Tracking Control of X-Z Inverted Pendulum with Block Backstepping

Abstract

As the extension of traditional linear (or X) inverted pendulum (IP), X-Z IP is a multiple-input multiple-output (MIMO), underactuated, open-loop unstable, and nonlinear system. In the tracking control of the X-Z IP, the equilibrium point changes with the pivot position of the pendulum. This makes linear control theories have difficulties in realization of the tracking control for the pendulum. The underactuated feature of the pendulum makes the feedback linearization unsuitable to simplify the control design. With the present model of the X-Z IP, there is no way to realize the backstepping design. This paper gives a novel state transformation method for the X-Z IP. Through the state transformation, the block backstepping can be easily deployed in the controller design of the X-Z IP. The proposed controller can achieve the tracking control in the vertical plane. Simulation results certify the rightness and effectiveness of the proposed tracking controller.