Finite time disturbance observer design and Lyapunov-based control design for overhead cranes with double-pendulum dynamics

Abstract

In this paper, a novel disturbance observer and a Lyapunov-based control approach are developed for the crane control. For existing works, the assumption on the disturbances is strong and the motivation of these methods is to reject disturbances by feedback control. To tackle these problems, this paper proposes a novel composite control strategy consisting of a nonlinear control method and a finite time disturbance observer. Specifically, first, based on the system dynamic equations, a disturbance estimator is put forward, which can exactly identify the unknown disturbances in finite time. Next, an elaborate Lyapunov function is constructed and a disturbance-compensation-based control approach is presented for the overhead crane system with double-pendulum dynamics. Then, rigorous theoretical analysis is given to prove that all of the states of the closed-loop system asymptotically converge to the origin. At last, simulation tests are included to verify the effectiveness and robustness of the proposed method.