Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm

This paper introduces a new version of the particle swarm optimization (PSO) method. Two basic modifications for the conventional PSO algorithm are proposed to improve the performance of the algorithm. The first modification inserts adaptive accelerator parameters into the original velocity update formula of the PSO which speeds up the convergence rate of the algorithm. The ability of the algorithm in escaping from local optima is improved using the second modification. In this case, some particles of the swarm, which are named the superseding particles, are selected to be mutated with some probability. The proposed modified PSO (MPSO) is simple to be implemented, fast and reliable. To validate the efficiency and applicability of the MPSO, it is applied for designing optimal fractional-order PID (FOPID) controllers for some benchmark transfer functions. Then, the introduced MPSO is applied for tuning the parameters of FOPID controllers for a five bar linkage robot. Sensitivity analysis over the fractional order of the PID controller is also provided. Numerical simulations reveal that the MPSO can optimally tune the parameters of FOPID controllers.     

基于PSO和BP复合算法的模糊神经网络控制器

为了克服单独应用粒子群算法（PSO）或BP算法训练模糊神经网络控制器参数时存在的缺陷,提出了一种训练模糊神经网络参数的PSO＋BP算法。该算法将二者相结合,即在PSO算法中加入一个BP算子,以充分利用PSO算法的全局寻优能力和BP算法的局部搜索能力,从而更有效地提高其收敛速度、训练效率和提高该模糊神经网络控制器的控制效果。最后的仿真实验结果验证了该基于PSO＋BP复合算法的模糊神经网络控制器的有效性和可行性。     

Non-linear system control using a recurrent fuzzy neural network based on improved particle swarm optimisation

This article introduces a recurrent fuzzy neural network based on improved particle swarm optimisation (IPSO) for non-linear system control. An IPSO method which consists of the modified evolutionary direction operator (MEDO) and the Particle Swarm Optimisation (PSO) is proposed in this article. A MEDO combining the evolutionary direction operator and the migration operation is also proposed. The MEDO will improve the global search solution. Experimental results have shown that the proposed IPSO method controls the magnetic levitation system and the planetary train type inverted pendulum system better than the traditional PSO and the genetic algorithm methods.     

基于PSO的模糊控制器参数优化设计

本文提出了将微粒群优化(PSO)算法应用于模糊控制器的参数优化设计中,针对常用的工业对象模型进行了仿真实验,仿真结果表明基于微粒群算法优化模糊控制器参数可以获得满意的控制效果,PSO算法为模糊控制器的设计提供了一种的新的思路.     

Acceleration Factor Harmonious Particle Swarm Optimizer

A Particle Swarm Optimizer (PSO) exhibits good performance for optimization problems, although it cannot guarantee convergence to a global, or even local minimum. However, there are some adjustable parameters, and restrictive conditions, which can affect the performance of the algorithm. In this paper, the sufficient conditions for the asymptotic stability of an acceleration factor and inertia weight are deduced, the value of the inertia weight ω is enhanced to (-1,1). Furthermore a new adaptive PSO algorithm - Acceleration Factor Harmonious PSO (AFHPSO) is proposed, and is proved to be a global search algorithm. AFHPSO is used for the parameter design of a fuzzy controller for a linear motor driving servo system. The performance of the nonlinear model for the servo system demonstrates the effectiveness of the optimized fuzzy controller and AFHPSO.     

一种基于粒子群算法的模糊隶属函数优化方法

在分析图像模糊增强算法对于隶属函数及其模糊区域选择方法不足的基础上,提出一种新的基于粒子群算法的模糊隶属函数优化方法。该方法给出一个新模糊熵的定义,这个新模糊熵定义不仅考虑到图像在模糊域中划分区域时随隶属函数变化而变化的情况,同时又考虑到图像在空域中划分区域时随隶属函数变化而变化的情况。这样就使得图像依照最大熵准则变换到模糊域更能够有效地反映图像的固有信息。另外,根据图像增强算法中使用double型数据类型的特点,采用改进粒子群优化算法寻求隶属函数的最优参数。将新算法应用于图像增强中,取得了优于现有大多数模糊增强算法的效果。     

