Fractional PID Controller Research Articles

Intelligent-based approach for parameters identification and control of fractional order systems

The optimization algorithms for identification and control processes take more and more place in the industrial domain. However, determining a control law for fractional systems remains challenging for researchers today. This paper presents a simple method for using a fractional PID (FOPID) corrector to regulate a class of fractional systems that show a stable step response. The procedure is based on an algorithmic identification to assimilate the fractional system into a simple model. Optimization methods were used. Using techniques like Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Artificial Bee Colony (ABC), and Ant Colony Optimization (ACO) to ascertain the parameters of the basic model, a first-order system with delay. Then, the FOPID controller will be calculated using Ziegler–Nichols methods and optimization algorithms to stabilize the real process. Better performance Overshoot and Settling time as well as minimal Energy control effort are benefits of the proposed design. To confirm that the fractional regulator is robust which is optimized by the best-chosen method (PSO), the parameters of the chosen process will be randomly varied. Through two numerical simulations, the efficiency of the suggested method has been confirmed.

Hover Flight Improvement of a Quadrotor Unmanned Aerial Vehicle Using PID Controllers with an Integral Effect Based on the Riemann–Liouville Fractional-Order Operator: A Deterministic Approach

The hovering flight of a quadrotor Unmanned Aerial Vehicle (UAV) refers to maintaining the aircraft in a fixed position in the air, without lateral, vertical, or rotational movements, using only the vehicle’s control systems to maintain proper balance in all spatial dimensions. Algorithms and control systems have been developed to continuously adjust motor speeds to counteract deviations from the desired position and achieve effective hovering flight. This paper proposes a set of PID controllers with an integral effect based on the Riemann–Liouville fractional-order approach to improve the hovering flight of a quadrotor UAV. This research innovates by introducing a set of fractional-order PID controllers for UAV hover stability, which offer better adaptability to non-linear dynamics and robustness than traditional PID controllers. Also presented is the development of new performance metrics (MSE, BQC-LR), which allow for more comprehensive control system evaluations. A thorough comparative analysis with conventional control methods demonstrates the superior performance of fractional-order control in real-world simulations. The numerical simulation results show the effectiveness of the proposed Fractional Integral Action PID Controller in the control of UAV hovering flight, while comparative analyses against a classical controller emphasize the benefits of the fractional-order approach in terms of control accuracy.

Fuzzy Logic-Based Smart Control of Wind Energy Conversion System Using Cascaded Doubly Fed Induction Generator

This paper introduces a robust system designed to effectively manage and enhance the electrical output of a Wind Energy Conversion System (WECS) using a Cascaded Doubly Fed Induction Generator (CDFIG) connected to a power grid. The solution that was investigated is the use of a CDFIG that is based on a variable-speed wind power conversion chain. It comprises the electrical and mechanical connection of two DFIGs through their rotors. The originality of this paper lies in the innovative application of a fuzzy logic controller (FLC) in combination with a CDFIG for a WECS. To demonstrate that this novel configuration enhances control precision and performance in WECSs, we conducted a comparison of three different controllers: a proportional–integral (PI) controller, a fractional PID (FPID) controller, and a fuzzy logic controller (FLC). The results highlight the potential of the proposed system in optimizing power generation and improving overall system stability. It turns out that, according to the first results, the FLC performed optimally in terms of tracking and rejecting disturbances. In terms of peak overshoot for power and torque, the findings indicate that the proposed FLC-based technique (3.8639% and 6.9401%) outperforms that of the FOPID (11.2458% and 10.9654%) and PI controllers (11.4219% and 11.0712%), respectively. These results demonstrate the superior performance of the FLC in reducing overshoot, providing better control stability for both power and torque. In terms of rise time, the findings show that all controllers perform similarly for both power and torque. However, the FLC demonstrates superior performance with a rise time of 0.0016 s for both power and torque, compared to the FOPID (1.9999 s and 1.9999 s) and PI (0.0250 s and 0.0247 s) controllers. This highlights the FLC’s enhanced responsiveness in controlling power and torque. In terms of settling time, all three controllers have almost the same performance of 1.9999. An examination of total harmonic distortion (THD) was also employed to validate the superiority of the FLC. In terms of power quality, the findings prove that a WECS based on an FLC (0.93%) has a smaller total harmonic distortion (THD) compared to that of the FOPID (1.21%) and PI (1.51%) controllers. This system solves the problem by removing the requirement for sliding ring–brush contact. Through the utilization of the MATLAB/Simulink environment, the effectiveness of this control and energy management approach was evaluated, thereby demonstrating its capacity to fulfill the objectives that were set.

