LQ optimal robust multivariable PID control for dynamic positioning of ships with norm-bounded parametric uncertainties

Abstract

The design of a suitable controller for dynamic positioning (DP) of ships is a challenging task keeping the hydrodynamic uncertainties in mind. The magnitude and rate constraints on the actuators make the problem more difficult. The present work employs a two-degree-of-freedom (2-DOF), multivariable, proportional–integral–derivative (PID) control for DP of a ship. To design the controller, first, the ship dynamics with hydrodynamic parameter uncertainties is represented in an uncertain state-space descriptor form. Then, the design of feedback gains of 2-DOF PID controller for the uncertain descriptor plant is converted into a state feedback design for an augmented uncertain descriptor plant. Next, a linear matrix inequality-based condition is obtained to solve this state feedback problem in order to ensure a desired linear quadratic (LQ) performance, even in presence of uncertainties. Finally, to further improve the tracking performance, the feedforward gain of the 2-DOF PID controller is designed using H∞ approach. The DP performance of the proposed controller is tested for the considered ship model along with uncertainties, actuator constraints, and environmental disturbances. A comparison with the existing PID controllers is also carried out to show superiority of the proposed controller.