UKF Based Nonlinear Offset-free Model Predictive Control for Ship Dynamic Positioning Under Stochastic Disturbances

Abstract

This paper presents the schemes of nonlinear offset-free model predictive control (MPC) for reference tracking of ship dynamic positioning (DP) systems, in the presence of slow-varying stochastic disturbances and input constraints. Two offset-free MPC strategies for nonlinear DP systems are proposed. The first approach, namely, the target calculation formulation, estimates the disturbance based on the augmented disturbance model, and employs a target calculator to address the MPC optimization problem. The second approach, namely, the delta input formulation, works with the augmented velocity model to lump the effects of disturbances into the input estimates. By successively on-line linearizing the state-space model at the current operating point, the future outputs are explicitly predicted, and then the nonlinear optimization problem becomes an easy quadratic optimization problem. The unscented Kalman filter is adopted for the state estimation. By implementing simulations for two scenarios of disturbances with parametric plant-model mismatch, the effectiveness of the two strategies is demonstrated. Results show that the closed-loop control performance of the delta input formulation method is superior, for its good robustness to the stochastic disturbance.