The equations for an armature-controlled dc motor are the following. The motorÃ¢â¬â¢s current is i and its
rotational velocity is Ãâ°.
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where L, R, and I are the motorÃ¢â¬â¢s inductance, resistance, and inertia; KT and Ke are the torque constant and back emf constant; c is a viscous damping constant; and v(t) is the applied voltage. Use the values R = 0.8 ÃÂ©, L = 0.003 H, KT = 0.05 N ÃÂ· m/A, Ke = 0.05 V ÃÂ· s/rad, c = 0, and I = 8 Ãâ 10Ã¢Ëâ5 kg ÃÂ· m2.
a. Suppose the applied voltage is 20 V. Plot the motorÃ¢â¬â¢s speed and current versus time. Choose a final time large enough to show the motorÃ¢â¬â¢s speed becoming constant.
b. Suppose the applied voltage is trapezoidal as given below.