Fractional Order PID Controller Research Articles

Supporting load frequency control process by using adaptive model reference virtual inertia controller when connecting renewable energy plants

Virtual inertia control can be used in combination with conventional load frequency controllers to support the system's inertia against the attenuation caused by renewables. As fractional-order controllers add more degrees of freedom, leading to a better response and improved controller robustness, this work proposes the implementation of a developed fractional-order model reference adaptive virtual inertia controller when integrating renewables in combination with fractional-order ID-P with filter controller as secondary controllers. To validate the introduced controllers, their results have been compared to those of using integer and fractional-order PID controllers as secondary controllers, in combination with adaptive and fixed parameters virtual inertia controllers. The Artificial Rabbits heuristic algorithm is used for the purpose of tuning secondary controllers and fixed parameters virtual inertia controllers. The proposed combination of adaptive model reference virtual inertia control with fractional-order ID-P with a filter achieves the best response among all the studied combinations. Using the proposed combination shows a relative percentage improvement in the cost function value of 26% to 160% compared to all the studied combinations. Additionally, the proposed combination shows a maximum frequency overshoot value of 0.04 Hz and a minimum undershoot value of -0.06 Hz.

An adaptive fractional controller design for automatic voltage regulator system: sigmoid-based fractional-order PID controller

AbstractThe primary objective of a power system is to provide safe and reliable electrical energy to consumers. This objective is achieved by maintaining the stability of the power system, a multifaceted concept that can be divided into three distinct classes. The focus of this study is on one of these classes, voltage stability. A critical component in maintaining voltage stability is the automatic voltage regulator (AVR) system of synchronous generators. In this paper, a novel control method, the sigmoid-based fractional-order PID (SFOPID), is introduced with the aim of improving the dynamic response and the robustness of the AVR system. The dandelion optimizer (DO), a successful optimization algorithm, is used to optimize the parameters of the proposed SFOPID control strategy. The optimization process for the DO-SFOPID control strategy includes a variety of objective functions, including error-based metrics such as integral of absolute error, integral of squared error, integral of time absolute error, and integral of time squared error, in addition to the user-defined Zwee Lee Gaing’s metric. The effectiveness of the DO-SFOPID control technique on the AVR system has been rigorously investigated through a series of tests and analyses, including aspects such as time domain, robustness, frequency domain, and evaluation of nonlinearity effects. The simulation results are compared between the proposed DO-SFOPID control technique and the fractional-order PID (FOPID) and sigmoid-based PID (SPID) control techniques, both of which have been tuned using different metaheuristic algorithms that have gained significant recognition in recent years. As a result of these comparative analyses, the superiority of the DO-SFOPID control technique is confirmed as it shows an improved performance with respect to the other control techniques. Furthermore, the performance of the proposed DO-SFOPID control technique is validated within an experimental setup for the AVR system. The simulation results show that the proposed DO-SFOPID control technique is highly successful in terms of stability and robustness. In summary, this study provides comprehensive evidence supporting the effectiveness and superiority of the DO-SFOPID control technique on the AVR system through both simulation and experimental results.

Correction to: Selection and Evaluation of FOPID Criteria for the X-15 Adaptive Flight Control System (AFCS) via Lyapunov Candidates: Optimizing Trade-Offs and Critical Values Using Optimization Algorithms

Recently, there has been a growing interest among academics worldwide in studying flight control systems. The advancement of tracking technologies, such as the X-15 adaptive flight control system developed at NASA (National Aeronautics and Space Administration), has sparked significant exploration efforts by scientists. The vast availability of aerial resources further contributes to the importance of studying adaptive flight control systems (AFCS). The successful operation of AFCS relies on effectively managing the three fundamental motions: pitch, roll, and yaw. Therefore, scientists have been diligently working on developing optimization algorithms and models to assist AFCS in achieving optimal gains during motion. However, in real-world scenarios, each motion requires its own set of criteria, which presents several challenges. Firstly, there are multiple criteria available for selecting appropriate optimization values for each motion. Secondly, the relative importance of these criteria influences the selection process. Thirdly, there is a trade-off between the performance of the criteria within a single optimization case and across different cases. Lastly, determining the critical value of the criteria poses another obstacle. Consequently, evaluating and selecting optimum methods for AFCS trajectory controls becomes a complex operation. To address the need for optimizing AFCS for various maneuvers, this study proposes a new selection process. The suggested approach involves utilizing black hole optimization (BHO), Jaya optimization algorithm (JOA), and sunflower optimization (SFO) as methods for detecting and correcting trajectories in adaptive flight control systems. These methods aim to determine the best launch of missiles from the AFCS based on the coordinate location for both long and short distances. Additionally, the methods determine the optimal gains for the FOPID (fractional order proportional integral derivative) controller and enhance protection against enemy attacks. The research framework consists of two parts. The first part focuses on improving the FOPID motion gains by employing optimization algorithms (BHO, JOA, and SFO) that are evaluated based on the FOPID criteria. Lower significant weighting values of the optimization algorithms demonstrate the best missile launching in a cosine wave trajectory within AFCS, while higher significant values indicate the best missile launching in a sine wave trajectory within AFCS. The FOPID controller criteria, including Kp_pitch, Ki_roll, Kd_yaw, λ_pitch, and µ_yaw, are considered in all situations. Furthermore, the study reports the best weights obtained for the "Kp_pitch" criterion across the motions as follows: (0.8147, 66.7190, and 54.4716). For the "Ki_roll" criterion, the best weights are (0.0975, 64.4938, and 64.7311), and for "Kd_yaw" the weights are (0.1576, 35.2811, and 54.3886). The results of the selection process by the BHO, JOA, and SFO algorithms also include λ_pitch (0.1419, 40.0791, and 72.1047) and µ_yaw (0.6557, 13.5752, and 52.2495). To ensure the validity of the proposed research framework, a systematic evaluation and precise analysis were conducted.

