Fractional Order PID Controller Research Articles

Enhanced decentralised fractional-order control using tree seed optimisation and singular value analysis

Higher-order multi-input multi-output systems pose challenges in terms of stability and control performance due to increased complexity and interactions between multiple subsystems. Hence, this research work proposes a novel comprehensive approach to design a decentralised fractional order control strategy for higher-order systems using tree seed algorithm. The design focuses on enhancing control performance by imposing constraints on performance indices – the integral of absolute error and closed-loop amplitude ratio. Further, this work incorporates stability analysis through the singular values of the sensitivity function. The proposed decentralised fractional-order proportional-integral-derivative (FOPID) controller parameters are optimised using the tree seed algorithm. Besides, the stability is examined using the singular values of the sensitivity function. The tree seed algorithm explores the parameter space and converges to optimal controller settings that satisfy the imposed constraints by ensuring system stability. Simulation studies are conducted on various higher-order systems to analyse the proposed approach. The findings demonstrate that the decentralised control with tree seed algorithm-based FOPID controller achieves improved control performance by reducing the loop interactions among subsystems with enhanced stability. Furthermore, robustness is ensured by considering output uncertainty and parameter variations.

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.

ANFIS-based FOPID controller to enhanced stability of cascaded converter for electric vehicle (EV) charger

In an electric vehicle (EV) charger system, a two-stage conversion process is integrated and cascaded with a voltage source converter (VSC) and a Dual active bridge converter (DAB). These impedances VSC outputs impedance (ZoutVSC(s)) and DAB have input impedance (ZinDAB(s)) interact, leading to voltage fluctuation and power loss. To address the cascaded converter’s impedance interaction, the modified controller that combines an adaptive Neuro-fuzzy inference system (ANFIS) based fractional order proportional integral derivative (FOPID) controller is used with effective active damping (AD). The modified controller (ANFIS + FOPID + AD) uses ANFIS’s skills to capture and predict the system’s nonlinear behaviour, using its trained data to guide the FOPID’s parameter. The presence of AD ensures the sorting out of impedance interaction problems. Compared to the PID controller, the FOPID controller includes two more degrees of freedom and offers superior adaptability and performance. The effectiveness of the modified controller is tested via frequency response analysis and time domain simulations. Time domain simulations underscore the advantage of the modified controller (ANFIS + FOPID + AD), revealing a remarkable 30% settling time and a 25% overshoot compared to the (FOPID + AD) controller. It is better regarding flexibility, faster response time, and improved system stability. The system performance has been validated and compared by simulation process and HIL technique OPAL RT OP44512.

Nature‐ınspired algorithms for optimizing fractional order PID controllers in time‐delayed systems

AbstractTime‐delayed systems frequently appear, especially in sectors such as fluid flow processes, chemical procedures, and the food industry. This paper addresses the optimization of parameters for a fractional order PID (FOPID) controller, which is used to control a time‐delayed system, using five distinct algorithms inspired by nature. These algorithms are NewBAT, Cuckoo search (CS), Firefly (FF), Gray Wolf Optimizer (GWO), and Whale optimization algorithm (WOA). The FOPID controller parameters, namely KP, KI, KD, λ and μ, have been optimized using these algorithms. During the optimization process, the integral of the time absolute error (ITAE) was considered as the primary measurement criterion. In addition to this value, the maximum overshoot, settling time, time to reach the maximum value, and error values were examined. Simulations conducted with the obtained parameters tested the system's resilience to disturbances introduced at the output, and the controller responses were also evaluated during these tests. The reactions of the determined parameters to different reference inputs were analyzed, and the results are presented in graphs and tables. The efficiency and reliability of the optimization algorithms were substantiated by comprehensive statistical analyses. These analyses play a critical role in algorithm selection and objective evaluation of the results. Simulation studies were conducted in the Matlab and Simulink environments. The FOMCON Toolbox was used for fractional‐order processes.

