Fractional Order Control of Fractional Diffusion Systems Subject to Input Hysteresis

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Necati Özdemir ◽  
Beyza Billur İskender
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Fractional Diffusion ◽  
Pid Controllers ◽  
Algebraic Equations ◽  
Proportional Integral Derivative ◽  
Diffusion Systems ◽  
Hysteresis Nonlinearity ◽  
Liouville Fractional Derivative ◽  
Fractional Order Pid

This paper concerns the control of a time fractional diffusion system defined in the Riemann–Liouville sense. It is assumed that the system is subject to hysteresis nonlinearity at its input, where the hysteresis is mathematically modeled with the Duhem operator. To compensate the effects of hysteresis nonlinearity, a fractional order Proportional+Integral+Derivative (PID) controller is designed by minimizing integral square error. For numerical computation, the Riemann–Liouville fractional derivative is approximated by the Grünwald–Letnikov approach. A set of algebraic equations arises from this approximation, which can be solved numerically. Performance of the fractional order PID controllers are analyzed in comparison with integer order PID controllers by simulation results, and it is shown that the fractional order controllers are more advantageous than the integer ones.

Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

2009 ◽  
Author(s):  
Bijoy K. Mukherjee ◽  
Santanu Metia ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
...  
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Pid Controllers ◽  
Integer Order ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

scholarly journals Performance Evaluation of Fractional Order Pid and Sliding Mode Control with Optimization Tuning Access

2019 ◽  
Vol 8 (2S8) ◽  
pp. 1448-1454
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
World Economy ◽  
Sliding Mode ◽  
Proportional Integral Derivative ◽  
Robust Controller ◽  
The Past ◽  
Control Schemes ◽  
Different Types ◽  
Fractional Order Pid

The statistical analyses in the past showing the important properties of the electrohydraulic actuator (EHA) system, especially in the growth of the world economy. Dealing with the existing drawback in the EHA system, various types of control schemes have been introduced in the past. In this paper, to produce a more insightful view of the performance and the capabilities of the controller, three different types of controllers have been designed and compared. The favourite controller in the industry field, which is the proportional-integral-derivative (PID) controller will be first introduced. Follow by the improved PID controller, named Fractional Order (FO-PID) controller will be designed. Then, the prominent robust controller in the control field, called sliding mode controller (SMC) will be established. Instead of obtaining the controller’s parameters without any appropriate technique, the well-known tuning technique in computer science, named particle swarm optimization (PSO) will be utilized. Referring to the performances produced by these controllers, it can be concluded that the SMC is capable to generate most desired control performance that produced the highest accuracy with the smallest error in the analyses.

scholarly journals Fractional-Order Approximation and Synthesis of a PID Controller for a Buck Converter

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 629 ◽  
Author(s):  
Allan G. Soriano-Sánchez ◽  
Martín A. Rodríguez-Licea ◽  
Francisco J. Pérez-Pinal ◽  
José A. Vázquez-López
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Order Approximation ◽  
Buck Converter ◽  
Step Response ◽  
Pid Controllers ◽  
Limited Frequency ◽  
Tuning Process ◽  
Band Limited ◽  
Fractional Order Pid

In this paper, the approximation of a fractional-order PIDcontroller is proposed to control a DC–DC converter. The synthesis and tuning process of the non-integer PID controller is described step by step. A biquadratic approximation is used to produce a flat phase response in a band-limited frequency spectrum. The proposed method takes into consideration both robustness and desired closed-loop characteristics, keeping the tuning process simple. The transfer function of the fractional-order PID controller and its time domain representation are described and analyzed. The step response of the fractional-order PID approximation shows a faster and stable regulation capacity. The comparison between typical PID controllers and the non-integer PID controller is provided to quantify the regulation speed introduced by the fractional-order PID approximation. Numerical simulations are provided to corroborate the effectiveness of the non-integer PID controller.

