On performance evaluation method and optimal control for vertical dynamic of a fast ferry

To decrease the vertical acceleration associated with pitch and heave, a multivariable PD controller is firstly designed in the paper, then parameters of the controllers are optimized according to the H₂ norm of the worst vertical acceleration (WVA) output. The non-linearity of the actuators (flaps and T-foil) is considered and included into the simulation process. In order to assess the closed-loop performance of the nonlinear system, an evaluation method based on the describing function and the variance gain is proposed. This evaluation approach provides, in the frequency domain, a clear picture of the closed-loop performance on the vertical acceleration. By using this evaluation approach to a specific example, it is indicated that this frequency domain closed-loop performance computation approach can more reasonably explain the simulation results of the system. This evaluation method can not only be used to quantitatively access the WVA reduction percentage, but also can be used to estimate the degree of Input/Output non-linearity of the closed-loop system.