Consensus Tracking and Vibration Control for Multiple Overhead Cranes With Flexible Cables Under Time-Varying Actuator Faults

This paper discusses consensus position tracking and vibration control issues of multiple overhead cranes equipped with flexible cables subject to unknown time-varying actuator faults, where each crane is modeled by partial differential equations (PDEs). To mitigate the effect of unknown simultaneous time-varying actuator faults, both multiplicative and additive, and external disturbances, an innovative adaptive fault-tolerant consensus tracking strategy was developed using a PDE based model. The proposed control scheme can move multiple overhead crane payloads to a required setpoint and eliminate the transverse deflections of flexible cables, where only some cranes know the setpoint. Furthermore, all closed-loop signals are shown to be uniformly bounded; additionally, consensus tracking errors and transverse deflections are shown to ultimately converge to small adjustable regions of the origin. Finally, numerical simulations are carried out to show the effectiveness of the developed control strategy.