DESIGN OF ADAPTIVE FUZZY FRACTIONAL ORDER PID CONTROLLER FOR AUTONOMOUS UNDERWATER VEHICLE (AUV) IN HEADING AND DEPTH ATTITUDES

2021 ◽  
Vol 158 (A1) ◽  
Author(s):  
M H Khodayari ◽  
S Balochian
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Autonomous Underwater Vehicle ◽  
Path Following ◽  
Transient State ◽  
Pid Controllers ◽  
Adaptive Fuzzy ◽  
Highly Nonlinear ◽  
Self Tuning ◽  
Fractional Order Pid

This paper deals with the design of new self-tuning Fuzzy Fractional Order PID (AFFOPID) controller based on nonlinear MIMO structure for an AUV in order to enhance the performance in both transient state and steady state of traditional PID controller. It is particularly advantageous when the effects of highly nonlinear processes, like high maneuver, parameters variation, have to be controlled in presence of sensor noises and wave disturbances. Aspects of AUV controlling are crucial because of Complexity and highly coupled dynamics, time variety and difficulty in hydrodynamic modeling. In this try, the comprehensive nonlinear model of AUV is derived through kinematics and dynamic equations. The scaling factor of the proposed AFFOPID Controller is adjusted online at different underwater conditions. Combination of adaptive fuzzy methods and PID controllers can enhance solving the uncertainty challenge in the PID parameters and AUV parameter uncertainty. The simulation results show that developed control system is stable, competent and efficient enough to control the AUV in path following with stabilized and controlled speed. Obtained results demonstrate that the proposed controller has good performance and significant robust stability in comparison to traditional tuned PID controllers.

scholarly journals Variable, Fractional-Order PID Controller Synthesis Novelty Method

2020 ◽  
Author(s):  
Piotr Ostalczyk ◽  
Piotr Duch
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Main Idea ◽  
Pid Controllers ◽  
Time Interval ◽  
Discrete Variable ◽  
Closed Loop Systems ◽  
The Stability ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

The novelty method of the discrete variable, fractional order PID controller is proposed. The PID controllers are known for years. Many tuning continuous time PID controller methods are invented. Due to different performance criteria there are optimized three parameters: proportional, integral and differentiation gains. In the fractional order PID controllers there are two additional parameters: fractional order integration and differentiation. In the variable, fractional order PID controller fractional orders are generalized to functions. Nowadays all PID controllers are realized by microcontrollers in a discrete time version. Hence, the order functions are discrete variable bounded ones. Such controllers offer better transient characteristics of the closed loop systems. The choice of the order functions is still the open problem. In this Section a novelty intuitive idea is proposed. As the order functions one applies two spline functions with bounded functions defined for every time subinterval. The main idea is that in the final time interval the variable, fractional order PID controller transforms itself to the classical one preserving the stability conditions and zero steady-state error signal. This means that in the last time interval the discrete integration order is −1 and differentiation is 1.

Design of Fractional Order PID Controller Based on Artificial Immune Algorithm

2011 ◽  
Vol 268-270 ◽  
pp. 1061-1066 ◽  
Author(s):  
You Rui Huang ◽  
Hai Bo Hu
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Immune Algorithm ◽  
Pid Controllers ◽  
Time Varying ◽  
Artificial Immune ◽  
Artificial Immune Algorithm ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller ◽  
Method Of Design

PID control scheme has been widely used in most of control system. The method of design PID controller is mature gradually. Due to the controlled object is nonlinear and time-varying, so the integer PID controller can not achieve the desired effect. After study people found that the application of fractional order PID controllers can solve the problem of time-varying and nonlinear very well and the controller has high control precision. Currently, the method of design fractional order PID controllers is little. This article describes an artificial immune algorithm and using MATLAB for simulation, the simulation results demonstrate that the artificial immune algorithm has little error and high optimization speed than traditional optimization algorithm, and the fractional order PID controller has a better control effect than traditional integer PID controller.

Fractional PID Controller Applied to a Chemical Plant with Level and pH Control

2018 ◽  
Vol 13 (4) ◽  
Author(s):  
Renato Aparecido Aguiar ◽  
Ivan Carlos Franco ◽  
Fabrizio Leonardi ◽  
Fábio Lima
Keyword(s):  
Fractional Order ◽  
Pid Control ◽  
Pid Controller ◽  
Ph Control ◽  
Dynamic Responses ◽  
Control Performance ◽  
Proportional Integral Derivative ◽  
Control Effort ◽  
Multivariable Process ◽  
Fractional Order Pid

Abstract One of the most important processes in the chemical, biological and petrochemical industries is the control of the potential of hydrogen (pH). As it is a multivariable process and non-linear, pH control gives rise to many challenges for designers in both dynamic responses and robustness issues. Despite all this complexity, in many circumstances pH control is performed by using a conventional proportional integral derivative (PID) control, which is very common in industry. This paper proposes using a fractional-order PID to improve the pH control performance of a lab-scale process, as it is more flexible, i. e., there is a higher number of variables to be adjusted. Results from a simulation have been compared to those from both conventional and fractional-order PID controls, which has shown the better performance of the latter related to important metrics such as the control effort and dynamic response of the controlled variables.

