Optimal control of a wind turbine by using linear matrix inequality method

Linear matrix inequalities (LMIs) are very important tools that allow us to numerically solve control engineering problems by means of computer tools and optimization techniques. LMIs are convex constraints for a semidefinite programming (SDP) which is subfield of convex optimization. In this thesis, LMI structure and problems related with LMIs were studied. Optimal control problem was written in the form of LMI eigenvalue problem. With the help of the relevant computer tools, controller design was done for linear systems by solving LMI problem. A wind turbine control problem was selected as a case study in order to reveal effectiveness of proposed optimal control solution. A nonlinear turbine model was linearized at an operating point. For linear wind turbine model, a controller design was performed by using linear quadratic regulator (LQR) method. In this design, the LQR problem was written as the LMI constraint of the SDP. By numerically solving the optimization problem, a state feedback gain matrix which minimizes the performance index was calculated. The designed controller was compared with the baseline gain scheduled PI controller on the nonlinear wind turbine model in the computer simulation. Results reveal that proposed optimal control solution performs satisfactorily well and optimal LMI based LQR control proves to be a suitable alternative in controlling nonlinear wind turbine systems. Key Words: Linear matrix inequality, linear quadratic regulator, wind turbine.