AN EFFICIENT EVOLUTIONARY NEURAL FUZZY CONTROLLER FOR THE INVERTED PENDULUM SYSTEM

In this article we propose an evolutionary neural fuzzy controller for the planetary train–type inverted pendulum system (IPS) and verify its effectiveness. The novel hybrid particle swarm optimization (HPSO) learning algorithm of the proposed controller is based on approaches of the fuzzy entropy clustering (FEC), the modified PSO (MPSO), and recursive singular value decomposition (RSVD). The FEC is applied to generate base particles and the MPSO is proposed to effectively improve the performance of the traditional PSO. There are mainly two different characteristics between the MPSO and its original version; that is, the initial parameters of the MPSO are calculated by an effective local approximation method (ELAM), and the global optimum is chosen by the multi-elites strategy (MES). In addition, we use the RSVD to determine the optimal consequent parameters of fuzzy rules, in order to reduce requirements of the computational time and space. Experimental results show that the proposed approach outperforms the proportional–integral–derivative (PID), PSO, and MPSO in terms of better abilities of tracking and noise rejection for planetary train–type IPS.     

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.     

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.     

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.     

改进的粒子群优化算法优化分数阶PID控制器参数

为了提高分数阶比例积分微分（FOPID）控制器的控制效果,针对FOPID控制器参数整定的范围广、复杂性高等特点,提出改进的粒子群优化（PSO）算法优化FOPID控制器参数的方法。该算法对PSO中惯权重系数的上下限设定范围并随迭代次数以伽玛函数方式非线性下降,同时粒子的惯性权重系数和学习因子根据粒子的适应度值大小动态调整,使粒子保持合理运动惯性和学习能力,提高粒子的自适应能力。仿真实验表明,改进的PSO算法优化FOPID控制器的参数较标准PSO算法具有收敛速度快和收敛精度高等优点,使FOPID控制器得到较优的综合性能。     

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.     

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.     

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.     

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.     

Conical tank level control using fractional order PID controllers: a simulated and experimental study

In this paper, simulated and experimental results on the conical tank level control are presented. PI/PID controllers of integer order (IO) as well as of fractional order (FO) are studied and compared. The tuning parameters are obtained first by using root locus (RL) and Ziegler and Nichols methods, for comparison purposes. Next, particle swarm optimization (PSO) is employed to determine the optimal controllers'' parameters using as fitness function the integral of the absolute value of tracking error (IAE). From the experimental results it is concluded that PI/FOPI are the controllers presenting the lowest IAE indexes, whereas PID/FOPID controllers present the lowest energy consumption by the control signal.     

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.     

引入多级扰动的混合型粒子群优化算法

为解决粒子群优化算法易陷入局部最优值的问题,提出一种引入多级扰动的混合型粒子群优化算法.该算法结合两种经典改进粒子群优化算法的优点,即带惯性参数的标准粒子群优化算法和带收缩因子的粒子群优化算法,在此基础上,引入多级扰动机制：在更新粒子位置时,引入一级扰动,使粒子对解空间的遍历能力得到加强;若优化过程陷入“局部最优”的情况,则引入二级扰动,使得优化过程继续,从而摆脱局部最优值.使用了6个测试函数——Sphere函数、Ackley函数、Rastrigin函数、Styblinski-Tang函数、Duadric函数及Rosenbrock函数来对所提出的混合型粒子群优化算法进行仿真运算和对比验证.模拟运算的结果表明：所提出的混合型粒子群优化算法在对测试函数进行仿真时,其收敛精度和收敛速度都优于另外两种经典的改进粒子群优化算法;另外,在处理多峰函数时,本算法不易被局部最优值所限制.     

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.     

基于改进BBO算法的分数阶PID控制器设计

针对分数阶PID(Fractional-Order Proportional-Integral-Derivative,FOPID)控制器参数整定,提出了一种改进生物地理学优化(Biogeography-Based Optimization,BBO)算法。该算法改进点主要包括:迁移操作中保留精英个体;变异操作中引入差分进化(Dtferential Evolution,ED)算法的变异策略;消除重复样本。仿真结果表明:在分数阶PID控制器参数整定中,与原始的BBO算法、遗传算法(Genetic Algorithm,GA)和粒子群算法(Particle Swarm Optimization,PSO)比较,提出的改进BBO算法具有超调量小、误差小,收敛更快的特点。     

电液伺服系统多PID控制器参数整定优化

为了解决挖掘机器人动臂、斗杆和铲斗不同电液伺服系统中多个比例–积分–微分(PID)控制器参数优化的难题, 提高挖掘机器人铲斗齿尖轨迹跟踪精度, 采用改进的粒子群算法(PSO)对多PID控制器参数进行整定优化. 首先, 建立电液伺服系统的数学机理模型, 在理论模型的基础上, 采用递推最小二乘辨识法(RLS)得到实际的机理模型. 其次, 提出一种改进的PSO算法, 采用非线性自适应惯性权重、引入异步变化策略、设计精英变异方法. 接着, 搭建仿真验证平台, 跟踪正弦轨迹, 比较传统Z-N参数整定方法、基本PSO算法和改进PSO算法的差别. 最后, 以挖掘机 器人最常见的整平为代表工况, 基于23 t挖掘机器人实验平台进行实验验证. 实验结果表明, 改进PSO算法的跟踪精度最高, 与基本PSO算法相比, 明显提高了轨迹跟踪精度     

