Adaptive Vibration Suppression for the Primary Girder of a Bridge Crane Under Time-Varying Actuator Failures

Bridge cranes are critical for industrial automation but suffer from vibrations that compromise safety and efficiency. Suppressing these vibrations remains a key challenge in crane control systems. This paper investigates the vibration suppression problem of the primary girder of a bridge crane. To address nonlinear time-varying actuator failures, we develop a novel adaptive fault-tolerant in-domain control scheme using the lower bound method, derived from the primary girder's partial differential equation (PDE) model. The proposed controller guarantees effective vibration suppression. Furthermore, Lyapunov stability analysis rigorously demonstrates the boundedness of all closed-loop signals. Numerical simulations validate the effectiveness of the proposed control scheme in suppressing vibrations under actuator failures. In addition, the method exhibits broad applicability to flexible mechanical systems with structural dynamics analogous to bridge crane girders.