Modeling and Simulation of Fractional PID Controller for Under-actuated Inverted Pendulum Mechanical System

The stabilization of the non-linear inverted pendulum system requires a robust control strategy, as this system is inherently unstable and sensitive to disturbances. This research utilizes Lagrangian mechanics, a powerful technique in analytical dynamics, to derive the mathematical representation of the system. By applying the principles of Lagrangian dynamics, we can accurately model the energies involved and derive the equations of motion that govern the pendulum’s behavior. Following this, state-space feedback is employed to determine the Proportional, Integral, and Derivative (PID) values essential for effective control. This control strategy is particularly useful due to its ability to minimize error over time and ensure stability. To further enhance the control process, a comprehensive mathematical model is developed to establish the transfer function that correlates the pendulum's angle with the displacement of the cart. This relationship is crucial for understanding how changes in the cart's position affect the pendulum's stability. To validate the proposed control law, extensive simulations are conducted, allowing for comparative analysis against an Integer Order Controller. These simulations not only highlight the effectiveness of the PID controller but also provide insights into the dynamic behavior of the system under various conditions. The results demonstrate significant improvements in settling time and overshoot, showcasing enhanced performance metrics for the selected objective functions. This research contributes to the broader field of control systems engineering, suggesting that advanced control strategies can effectively manage complex, non-linear systems.

Evaluation of Fractional Proportional-Integral-Derivative and Integer Proportional-Integral-Derivative Control for a Drone-Based Cable Suspended Payload System

Abstract Arctic remote sensing is crucial for studying and preserving the vulnerable Arctic environment. Researchers use ground penetrating radars (GPRs) to understand climate change and ice properties, but maneuvering a bulky GPR on the inhospitable Arctic terrain is difficult. Suspending the GPR from a drone can be a solution to operating a large GPR, however, proper control and stabilization of the drone-GPR system pose a challenge. In this paper, we contribute to the literature by analyzing the response of closed-loop feedback fractional-order and integer-order proportional-integral-derivative (PID) controllers at minimizing the payload sway for a drone-based cable-suspended payload system. Both controllers were tuned using particle swarm optimization and simulated to experience delays and external disturbances. Results indicate that both controllers had comparable time responses. The fractional-order controller was more robust to disturbances but was also sensitive to system delays. The findings of this study can be considered for future drone development.

Performance Evaluation of Fractional Proportional–Integral–Derivative Controllers Tuned by Heuristic Algorithms for Nonlinear Interconnected Tanks

This article presents an in-depth analysis of three advanced strategies to tune fractional PID (FOPID) controllers for a nonlinear system of interconnected tanks, simulated using MATLAB. The study focuses on evaluating the performance characteristics of system responses controlled by FOPID controllers tuned through three heuristic algorithms: Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Flower Pollination Algorithm (FPA). Each algorithm aims to minimize its respective cost function using various performance metrics. The nonlinear model was linearized around an equilibrium point using Taylor Series expansion and Laplace transforms to facilitate control. The FPA algorithm performed better with the lowest Integral Square Error (ISE) criterion value (297.83) and faster convergence in constant values and fractional orders. This comprehensive evaluation underscores the importance of selecting the appropriate tuning strategy and performance index, demonstrating that the FPA provides the most efficient and robust tuning for FOPID controllers in nonlinear systems. The results highlight the efficacy of meta-heuristic algorithms in optimizing complex control systems, providing valuable insights for future research and practical applications, thereby contributing to the advancement of control systems engineering.

Implementation of AI Tuned PID Controller for Speed and Direction Control of BLDC Motor

This paper explores BLDC motor control using MATLAB Simulink, focusing on AI tuned PID and fractional PID controllers for closed-loop speed regulation and direction . It involves designing a feedback system comprising sensor feedback, controller, and BLDC motor model. Through iterative tuning, optimal controller parameters are determined for enhanced performance. Simulations were carried out to evaluate response characteristics, stability, and robustness across varying conditions. Experimental validation though hardware-in-the-loop experiments corroborates simulation findings. Performance metrics, including speed accuracy and disturbance rejection, are analyzed to compare the effectiveness of PID and fractional PID controllers. This work provides insights into advanced control techniques for BLDC motors, aiding in the selection of suitable strategies for real-world applications.

