Studies On Inverted Pendulum System By The Fuzzy Control

The inverted pendulum system is a natural instability system of multivariable, nonlinear and strong-coupling. The research of the inverted pendulum is always a hotspot in control field in recent years. As a controlled object, it has very important value, not only the theory but also the realistic meaning in the research such as the walking of biped robot, the lunching process of rocket and flying control of helicopter.The energy controller is introduced to study swinging up characteristics of the single inverted pendulum in the paper. The fuzzy controller is designed to realize the stabilization control of both the single inverted and double inverted pendulums. The success of control of hardware pendulum system proves that these controllers have very good stability, robustness and adaptability. The main research work is as follows:1) The mathematical models of both single inverted and double inverted pendulum are proposed. The qualitative analysis done for the inverted pendulum. It is proved that open-loop control inverted pendulum system is instability, but it is controllable and observable on the equilibrium point. At the same time comparative controllability of the double inverted pendulum is more difficult.2) Research on controller of single inverted pendulum. At first, the swinging up controller is designed, which is based energy viewpoint. And then, according to the principle of standing up pendulum and stabilizing cart, the control strategy of double fuzzy controllers and the concept of dummy angle are proposed. The important parameters are optimized through simulation debugging. At last, after doing real-time control it can realize the pendulum from swinging up automatically to standing up steadily.3) Research on the controller of the double inverted pendulum. Because the double inverted pendulum has six state variables, the request for designing fuzzy controller is higher. The input dimension of the controller should not be too high, otherwise there occur to the problem of rule explosion. The rules must be effective and complete. So, based on LQR theory the stable variables are effectively merged. At the same time, this paper calculates fuzzy the rules by means of a set of input-output data. At last, the fuzzy stable controller of the double inverted pendulum is designed. After testing, the Successcontrol of the double inverted pendulum hardware system proves that the controller iseffective.