Optimum design of fractional order PID controller for AVR system using chaotic ant swarm

Fractional-order PID (FOPID) controller is a generalization of standard PID controller using fractional calculus. Compared to PID controller, the tuning of FOPID is more complex and remains a challenge problem. This paper focuses on the design of FOPID controller using chaotic ant swarm (CAS) optimization method. The tuning of FOPID controller is formulated as a nonlinear optimization problem, in which the objective function is composed of overshoot, steady-state error, raising time and settling time. CAS algorithm, a newly developed evolutionary algorithm inspired by the chaotic behavior of individual ant and the self-organization of ant swarm, is used as the optimizer to search the best parameters of FOPID controller. The designed CAS-FOPID controller is applied to an automatic regulator voltage (AVR) system. Numerous numerical simulations and comparisons with other FOPID/PID controllers show that the CAS-FOPID controller can not only ensure good control performance with respect to reference input but also improve the system robustness with respect to model uncertainties.     

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.     

Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization

In this paper, two lbests multi-objective particle swarm optimization (2LB-MOPSO) is applied to design multi-objective robust Proportional-integral-derivative (PID) controllers for two MIMO systems, namely, distillation column plant and longitudinal control system of the super maneuverable F18/HARV fighter aircraft. Multi-objective robust PID controller design problem is formulated by minimizing integral squared error (ISE) and balanced robust performance criteria. During the search, 2LB-MOPSO can focus on small regions in the parameter space in the vicinity of the best existing fronts. As the lbests are chosen from the top fronts in a non-domination sorted external archive of reasonably large size, the offspring obtained can be more diverse with good fitness. The performance of various optimal PID controllers is compared in terms of the sum of ISE and balanced robust performance criteria. For the purpose of comparison, 2LB-MOPSO, NSGA-II as well as earlier reported Riccati, IGA and OSA methods are considered. The performance of PID controllers obtained using 2LB-MOPSO is better than that of others. In addition, Hypervolume-based comparisons are carried out to show the superior performance of 2LB-MOPSO over NSGA-II. The results reveal that 2LB-MOPSO yields better robustness and consistency in terms of the sum of ISE and balanced robust performance criteria than various optimal PID controllers.     

Statistically optimized FOPID for output force control of SEAs

Fractional order PID (FOPID) controllers have recently found an increasing application in different fields of control. Comparing to traditional PID algorithms, FOPID controllers provide more flexibility and better performances. The simple and non-model-based structure of FOPID controllers has boosted their usage in real-world applications. However, due to having two more control parameters than regular PID controllers and the non-linear structure of FOPID controllers, the tuning procedure of these controllers is still a challenge. The authors of the present paper have recently proposed a Taguchi-based gain tuning algorithm for tuning of control parameters of FOPID controller. The present paper is an experimental evaluation of the proposed method. A custom made SEA, FUM-LSEA, is used as the test bed in this study. Deriving a dynamic model of the FUM-LSEA, feed-forward terms are added to the controller to compensate for disturbances from motions of the output block. Optimal gains and orders of the controller are obtained through a set of experiments suggested by the Taguchi method. The Taguchi optimized controller is also compared to a Ziegler–Nichols tuned controller. The experimental results indicate 45% improvements in force tracking error.     

用改进的人工蜂群算法设计AVR系统最优分数阶PID控制器

分数阶PID控制器（FOPID）是标准PID控制器的一般形式.与PID控制器相比,FOPID有更多的参数,其参数整定也更复杂.本文提出一种基于环交换邻域和混沌的人工蜂群算法（CNC-ABC）,用于FOPID控制器的参数整定.CNC-ABC算法由于应用了环交换邻域,增加了解的搜索范围,从而能加快人工蜂群算法的收敛速度;同时利用混沌的遍历性使算法跳出局部最优解.用CNC-ABC算法优化AVR系统的FOPID控制器的参数.仿真结果表明,CNC-ABC算法整定的FOPID控制器比其它FOPID及PID控制器有较好的性能.     

Design of a fractional order PID controller for an AVR using particle swarm optimization

Application of fractional order PID (FOPID) controller to an automatic voltage regulator (AVR) is presented and studied in this paper. An FOPID is a PID whose derivative and integral orders are fractional numbers rather than integers. Design stage of such a controller consists of determining five parameters. This paper employs particle swarm optimization (PSO) algorithm to carry out the aforementioned design procedure. PSO is an advanced search procedure that has proved to have very high efficiency. A novel cost function is defined to facilitate the control strategy over both the time-domain and the frequency-domain specifications. Comparisons are made with a PID controller and it is shown that the proposed FOPID controller can highly improve the system robustness with respect to model uncertainties.     

Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region (PSR) analysis. Firstly, the PSR is presented to improve the existing stability region (SR) in D‐decomposition method. Then, the optimal fractional orders λ and μ of FOPID controller are achieved at the biggest three‐dimensional PSR, which means the best robustness. Given the optimal λ and μ, the other FOPID controller parameters k_p, k_i, k_d can be solved under the control specifications, including gain crossover frequency, phase margin, and an extended flat phase constraint. In addition, the steps of the proposed robust FOPID controller design process are listed at length, and an example is given to illustrate the corresponding steps. At last, the control performances of the obtained robust FOPID controller are compared with some other controllers (PID and FOPI). The simulation results illustrate the superior robustness as well as the transient performance of the proposed control algorithm.     

Robust adaptive control of a bio-inspired robot manipulator using bat algorithm

This paper proposes a novel adaptive fractional order PID sliding mode controller (AFOPIDSMC) using a Bat algorithm to control of a Caterpillar robot manipulator. A fractional order PID (FOPID) control is applied to improve both trajectory tracking and robustness. Sliding mode controller (SMC) is one of the control methods which provides high robustness and low tracking error. Using hybridization, a new combined control law is proposed for chattering reduction by means of FOPID controller and high trajectory tracking through using SMC. Then, an adaptive controller design motivated from the SMC is applied for updating FOPID parameters. A metaheuristic approach, the Bat search algorithm based on the echolocation behavior of bats is applied for optimal design of the Caterpillar robot in order to tune the parameter AFOPIDSMC controllers (BA-AFOPIDSMC). To study the effectiveness of Bat algorithm, its performance is compared with five other controllers such as PID, FOPID, SMC, AFOPIDSMC and PSO-AFOPIDSMC. The stability of the AFOPIDSMC controller is proved by Lyapunov theory. Numerical simulation results completely indicate the advantage of BA-AFOPIDSMC for trajectory tracking and chattering reduction.     

在线自调整模糊-PID控制器的设计

提出一种带修正因子的在线自调整模糊－ＰＩＤ控制器的设计,即将模糊控制器与ＰＩＤ控制器考虑一个系统中,通过在线调整协调因子改变上述两个控制器输出的权重,同时在模糊控制器环节采用修正因子对其输出在线调整。仿真证明,该方法具有算法简单、控制器质较好等优点。     

一类模糊P I D 控制器的鲁棒优化设计

研究一类模糊 PID控制器的鲁棒设计。以小增益定理分析得到该模糊 PID控制系统稳定性条件。针对参数摄动系统的“最坏点”,用该稳定性条件作为约束 ,采用遗传算法对标称系统的性能进行优化 ,求得优化鲁棒控制器。以倒立摆为例进行鲁棒模糊 PID控制器的设计 ,实验结果表明了该方法的有效性     

Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 23 factorial experimental design for a fractional order proportional integral and derivative controller (FOPID), integer order proportional integral and derivative controller (IOPID) and the Skogestad internal model control controller (SIMC). The factors assumed in experiment are the presence of random noise, external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.      

Discrete-time fractional-order PID controller: Definition,tuning, digital realization and some applications

In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID (FOPID). Commonly, after tuning the parameters of FOPID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discrete-time version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems.     

A genetic-multivariable fractional order PID control to multi-input multi-output processes

A multivariable fractional order PID controller is designed and to get suitable coefficients for the controller, a genetic algorithm with a new topology to generate a new population is proposed. The three parts of the genetic algorithm such as reproduction, mutation, and crossover are employed and some variations in the methods are fulfilled so that a better performance is gained. The genetic algorithm is applied to design FOPID controllers for a multivariable process and the results are compared with the responses of a H_∞ based multivariable FOPID controller. The simulation responses show that in all cases, the genetic-multivariable FOPID controller has suitable performance, and the output of the system has a smaller error. Also, in the proposed method, variations in one output have a smaller effect on another output which is shown the ability of the proposed method to overcome the interaction in the multivariable processes.     

