Calculate and plot the waveform of the pole voltage vat

Question

Problem

Consider a permanent magnet dc motor with the following parameters: R_a = 0.25, L_a = 1.45mH. k_E = 0.5V/rad/s, k_T = 0.5 Nm/A, J_m = 0.02kg-m² and J_L = 0.03 kg-m². The load torque stays steady at T_L = 2 Nm. The motor is operating in steady-state with a speed of 250rad/s. This motor is supplied by a switch-mode de-dc converter (single-pole, two-quadrant), which has a do bus voltage of V_d = 200V. The switching frequency is F_s = 25 KHz. Calculate and plot the waveform of the pole voltage V_A(t) (voltage applied to the motor). You may assume the triangular carrier waveform has a peak-to-peak of 1V.