Constrained H∞ control of gyroscopic ship stabilization systems

Abstract

We suggest a constrained ${\mathcal{H}}_{\infty }$ control scheme for gyroscopic marine vehicle stabilization systems with output and control constraints. The ${\mathcal{H}}_{\infty }$ performance is used to measure the roll angle reduction of the vessel relative to wave disturbances in regular beam seas. Time-domain constraints, representing requirements for precession angle of gyroscopes and for actuator saturation, are captured using the concept of reachable sets and state-space ellipsoids. A state feedback solution to the constrained ${\mathcal{H}}_{\infty }$ stabilization control problem is proposed in the framework of linear matrix inequality optimization and multiobjective control. This approach can potentially achieve the best possible vessel comfort with respect to roll motion by allowing constrained variables free as long as they remain within given bounds. Analysis and simulation results for roll dynamics of the vessel coupled with the gyroscopic actuator control system show possible improvements on roll motion stabilization while respecting time-domain hard constraints.