Problem 3. Obtain the closed loop transfer function C(s)/R(s) for the positional servomechanism is shown in Figure 3. Assume the input and output of the system are the input shaft position

and the output shaft position, respectively. Assume the following numerical values for the system constantans: r с 0 K₁ Kp Kb R₂ La Km Jm Bm JL BL N2/N1 angular displacement of the reference input shaft, radian angular displacement of the reference output shaft, radian angular displacement of the motor shaft, radian gain of the potentiometric error detector, 24/ V/rad amplification gain 10 V/V back emf constant = 5.5 x 102 V-sec/rad armature-winding resistance = 0.22 armature-winding inductance 0 motor torque constant = 6 x 10-5 lb-ft moment of inertia of the motor = 10-5 lb-ft-sec² viscous friction coefficient of the motor ≈ 0 moment of inertia of the load = 4.4 × 10-³ lb-ft-sec² viscous friction coefficient of the load = 4. × 10-² lb-ft-sec² Gear ratio = 10 Reference input Input potentiometer -Output potentiometer Feedback signal [2²] R₂ www.roo K₁ Kjer Input device Error measuring device Amplifier Figure 3 Motor Gear train Load