Problem 5: The DC motor you used in Lab 3 generates a torque of T = ½-½ (V - kw), where k is the motor constant, R is the winding resistance, V is the applied voltage, and w is the angular velocity. Suppose the rotor and wheel have a combined rotational inertia I. a) Find the transfer function from motor voltage V to angular velocity w. P = b) You decide to use open-loop control to achieve a desired speed using the control law V = Fwd. What value for the constant gain F will result in zero steady-state error? Wa V F P. 3 F = c) Do you think this open-loop control system will work well to drive a robot? Why or why not? d) You decide to add a feedback loop with integral action in addition to the feedforward gain such that the total motor voltage is V = Fwd + K₁f (wa - w)dt. Draw a block diagram for this system and find the closed-loop transfer function from desired speed to speed Twa→w. Twa→w = e) The controller is limited to a voltage of ±10 V. What potential issues could this cause?