Application Study Of Fuzzy Control On Inverted Pendulun System

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.