A Low Power Analog Integrated Fractional Order Type-2 Fuzzy PID Controller

A Low Power Analog Integrated Fractional Order Type-2 Fuzzy PID Controller

Optimization of PEMFC pressure control using fractional PI/D controller with non-integer order: design and experimental evaluation

The fuel-based proton exchange membrane (PEM) fuel cell is a promising technology for clean energy production owing to the several advantages including high efficiency (around 80% theoretical), quiet in operation, and almost zero emission as compared to conventional internal combustion engine. Only hydrogen and oxygen are supplied at the anode and cathode, respectively to generate power and water is produced as by product. However, it suffers to achieve its maximum theoretical efficiency due to lack of flow/pressure management of hydrogen and oxygen in the PEMFC stack which also causes flooding within the cell and reduce the performance of the catalyst and reduces the efficiency. The higher efficiency can be achieved with the proper control of the hydrogen and oxygen inlet flow rate and pressure at the PEMFC. Since it’s crucial to maintaining a consistent supply of exponential pressure, the main focus of this work is pressure regulation at the PEMFC cathode side. A fractional PI/D controller is designed to operate the PEMFC system more realistically. There are three primary objectives of this research work. In the first step, monitoring the PEMFC operating pressure to find out the suitable fractional PI-D controller for a given resilience level, which has the lowest Integration Absolute Error (IAE) to disturbances. The robustness level and/or threshold peak is considered as a tuning parameter for the evaluation. Second, compare the best IAE performance of the fractional PI-D controller with that of simple SIMC rules, where a certain level of resilience is achieved by varying the SIMC tuning variable. Through this comparison, the effectiveness of the recommended controller in achieving the optimal plant performance is evaluated. Thirdly, design a non-integer order PEMFC plant with a fractional controller using MATLAB software and compare the results with existing models. This comparison provides insight into the practical performance of the proposed controller. The results shows that the developed fractional PI/D controller is able to control the pressure very efficiently at the PEMFC cathode side. The findings further emphasise on the important to consider the resilience and robustness levels at the time of developing control systems for PEMFCs. The efficacy of the suggested unique technique is further confirmed by contrasting the suggested controller with the developed models.

Fractional PID with Genetic Algorithm Approach for Industrial Tank Level Control Process

Process control is used in various types of industries to boost production while using current resources, product quality, and safety, with level control being one of the most important schemes. It is suggested that study be conducted on nonlinear continuous processes, particularly in process control applications such as conical tank level control. Initially, each process receives one set of Proportional-Integral (PI) controller settings and a First Order Plus Dead-Time (FOPDT) model using the Ziegler Nicholas (ZN) step response tuning method. The numerous FOPDT models and parameter sets are also obtained. Responses obtained with a single set of parameters and responses obtained with many sets of parameters are compared. By creating a Fractional PID Controller (FPID) with Genetic Algorithm (GA), a simulation-based tuning strategy is proposed. The step responses are acquired through experimental research using fine-tuned settings. At most operational points, the Fractional PID Controller with Genetic Algorithm-based tuning approach outperforms, with lowest oscillation, extremely tiny overshoot, minimum average ISE, and minimum average IAE. The proposed FPID with GA method provides better setpoint and regulatory tracking performance compared to ZN-PID.

Design of Fuzzy Fractional Order-based PID Controller for Higher Order Systems

The conventional Integer Order-based Proportional Integral Derivative (IO-PID) control is mostly used in process control and manufacturing industries. However, it has been analyzed after an in-depth review of the literature that traditional IO-PID control is not worthwhile for non-linear and higher-order applications. The Controlling of higher-order systems is a critical issue in many industrial plants. The foremost objective of Controllers in complex systems is the reduction of settling time, overshoot, etc for higher-order systems. A novel Fuzzy fractional order-based PID (FFOPID) controller is designed to resolve all the significant issues of control systems. The traditional controller and the novel controller are given the same unit step input and the simulation had been done using MATLAB. The comparison between the output response of the two controllers revealed that the designed novel controller works better than the traditional IO-PID controllers.

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.

On PID Controllers for a Complex-Order Fractional Model of an Automotive Injection System

Recent studies have shown that complex-order fractional operators allow for compact modeling with simpler structures and less parameters than models based on integer-order operators and even non-integer real-order operators. This work verifies the usefulness and potential of a complex-order fractional model when used to set parameters of a PID controller regulating the common-rail pressure in the injection system of a compressed natural gas engine. Parameters are derived by a general particle swarm optimization that considers a cost function weighting the performance and robustness measures. Simulation results show the effectiveness of the complex-order fractional model-based PID controller through the response to step references, the rejection of disturbances, the low sensitivity to variations of the injection system parameters.

Optimization of Third Order System with a Novel Fuzzy-based Fractional PID Controller

The conventional Integer Order-based Proportional Integral Derivative (IO-PID) control has been widely employed in process control and manufacturing industries. However, upon thorough review, it is evident that traditional IO-PID control falls short when applied to non-linear and higher-order systems. This paper addresses the challenge of controlling higher-order systems prevalent in numerous industrial plants. The primary goal of controllers in intricate systems is to minimize settling time, overshoot, and related parameters for higher-order systems. To tackle these issues, a novel Fuzzy fractional order-based PID (FFOPID) controller is introduced through this work. This controller aims to provide solutions for the significant challenges encountered in control systems. By subjecting both the traditional controller and the novel controller to the same unit step input, simulations are carried out using MATLAB. The comparative analysis of the output responses highlights the superior performance of the designed novel controller works over the traditional IO-PID controllers. There is a reduction of overshoot by 15% and settling time by more than one second by the FFOPID controller compared to the IO-PID controller.

