Variable Structure Control Theory And Its Application To Double Inverted Pendulum System

In the 1950s,Emelyanov, a soviet researcher, first proposed variable structure control(VSC)based on sliding mode(SM).Then Utkin and Itkis developed the theory. Significant interest on VSC with SM has been generated in the control research realm on account of its excellent robustness and complete adaptability to the uncertainties and external disturbance in the 1970s.So far, VSC with SM has been deeply studied as an important branch of nonlinear control theory. It has been employed to control discrete鈥攖ime systems, distributed parameters systems and time鈥攄elay systems etc.. However, the chattering with high frequency in sliding mode control systems is a barrier for the application to the practice engineering problems. Therefore, many advanced control theories, such as adaptive control, fuzzy control, NN etc.. have been applied to variable structure system to reduce the chattering.Considering the current developed VSC theory and the requirements for the practice, this paper proposes a method which using fuzzy system to reduce the chattering. The double inverted pendulum has been controlled by the sliding mode controller successfully. The main contents of this paper are as follows:A SM based adaptive fuzzy system is presented to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems. The results of simulation show this method is efficacious.The double inverted pendulum is successfully balanced by VSC with SM. Two different methods are employed to reduce the chattering. One is using saturation function to replace sign function; the other is using fuzzy system to adjust the speed of reaching sliding mode surface. Simulation researches reach to a conclusion that the method using fuzzy system is more robust.