Fractional-Order PIλDμ Control to Enhance the Driving Smoothness of Active Vehicle Suspension in Electric Vehicles

The suspension system is a crucial part of an electric vehicle, which directly affects its handling performance, driving comfort, and driving safety. The dynamics of the 8-DoF full-vehicle suspension with seat active control are established based on rigid-body dynamics, and the time-domain stochastic excitation model of four tires is constructed by the filtered white noise method. The suspension dynamics model and road surface model are constructed on the Matlab/Simulink simulation software platform, and the simulation study of the dynamic characteristics of active suspension based on the fractional-order PIλDμ control strategy is carried out. The three performance indicators of acceleration, suspension dynamic deflection, and tire dynamic displacement are selected to construct the fitness function of the genetic algorithm, and the structural parameters of the fractional-order PIλDμ controller are optimized using the genetic algorithm. The control effect of the optimized fractional-order PIλDμ controller based on the genetic algorithm is analyzed by comparing the integer-order PID control suspension and passive suspension. The simulation results show that for optimized fractional-order PID control suspension, compared with passive suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions reaches over 25%, the average optimization of suspension dynamic deflection exceeds 30%, and the average optimization of tire dynamic displacement is 5%. However, compared to the integer-order PID control suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions decreased by 5%, the average optimization of suspension dynamic deflection increased by 3%, and the average optimization of tire dynamic displacement increased by 2%.

Enhanced FOPID Controller Based Cascaded Inverter for Grid-Connected Photovoltaic System

An enhanced controller is proposed to investigate grid-connected photovoltaic systems employing cascaded two-level inverters. The primary focus is on optimizing power output, achieved through the development, modeling, and testing of photovoltaic systems using the suggested upgraded controller. This advanced controller, specifically a Fractional Order PID (FOPID) controller, incorporates the Ant-Lion Optimizer (ALO) algorithm for enhanced performance compared to conventional controllers. The FOPID controller’s reliability is emphasized, and further improvements are pursued by optimizing gain parameters through the prescribed method. Power supply under both schemes is examined, and the controller’s performance in extracting maximum power under specified operating conditions is deemed satisfactory. To validate the proposed approach, practical implementation is conducted using the MATLAB/Simulink platform. The effectiveness of proposed and conventional methodologies for analyzing the id and iq currents is assessed. A comparison is drawn between the suggested approach and current methods such as the base controller, GSA, and ABC methodologies. In comparison to the existing methods, the suggested FOPID controller demonstrates superior performance in maintaining the DC link voltage, achieving an efficiency of 94%, while the GSA method reaches 91.5%, the ABC method achieves 91%, and the base controller achieves 90%.

Designing Heuristic-Based Tuners for Fractional-Order PID Controllers in Automatic Voltage Regulator Systems Using a Hyper-Heuristic Approach