A multilevel image thresholding segmentation algorithm based on two-dimensional K–L divergence and modified particle swarm optimization

Multilevel image segmentation is a technique that divides images into multiple homogeneous regions. In order to improve the effectiveness and efficiency of multilevel image thresholding segmentation, we propose a segmentation algorithm based on two-dimensional (2D) Kullback–Leibler(K–L) divergence and modified Particle Swarm Optimization (MPSO). This approach calculates the 2D K–L divergence between an image and its segmented result by adopting 2D histogram as the distribution function, then employs the sum of divergences of different regions as the fitness function of MPSO to seek the optimal thresholds. The proposed 2D K–L divergence improves the accuracy of image segmentation; the MPSO overcomes the drawback of premature convergence of PSO by improving the location update formulation and the global best position of particles, and reduces drastically the time complexity of multilevel thresholding segmentation. Experiments were conducted extensively on the Berkeley Segmentation Dataset and Benchmark (BSDS300), and four performance indices of image segmentation – BDE, PRI, GCE and VOI – were tested. The results show the robustness and effectiveness of the proposed algorithm.     

Optimal fuzzy controller parameters using PSO for speed control of Quasi-Z Source DC/DC converter fed drive

The conventional controller suffers from uncertain parameters and non-linear qualities of Quasi-Z Source converter. However they are computationally inefficient extending to optimize the fuzzy controller parameters, since they exhaustively search the optimal values to optimize the objective functions. To overcome this drawback, a PSO based fuzzy controller parameter optimization is presented in this paper. The PSO algorithm is used to find the optimal fuzzy parameters for minimizing the objective functions. The feasibility of the proposed PSO technique has been simulated and tested. The results are bench marked with conventional fuzzy controller and genetic algorithm for two types of DC/DC converters namely double input Z-Source converter and Quasi-Z Source converter. The results of both the DC/DC converters for several existing methods illustrate the effectiveness and robustness of the proposed algorithm.     

A modified particle swarm optimization for production planningproblems in the TFT Array process

In this study, a practical production planning problem in the TFT (thin film transistor) Array process is introduced. Several researchers have referred to the capacitated production lot-sizing allocation problems as NP-Hard. Naturally, it is harder to solve the capacitated production allocation problem considering its practical characteristics and constraints, such as allocation problems among bottleneck machines, photo masks, and products with different re-entrant layers. In response to this, we proposed a novel variation of the particle swarm optimization (PSO) model called the modified PSO (MPSO), which is a binary PSO model with dynamic inertia weight and mutation mechanism. It improves some weaknesses as opposed to the original version of the PSO, including a propensity for obstruction near the optimal solution regions that hardly improve solution quality by fine tuning. In addition, it is converted to be able to solve the model of binary decision variables. In order to illustrate effectiveness, the traditional PSO (TPSO), genetic algorithm (GA), and the proposed MPSO are compared by application of the literature’s well-known test problems as well as the practical production planning problem in the TFT Array process. Based on the results of the investigation, it can be concluded that the proposed MPSO is more effective than the other approaches in terms of superiority of solution and required CPU time.     

基于粒子群优化的自适应模糊制冷控制算法

为解决空间斯特林制冷机和探测器热负载不确定及存在变化的问题,提出了自适应模糊PID制冷控制。在空间环境中使用的斯特林制冷机参数会随着时间的变化而发生改变,探测器负载也会随着工作模式和工作时间的变化而变化,整个制冷系统涉及的变量多,参数非线性。采用传统的控制方法,在固定的单一条件、环境下得到的控制参数,环境和负载发生变化后容易性能变差甚至不稳定,控制精度和稳定性不能满足使用要求。设计了一种自适应斯特林制冷机控制器,通过综合自适应模糊PID控制的方法,采用粒子群优化算法调整控制参数以减小代价函数。通过仿真和试验验证算法的有效性和鲁棒性。     

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.     

