Modelling and vibration control for deep-sea robot lifting system with time variable length and nonlinear disturbance observer

In this paper, we propose a mathematical model meant to eliminate the vibration of deep-sea robot lifting system with time-variant length and harsh environmental conditions. The variable-length umbilical cable is modelled as a moving string with additional lumped-mass that has a partial differential equation (PDE) theoretically, spatially discretized by the modified assumed modes method (AMM). Three features of the deep-sea robots are considered in the control schema i.e. non-matched uncertainties, rigid-flexible couplings, and input saturation. By combining Lyapunov theory and LaSalle's invariance theorem, a robust adaptive feedback control is proposed to eliminate vibration of the deep-sea robot. In-addition, a nonlinear disturbance observer (NDO) is scientifically designed to estimate the unknown boundary uncertainties and their couplings, where the stability of whole control system is simultaneously presented. A nonlinear function is further developed to settle out the potential problem of input nonlinearities for the actuator. The dynamic modelling of the system is first illustrated by the ADAMS simulation and followed by more detailed analyses of different cases to demonstrate the effectiveness of the current method. © 2022