Answer Happy

A doubly-fed actuator has two windings with current 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 Tlood, and J is its moment of inertia. The flux linkages and induced voltages at the windings are respectively A₁, A₂ and ₁. 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 W; (0). Assuming the core is magnetically linear, choose the correct statement. Spring Electrical source 1 A₂₂ Tuxt/ Rotor Stator O The energy can be obtained as W₁ (0) = 0.5[L₁(0) + L₂ (0)² + L12 (0)i1i2] O The electromechanical system has a state-space model of order n = 2 with two state variables, i.e. currents and ₁ and 22. o Th motion equation of the system is dWy(0) -Tload-J 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) + L₂ (0)i? − 2L12 (0)i₁i₂] Electrical source 2