# RESULTS AND DISCUSSIONS To test the superiority of the constrained FRHC on Essay

4. RESULTS AND DISCUSSIONS To test the superiority of the constrained FRHC on the wind-turbine system, two case studies are composed. Firstly, stepwise varying wind-speed is first used on the mathematical model. Secondly, the benchmark wind-turbine simulator [18] is used to test controller superiority under turbulent wind-speed profile. The online quadratic optimization problem in (29) is solved using commercial solver Gurobi version 7.5.2 and YALMIP version R21081012 [19]. For the pitch angle constraint ( ) is ( and the rate of change of pitch angle constraint ( ) is ( ).

The state constraint ( ) is ( ). The state constraint ( ) is ( . According to the simulation, the wind-speed profiles changes each 0.05 second, thus the model sampling time is chosen to equal 0.0125 seconds. To find the best performance of constrained FRHC, the optimization parameters are chosen as follows; the predicted control action penalty ( ), for the predicted state variables penalty ( ), prediction horizons ( ), and control horizon ( ).4.1 Case 1: Stepwise Wind-speed ProfileThe wind-turbine mathematical model of Eq. (8) is the plant which has six states, three output, and three inputs. In region 3, the first input is the torque which is assumed constant.

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