A novel opposition-based hybrid cooperation search algorithm with Nelder–Mead for tuning of FOPID-controlled buck converter

This paper introduces a novel metaheuristic algorithm named the opposition-based cooperation search algorithm with Nelder–Mead (OCSANM). This enhanced algorithm builds upon the cooperation search algorithm (CSA) by incorporating opposition-based learning (OBL) and the Nelder–Mead simplex search method. The primary application of this algorithm is the design of a fractional-order proportional–integral–derivative (FOPID) controller for a buck converter system. A comprehensive evaluation is conducted using statistical boxplot analysis, nonparametric statistical tests and convergence response comparisons to assess the algorithm’s performance and confirm its superiority over CSA. Furthermore, the FOPID-controlled buck converter system based on OCSANM is compared with two top-performing algorithms: one using a hybridized approach of Lévy flight distribution with simulated annealing (LFDSA) and the other employing the improved hunger games search (IHGS) algorithm. This comparison encompasses transient and frequency responses, performance indices and robustness analysis. The results reveal the notable advantages of the proposed OCSANM-based system, including 25.8% and 8.7% faster rise times, 26% and 8.8% faster settling times compared with the best-performing approaches, namely LFDSA and IHGS, respectively. In addition, the OCSANM-based system exhibits a 34.7% and 9.6% wider bandwidth than the existing approaches-based systems. Incorporating voltage and current responses of the buck converter’s switched circuit with the OCSANM-based FOPID controller further underscores the algorithm’s effectiveness. To provide a comprehensive assessment, the paper also compares the proposed approach’s time and frequency domain responses with those of 17 other state-of-the-art approaches attempting to control buck converter systems similarly. These findings affirm the effectiveness of the OCSANM in designing FOPID controllers for buck converter systems.

Data-Driven Robust Servo Tuning Method Using Fractional-Order PID Controller

This paper proposes a data-driven method using a Fractional-Order Proportional-Integral-Derivative (FOPID) controller. The proposed method simultaneously obtains FOPID controller and reference model parameters to achieve tracking performance and specified robust stability from only one-shot closed-loop input-output data. The proposed control law is designed by solving an optimization problem, subject to the constraint condition of using the maximum value of the sensitivity function. Therefore, the proposed method provides trade-off design between tracking performance for the reference input and robust stability by selecting robust stability. By comparing numerical example results obtained for FOPID and integer-order controllers, it is shown that the use of the FOPID controller is effective in improving tracking performance for reference output.

Robust Fractional Order PID Controller Coupled with a Nonlinear Filtered Smith Predictor for Solar Collector Fields

This work introduces a Fractional Order PID (FOPID) controller associated with a nonlinear Filtered Smith Predictor (FSP) to control a Solar Collector Field (SCF) system. The combined approach enhances the control performance by decoupling model uncertainties. First, the FOPID addresses linear model uncertainties through optimal robust design across the operational conditions, while the FSP compensator adeptly manages the system’s varying time delays. Rigorous tuning in the frequency domain considering closed-loop, robustness, and disturbance rejection performances is developed using a bi-level optimization approach to obtain the FOPID control parameters. Experimental results of the FOPID + nonlinear FSP demonstrate low rise time for reference tracking and robust stability across several operating conditions, even in the face of high-frequency disturbances in the solar irradiance due to passing clouds. Moreover, the nonlinear FSP effectively handles variations in time delays undergone by the water flow variation during the experiment. The achieved outcomes of the overall control structure, comprising the FOPID + FSP, demonstrate a promising approach for SCF system control, obtaining robust behavior in the presence of model uncertainties and disturbances while offering satisfactory reference tracking capabilities across an extensive range of plant operations.

Optimising liquid level in two tank spherical interacting system with fractional order PID control via hybrid POA-RERNN approach

Optimising liquid level in two tank spherical interacting system with fractional order PID control via hybrid POA-RERNN approach

Auto-Tuning Software Tool for Inverse Response Model Robust Tuning of 1-DoF PID and FOPID Controllers

The main objective of this work is to present a software tool that allows to perform the tuning process of PID and Fractional Order PID controllers in an automated method. The tool tunes 1DoF PID and FOPID controllers for a controlled process with a inverse response second-order plus dead time model. This tuning is based on the Inverse Response Model Robust Tuning (IRM-RoT) rule, which aims to achieve optimal control system performance while ensuring a target robustness. Additionally, the tool measures the performance obtained from the control system, as well as the robustness achieved, and displays the control signal obtained by implementing the tuned controller. The examples used show the main characteristics of the tool and conclude that it can be a very useful contribution for educational purposes in fields such as electrical engineering.

