Lyapunov approach for the control of overhead crane systems with double-pendulum dynamics and uncertain disturbances

Abstract

In this paper, a new composite control strategy, consisting of a disturbance observer and a nonlinear anti-swing control approach, is presented for underactuated overhead crane systems. Compared with existing control strategies for overhead crane systems, both the double-pendulum dynamics and unknown disturbances of which are taken into consideration. In addition, the unknown disturbances are handled by a feedforward compensation control method. Specifically, first, based on the system dynamic equations, an auxiliary signal is constructed and a nonlinear disturbance observer is presented, which can exactly estimate the unknown disturbances in finite time. Next, an elaborate Lyapunov function is introduced and a disturbance-observer-based control approach is presented for the overhead crane system with double-pendulum dynamics. Then, rigorous theoretical analysis is given to prove the convergence of the system states. At last, simulation tests are included to verify the effectiveness and robustness of the devised approach.