jaya grey wolf hybrid algorithm (GWJA). The primary objectives of this study, aimed at enhancing power quality (PQ), include: (1) ensuring swift stabilization of DC link capacitor voltage (DCLCV); (2) reducing harmonics and improving power factor (PF); (3) maintaining satisfactory performance under different combinations of loads like EV charging load, non linear load and solar irradiation conditions. The proposed controller's performance is evaluated through three test scenarios featuring different load configurations and irradiation levels. Additionally, the HAPF is subjected to design using other optimization algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), and ant colony optimization (ACO) to assess their respective contributions to PQ improvement.

Jellyfish Search Optimized Gated Recurrent Unit Based FOPID/PID for Enhanced Automatic Voltage Regulator

The most essential mechanism for regulation in power systems is the Automatic Voltage Regulator (AVR) device, which maintains generator terminal voltage within predefined parameters. This research paper introduces an innovative approach to enhance AVR system performance through the ideal setting for a fractional-order PID (FOPID) controller that leverages Bidirectional Gate Recurrent Unit (BiGRU)-based deep learning techniques in conjunction with the Jellyfish Search Optimization (JSO) algorithm. To enhance flexibility and precision in control, the conventional proportional integral derivative (PID) controller is replaced with a FOPID controller, whose parameters are optimized by means of the JSO algorithm. The effectiveness of the proposed Jellyfish Search Optimization-based most advanced controllers (JSO-FOPID/PID) is compared with the existing FOPID controller implemented using the Seagull Optimization Algorithm (SOA-FOPID). Comprehensive analyses, including transient time, robustness, stability, and convergence analysis, are conducted subject to applying both stable and alternating load situations to validate the proposed approach. Experimental validation is performed using the MATLAB R2022a application with FOMCON tools and a laboratory prototype for testing. The simulations and experiments demonstrate that the projected AVR consistently delivers optimum dynamic responses and enhances overall stability when compared to existing methods, underscoring its efficacy in voltage regulation and power system control.

Improved Decentralized Fractional-Order Control of Higher-Order Systems Using Modified Flower Pollination Optimization

Due to increased complexity and interactions between various subsystems, higher-order MIMO systems present difficulties in terms of stability and control performance. This study effort provides a novel, all-encompassing method for creating a decentralized fractional-order control technique for higher-order systems. Given the greater number of variables that needed to be optimized for fractional order control in higher-order, multi-input, multi-output systems, the modified flower pollination optimization algorithm (MFPOA) optimization technique was chosen due to its rapid convergence speed and minimal computational effort. The goal of the design is to improve control performance. Maximum overshoot (Mp), rising time (tr), and settling time (ts) are the performance factors taken into consideration. The MFPOA approach is used to improve the settings of the proposed decentralized fractional-order proportional-integral-derivative (FOPID) controller. By exploring the parameter space and converging on the best controller settings, the MFPOA examines the parameter space and satisfies the imposed constraints by maintaining system stability. To evaluate the suggested approach, simulation studies on two systems are carried out. The results show that by decreasing the loop interactions between subsystems with improved stability, the decentralized control with the MFPOA-based FOPID controller provides better control performance.

Pelican-FOPID Based DSTATCOM for real-time load compensation and harmonics mitigation in three-phase distribution system

Power quality (PQ) explores the issues resulting from current and voltage deviations. Non-sinusoidal currents were drawn from the electric grid by the nonlinear loads. These non-sinusoidal currents contain harmonics and reactive power that lower the system's overall power quality. Distribution Static Compensator (DSTATCOM) emerged as a promising compensator to provide solution for all PQ issues. Yet the controlling strategy of this compensator was still complex to design. Here, an optimization-based Fractional Order Proportional Integral Derivative (FOPID) was introduced to manage the DSTATCOM process to improve PQ in a standard bus system. The optimal problem of FOPID controller was solved through the use of novel optimization approach. The DSTATCOM with FOPID was linked to the weak bus system. The pulse-signal of DSTATCOM was done using the optimal controller, which analyzes the error value of reference voltage and bus voltage to generate-pulses. The proposed model was designed, and the performance was analyzed under two cases, like IEEE 33 bus system and IEEE 13 bus system. The proposed optimal controller-based DSTATCOM performance was validated under various conditions such as interruption, swell, harmonics and sag. The optimal controller offered Total Harmonic Distortion (THD) value at sag, swell, and interruption period was 0.46%, 1.36% and 0.46% in IEEE 13 bus system, and 1.79%, 2.10% and 2.67% THD in IEEE 33 bus system. Moreover, the issues mitigation performance was compared to another present approach. The validated outcome demonstrates the proposed model provides a good mitigation performance in all PQ issues conditions, so it was well fit for real-time implementation.

System Identification and Fractional-Order Proportional–Integral–Derivative Control of a Distributed Piping System

The vibration of piping systems is one of the most important causes of accelerated equipment wear and reduced work efficiency and safety. In this study, an active vibration control method based on a fractional-order proportional–integral–derivative (PID) controller was proposed to suppress pipeline vibration and reduce pipeline damage. First, a mathematical model of the distributed piping system was established using the finite element analysis method, and the characteristics of the distributed piping system were studied effectively. Further, the time-frequency domain parameter identification method was used to realise the system identification of the cross-point vibration transfer function between the brake and sensor, and the particle swarm optimisation algorithm was utilised to further optimise the transfer function parameters to improve the system identification accuracy. Therefore, a fractional-order PID controller was designed using the D-decomposition method, and the optimal controller parameters were obtained. The experimental and numerical simulation results show that the improved system identification algorithm can significantly improve modelling accuracy. In addition, the designed fractional-order PID controller can effectively reduce the system’s overshoot, oscillation time, and adjustment time, thereby reducing the vibration response of piping systems.

Black-hole optimisation algorithm with FOPID-based automation intelligence photovoltaic system for voltage and power issues

ABSTRACT The article discusses the challenges related to voltage and power management in automated intelligent photovoltaic (PV) systems. It suggests that Fractional Order Proportional Integral Derivative (FOPID) controllers can help address these challenges effectively. The research aims to create a highly adaptable and precise automated intelligent PV system that focuses on managing voltage and power issues. It introduces a novel approach using the Black Hole Optimization (BHO) algorithm and leverages the advantages of FOPID controllers for automation. The study also considers thermal models for batteries within the automated intelligent PV system and explores different options to handle voltage and power issues stemming from PV panels. It involves fine-tuning 15 parameters using the BHO algorithm and concludes that one configuration (Instance 1) is preferable due to its superior accuracy and scalability. This choice is supported by objective validation. In essence, your abstract is about improving the performance and automation of PV systems, particularly in dealing with voltage and power challenges, through the application of FOPID controllers and the innovative BHO algorithm.

Analysis of Networked Control System With Integer-order and Fractional-order PID Controllers

Analysis of Networked Control System With Integer-order and Fractional-order PID Controllers

Achieving improved stability for automatic voltage regulation with fractional-order PID plus double-derivative controller and mountain gazelle optimizer

Achieving improved stability for automatic voltage regulation with fractional-order PID plus double-derivative controller and mountain gazelle optimizer