基于LQR球杆系统的控制方法研究与设计仿真
关键字：球杆系统；数学模型；频率响应；二次最优控制
Research and design of ball and beam system’s control method
Abstract: Ball-beam system is a typically nonlinear and unstable system in the field of control; what the objective of the control is to locate the ball at the given position of the guide rail. By building the models of machines, the relationship of angles and the model of motor, the nonlinear model of the ball-beam system can be obtained. Linearizing the ball-beam system near the equilibrium point contributes to getting the ball-beam system’s linear model. The purposes of this paper are to analyze the response of its open-loop step input and design two controllers. One is based on frequency response and the other is based on the quadratic optimal control. Frequency response controller which uses the lead compensation can successfully implement the real-time control. In allusion to the instability and non-linear characteristics of the ball-beam system, we use the theory of quadratic, with selecting the location of the ball, the speed of the ball, the gear's angle and gear's angular velocity as the state variable, to design the controller based on LQR. Meanwhile I conduct the simulated experiments using MATLAB and make contrastive analysis from the control effects of two controllers.
Keywords: Ball-beam system；Mathematical model; Frequency response；Quadratic optimal control
目录
1 绪论 1
1.1 球杆系统的研究意义 1
1.2 国内外球杆系统的研究现状 1
1.3 本课题的主要工作 2
2 球杆系统的建模 4
2.1 球杆系统的特性分析 4
2.2 球杆系统的数学模型 4
2.2.1 机械部分的数学模型 4
2.2.2 角度关系模型 6
2.2.3 电机模型 7
3 球杆系统的频率响应控制方法研究 11
3.1 球杆系统的开环模型 11
3.2 基于频率响应控制方法研究 11
4 二次最优控制理论基础 17
4.1 最优控制简介 17
4.2 线性二次型问题 17
4.3 二次最优控制的MATLAB应用 20
4.3.1 MATLAB软件介绍 20
4.3.2 MATLAB程序设计 20
4.3.3 Simulink的简介 20
4.3.4 MATLAB/Simulink在线性二次型最优控制中的应用 21
5 球杆系统的二次最优控制设计 22
5.1 球杆系统的状态空间模型 22
5.1.1 线性化系统模型 22
5.1.2 状态空间模型 22