Abstract
A relatively simple, optimal, and robust nonlinear Sliding Mode Control (SMC) is developed in this paper for a novel nonlinear Wave Energy Converter (WEC). Giving that deriving an optimal control for a complex system is very cumbersome or nearly impossible, an SMC (purely switching only) is thus implemented with the sliding surface defined in an optimal sense. Despite it is simple, the optimality of this control is proved by using a new equivalent control analysis mathematically and also demonstrated numerically. In addition, the robustness of the control is shown mathematically with Lyapunov analysis and by simulations with uncertainties. The main contributions of this paper are: (1) a novel Sliding Mode Control is developed which is simple, optimal, and robust;(2) the robustness and optimality of the proposed control are both proved mathematically and verified numerically; (3) a weakly nonlinear model is developed for a nonlinear WEC which is utilized to validate the performance of the proposed nonlinear control. The numerical simulations are then conducted on a weakly nonlinear model developed for the nonlinear WEC. The results show the robustness and optimality of the proposed control (compared with a nonlinear damping control) subject to uncertainties and nonlinearities.