Fuzzy control of a double inverted pendulum based on hyper topology space

The control of double-inverted pendulum is one of the most difficult control problems, especially for the control of parallel-type one, because of the high complexity of control systems. To attain the prescribed accuracy in reducing control complexity, a new fuzzy controller for stabilizing a double inverted pendulum system is presented based on the model of hyper topology space. It is a universal multi-granular fuzzy adaptive controller which represents the process of reaching goal at different spaces of the information granularity. When the prescribed accuracy is low, a coarse fuzzy controller can be used. As the process moves from high level to low level, the prescribed accuracy becomes higher and the information granularity to fuzzy controller becomes finer. In this controller, a rough plan is generated to reach the final goal firstly. Then, the plan is decomposed to many sub-goals which are submitted to the next lower level of hierarchy. And the more refined plans to reach these sub-goals are determined. If needed, this process of successive refinement continues until the final prescribed accuracy is obtained. Analysis and design of the fuzzy controller is discussed. Finally, simulation results indicate the effectiveness of the proposed controller.