Robust Control Designs of Payload’s Skew Rotation in a Boom Crane System

In this paper, a robust nonlinear integral sliding mode control (ISMC) is proposed as a vibration controller for the payload’s skew rotation process of a boom crane to cope with parametric uncertainties in the system parameters. By using the indirect Lyapunov method, algebraic inequality constraints for the ISMC gains are formulated to ensure the robust stability of the closed-loop system under the sliding mode and in a context where the reaching phase is completely eliminated. Moreover, a robust output feedback <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control is introduced as a benchmark to compare with the nonlinear ISMC. Specifically, <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synthesis is utilized to establish the robust stabilization for the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller. An optimization routine based on the metaheuristic particle swarm optimization mechanism is established, which adopts the robust stability conditions with regard to each controller as the nonlinear constraints. By means of the proposed optimization procedure, minimization of desirable performance index and robust stabilization of the closed-loop system are guaranteed simultaneously in a single framework. Through both random simulation and experimental results, ISMC shows its superiority to the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control; hence, ISMC is the preferable candidate for the actual implementation on the real-size system in use at the harbor.