Design and analysis of improved mountain gazelle optimization tuned PID and FOPID controllers for PV MPPT system

The solar photovoltaic (PV)-based Maximum Power Point Tracking (MPPT) systems have gained popularity in recent times. This work proposes the improvement and implementation of a newly introduced optimization technique, the Improved Mountain Gazelle Optimization (IMGO) algorithm, for tuning the Fractional Order Proportional-Integral-Derivative (FOPID) and Proportional-Integral-Derivative (PID) controllers for the MPPT control strategy. The performances of the controllers were evaluated with reference to error criteria and settling time of the response. The performance parameters mentioned above are compared with those of PID and FOPID controllers tuned using Genetic Algorithm (GA) and Grey-Wolf Optimization (GWO) algorithms. The simulation study was carried out in the MATLAB/SIMULINK environment. The analysis found that the FOPID controller tuned using the Improved Mountain Gazelle Optimization algorithm provides better results in terms of settling time and error when compared to the PID controller.

Performance Comparison of Robust PID and FOPID for an Inverse Response Process Model

This paper provides a quantitative comparison between the performance provided by the use of Proportional-Integral-Derivative (PID) and Fractional-Order Proportional-Integral-Derivative (FOPID) controllers for the control of second-order processes with inverse response based on the integrated absolute value of the error (IAE index). These controllers are designed in order to achieve an optimal performance in both, set-point tracking task and regulatory control operation, while robustness considerations are taken into account, and, therefore, also the trade-of between robustness and performance of the control system is considered. The performance comparison and example, show that FOPID controllers achieve higher performance that PID controllers mainly for processes with larger normalized dead times as well when more robustness should be considered in the closed-loop system. These advantages are due to the use of the fractional parameter µ associated to the derivative part of the FOPID controller.

Hybrid controller with neural network PID/FOPID operations for two-link rigid robot manipulator based on the zebra optimization algorithm.

The performance of the robotic manipulator is negatively impacted by outside disturbances and uncertain parameters. The system's variables are also highly coupled, complex, and nonlinear, indicating that it is a multi-input, multi-output system. Therefore, it is necessary to develop a controller that can control the variables in the system in order to handle these complications. This work proposes six control structures based on neural networks (NNs) with proportional integral derivative (PID) and fractional-order PID (FOPID) controllers to operate a 2-link rigid robot manipulator (2-LRRM) for trajectory tracking. These are named as set-point-weighted PID (W-PID), set-point weighted FOPID (W-FOPID), recurrent neural network (RNN)-like PID (RNNPID), RNN-like FOPID (RNN-FOPID), NN+PID, and NN+FOPID controllers. The zebra optimization algorithm (ZOA) was used to adjust the parameters of the proposed controllers while reducing the integral-time-square error (ITSE). A new objective function was proposed for tuning to generate controllers with minimal chattering in the control signal. After implementing the proposed controller designs, a comparative robustness study was conducted among these controllers by altering the initial conditions, disturbances, and model uncertainties. The simulation results demonstrate that the NN+FOPID controller has the best trajectory tracking performance with the minimum ITSE and best robustness against changes in the initial states, external disturbances, and parameter uncertainties compared to the other controllers.

Robust FOPID Control of an After-Cooler Heat Exchanger with TES

In this paper the temperature control of an after-cooler heat exchanger (AHX) with Thermal Energy Storage (TES) is considered. The AHX can be modelled as a nonlinear system whose gain strongly depends on the operating point. This can cause the reduction of the phase margin which translates into the risk of excessive temperature overshoots. The generalized isodamping approach has been applied to design a fractional-order robust PID controller that guarantees the invariance of the phase margin despite the gain variations. Simulation results performed on a realistic model of the system demonstrate the effectiveness of the proposed design approach.