基于模糊c-means与自适应粒子群优化的模糊聚类算法

已有的粒子群模糊聚类算法需要设置粒子群参数并且收敛速度较慢,对此提出一种基于改进粒子群与模糊c-means的模糊聚类算法。首先,使用模糊c-means算法生成一组起始解,提高粒子群演化的方向性;然后,使用改进的自适应粒子群优化方法对数据进行训练与优化,训练过程中自适应地调节粒子群参数;最终,采用模糊c-means算法进行模糊聚类过程。对比实验结果表明,所提方法大幅度提高了计算速度,并获得了较高的聚类性能。     

基于模糊文化算法的自适应粒子群优化

为解决粒子群优化中惯性权重的调整机制在具体优化问题中的自适应问题,本文建立了一种全新的基于模糊文化算法的自适应粒子群优化算法;利用模糊规则表示个体粒子在演化过程中获取的经验,经验共享形成群体文化,并利用遗传算法来实现文化的进化;通过信念空间中以模糊规则表示的知识建立模糊系统来逼近与实际问题相适应的惯性权
权重控制器。在测试函数集上的仿真实验对比结果证明,该算法相对于现有算法有优势。     

A Hybrid Approach for Design of Stable Adaptive Fuzzy Controllers Employing Lyapunov Theory and Particle Swarm Optimization

This paper proposes a new approach for designing stable adaptive fuzzy controllers, which employs a hybridization of a conventional Lyapunov-theory-based approach and a particle swarm optimization (PSO) based stochastic optimization approach. The objective is to design a self-adaptive fuzzy controller, optimizing both its structures and free parameters, such that the designed controller can guarantee desired stability and can simultaneously provide satisfactory performance. The design methodology for the controller simultaneously utilizes the good features of PSO (capable of providing good global search capability, required to provide a high degree of automation) and Lyapunov-based tuning (providing fast adaptation utilizing a local search method). Three different variants of the hybrid controller are proposed in this paper. These variants are implemented for benchmark simulation case studies and real-life experimentation, and their results demonstrate the usefulness of the proposed approach.     

Comparative performance analysis of various binary coded PSO algorithms in multivariable PID controller design

In this paper, comparative performance analysis of various binary coded PSO algorithms on optimal PI and PID controller design for multiple inputs multiple outputs (MIMO) process is stated. Four algorithms such as modified particle swarm optimization (MPSO), discrete binary PSO (DBPSO), modified discrete binary PSO (MBPSO) and probability based binary PSO (PBPSO) are independently realized using MATLAB. The MIMO process of binary distillation column plant, described by Wood and Berry, with and without a decoupler having two inputs and two outputs is considered. Simulations are carried out to minimize two objective functions, that is, time integral of absolute error (ITAE) and integral of absolute error (IAE) with single stopping criterion for each algorithm called maximum number of fitness evaluations. The simulation experiments are repeated 20 times with each algorithm in each case. The performance measures for comparison of various algorithms such as mean fitness, variance of fitness, and best fitness are computed. The transient performance indicators and computation time are also recorded. The inferences are made based on analysis of statistical data obtained from 20 trials of each algorithm and after having comparison with some recently reported results about same MIMO controller design employing real coded genetic algorithm (RGA) with SBX and multi-crossover approaches, covariance matrix adaptation evolution strategy (CMAES), differential evolution (DE), modified continuous PSO (MPSO) and biggest log modulus tuning (BLT). On the basis of simulation results PBPSO is identified as a comparatively better method in terms of its simplicity, consistency, search and computational efficiency.     

