An Adaptive Controller Based on IDA-PBC for Underactuated Mechanical Systems: Application to the Ball and Beam System

In this paper, an adaptive technology and the interconnection and damping assignment passivity-based control method are combined to solve the stabilization problem for underactuated mechanical systems with uncertainties (including matched and unmatched). Uncertainties include unknown friction coefficients and unknown terms in kinetic energy and potential energy. A novel adaptive interconnection and damping assignment passivity-based control scheme is proposed and an adaptive stabilization controller is designed to make the closed-loop system locally stable. Verification is conducted on the ball and beam system, taking into account uncertainties of friction coefficients, kinetic energy, and potential energy. The locally asymptotic stability is demonstrated using the LaSalle’s invariance principle and approximate linearization. The effectiveness of the proposed control law is verified through numerical simulations.