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Problem 4. (20 pts.) The transfer function for the shaft torque, OS (s) , of a 250 kW grid- connected, variable pitch wind turbine with an induction generator as a function of the aerodynamic torque, aW(s) , is: es (s ) 49(s +96.92) all' (s) (s+97.154)s? +5.109s + 48.88 a) Using Simulink, provide a plot of the open-loop system response to a unit step increase in aW(s). b) Verify the result using the Final Value Theorem presented in class. Note that F(s) is the step response of the system, not the response of the system alone lim sF(s) = lim f(t) s-+0 t-+00 c) Provide a closed-loop control system that rejects unit step disturbances on the input aerodynamic torque, a W(s), and provides zero steady-state deviation from demanded aW(s), with a reasonable response time. Demonstrate using a Simulink model