Prescribed performance ADRC position stabilization control of gangway tips under velocity constrains

Consider an offshore gangway with vessel-motion-induced disturbances, dynamic uncertainties and friction force uncertainties under velocity constrains of the gangway tip (GT). A prescribed-time extended state observer (PTESO) is innovatively constructed by means of an error mapping function with respect to a prescribed performance function (PPF) where the problem that the gains of the existing PTESOs approach to infinity at a prescribed time is solved. The constructed PTESO with prescribed-time convergent estimation errors can provide the estimates of the GT motion states and the gangway total disturbances, respectively. Further, a new barrier function with respect to the PPF, the gangway tip position stabilization (GTPS) error and the GT velocity is proposed to handle the velocity constrains of the GT. Based on the above, a prescribed-performance control law for the GTPS is developed such that the GTPS errors converge to a prescribed tolerance steady-state error band in a prescribed settling time. Therein, our proposed barrier function is used as the component of the gain of the developed control law, unlike in the existing literatures used as the barrier Lyapunov functions, such that the developed control law is easy to implement. Simulation results exhibit that the GTPS errors under our developed control law are decreased by 16 % and 19 % in two cases with different sea states and model parameters, respectively.