This work introduces an alternative approach for developing a customized Metaheuristic (MH) tailored for tuning a Fractional-Order Proportional-Integral-Derivative (FOPID) controller within an Automatic Voltage Regulator (AVR) system. Leveraging an Automated Algorithm Design (AAD) methodology, our strategy generates MHs by utilizing a population-based Search Operator (SO) domain, thus minimizing human-induced bias. This approach eliminates the need for manual coding or the daunting task of selecting an optimal algorithm from a vast collection of the current literature. The devised MH consists of two distinct SOs: a dynamic swarm perturbator succeeded by a Metropolis-type selector and a genetic crossover perturbator, followed by another Metropolis-type selector. This MH fine-tunes the FOPID controller’s parameters, aiming to enhance control performance by reducing overshoot, rise time, and settling time. Our research includes a comparative analysis with similar studies, revealing that our tailored MH significantly improves the FOPID controller’s speed by 1.69 times while virtually eliminating overshoot. Plus, we assess the tuned FOPID controller’s resilience against internal disturbances within AVR subsystems. The study also explores two facets of control performance: the impact of fractional orders on conventional PID controller efficiency and the delineating of a confidence region for stable and satisfactory AVR operation. This work’s main contributions are introducing an innovative method for deriving efficient MHs in electrical engineering and control systems and demonstrating the substantial benefits of precise controller tuning, as evidenced by the superior performance of our customized MH compared to existing solutions.

Design of fractional MOIF and MOPIF controller using PSO algorithm for the stabilization of an inverted pendulum‐cart system

AbstractThe topic of this paper is the design of two fractional order schemes, based on a state feedback for linear integer order system. In the first one of the state feedback is associated with a fractional order integral () controller. In the second structure the state feedback is associated with a fractional order proportional integral () controller. With such controllers, the closed loop system with state feedback described by the state equations splits in n‐subsystems with different fractional orders derivatives of the state variable. In order to find the optimal parameters value of both controllers () and (), a multi‐objective particle swarm optimization algorithm is used, with the integral of absolute error, the overshoot , the Buslowicz stability criterion are considered as objective functions. The multi‐objective integral fractional order controller and the multi‐objective proportional integral fractional order controller are applied to stabilize the inverted pendulum‐cart system (IP‐C), and their performance is compared to the fractional order controller. The simulation results of these innovative controllers are also compared with those obtained by conventional proportional–integral–derivative and fractional order proportional–integral–derivative controllers. The robustness of the proposed controllers against disturbances is investigated through simulation runs, considering the non‐linear model of the IP‐C system. The obtained results demonstrate that our approach not only leads to high effectiveness but also showcases remarkable robustness, supported by both simulation and experimental results.

Analysis, Performance Improvement and Control Design of Heliostat System Based on Fractional Order PID Controller

Analysis, Performance Improvement and Control Design of Heliostat System Based on Fractional Order PID Controller

Modified fractional order PID structure for non‐integer model bioreactor control

AbstractTemperature control for fermentation is crucial as it directly affects microorganism growth, productivity, and metabolic activity. This work proposes a modified fractional order proportional‐integral‐derivative (FOPID‐DF) controller that incorporates the system model in the control loop configuration utilizing a differential filter for precise temperature control within a narrow operating range. PID, fractional order PID (FOPID), modified fractional order PID (MFOPID), and fractional order internal model control (IMC) controllers were also designed for comparative analysis. The simulation results demonstrated that the proposed FOPID‐DF controller outperforms the other designed controllers, shown by a 22.33% reduction in integral absolute error (IAE) and a 29.06% decrease in integral square error (ISE) compared to the FOPID controller and various other improved performance indicators. Parameter variation and noise analysis highlighted the ability of the controller to maintain stability and performance under changing conditions. The simulation outcomes suggested that the FOPID‐DF controller excels in temperature control, ensuring optimal microorganism growth and metabolic activity.

An Analysis on Integration of Solar and Wind Power into a Single-Phase Grid with an Optimal Parameterized Fractional-Order Pid Controller

Because of the complimentary nature of solar and wind electricity, hybrid solar-wind power systems are the most effective renewable energy sources. Weather conditions have a significant impact on the amount of power that can be generated by wind and solar photovoltaic systems. Their intermittent nature causes output fluctuations. The purpose of this research is to offer a technique for a hybrid wind–solar power plant that makes the most efficient contribution of renewable energy resources and is backed by technology that allows batteries to store energy. The fact that solar and wind power display power profiles that are complimentary was the driving force for the construction of the hybrid solar–wind power system.

Surrogate Optimal Fractional Control for Constrained Operational Service of UAV Systems

In the expeditiously evolving discipline of autonomous aerial robotics, the efficiency and precision of drone control deliveries have become predominant. Different control strategies for UAV systems have been thoroughly investigated, yet PID controllers still receive significant consideration at various levels in the control loop. Although fractional-order PID controllers (FOPID) have greater flexibility than integer-order PID (IOPID) controllers, they are approached with caution and hesitance. This is due to the fact that FOPID controllers are more computationally intensive to tune, as well as being more challenging to implement accurately in real time. In this paper, we address this problem by developing and implementing a surrogate-based analysis and optimization (SBAO) of a relatively high-order approximation of FOPID controllers. The proposed approach was verified through two case studies; a simulation quadrotor benchmark model for waypoint navigation, and a real-time twin-rotor copter system. The obtained results validated and favored the SBAO approach over other classical heuristic methods for IOPID and FOPID.

