Modelling and control of flexible guided lifting system with output constraints and unknown input hysteresis

Abstract

Modelling and control vibration is studied for the flexible guided lifting system in the presence of output constraints, input hysteresis, guided rope fault, etc. Flexible guided lifting system, subjected to external disturbances from the boundary disturbance or fluid interaction, is an inherent distributed parameter system with time-varying length and infinite dimensions. According to extended Hamilton’s principle, the governing equation in the form of hybrid partial differential equations and ordinary differential equations is derived to reflect the dynamic response of such multiple ropes under the boundary disturbances and multiple constraints. Adaptive neural network control combining with backstepping technique is subsequently designed to suppress undesirable vibration and stabilise the system, where the neural network is provided as a feedforward compensator for the unknown hysteresis nonlinearities in the control input. Asymptotic stability and uniform boundedness of the system are guaranteed through the Lyapunov theorem, which indicates that all states are uniformly convergent by LaSalle’s invariance principle. The original governing equation is solved numerically by using the finite difference method, where simulation results are illustrated to validate the efficiency of the hybrid partial differential equation and ordinary differential equation model and the adaptive stabilisation design.