Convex optimization design of multi-model controller for pitch-regulated wind turbine systems

In this paper, a convex optimization approach to controller design is addressed. Specifically, a family of LQR-based controllers namely; LQR with integral action (LQRI) and LQR with disturbance rejection and integral action (LQRI+) are designed for pitch control of wind turbine systems. The LQRI+ incorporates an extra term in the formulation of the LQRI controller to compensate for the effect of disturbance on the system. Both controllers were designed using LMI formalism. To guarantee satisfactory performance including stability and reference tracking across all operating regimes of the turbine, a multi-model approach was employed using linear models obtained at multiple wind speeds designating different operating regions of the turbine. The performance of both controllers were then compared using FAST, an aero-elastic tool and a benchmark NREL 5MW wind turbine developed by the National Renewable Energy Laboratory, USA.