Optimizing blood glucose regulation in type 1 diabetes: A fractional order controller approach

This study presents the design and implementation of a Fractional Order Proportional, Integral, and Derivative (FOPID) controller intended for the regulation of blood glucose levels in individuals with type 1 diabetes mellitus (T1DM). The efficacy of this controller is evaluated through its application to a nonlinear Stolwijk–Hardy model simulating T1DM patients, accounting for a range of physiological conditions. Utilizing a genetic algorithm, the parameters of the FOPID controller are fine-tuned. By conducting a comparative analysis with previously established control algorithms, the performance of the proposed controller is validated, demonstrating its superior performance. The results underscore the significant improvements achieved by the proposed controller in maintaining blood glucose concentrations within safe thresholds, particularly in scenarios involving disruptions due to meals.

Design and performance evaluation of a novel fractional order PID control strategy for vehicle semi-active suspension

Design and performance evaluation of a novel fractional order PID control strategy for vehicle semi-active suspension

Momentum Adaption and Metalearning-Based DVR With Optimized Gains of Fractional-Order PID Controller

Momentum Adaption and Metalearning-Based DVR With Optimized Gains of Fractional-Order PID Controller

An Analysis on Integration of Solar and Wind Power into A Single-Phase Grid with an Optimal Parameterized Fractional-Order Pid Controller

Because of the complimentary nature of solar and wind electricity, hybrid solar-wind power systems are the most effective renewable energy sources. Weather conditions have a significant impact on the amount of power that can be generated by wind and solar photovoltaic systems. Their intermittent nature causes output fluctuations. The purpose of this research is to offer a technique for a hybrid wind–solar power plant that makes the most efficient contribution of renewable energy resources and is backed by technology that allows batteries to store energy. The fact that solar and wind power display power profiles that are complimentary was the driving force for the construction of the hybrid solar–wind power system.

Improvisation of artificial hummingbird algorithm through incorporation of chaos theory in intelligent optimization of fractional order PID controller tuning

Improvisation of artificial hummingbird algorithm through incorporation of chaos theory in intelligent optimization of fractional order PID controller tuning

Joint contribution of RTEM and AGC system for frequency stabilisation in renewable energy integrated power system

AbstractIncreasing penetration of variable renewable generations will diminish system inertia thereby degrading the conventional frequency regulation capability. As a result, maintaining frequency stability will be more and more challenging with traditional approaches. Even though renewable sources integration would jeopardise the grid stability, it also presents several opportunities as well. For example, converter‐interfaced generators can bid in real‐time electricity markets (RTEM) and provide short‐time dispatch to minimise load‐generation mismatch. In this paper, an integrated approach that accommodates discrete automatic generation control (AGC) system with a regulation mileage framework and RTEM model to balance generation and consumption is proposed. The RTEM model is assumed to have a five‐minute dispatch trading interval which is to some extent comparable to the discrete AGC system. Furthermore, a fractional order PID (FOPID) controller is equipped in the AGC system whose parameters are tuned using a novel metaheuristic‐based optimisation called Lichtenberg Algorithm (LA). The proposed framework is tested in a three‐area system under several operating conditions to reveal the improvement in the dynamic performance of the system. The objective function is also incorporated with mileage payment that allows a fair compensation rule for all the units.

A Comparative performance evaluation of a complex-order PI controller for DC–DC converters

Switched-mode DC–DC converters are required to maintain constant output under uncertainties and variations in input voltage and load. The controller’s robustness is crucial in such systems, and hence various controllers have been proposed in the past few decades for DC–DC converter control. Fractional order PID controllers have attracted the attention of researchers due to their robustness and flexibility in control of power converters. Such controllers use fractional orders of integration and differentiation. Complex order controllers are the generalized form of the fractional order PID controllers and have complex orders of integration and differentiation. These controllers are very robust in the control of nonlinear systems with time-varying parameters. But complex order controllers have been very sparingly used in power electronic control. This paper proposes a complex order PI controller with a complex order integrator for controlling DC–DC buck and boost converters. The complex PID controller has four parameters to be tuned. The complex order PI controller is designed by optimization using the metaheuristic Cohort Intelligence algorithm. The results are compared with that of a fractional-order PID controller. It was observed that the complex PI controller gave a better response than the FOPID controller and was more robust to parameter variations.

Wykorzystanie rachunku niecałkowitego rzędu w sterowaniu suwnicą 3D

The 3D crane is an object used in various industries. From a control point of view, it is a dynamic, non-linear and multidimensional system. In this paper, two control systems are designed: with a classical PID controller and with a fractional-order PID controller. A comparative analysis of the designed control systems is presented.

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.