【作者】 焦灵侠；

【导师】 张荷芳；

【作者基本信息】 西安工业大学 ， 控制理论与控制工程， 2010， 硕士

【摘要】 倒立摆控制系统是检验控制算法的一个典型的对象,其中倒立摆摆杆级数的增加和其控制算法的更新都是倒立摆控制系统的重要研究内容。倒立摆系统本身是一个多变量、非线性、强耦合和自然不稳定的系统。由于倒立摆系统与机器人的站立、行走和火箭的飞行等有很大的相似性,所以对倒立摆控制问题的研究具有重要的理论和实际指导意义。本文以深圳固高公司提供的倒立摆控制系统为研究对象,在讨论直线倒立摆系统数学模型的基础上,采用了LQR(Linear Quadratic Regulation)线性二次型调节器控制算法和模糊控制算法分别实现了对一级倒立摆和二级倒立摆系统的仿真和实时控制研究。主要的研究内容包括：讨论了一级倒立摆和二级倒立摆系统的数学模型,并分析了一级倒立摆和二级倒立摆系统的稳定性、能控性、能观性和可控性,分析表明倒立摆系统在开环状态下是不稳定的,但是在其平衡点位置附近是可控制、可观测的,而且一级倒立摆系统比二级倒立摆系统可控度更高。进行了倒立摆系统的LQR控制算法的研究,介绍了如何利用Matlab/Simulink建立倒立摆系统的仿真模型,讨论了加权矩阵Q和R的选取方法,进行一级倒立摆和二级倒立摆LQR控制器的设计、仿真和实物的实时控制,得到稳定时倒立摆系统的响应曲线,实验表明LQR算法控制倒立摆效果较好。对于一级倒立摆系统,进行模糊控制方法的研究,设计了一级倒立摆系统的Simulink模型和模糊控制器,并对其进行仿真研究。对于二级倒立摆系统,进行模糊控制算法的研究,为降低模糊控制器的维数,解决“规则爆炸”问题,利用最优控制方法设计了融合函数,即把小车位移、下摆摆角和上摆摆角合成为一个变量E,而把小车速度、下摆角速度和上摆角速度合成为一个变量EC,从而设计了二维模糊控制器,提升了模糊控制器的性能。对二级倒立摆系统进行了仿真及实物的实时控制,最后对二级倒立摆系统进行了抗干扰性研究并与LQR控制算法进行了比较。研究结果表明,模糊控制倒立摆系统使其具有很好的稳定性。更多还原

【Abstract】 Inverted pendulum system is a typical object of the verifying control algorithm. The increasement of the inverted pendulum series and updating control algorithm are the major research project of the inverted pendulum control system. Inverted pendulum system has the performances of multivariable, nonlinear, strong coupling and natural instability. Because the Inverted pendulum system is great similarity with the robot standing, walking and flying rockets, etc, it has important theoretical and practical significances to research on the inverted pendulum control problems.The inverted pendulum system was provided by GoogolTech of Shenzhen in this paper. Based on the mathematical model of linear inverted pendulum system, LQR(Linear quadratic regulator) control algorithm and fuzzy control algorithm are adopted to achieve the simulation and real-time control of one-stage inverted pendulum and two-stage inverted pendulum system. In this paper, we focus on the following problems:Firstly, the mathematical models of one-stage inverted pendulum and two-stage inverted pendulum system were setted up. Then, the stability, controllability and observability of the system were analyzed. The result showed that the inverted pendulum system was unstable under open-loop stage, but it can be controlled and observed near the equilibrium point, and the controllability of one stage inverted pendulum system was better than two stage inverted pendulum system.Secondly, LQR control algorithm of inverted pendulum system was researched. The inverted pendulum system model established by matlab/simulink was introduced, the method of how to select the Q and R weighting matrix was discussed. The LQR of the one-stage inverted pendulum and two-stage inverted pendulum system were designed, simulated and real-time controlled, the response curve of the stabilized inverted pendulum system was obtained. The experimental result showed that the inverted pendulum system with LQR algorithm had better performance. Thirdly, the fuzzy control algorithm both for the one-stage inverted pendulum and the two-stage inverted pendulum system were researched, their simulink models and fuzzy controller were designed, both the two systems were simulated and real-time controlled. In order to reduce the dimension of the fuzzy controller and resolve the "rule explosion", the fusion function was designed by adopting the optimal control method. That is to synthesize the displacement of the car, the upper swing angle and the bottom swing angle as a variable E, synthesize the speed of the car, the upper angular velocity and the bottom angular velocity as a variable EC. The two-dimensional fuzzy controller was designed by employing the two velocities, and its performance was enhanced. The anti-interference performance of the two-stage inverted pendulum system was researched. Finally, compared with the LQR algorithm, the fuzzy control inverted pendulum system had the better stability than the system with LQR algorithm.更多还原