[倒立摆论文.doc

倒立摆控制器的设计与研究 摘要 倒立摆系统是非线性、强耦合、多变量和自然不稳定的系统，是机器人技术、控制理论、计算机控制等多个领域、多种技术的有机结合。在控制过程中，它能有效地反映诸如可镇定性、鲁棒性、随动性以及跟踪等许多控制中的关键问题，是检验各种控制理论的理想模型。控制器的设计是倒立摆系统的核心内容。目前典型的控制器设计理论有PID控制、根轨迹以及频率响应法、状态空间法、最优控制理论等。 本文详细介绍了一级倒立摆系统的控制器设计过程，首先概述了倒立摆系统的数学模型，其次，分别采用PID控制算法和状态空间极点配置法对倒立摆系统进行了控制器设计。在设计控制器的过程中，采用Matlab软件对控制系统进行编程仿真，并用M文件以及Simulink工具箱对所采用的设计方法进行仿真。仿真结果验证了算法的有效性，同时表明采用状态空间极点配置法所设计的控制器能够同时控制摆杆的角度以及小车的位置，较经典的PID控制算法好。 关键词：倒立摆；PID控制；极点配置；状态空间 DESIGN AND RESEARCH OF INVERTED PENDELUM ABSTRACT Inverted Pendulum is a nonlinear, coupling, variable and natural unsteadiness system, which includes robot technology, control theory, computer control and so on. During the control process, pendulum can effectively reflect many pivotal problems such as equanimity, robust, follow-up and track. Therefore, it is a perfect model used to testing various control theories. The design of controller is a main work of pendulum system. At present, the methods of controller design include: PID control, root locus and frequency respond, state-space method, optimal control theory and so on. The process of a controller design for the first-level inverted pendulum system is introduced. In this paper, a PID control and a pole assignment with state-space design are proposed. The Matlab software is used to carring out a program and simulation in the process of the controller design. The M-file and simulink tool box are applied, and the result shows that these methods are effective. Form this paper, the controller designed by pole assignment with state-space is able to control the angle of pendulum bar and the location of handcart at the same time. The simulation shows that the method of state-space is better than traditional PID control algorithm. Key words: Inverted pendulum; PID control; Pole assignment; State-space 第1章 绪论 1.1 引言 杂技顶杆表演之所以为人们熟悉，不仅是其技术的精湛引人入胜，更重要的是其物理本质与控制系统的稳定性密切相关。它深刻揭示了自然界一种基本规律，即一个自然不稳定的被控制对象，通过控制手段可使之具有良好的稳定性。由此不难看出杂技演员顶杆表演的物理机制可简化为一个倒置的倒立摆装置，也就是人们常称的倒