Eliminating steady-state error in ship trajectory control problem via integral sliding mode control

Abstract

This paper presents the design and analysis of an Integral Sliding Mode Control (ISMC) to address the trajectory tracking problem for a six-degree-of-freedom (6-DOF) ship model. Traditional Sliding Mode Control (SMC), despite its high robustness against disturbances and model uncertainties, often suffers from steady-state errors when the system is subjected to constant or slowly varying disturbances. By integrating an integral component into the sliding surface, the proposed ISMC is capable of completely eliminating these steady-state errors, ensuring superior trajectory tracking accuracy. The stability of the system is rigorously proven based on Lyapunov stability theory. Simulation results in MATLAB/Simulink are presented to compare the performance of theproposed ISMC with traditional SMC and PID controllers, thereby confirming the superiority of the proposed method.