11. Optimal Speed and Heading Control for Stabilization of Parametric Oscillations in Ships

In this chapter, two strategies to actively control ships experiencing parametric roll resonance are proposed. Both approaches aim at changing the frequency of the parametric excitation by controlling the Doppler shift, which, in recent results, has been shown to be effective to reduce the roll angle significantly. However, exactly how to change the frequency of the parametric excitation to stabilize the parametric oscillations has remained an open research topic. Thus, two optimal control philosophies that alter the ship’s forward speed and heading angle, which in turn changes the encounter frequency and consequently the frequency of the parametric excitation, are presented. This is referred to as frequency detuning. As a first approach, the methodology of extremum seeking (ES) control is adapted for ships in parametric roll resonance to iteratively determine the optimal setpoint of the encounter frequency in order to avoid one of the conditions for parametric roll. The encounter frequency is consequently mapped to the ship’s forward speed and heading angle by a control allocation. This is formulated as a constrained nonlinear optimization problem. Second, the use of a model predictive control (MPC) is proposed. By addressing both states and input constraints explicitly, the MPC formulation is used to change the ship’s forward speed and heading angle in an optimal manner to reduce parametric roll oscillations. The effectiveness of the proposed control approaches to stabilize parametric oscillations, by simultaneously changing the ship’s forward speed and heading angle optimally, is illustrated by computer simulations. This clearly verifies the concept of frequency detuning.