基于能量控制与近似输出调节的二级倒立摆起摆和跟踪控制

二级倒立摆是一个典型的欠驱动非线性系统,其控制问题具有一定的挑战性.为了解决时变参考信号下二级倒立摆的起摆和跟踪控制问题,本文提出了一种基于能量控制与近似输出调节方法的起摆和三阶控制器设计方案.首先,采用能量控制方法将第1级摆杆从下垂位置摆起到倒立位置附近;其次,采用滑模控制方法将第1级摆杆稳定在倒立位置,同时,采用等效小车与能量控制相结合的方法将第2级摆杆摆起到倒立位置附近;最后,采用基于近似输出调节理论的多项式近似方法设计三阶控制器实现二级倒立摆的位置跟踪控制.仿真和实验结果均验证了该控制方案的有效性.     

单神经元PID倒立摆系统

为解决双PD倒立摆控制器参数不可调的难题,利用单神经元PID控制算法简单、权值可调的特点,针对倒立摆系统,设计出基于小车位移和摆杆摆角两个回路的单神经元PID控制器。通过仿真实验研究,证明了该控制方案的可行性和有效性。最后,将该控制方案与目前常使用的双PD控制及LQR控制进行了比较。     

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。     

单神经元PID算法在倒立摆控制系统中的应用

倒立摆是非线性、不稳定的系统.本文使用单神经元PID控制算法,设计出基于小车位移和摆杆摆角两个回路的单神经元PID控制器,并与传统的PD控制策略相比较,验证了其有效性和可行性.     

一种基于鲁棒性设计的一阶倒立摆双闭环控制方法

本文在利用牛顿运动定律建立起一阶倒立摆数学模型的基础上．对精确模型进行了工作点附近的线性化与降阶处理；以摆角为内环、小车位移为外环．利用鲁棒控制理论设计出确定参数(摆长L和摆杆质量m)下的内、外环PD控制器；数字仿真实验证明了该方法的有效性。     

车轨长度受限的并行双摆能量控制

采用牛顿-欧拉方法建立并行二级倒立双摆系统的数学模型.针对车轨长度受限的并行二级倒立摆系统,本文提出了一种基于能量控制思想和直接李雅普诺夫函数方法的摆起控制策略.所设计的控制器保证了小车的速度收敛到零和摆杆在达到垂直向上的位置时摆杆的能量为零.同时,它能实现对并行双摆的稳摆控制.控制器简单易行,参数调节方便.在并行二级倒立摆摆起控制器设计的基础上,简述了三级车摆的摆起控制器设计过程.最后,通过计算机仿真验证了控制方法在工作效率和抗干扰方面能保持良好的控制性能.     

单级倒立摆的简化模糊控制及仿真研究

单级倒立摆系统是一种广泛应用的物理模型,为了研究其特性,应用拉格朗日方程建立了其精确数学模型,建模中考虑了摩擦力.同时为解决模糊多变量控制中的"维数灾"问题,利用单输入规则动态加权推理模糊控制器(SIRMs)实现了单级倒立摆系统的控制,SIRMs将多维模糊控制问题化简成单维模糊控制问题来解决,大大减少了模糊规则数.利用随机优化搜索法优化了控制参数,其中,所建立的动态参数权重使得摆杆角度控制优先于小车位移控制,故倒立摆不会因为同时控制角度与小车位移而失去稳定性.利用Vissim对基于SIRMs模糊控制器的倒立摆系统进行了仿真实验,结果表明该方法能够较好地完成倒立摆的运动控制,系统跟踪速度快,超调量小,具有很强的鲁棒性和更好的动静态特性,验证了模型和控制算法的有效性.     

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。     

平面倒立摆自适应滑模模糊控制

采用拉格朗日方程建立平面倒立摆的动力学模型，并将其在平衡位置进行线性化，得到了系统在X和Y两个正交控制方向解耦的近似模型．针对每一个控制方向上由互相耦合的基座小车定位子系统和摆杆镇定子系统组成的欠驱动系统，设计了自适应滑模模糊控制器，实现了基座小车沿圆周行走条件下摆杆的运动平衡控制．行走实验验证了所提出控制算法的有效性．     

平面一级倒立摆的稳定控制

平面倒立摆系统是进行控制理论研究的理想实验平台.在对平面一级倒立摆进行运动学和动力学分析的基础上,采用拉格朗日方程建立了它的动力学模型.分别设计了LQR控制器和模糊控制器,应用所设计的控制器对倒立摆系统进行了实时控制实验.验证了两种控制方法的优缺点.     

