摘要：倒立摆是一个典型的开环不稳定系统。系统本身的复杂性和非线性特点对控制系统的设计具有很大的挑战性。本课题以单级倒立摆模型为研究对象，采用机理建模的方法推导出倒立摆系统的状态空间模型，并对系统的开环不稳定性进行了分析。课题采用二次最优控制和模糊推理设计了控制器。围绕倒立摆控制系统主要探讨了以下两点：第一，设计了倒立摆系统的二次最优控制，并在实验设备上进行了实时控制。最后，分析了加权矩阵对控制系统的影响。第二，利用二次最优控制得到的反馈矩阵设计了分层控制，成功解决了模糊规则不能穷举问题并结合相关的模糊控制设计了模糊控制器。通过对两种控制器的仿真，比较了两种控制器的优劣和差异。仿真结果表明：采用了分层控制技术的模糊控制能够较好控制倒立摆系统，使整个系统具有较高的抗干扰性。24557
毕业论文关键词：单级倒立摆；最优二次控制；模糊控制；融合函数
Design the controller of the Single-stage inverted pendulum
Abstract: The inverted pendulum is a typical open-loop unstable systems. The complexity of the system itself and nonlinear characteristics of the inverted pendulum system has a great challenge for designing controller. The topics used single-stage inverted pendulum model for the study, using the mechanism modeling method to derive the inverted pendulum system state space model, and analyzed open-loop instability of the system. Topic quadratic optimal control and fuzzy reasoning designed controller. Around the inverted pendulum control system focuses on the following points: First, to design the optimal control of secondary inverted pendulum system, and take real-time control on the experimental equipment. Finally, analyzed the influence of the weighting matrix of the control system. Second, using the feedback matrix of the LQR controller designd hierarchical controller ,successfully solves the problem that the fuzzy rules can not be exhaustive and with the knowledge of the fuzzy controller ,we designd the fuzzy controller .Compared the merits and differences between the two controllers though simulake the two controllers,. Simulation results show that: the use of hierarchical fuzzy control technology can better control the inverted pendulum control system, so that the whole system has high noise immunity.
Key Words:  Single-stage inverted pendulum;Optimal control ; Fuzzy controller; Fusion function
目录
1  绪论    1
1.1  倒立摆控制系统研究设计的意义    1
1.2  倒立摆系统的发展过程及现状    1
1.3  本课题研究的主要难点和内容    2
1.3.1  倒立摆系统的难点    2
1.3.2  本课题要研究的内容    2
2  倒立摆系统简介    4
2.1  倒立摆的类型及特点    4
2.2  倒立摆系统介绍    5
2.3  MATLAB/SIMULINK的介绍    6
3  倒立摆系统的建模和可控性分析    8
3.1   倒立摆数学模型的建立    8
3.1.1  倒立摆模型推导原理    8
3.1.2  倒立摆模型的建立    8
3.2  一级倒立摆的可控制性分析    11
4  LQR控制    14
4.1 线性二次最优控制原理    14
4.2 单级倒立摆的LQR控制器设计    16
4.3  一级倒立摆LQR实时控制    17
5  模糊控制器设计    20
5.1模糊控制的基本思想    20
5.2模糊控制的基本原理    20
5.3 模糊控制器设计的基本方法    21 单级倒立摆的控制系统设计+源程序:http://www.youerw.com/wuli/lunwen_18101.html