Optimal power extraction of a two-stage tidal turbine system based on backstepping disturbance rejection control

Abstract

This paper investigates the optimal power generation control for a two-stage horizontal-axis tidal turbine system based on backstepping disturbance rejection control (BDRC), which is a new control framework for high-order nonlinear systems. The tidal turbine system is designed with the main structure being described. The dynamics of the tidal turbine system is then formulated based on the integration of the dynamics of its constitute components. The tidal turbine experiences large uncertainties and unknown dynamics from non-uniform operating thrust and fatigue forces, variations and turbulence in tidal flow velocities induced by waves and wind. The proposed BDRC is a unique control concept which has superior performance in dealing with these large uncertainties without requiring much information about the turbine dynamics. Consequently, the BDRC system is synthesized in two control loops for the control of the turbine dynamics (outer loop) and the q-axis current dynamics (inner loop) respectively to track the optimal tidal turbine speed and hence maintain the optimal power generations. Both the stability and convergence of the two closed control loops are subsequently analyzed and proved. The simulations are conducted in MATLAB/Simulink to compare the performance of the developed BDRC system with a sliding mode control method used in the literature. In addition, the proposed BDRC algorithm is extended to a general nonlinear strict-feedback system with high uncertainties and external/internal disturbances. The proposed BDRC has significantly extended the traditional ADRC and does not need any differential operations, thereby totally eliminating the inherent problems of “explosion of complexity” and repeated differentiations of virtual control variables in traditional backstepping control.