Design of optimized fuzzy cascade controllers by means of Hierarchical Fair Competition-based Genetic Algorithms

In this study, we present a design of an optimized fuzzy cascade controller based on Hierarchical Fair Competition-based Genetic Algorithms (HFCGA) for a rotary inverted pendulum system. In this system, one controls the movement of a pendulum through the adjustment of a rotating arm. The objective is to control the position of the rotating arm and to make the pendulum maintain the unstable equilibrium point at vertical position. To control the system, we design a fuzzy cascade controller scheme which consists of two fuzzy controllers arrange in a cascaded topology. The parameters of the controller are optimized by means of the HFCGA algorithm. The fuzzy cascade scheme comprises two controllers located in two loops. An inner loop controller governs the position of the rotating arm while an outer controller modifies a set point of the inner controller implied by the changes of the angle of pendulum. The HFCGA being a computationally effective scheme of the Parallel Genetic Algorithm (PGA) has been developed to eliminate an effect of premature convergence encountered in Serial Genetic Algorithms (SGA). It has emerged as an effective optimization vehicle to deal with very large search spaces. A comparative analysis involving computing simulations and practical experiment demonstrates that the proposed HFCGA based fuzzy cascade controller comes with superb performance in comparison with the conventional Linear Quadratic Regulator (LQR) controller as well as HFCGA-based PD cascade controller.     

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     

Systematic design method of stabilization fuzzy controllers for pendulum systems

A systematic method to construct stabilization fuzzy controllers for a single pendulum system and a series-type double pendulum system is presented based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model. The angle and angular velocity of each pendulum and the position and velocity of the cart are selected as the input items. Each input item is given with a SIRM and a dynamic importance degree. All the SIRMs have the same rule setting. The dynamic importance degrees use the absolute value(s) of the angle(s) of the pendulum(s) as the antecedent variable(s). The dynamic importance degrees are designed such that the upper pendulum angular control takes the highest priority and the cart position control takes the lowest priority when the upper pendulum is not balanced upright. The control priority orders are automatically adjusted according to control situations. The simulation results show that the proposed fuzzy controllers have high generalization ability to completely stabilize a wide range of single pendulum systems and series-type double pendulum systems in short time. By extending the architecture, a stabilization fuzzy controller for a series-type triple pendulum system is even possible. © 2001 John Wiley & Sons, Inc.     

Robust stabilisation of rotary inverted pendulum using intelligently optimised nonlinear self-adaptive dual fractional-order PD controllers

This article presents an intelligently optimised self-tuning fractional-order control scheme to improve the attitude-stabilisation of an inverted pendulum. Primarily, the scheme employs two Fractional-order Proportional-Derivative (FPD) controllers acting concurrently on the system to minimise the deviations in its state-trajectories. Wherein, one FPD controller compensates the variations in pendulum-angle and its fractional-order derivative to vertically balance the pendulum, where as the other FPD controller acts as a position controller and regulates the variations in arm-angle and its fractional-order derivative. The integration of fractional calculus with conventional PD controllers optimises the reference-tracking performance of the control scheme by increasing its degrees-of-freedom and design flexibility. In order to further improve the system’s immunity against exogenous disturbances, the PD gains of each controller are dynamically adjusted after each sampling interval using piecewise nonlinear functions of their respective state-variations. The hyper-parameters of the nonlinear gain-adjustment functions as well as the fractional-number power of the derivative-operator of each controller are selected via Particle-Swarm-optimisation (PSO) algorithm. The proposed adaptive control scheme is tested on the QNET Rotary Inverted Pendulum setup via ‘hardware-in-the-loop’ experiments. The optimality and robustness of the proposed control scheme are validated by comparing its performance with PSO-based fixed-gain dual-PD and dual-FPD control schemes.     

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.     

Neural network control for position tracking of a two-axis inverted pendulum system: experimental studies.

In this paper, experimental studies of a decentralized neural network control scheme of the reference compensation technique applied to control a 2-degrees-of-freedom (2-DOF) inverted pendulum on an x - y plane are presented. Each axis is controlled by two separate neural network controllers to have a decoupled control structure. Neural network controllers are applied not only to balance the angle of pendulum, but also to control the position tracking of the cart. The decoupled control structure can compensate for uncertainties and cancel coupling effects. Especially, a circular trajectory tracking task is tested for position tracking control of the cart while maintaining the angle of the pendulum. Experimental result shows that position control of the inverted pendulum and cart is successful.     

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.     

Speed control of induction motors using a novel fuzzy sliding-modestructure

This paper presents a new approach to indirect vector control of induction motors. Two nonlinear controllers, one of sliding mode type and the other PI-fuzzy logic-based, define a new control structure. Both controllers are combined by means of an expert system based on Takagi-Sugeno fuzzy reasoning. The sliding-mode controller acts mainly in a transient state while the PI-like fuzzy controller acts in the steady state. The new structure embodies the advantages that both nonlinear controllers offer: sliding-mode controllers increasing system stability limits, and PI-like fuzzy logic based controllers reducing the chattering in permanent state. The scheme has been implemented and experimentally validated