三级倒立摆的加权变量模糊神经网络控制

为了提高三级倒立摆系统控制的响应速度和稳定性,在设计Mamdani型摸糊推理规则控制器控制倒立摆系统稳定的基础上,设计了一种更有效率的基于Sugeno型模糊推理规则的模糊神经网络控制器。该控制器使用BP神经网络和最小二乘法的混合算法进行参数训练,能够准确归纳输入输出量的模糊隶属度函数和模糊逻辑规则。通过与Mamdani型控制器的仿真对比,表明该Sugeno型模糊神经网络控制器对三级倒立摆系统的控制具有良好的稳定性和快速性,以及较高的控制精度。     

Adaptive fuzzy sliding mode controller for a class of SISO nonlinear time-delay systems

In this paper, we propose an adaptive fuzzy controller for a class of nonlinear SISO time-delay systems. The plant model structure is represented by a Takagi–Sugeno (T–S) type fuzzy system. The T–S fuzzy model parameters are adjusted online. The proposed algorithm utilizes the sliding surface to adjust online the parameters of T–S fuzzy model. The controller is based on adjustable T–S fuzzy parameters model and sliding mode theory. The stability analysis of the closed-loop system is based on the Lyapunov approach. The plant state follows asymptotically any bounded reference signal. Two examples have been used to check performances of the proposed fuzzy adaptive control scheme.     

A framework for designing cognitive trajectory controllers using genetically evolved interval type-2 fuzzy cognitive maps

In this paper, we provide a complete framework for the design of genetically evolved cognitive tracking controller based on interval type-2 (IT2) fuzzy cognitive map (FCM). We construct the cognitive controller based on a nonlinear controller by transforming its representation into a FCM. This representation gives the opportunity to prove the stability of the cognitive controller in the framework of nonlinear control theory. Moreover, with the deployment of IT2-fuzzy sets which are known to be capable to handle high level of uncertainty, the proposed cognitive controller has the ability to deal with uncertainty that are encountered in real-time world applications. To accomplish the design of the cognitive controller, we present a systematic approach based on genetic algorithm to optimize its parameters and learn fuzzy rules by extracting them from model space (e.g., a set of rules). Within the paper, all steps in constructing and designing the IT2-FCM-based cognitive controller are presented. We first show the performance improvements of the proposed IT2-FCM-based tracking controller with extensive and comparative simulation results and then with experimental results that were collected on real-world mobile robot. The results clearly show the superiority of proposed cognitive control systems when compared to its conventional and fuzzy controller counterparts. We believe that the proposed genetically evolved design approach of the IT2-FCM-based cognitive controller will provide a bridge between the well-developed cognitive sciences and control theory.     

Automatically extracting T–S fuzzy models using cooperative random learning particle swarm optimization

This paper proposes a methodology for automatically extracting T–S fuzzy models from data using particle swarm optimization (PSO). In the proposed method, the structures and parameters of the fuzzy models are encoded into a particle and evolve together so that the optimal structure and parameters can be achieved simultaneously. An improved version of the original PSO algorithm, the cooperative random learning particle swarm optimization (CRPSO), is put forward to enhance the performance of PSO. CRPSO employs several sub-swarms to search the space and the useful information is exchanged among them during the iteration process. Simulation results indicate that CRPSO outperforms the standard PSO algorithm, genetic algorithm (GA) and differential evolution (DE) on the functions optimization and benchmark modeling problems. Moreover, the proposed CRPSO-based method can extract accurate T–S fuzzy model with appropriate number of rules.     

Adaptive intelligent cascade control of a ball-riding robot for optimal balancing and station-keeping

This paper presents an adaptive intelligent cascade control strategy to maintain the dynamic stability of a ball-riding robot (BRR). The four-wheeled mechanism beneath the robot body balances it on a spherical wheel. The BRR is modeled as a combination of two decoupled inverted pendulums. Therefore, two independent controllers are used to control its pitch and roll rotations. An incremental proportional–integral–derivative (PID) is implemented in the inner loop of the cascade to maintain the vertical balance. A generic PD controller is used in the outer loop to keep the station by controlling its spatial position. The controller parameters are automatically tuned via a fuzzy adaptation mechanism. The centers of fuzzy output membership functions are dynamically updated via an extended Kalman filter (EKF). The proposed controller quickly responds to changes in system’s state and effectively rejects the exogenous disturbances. The results of real-time experiments are presented to validate the effectiveness of the proposed hybrid controller over the conventional classical controllers.