Pareto Optimal Robust Design of Fuzzy Fractional-Order Pid Controllers

2011 ◽  
Vol 403-408 ◽  
pp. 4735-4742
Author(s):  
Nader Nariman Zadeh ◽  
Amir Hajiloo
Keyword(s):  
Fractional Order ◽  
Robust Design ◽  
Pid Controller ◽  
Pid Controllers ◽  
Pareto Optimum ◽  
Pareto Optimal ◽  
Objective Functions ◽  
Trade Off ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

In this paper, a multi-objective uniform-diversity genetic algorithm (MUGA) is used for Pareto optimum design of fuzzy fractional-order PID controllers for plants with parametric uncertainties. Two conflicting objective functions have been used in Pareto design of the fuzzy fractional-order PID controller. The results clearly show that an effective trade-off can be compromisingly achieved among the different fuzzy fractional-order PID controllers obtained using the methodology of this work and to achieve a robust design against the plant’s uncertainties.

scholarly journals Design of a Fractional Order PID Controller for Electric Hydraulic Actuator

2021 ◽  
pp. 59-68
Author(s):  
Erinna Dyah Atsari ◽  
Abdul Halim
Keyword(s):  
Steady State ◽  
Fractional Order ◽  
Pid Controller ◽  
Pid Controllers ◽  
System Response ◽  
Hydraulic Actuator ◽  
Fluid Flow Control ◽  
Two Parameters ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

Electric hydraulic actuators are more used especially in industries that demand high levels of accuracy. A common problem with this type of actuator is consistency in fluid flow control. PID controllers can accelerate the achievement of defined output values, eliminate offsets, and reduce maximum overshoots but result in considerable errors. Therefore, it is necessary to design controllers that can reduce errors significantly. In this research, a Fractional Order PID controller is developed to reduce maximum overshoots and steady state. Unlike conventional PID controllers that have three  parameters, in the Fractional Order PID controller, there are extra two parameters of the λ and μ. The   parameters were selected using the Ziegler Nichols method with a 1st order approach with a delay time. Meanwhile, the λ and μ parameters were selected the best value to make the system response better. The results of the design of the Fractional Order PID controller were evaluated using matlab simulation. The simulation results showed that the Fractional Order PID controller was able to reduce the steady state error response by 0.5 %, and the maximum overshoots by 17.4 %. From this result, it can be noted that the Fractional Order PID controller is better than conventional PID.

Grasshopper Algorithm Optimized Fractional Order Fuzzy PID Frequency Controller for Hybrid Power Systems

2019 ◽  
Vol 12 (6) ◽  
pp. 519-531
Author(s):  
Deepak Kumar Lal ◽  
Ajit Kumar Barisal
Keyword(s):  
Power Systems ◽  
Power System ◽  
Fractional Order ◽  
Pid Controller ◽  
Load Frequency Control ◽  
Pid Controllers ◽  
Fuzzy Pid ◽  
Fuzzy Pid Controller ◽  
Hybrid Power ◽  
Increasing Demand

Background: Due to the increasing demand for the electrical power and limitations of conventional energy to produce electricity. Methods: Now the Microgrid (MG) system based on alternative energy sources are used to provide electrical energy to fulfill the increasing demand. The power system frequency deviates from its nominal value when the generation differs the load demand. The paper presents, Load Frequency Control (LFC) of a hybrid power structure consisting of a reheat turbine thermal unit, hydropower generation unit and Distributed Generation (DG) resources. Results: The execution of the proposed fractional order Fuzzy proportional-integral-derivative (FO Fuzzy PID) controller is explored by comparing the results with different types of controllers such as PID, fractional order PID (FOPID) and Fuzzy PID controllers. The controller parameters are optimized with a novel application of Grasshopper Optimization Algorithm (GOA). The robustness of the proposed FO Fuzzy PID controller towards different loading, Step Load Perturbations (SLP) and random step change of wind power is tested. Further, the study is extended to an AC microgrid integrated three region thermal power systems. Conclusion: The performed time domain simulations results demonstrate the effectiveness of the proposed FO Fuzzy PID controller and show that it has better performance than that of PID, FOPID and Fuzzy PID controllers. The suggested approach is reached out to the more practical multi-region power system. Thus, the worthiness and adequacy of the proposed technique are verified effectively.

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