Stabilization controller for a cart-type inverted pendulum via a partial linearization method

In this paper, a stabilization control problem of a cart-type inverted pendulum system is discussed. For the stabilizing control of the inverted pendulum system, in general, a state feedback controller with linearization of the pendulum system around its equilibrium point is used. However, in case of a controlling in states away from the equilibrium point, the guarantee of stability is difficult or a large amount of the control input is needed to system. Then, in this paper, a new stabilizing controller which guarantees stabilizing for widespread states of the systems is proposed using a partial linearization method. In the proposed controller, at first, we decide a reference angular position of the pendulum in order to converge an angular position and a cart position to 0, and pendulum can track to its reference angular position using partial linearization method. By analyzing a ZeroDynamics of system, achieving of the stabilizing control of the pendulum and the cart are proved. Simulation results are given to show the effectiveness of the proposed controller.