Research Of The Inverted Pendulum Control Based On Robust H_∞ Control Theory

The inverted pendulum system has the characteristics of multiple variables, the high-end, serious nonlinear, absolute instability; it can reflect many key issues in the progress of control, such as stabilization, nonlinear and robust problems etc. Therefore, the inverted pendulum system, which research not only has the far-reaching significance of the theoretical value but also has the important engineering background and practical significance, is often used to test the effectiveness of control theory. Obviously, the research on a classic non-linear unstable system has the important significance both in theory and methodology. And the built of mathematical model of double inverted pendulum plays a guiding role on the stability of the system. LMI method is widely used in the solution of robust H_∞control problems, Using the LMI method to solve the control system problems has become a research focus in these fields.Firstly, in this paper, the movement of the inverted pendulum system is analyzed, and using dynamic knowledge and real data of pendulum experiment device to build the mathematic model of the double inverted pendulum. Then the H_∞robust control theory and LMI method are described in detail. Besides, fuzzy control theory and variable structure theory are introduced. Using the fuzzy control theory to design the fuzzy controller of the double inverted pendulum, also using the pole placement method of variable structure to design a variable structure controller. And then, the simulation experiments are made through H_∞feedback control, fuzzy control, variable structure control and LMI method. Through analyzing the results of the simulations, the advantages and disadvantages are given out, so as to verify the application of the main method in this paper-LMI method, in the actual control of inverted pendulum.