The use of feedback control to vary the pitch angle in the blades of a variable speed wind turbine allows power generation optimization under variable wind conditions (Liu, 2008). At a specific operating point, it is possible to linearize turbine models. For example, the model of a three-blade turbine with a 15 m radius working in 12 m/s wind-speed and generating 220 V can be expressed as

where the state variable vector is given by

Here, β = pitch angle of the wind turbine blades, ξ = relative angle of the secondary shaft, ω_g = generator speed, and ω_gm = generator measurement speed. The system input is u, the pitch angle reference, and the output is y, the active power generated.

a. Find a state feedback vector gain such that the system responds with a 10% overshoot and a settling time of 2 seconds for a step input.

b. Use MATLAB to verify the operation of the system under state feedback.

Transcribed Image Text:

-5 1 x=-10.5229 -1066.67 -3.38028 23.5107 993.804 3.125 -23.5107 0 10 -10] + 0 u y= [0 0 0 1.223x10 0]x