The design of a fuzzy cascade controller for ball and beam system: A study in optimization with the use of parallel genetic algorithms

In this study, we introduce a design methodology for an optimized fuzzy cascade controller for ball and beam system by exploiting the use of hierarchical fair competition-based genetic algorithm (HFCGA). The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball and exhibits a number of interesting and challenging properties when considered from the control perspective. The position of ball is determined through the control of a servo motor. The displacement change of the position of ball requires the change of the angle of the beam which determines the position angle of a servo motor. Consequently, the variation of the position of the moving ball and the ensuing change of the angle of the beam results in the change of the position angle of a servo motor. We introduce the fuzzy cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller in a cascaded architecture. Auto-tuning of the parameters of the controller (viz. scaling factors) of each fuzzy controller is realized with the use of the HFCGA. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as a reference value which enters into the inner controller as the 2nd controller of the two cascaded controllers. HFCGA is a kind of a parallel genetic algorithm (PGA), which helps alleviate an effect of premature convergence being a potential shortcoming present in conventional genetic algorithms (GAs). A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy cascade controller and the conventional PD cascade controller whose design relied on the use of the serial genetic algorithms.     

倒立摆的双闭环模糊控制

对倒立摆采用双闭环的模糊控制方案，内环控制倒立摆的角度，外环控制倒立摆的位置，两个模糊控制器的设计都很简单，执行时间很短。在实际倒立摆装置上的实验结果验证了该方案的可行性和良好的控制性能。     

Optimized fuzzy PD cascade controller: A comparative analysis and design

In this study, we develop a design methodology for a fuzzy PD cascade controller for a ball & beam system by using particle swarm optimization (PSO). The ball & beam system is a well-known control engineering experimental setup, which consists of servo motor, beam, and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball & beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor. Consequently the variation of the position of the moving ball and the ensuing change of the angle of the beam results in the change of the position angle of a servo motor. We introduce a fuzzy PD cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller arranged in a cascaded architecture. Auto-tuning of the parameters of the controller (scaling factors) as well as fuzzy rules of each fuzzy PD controller is realized with the use of the PSO. Moreover the comparative analysis of results of optimization realized by PSO and GA based on SGA (Serial Genetic Algorithms) is discussed from the viewpoint of control performance. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as reference value, which enters into the inner controller as the 2nd controller of the two cascaded controllers. The optimization process takes advantage of a rapid convergence of PSO being used here as a generic search mechanism. A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy PD cascade controller and the conventional PD cascade controller whose design exploited serial genetic algorithms.     

倒立摆的一种模糊控制方法

提出一种模糊控制方案,实现对倒立摆系统的平衡控制.针对倒立摆系统多变量的特性,采用双模糊控制器方案,分别对摆杆倾角和小车位移设计模糊控制器,大大降低了设计难度;为了实现对摆角和位移双重控制的功能,采用两个控制器轮流控制的策略,当摆角偏差或角速度值较大时,摆角控制器起作用,保持摆杆的垂直,反之,位移控制器起作用,调整小车位置不越界.在实际的物理设备上进行了实时控制实验,实验结果验证了方案的正确性和有效性.     

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.     

基于变量分组模糊控制算法的倒立摆系统

采用模糊控制理论研究了直线一级倒立摆控制问题。直线一级倒立摆系统是多变量不稳系统,为了解决模糊规则爆炸问题,本文采用了变量分组的方法完成倒立摆模糊控制器的设计方案。要使直线一级倒立摆系统稳定,必须对小车位置和摆杆角度同时进行闭环控制,而单一的控制只能控制一个控制量,本文提出了两回路的模糊控制方案。仿真和实验结果证明了该方案的可行性和良好的控制性能。     

A Study on Lateral Control of Autonomous Vehicles via Fired Fuzzy Rules Chromosome Encoding Scheme

In this paper, we propose a novel Fired Rules Chromosomes (FRC) encoding scheme for a fuzzy controller tuned by Genetic Algorithms (GA). The proposed method improves the optimization speed through the reduction of the search space. In addition, an improvement in convergence is demonstrated. The fuzzy controller optimized by the FRC scheme is employed to maintain the lateral position of an autonomous vehicle. The robustness of the controller to parameter variation is studied by Monte-Carlo analysis. Simulation and experimental studies demonstrate the performance of the lateral controller.     

