Sliding Mode Observe and Control for the Underactuated Inertia Wheel Pendulum System

The inertia wheel pendulum (IWP) is a widely studied nonlinear benchmark underactuated system and its control problem is a challenging task for its underactuated nature. This paper considers the IWP stabilization problem with the classic sliding mode method. The nonlinear canonical model of the underactuated IWP is obtained through a collocated partial feedback linearization and two global changes of coordinates. In order to obtain the unmeasurable states of the newly derived model, two classic sliding mode observers are designed and it is ensured that the observing errors are convergent in finite time to meet the separation principle. In order to reduce the high frequency component of the observing output, the first-order filters are introduced from the view of practical applications. A simple sliding mode controller is proposed with the output of the first-order filters. It is proved that the proposed approach can guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system and the convergence speed can be improved by appropriately choosing design parameters. The simulation results demonstrate the effectiveness of the proposed approach.