PID/FOPID Tuning Rule Based on a Second Order Inverse Response Process Model with Robustness Considerations

This paper deals with the design of a proportional-integral-derivative (PID) and fractional-order proportional-integral-derivative (FOPID) controller tuning rule for second-order controlled processes with inverse response. The design of the rules takes into account specific levels of robustness and performance for both load disturbance rejection and set-point tracking tasks. In the first step, the optimal parameters for both controllers are obtained from optimizations that seek to minimize the error in both control modes while maintaining the robustness constraint. Subsequently, fitting functions to the optimal parameters are sought to capture their behavior with the possibility of finding optimal parameters with the tuning rule designed between certain ranges of the model parameters. For FOPID and PID controllers, the rule IRM-RoT (Inverse Response Model Robust Tuning) have been developed. The performance of the controllers was compared using examples, and the results showed that fractional order controllers provide a novel solution for inverse response dynamics in process control.

Fractional Order PID Control of Propofol Dosage and Optimization in Lean and Obese Patients

This paper outlines the design of a fractional-order proportional–integral–derivative controller for regulating the induction phase of Propofol infusion in lean and obese patients. The obtained controller is implemented within the pharmacokinetic-pharmacodynamic model and the nonlinear Hill function to conduct closed-loop simulations. The latter are employed using a dataset comprising 24 patients to obtain clinical evaluation results. The design of the controller relies on a generic second-order plus dead time approximation model, which characterizes interpatient variability in response to Propofol infusion within the studied population. The fractional-order proportional–integral–derivative is tuned to achieve sufficient robustness margins ie phase margin, cutoff frequency, and the consideration of the iso-damping properties. The results show no undershoot and a smooth convergence to the desired value of the bispectral index, which indicates the depth of hypnosis.

Salp Swarm Algorithm-Based Fractional Order PID Controller for Grid-Connected Hybrid Renewable Energy System

Salp Swarm Algorithm-Based Fractional Order PID Controller for Grid-Connected Hybrid Renewable Energy System

First-Hand Design of a Fractional order PID for Controlling the Depth of Hypnosis during Induction

The integration of information technology and control engineering has significantly increased in the research field of clinical practice, including the management of medication dosing for general anesthesia. To achieve effective drug dosing, it is necessary to have appropriate controllers for closed loop control methods. A multitude of control mechanisms have been devised to manage hypnosis, with most of them based on pharmacokinetic-pharmacodynamic (PK-PD) models. This study presents a novel structure of a fractional order PID controller tuned for inducing hypnosis. The tuning algorithm uses a novel fractional order model instead of the classical PK-PD models. The main goal is to control the Bispectral Index by delivering Propofol during the hypnotic stage of anesthesia. Closed loop simulation results show that the proposed controller manages to ensure little undershoot and time to target for a nominal patient model. Robustness tests are also performed. The analysis shows that the proposed controller is suitable to maintain BIS signal within a safe operating range but fails to meet the time to target requirement for significant patient variability (greater than 2 orders of magnitude). Online adaptation rules are suggested as a solution.

Voltage Control of PEM Fuel Cell in a DC Microgrid Using Optimal Artificial Rabbits Algorithm-Based Fractional Order PID Controller

Voltage Control of PEM Fuel Cell in a DC Microgrid Using Optimal Artificial Rabbits Algorithm-Based Fractional Order PID Controller

Analog real time tunable and configurable fractional order PID controller realization

Fractional-order controllers are modeled using irrational continuous-time transfer functions. Implementing these controllers in analogue form can be challenging, particularly if their parameters need to be adjusted in real-time. This paper presents an analogue implementation of a fractional PID controller that can be adjusted and configured in real-time. The controller can be configured as PIαDf, PIDβ, PIα, PDβ, Iα, Dβ. The signal within the proposed controller’s circuit stays analog and is not converted into discrete values. A prototype of the controller is tested. The results of the frequency and time domain validations indicated similarity between the theoretical, simulated and experimental measurements.

Fractional-Order PID Optimal Tuning Rule based on a FOPDT Process Model with Robustness Constraints

This paper introduces a tuning rule design for fractional order PID controllers. The design is based on a first order plus dead time model for the controlled process. The control problem presented, requires minimizing the integrated absolute error for each control mode, then making a different set of rules for set-point and load-disturbance response. For the proposed optimization, a robustness constraint based on the maximum value of the sensitivity function has been considered so that the tuned controllers have an optimal performance and guarantee the stability of the control system at the time of implementation. By performing a curve fitting process towards the optimal controller parameters, the Model based Robust Tuning rule was designed and its improvement over other tuning methods is validated through examples.