无人直升机基于视觉的静止点目标跟踪*

针对带有摄像机的直升机进行静止点目标跟踪的情况,提出了一种层级控制器。该控制器共有三个回路：内回路采用四个独立的PD控制器控制直升机的高度和姿态;中间回路利用两个Mamdani型模糊控制器控制直升机的位置;外回路利用视觉反馈获得直升机下一步的期望位置,其不需要已知摄像机的内参数和平移外参数以及目标点的坐标,只需已知粗略标定的旋转外参数。仿真结果表明了该控制器的可行性。     

倒立摆的双闭环选择型模糊控制设计及仿真

针对多变量、非线性、强耦合性的倒立摆系统 ,采用牛顿 -欧拉法建立了其动力学方程 ,并进行了线性化处理 ,得到了状态空间模型 ,并提出一种双闭环选择型模糊控制方案。该方案通过一个选择型开关将两个模糊控制器的工作有机地统一起来 ,实现了摆杆角度与小车位置的双重控制功能 ,而且降低了模糊控制器的设计难度。最后在MATLAB环境下进行了计算机仿真 ,仿真结果表明 ,摆杆角度和小车位置的控制过程均具有良好的动态性能和稳态性能 ,验证了建模的正确性和控制方案的有效性     

Simplifying the automatic design of a fuzzy logic controller using evolutionary programming

With the availability of a wide range of Evolutionary Algorithms such as Genetic Algorithms, Evolutionary Programming, Evolutionary Strategies and Differential Evolution, every conceivable aspect of the design of a fuzzy logic controller has been optimized and automated. Although there is no doubt that these automated techniques can produce an optimal fuzzy logic controller, the structure of such a controller is often obscure and in many cases these optimizations are simply not needed. We believe that the automatic design of a fuzzy logic controller can be simplified by using a generic rule base such as the MacVicar-Whelan rule base and using an evolutionary algorithm to optimize only the membership functions of the fuzzy sets. Furthermore, by restricting the overlapping of fuzzy sets, using triangular membership functions and singletons, and reducing the number of parameters to represent the membership functions, the design can be further simplified. This paper describes this method of simplifying the design and some experiments performed to ascertain its validity.     

Fuzzy logic controller design for spacecraft proximity operations

A Genetic Algorithms (GAs) based method is presented in this paper for concurrent design of rule sets and membership functions for a fuzzy logic controllers to be used in spacecraft proximity operations. The heuristic nature of fuzzy logic makes GAs a natural candidate for logic design in which both rule sets and membership functions are optimized simultaneously. The employment of GAs natural genetic operations provides a means to search in a complex system space that is difficult to described mathematically. A one-dimensional controller for spacecraft proximity operations is implemented for examination in detail. The expension of the algorithm for a 6 DOP controller is discussed.     

A comparative experimental study of type-1/type-2 fuzzy cascade controller based on genetic algorithms and particle swarm optimization

In this study, we introduce the design methodology of an optimized fuzzy controller with the aid of particle swarm optimization (PSO) for ball and beam system.The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball and beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor.The fixed membership function design of type-1 based fuzzy logic controller (FLC) leads to the difficulty of rule-based control design when representing linguistic nature of knowledge. In type-2 FLC as the expanded type of type-1 FL, we can effectively improve the control characteristic by using the footprint of uncertainty (FOU) of the membership functions. Type-2 FLC exhibits some robustness when compared with type-1 FLC.Through computer simulation as well as real-world experiment, we apply optimized type-2 fuzzy cascade controllers based on PSO to ball and beam system. To evaluate performance of each controller, we consider controller characteristic parameters such as maximum overshoot, delay time, rise time, settling time, and a steady-state error. In the sequel, the optimized fuzzy cascade controller is realized and also experimented with through running two detailed comparative studies including type-1/type-2 fuzzy controller and genetic algorithms/particle swarm optimization.     

Design of optimized cascade fuzzy controller based on differential evolution: Simulation studies and practical insights

In this study, we discuss a design of an optimized cascade fuzzy controller for the rotary inverted pendulum system and ball & beam system by using an optimization vehicle of differential evolution (DE). The structure of the differential evolution optimization environment is simple and a convergence to optimal values realized here is very good in comparison to the convergence reported for other optimization algorithms. DE is easy to use given its mathematical operators. It also requires a limited computing overhead. The rotary inverted pendulum system and ball & beam system are nonlinear systems, which exhibit unstable motion. The performance of the proposed fuzzy controller is evaluated from the viewpoint of several performance criteria such as overshoot, steady-state error, and settling time. Their values are obtained through simulation studies and practical, real-world experiments. We evaluate and analyze the performance of the proposed optimal fuzzy controller optimized by Genetic Algorithm (GA), and DE. In this setting, we show the superiority of DE versus other methods being used here as well as highlight the characteristics of this optimization tool.     

