This paper presents the design of a linear quadratic (LQ) optimal controller for a spar-type floating offshore wind turbine (FOWT). The FOWT is exposed to different sea states and constant wind turbulence intensity above rated wind speed. A new LQ control objective is specified for the floater-turbine coupled control, in accordance with standard requirements, to reduce both rotor speed fluctuations and floater pitch motion in each relevant sea state compared with a baseline proportional-integral (PI) controller. The LQ weighting matrices are selected using time series of the wind/wave disturbances generated for the relevant sea states. A linearized state-space model is developed, including the floater surge/pitch motions, rotor speed, collective blade pitch actuation, and unmeasured environmental disturbances. The wind disturbance modeling is based on the Kaimal spectrum and aerodynamic thrust/torque coefficients. The wave disturbance modeling is based on the Pierson-Moskowitz spectrum and linearized Morison equation. A high-fidelity FOWT simulator is used to verify the control-oriented model. The simulation results for the OC3-Hywind FOWT subjected to turbulent wind show that a single LQ controller can yield both rotor speed fluctuation reduction of 32-72% and floater pitch motion reduction of 22-44% in moderate to very rough sea states compared with the baseline PI controller.

This paper investigates the effects of nonlinearities on the design of a constrained optimal controller for spar-type floating wind turbines. The considered nonlinearities are due to wind speed variation and actuator saturation. The collective blade pitch actuator, usually employed for aerodynamic rotor speed regulation, is adopted for the mitigation of platform pitch vibrations as well. The wind speed effects and the control law are obtained from a linearized rigid-body dynamic model, taking into account persistent disturbances related to wind turbulence and wave induced loads, which are estimated using the Blade Element Momentum aerodynamic theory and Morison equation, respectively. A performance analysis is carried out for several operating points in the above rated wind speed region, considering the reduction of the platform pitch motion as the main control objective. The simulation results show that the designed fixed-gain multivariable controller can yield significant vibration reduction in comparison with a baseline gain-scheduled proportional-integral controller in the presence of the considered nonlinearities.

A state feedback aerodynamic controller is proposed for the stabilization and reduction of platform/tower pitch vibrations of a spar-type floating wind turbine, considering blade pitch saturation effects. The controller is synthesized from a linearized rigid body model developed for a NREL 5-MW offshore wind turbine operating at the above rated condition (region 3). Wind turbulence and wave induced loads are obtained from the blade element momentum (BEM) aerodynamic theory and Morison’s equation, respectively. The simulation results show that the proposed nonlinear control system yields significant vibration reduction in comparison to a proportional-integral controller.

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