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12 pts Question 1 A doubly-fed actuator has two windings with current i, at the stator and current 12 at the rotor as shown in the figure below. Its mechanical output is the angular displacement between the stator magnetic axis and rotor magnetic axis. The inputs are the two electrical voltage sources 1 and 2. The electromagnetic torque developed by the actuator is T, its load torque is Tload, and J is its moment of inertia. The flux linkages and induced voltages at the windings are respectively A₁, A2 and e₁, €2. The self and mutual inductances of the windings are respectively L₁ (0), L₂ (0) and L12 (0). The energy stored in the electromagnetic field of the system is Wƒ (0). Assuming the core is magnetically linear, choose the correct statement. Spring Electrical source 1 T Rotor Stator O The energy can be obtained as W₁ (0) = 0.5 [L₁ (0)² + L2 (0)i² + L12 (0)i1i2] 2 with two O The electromechanical system has a state-space model of order n = state variables, i.e. currents and ₁ and 12. O The motion equation of the system is dW; (6) - Tload=J do O Since the core is magnetically linear, the dynamic model of the electromechanical system should be linear. O The energy can be obtained as W₁ (0) = 0.5[L₁(0)² + L2 (0)i? — 2L12 (0)i1i2] Electrical source 2