Multi-loop design of multi-scale controllers for multivariable processes

Based on the recently proposed (SISO) multi-scale control scheme, a new approach is introduced to design multi-loop controllers for multivariable processes. The basic feature of the multi-scale control scheme is to decompose a given plant into a sum of basic modes. To achieve good nominal control performance and performance robustness, a set of sub-controllers are designed based on the plant modes in such a way that they are mutually enhanced with each other so as to optimize the overall control objective. It is shown that the designed multi-scale controller is equivalent to a conventional PID controller augmented with a filter. The multi-scale control scheme offers a systematic approach to designing multi-loop PID controllers augmented with filters. Numerical studies show that the proposed multi-loop multi-scale controllers provide improved nominal performance and performance robustness over some well-established multi-loop PID controller schemes.     

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional–Integral–Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.     

基于PLC的过程控制实验装置温度模糊PID控制

本文介绍了用S7-200实现过程控制系统实验装置中锅炉夹套的温度模糊控制设计思想,对模糊PID控制的结构、模糊PID控制器的设计、模糊PID控制的PLC实现进行了分析,文中详细介绍了模糊控制器程序的编写方法,结果表明,用PLC实现的模糊控制器简单实用。     

Adaptive hierarchical tuning of fuzzy controllers

Fuzzy controller design includes both linear and non-linear dynamic analysis. The knowledge base parameters associated within the fuzzy rule base influence the non-linear control dynamics while the linear parameters associated within the fuzzy output signal influence the overall control dynamics. For distinct identification of tuning levels, an equivalent linear controller output and a normalized non-linear controller output are defined. A linear proportional-integral-derivative (PID) controller analogy is used for determining the linear tuning parameters. Non-linear tuning is derived from the locally defined control properties in the non-linear fuzzy output. The non-linearity in the fuzzy output is then represented in a graphical form for achieving the necessary non-linear tuning. Three different tuning strategies are evaluated. The first strategy uses a genetic algorithm to simultaneously tune both linear and non-linear parameters. In the second strategy the non-linear parameters are initially selected on the basis of some desired non-linear control characteristics and the linear tuning is then performed using a trial and error approach. In the third method the linear tuning is initially performed off-line using an existing linear PID law and an adaptive non-linear tuning is then performed online in a hierarchical fashion. The control performance of each design is compared against its corresponding linear PID system. The controllers based on the first two design methods show superior performance when they are implemented on the estimated process system. However, in the presence of process uncertainties and external disturbances these controllers fail to perform any better than linear controllers. In the hierarchical control architecture, the non-linear fuzzy control method adapts to process uncertainties and disturbances to produce superior performance.     

Chaos synchronization of nonlinear gyros using self-learning PID control approach

Since chaotic systems are important nonlinear deterministic systems that display complex, noisy-like and unpredictable behavior, synchronizing chaotic systems has become an important issue in the engineering community. Due to the proportional-integral-derivative (PID) controller has a simple architecture and easily designed, it was widely used in the industrial applications. However, the traditional PID controller usually needs some manual retuning before being used to practically application. To tackle this problem, this paper proposes a self-learning PID control (SLPIDC) system which is composed of a PID controller and a fuzzy compensator. The PID controller which is used to online approximate an ideal controller is the main controller. The controller gain factors of the PID controller can automatically tune based on the gradient descent method. The fuzzy compensator is designed to dispel the approximation error between the ideal controller and PID controller upon the system stability in the Lyapunov sense. From the simulation results, it is verified that the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized by the proposed SLPIDC scheme without the chattering phenomena in the control effort after the controller parameters learning.     

Optimum Design of Fractional Order Pid Controller Using Chaotic Firefly Algorithms for a Control CSTR System

A fractional‐order PID controller is a generalization of a standard PID controller using fractional calculus. Compared with the standard PID controller, two adjustable variables, “differential order” and “integral order”, are added to the PID controller. Fractional‐order PID is more flexible, has better responses, and the precise adjustment closed‐loop system stability region is larger than that of a classic PID controller. But the design and stability analysis is more complicated than for the PID controller. Therefore, the optimal setting of parameters is very important. A firefly algorithm in standard mode has only local optimization and accuracy is low. In order to fix this flaw an improved chaotic algorithm firefly is proposed for a design controller FOPID. To evaluate the performance of the proposed controller, it has been used in the control of a CSTR system with a variety of fitness functions. Simulations confirm the optimal performance of the proposed controller.     

一种新型的二维PID模糊控制器

通过对常规PID控制器的结构分析,设计出一种新型的二维PID模糊控制器,其结构形式简称为fuzzy PD+ fuzzy ID型.根据模糊规则的图解分析,提出fuzzy ID控制嚣的输入变量(偏差和偏差变化加速率)与输出变量之间的控制结构,并确定两控制器的模糊控制规则的相似性.通过对该PID模糊控制器的结构分析,给出与常...