Control of an inverted pendulum using grey prediction model

A 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 highly nonlinear property. In this paper, a grey prediction model combined with a proportional plus derivative 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 a stable position to an 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, respectively, based upon the angular and velocity values of the pendulum. 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 at an upright position in suffering an external impact acting on the pendulum.