Performances Improvement of Fractional order Systems using the Fractional Order Adaptive PID Controller

Performances Improvement of Fractional order Systems using the Fractional Order Adaptive PID Controller

Robust Adaptive Fuzzy Fractional Control for Nonlinear Chaotic Systems with Uncertainties

The control of nonlinear chaotic systems with uncertainties is a challenging problem that has attracted the attention of researchers in recent years. In this paper, we propose a robust adaptive fuzzy fractional control strategy for stabilizing nonlinear chaotic systems with uncertainties. The proposed strategy combined a fuzzy logic controller with fractional-order calculus to accurately model the system’s behavior and adapt to uncertainties in real-time. The proposed controller was based on a supervised sliding mode controller and an optimal robust adaptive fractional PID controller subjected to fuzzy rules. The stability of the closed-loop system was guaranteed using Lyapunov theory. To evaluate the performance of the proposed controller, we applied it to the Duffing–Holmes oscillator. Simulation results demonstrated that the proposed control method outperformed a recently introduced controller in the literature. The response of the system was significantly improved, highlighting the effectiveness and robustness of the proposed approach. The presented results provide strong evidence of the potential of the proposed strategy in a range of applications involving nonlinear chaotic systems with uncertainties.

Experimental Validation of Fractional PID Controllers Applied to a Two-Tank System

An experimental validation of fractional-order PID (FOPID) controllers, which were applied to a two coupled tanks system, is presented in this article. Two FOPID controllers, a continuous FOPID (cFOPID) and a discrete FOPID (dFOPID), were implemented in real-time. The gains tuning process was accomplished by applying genetic algorithms while considering the cost function with respect to the tracking error and control effort. The gains optimization process was performed directly to the two-tanks non-linear model. The real-time implementation used a National Instruments PCIe-6321 card as a data acquisition system; for the interface, we used a Simulink Matlab and Simulink Desktop Real-Time Toolbox. The performance of the fractional controllers was compared with the performance of classical PID controllers.

Performance Improvement of Aircraft pitch angle using the Fractional Order Adaptive PID Controller

Performance Improvement of Aircraft pitch angle using the Fractional Order Adaptive PID Controller

Fractional Order Internal Model PID Control for Pulp Batch Cooking Process

Pulp batch cooking is performed in a sealed high-temperature and high-pressure digester and is a complex black-box process. Based on the analysis of the mechanism of batch cooking, a model with nonlinear characteristics was established. To optimize the nonlinear part of the model, function fitting and numerical approximation were used for the simple cooking process. A novel fractional-order model is proposed to solve the problems of model inaccuracy and uncertain system parameters during batch cooking. For fractional-order systems, a two-degree-of-freedom fractional-order PID (FO-PID) controller based on internal model control is designed. The internal model control simplifies the number of parameter settings of the fractional-order controller and allows accurate adjustment of the adjustable parameters of the FO-PID controller based on the maximum sensitivity and stability margin. The simulation results show that the fractional-order internal model control in the batch cooking process is superior to the integer-order control in terms of overshoot, response speed, and robustness. Compared to internal model control, it provides better setpoint tracking dynamics and better robustness to system parameter disturbances. The practical application results in paper mills are given to illustrate the effectiveness of the method.

Design of an Optimal Fractional Complex Order PID Controller for Buck Converter

Dynamic and robust controllers are the inherent requirement of power electronic converters, which are subjected to dynamic variations and nonlinearities. The effectiveness of fractional order controllers in non-linear system control has been well-established by studies in the past few decades. Various forms of fractional order controllers have been used in power-electronic control. Recent research indicates that complex order controllers, extensions of fractional controllers, are more robust against uncertainties and non-linearities than their integer and fractional order counterparts. Though complex order controllers have been employed in various nonlinear plants, they have not been extensively tested on power electronic applications. Also, the design and tuning of the controller is difficult. This paper investigates the effectiveness of a complex order PID controller on a typical power electronic DC-DC buck converter for the first time. Two types of complex order controllers of the form PI^{a+ib}D^c and PI^{a+ib}D^{c+id} were designed for a power electronic buck converter. The complex order controllers were implemented in Simulink and the optimal tuning of the complex order controller parameters for various performance indices was performed using different optimization algorithms. The Cohort Intelligence algorithm was found to give the most optimal results. Both the complex controllers showed more robustness towards uncertainties than the linear and fractional PID controllers. The PI^{a+ib}D^c controller gave the smoothest and fastest response under non-linearities. The dynamic performance of the complex order controller is the best and can be expected to be useful for more power electronic applications.