基于遗传算法的模糊控制器的优化设计——采用模糊数据挖掘技术

论文为模糊系统建模提出了一种新颖的方法——由输入输出数据集合设计基于遗传算法的模糊控制器,该方法采用模糊数据挖掘技术,从大量的输入输出数据集合中自动地提取模糊规则模型,确定模糊分割点及各变量的隶属度函数;并利用实数编码的遗传算法RGA对隶属度函数参数进行全面优化。最后通过实例及仿真验证了该方法的有效性。     

一种基于遗传算法优化的模糊控制器研究

模糊控制中的模糊推理规则和隶属函数的选取往往依据相关专家或技术人员的实际经验,具有较大的人为主观性,尤其在面对具有较强的非线性系统和未知动态环境条件下,其控制性能达不到客观要求。本文采用改进的遗传算法优化模糊控制中的比例因子,从而对控制规则和隶属函数进行优化。仿真结果表明,经过优化后的模糊控制器和传统的Fuzzy-PID控制器相比,其控制规则和隶属函数更加客观合理,控制系统的动、静态性能都有较大提高。     

五种倒立摆控制器对比研究

针对水平导轨直线型倒立摆的稳定控制问题,论文设计了线性二次型调节器LQR和LQY、拟人智能控制器和模糊控制器,提出了一种基于泛组合模型的智能控制器。用这五种控制器对系统进行控制,实验证明了所提出的智能控制模型的有效性。对各控制器控制效果的比较研究说明智能控制比线性控制更适合解决这类非线性控制问题。     

基于基因算法的多变量模糊控制器的设计*

本文提出了一种通用的模糊控制器的设计方法，这种方法运用基因算法进行寻优，具有设计速度快、人工干预少，可获得一个基于一定性能指标的次优或最优模糊控制器。它可以对多输入多输出（ＭＩＭＯ）系统进行设计，不需要被控对象的精确数学模型，本文最后以二级倒立摆系统为控制对象给出了一个设计实例和实际控制的结果。     

Incremental Evolutionary Design of TSK Fuzzy Controllers

This paper proposes a novel method for the incremental design and optimization of first order Tagaki-Sugeno-Kang (TSK) fuzzy controllers by means of an evolutionary algorithm. Starting with a single linear control law, the controller structure is gradually refined during the evolution. Structural augmentation is intertwined with evolutionary adaptation of the additional parameters with the objective not only to improve the control performance but also to maximize the stability region of the nonlinear system. From the viewpoint of optimization the proposed method follows a divide-and-conquer approach. Additional rules and their parameters are introduced into the controller structure in a neutral fashion, such that the adaptations of the less complex controller in the previous stage are initially preserved. The proposed scheme is evaluated at the task of TSK fuzzy controller design for the upswing and stabilization of a rotational inverted pendulum. In the first case, the objective is a time optimal controller that upswings the pendulum in to the upper equilibrium point in shortest time. The stabilizing controller is designed as a state optimal controller. In a second application the optimization method is applied to the design of a fuzzy controller for vision-based mobile robot navigation. The results demonstrate that the incremental scheme generates solutions that are similar in control performance to pure parameter optimization of only the gains of a TSK system. Even more important, whereas direct optimization of control systems with more than 35 rules fails to identify a stabilizing control law, the incremental scheme optimizes fuzzy state-space partitions and gains for hundreds of rules.     

Teaching–learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system

This paper deals with the design of a novel fuzzy proportional–integral–derivative (PID) controller for automatic generation control (AGC) of a two unequal area interconnected thermal system. For the first time teaching–learning based optimization (TLBO) algorithm is applied in this area to obtain the parameters of the proposed fuzzy-PID controller. The design problem is formulated as an optimization problem and TLBO is employed to optimize the parameters of the fuzzy-PID controller. The superiority of proposed approach is demonstrated by comparing the results with some of the recently published approaches such as Lozi map based chaotic optimization algorithm (LCOA), genetic algorithm (GA), pattern search (PS) and simulated algorithm (SA) based PID controller for the same system under study employing the same objective function. It is observed that TLBO optimized fuzzy-PID controller gives better dynamic performance in terms of settling time, overshoot and undershoot in frequency and tie-line power deviation as compared to LCOA, GA, PS and SA based PID controllers. Further, robustness of the system is studied by varying all the system parameters from −50% to +50% in step of 25%. Analysis also reveals that TLBO optimized fuzzy-PID controller gains are quite robust and need not be reset for wide variation in system parameters.     

A novel hybrid DEPS optimized fuzzy PI/PID controller for load frequency control of multi-area interconnected power systems

In this paper, a novel hybrid Differential Evolution (DE) and Pattern Search (PS) optimized fuzzy PI/PID controller is proposed for Load Frequency Control (LFC) of multi-area power system. Initially a two-area non-reheat thermal system is considered and the optimum gains of the fuzzy PI/PID controller are optimized employing a hybrid DE and PS (hDEPS) optimization technique. The superiority of the proposed controller is demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as DE, Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI controllers for the same interconnected power system. Furthermore, robustness analysis is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Additionally, the proposed approach is further extended to multi-area multi-source power system with/without HVDC link and the gains of fuzzy PID controllers are optimized using hDEPS algorithm. The superiority of the proposed approach is shown by comparing the results with recently published DE optimized PID controller and conventional optimal output feedback controller for the same power systems. Finally, Reheat turbine, Generation Rate Constraint (GRC) and time delay are included in the system model to demonstrate the ability of the proposed approach to handle nonlinearity and physical constraints in the system model.