Control of an inverted pendulum using grey prediction model

The system with partial unknown structure, parameters and characteristics is called a grey system. The grey theory can be employed to improve the control performance of a system without sufficient information or with a highly nonlinear property. In this paper, the grey prediction model combined with a PD controller is proposed to balance an inverted pendulum which is a classic example of an inherently nonlinear unstable system. The control objective is to swing up the pendulum from the stable position to the unstable position and bring its slider back to the origin of the track. The overall control algorithm is decomposed into two separate grey model controllers for swinging up and balancing based upon the angular and velocity values of the pendulum. The actuator is a Nippon Seiko Co. (NSK) linear motor. The experimental results show that this grey model controller is able to swing up and balance the inverted pendulum and guide its slider to the center of the track. It also has the robustness to balance the inverted pendulum in suffering an external impact acting on the pendulum