preparatory work of the relevant theory, which include the introduction of the PID and fuzzy theory. In chapter3, we establish the mathematical model of inverted pendulum control system (state equation) and by using modern control theory analysis the controllability, observability and stability of two level inverted pendulum system. In chapter4, the fuzzy PID controller design process is given, the fuzzy controller

parameters are described and the fuzzy control rules and the reasoning process are developed. In chapter5, the fuzzy PID controller is applied to the double inverted pendulum model by using MATLAB as the simulation tool, and then the fuzzy PID controller is applied to the actual double inverted pendulum system.The simulation and physical experiment results show that the fuzzy PID controller has higher stabilizability. Compared to PID controller, the fuzzy PID controller can avoid the drawbacks of manual adjustment parameter and not timely changing the parameter to meet the system requirements. The fuzzy PID controller designed in this thesis is superior to a single fuzzy control and PID control, and it is a very effective control method and the fast control and no error control are gotten.