Problem 2. A linearized state space model of a three blade speed wind turbine with a 15 m radius working at 12 m/s wind-speed and generating 220 V is -5 1 -10.5229 -1066.67 -3.38028 23.5107 993.804 3.125 -23.5107 Wgm 10 -10 Wgm y = [0 0 0 1.223 x 10 0] Wym where 3 is the pitch angle of the wind turbine blades, § is the relative angle of the sec- ondary shaft, į is the angular velocity of the secondary shaft, wg is the generator speed, wgm is the generator measurement speed, u is the pitch angle reference, and y is the active power generated. (a) What is the maximum number of poles that the transfer function could have? How many poles does it have?

Q9/ A thermocouple has the following characteristics when it is immersed in a stirred bath: Mass of thermocouple = 1 g Heat capacity of thermocouple = 0.25 cal/(g 'C) Heat transfer coefficient = 20 cal/(cm?h 'C) (for thermocouple and bath) Surface area of thermocouple = 3 cm? (a) Derive a transfer function model for the thermocouple relating the change in its indicated output T to the change in the temperature of its surroundings T, assuming uniform temperature (no gradients in the thermocouple bead), no conduction in the leads, constant physical properties, and conversion of the millivolt-level output directly to a C reading by a very fast sensor. (b) If the thermocouple is initially out of the bath and at room temperature (23 'C), what is the maximum temperature that it will register if it is suddenly plunged into the bath (80 °C) and held there for 20 s?