Numerical simulation for Fuzzy-PID controllers and helping EP reproduction with PSO hybrid algorithm

Many Fuzzy-PID controller schemes used in industry today are based on some sort of simplified fuzzy reasoning methods and PID parameters. We present a design for Fuzzy-PID controllers using a novel PSO-EP-based hybrid algorithm. We succeed in making mathematical calculations and in encouraging EP reproduction with PSO. The main advantage of our design is that the integration of the PSO-EP-based hybrid algorithm structure generates new parameters for the Fuzzy-PID control schemes. The proposed algorithm is an improved variant of PSO, a relatively recently introduced stochastic optimization strategy for Fuzzy-PID controllers that is investigated in this study. The function of Fuzzy-PID controllers is illustrated by means of a model of the induction motor control system and a higher-order numerical model.     

多策略粒子群优化算法

为了克服粒子群优化算法易早熟、局部搜索能力弱的问题,提出了一种改进的粒子群优化算法--多策略粒子群优化算法。在群体寻优过程中,各粒子根据搜索到的最优位置的变动情况,从几种备选的策略中抉择出当代的最优搜索策略。其中,最优粒子有最速下降策略、矫正下降策略和随机移动策略可以选择,非最优粒子有聚集策略和扩散策略可以选择。四个典型测试函数的数值实验结果表明,新提出的算法比标准粒子群优化算法具有更强和更稳定的全局搜索能力。     

Fractional-order load-frequency control of interconnected power systems using chaotic multi-objective optimization

Fractional-order proportional-integral-derivative (FOPID) controllers are designed for load-frequency control (LFC) of two interconnected power systems. Conflicting time-domain design objectives are considered in a multi-objective optimization (MOO)-based design framework to design the gains and the fractional differ-integral orders of the FOPID controllers in the two areas. Here, we explore the effect of augmenting two different chaotic maps along with the uniform random number generator (RNG) in the popular MOO algorithm—the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Different measures of quality for MOO, e.g. hypervolume indicator, moment of inertia-based diversity metric, total Pareto spread, spacing metric, are adopted to select the best set of controller parameters from multiple runs of all the NSGA-II variants (i.e. nominal and chaotic versions). The chaotic versions of the NSGA-II algorithm are compared with the standard NSGA-II in terms of solution quality and computational time. In addition, the Pareto optimal fronts showing the trade-off between the two conflicting time domain design objectives are compared to show the advantage of using the FOPID controller over that with simple PID controller. The nature of fast/slow and high/low noise amplification effects of the FOPID structure or the four quadrant operation in the two inter-connected areas of the power system is also explored. A fuzzy logic-based method has been adopted next to select the best compromise solution from the best Pareto fronts corresponding to each MOO comparison criteria. The time-domain system responses are shown for the fuzzy best compromise solutions under nominal operating conditions. Comparative analysis on the merits and de-merits of each controller structure is reported then. A robustness analysis is also done for the PID and the FOPID controllers.     

A modified particle swarm optimization for aggregate production planning

Particle swarm optimization (PSO) originated from bird flocking models. It has become a popular research field with many successful applications. In this paper, we present a scheme of an aggregate production planning (APP) from a manufacturer of gardening equipment. It is formulated as an integer linear programming model and optimized by PSO. During the course of optimizing the problem, we discovered that PSO had limited ability and unsatisfactory performance, especially a large constrained integral APP problem with plenty of equality constraints. In order to enhance its performance and alleviate the deficiencies to the problem solving, a modified PSO (MPSO) is proposed, which introduces the idea of sub-particles, a particular coding principle, and a modified operation procedure of particles to the update rules to regulate the search processes for a particle swarm. In the computational study, some instances of the APP problems are experimented and analyzed to evaluate the performance of the MPSO with standard PSO (SPSO) and genetic algorithm (GA). The experimental results demonstrate that the MPSO variant provides particular qualities in the aspects of accuracy, reliability, and convergence speed than SPSO and GA.     

Hyperchaos synchronization using PSO-optimized RBF-based controllers to improve security of communication systems

This paper studies the Lorenz hyperchaos synchronization and its application to improve the security of communication systems. Two methods are proposed to synchronize the general forms of hyperchaotic systems, and their performance in secure communication application is verified. These methods use the radial basis function (RBF)-based neural controllers for this purpose. The first method uses a standard RBF neural controller. Particle swarm optimization (PSO) algorithm is used to derive and optimize the parameters of the RBF controller. In the second method, with the aim of increasing the robustness of the RBF controller, an error integral term is added to the equations of RBF neural network. For this method, the coefficients of the error integral component and the parameters of RBF neural network are also derived and optimized via PSO algorithm. For better comparison, the proposed methods and an optimal PID controller optimized by PSO are applied to the Lorenz hyperchaotic system for secure communication. Simulation results show the effectiveness and superiority of the proposed methods in both performance and robustness in comparison with the PID controller.