MIMO PID compensation for dynamic positioning of a ship

The design of a suitable controller for dynamic positioning (DP) of a ship is a challenging task because of the presence of nonlinearity, model uncertainty, high channel interaction, environmental disturbances (wind, waves), etc. This paper is concerned with multivariable PID compensation for dynamic positioning control of a ship. For this purpose, a 3-Degree-of-Freedom (DoF) nonlinear model suitable for dynamic ship positioning is obtained from rigid body and hydrodynamic equations of motion in 6-DoF. The multi-input multi-output (MIMO) PID control is designed for the linearized system obtained from nonlinear system around an operating point. For design of PID gains, the PID control problem is transformed into state feedback control design. The state feedback gains are designed using optimal linear quadratic regulator (LQR) method. To improve the reference input to output characteristics of the control system, a feedforward gain is added to the PID controller and designed using LMI-based method. The performance of the control system designed is studied through simulations of the nonlinear system in presence of low frequency and high frequency environmental disturbances that occur in ship dynamic positioning system. Robustness of the system is also studied.