Consider the system shown in Figure 3-42 An armature-controlled dc servomotor drives a load consisting of the moment of inertia JL. The torque developed by the motor is T. The moment of inertia of the motor rotor is Jm. The angular displacements of the motor rotor and the load element are e(s)/ E(s). , respectively. The gear ratio is L R all ei Jm . Obtain the transfer function JL Figure 3-42 Armature-controlled de servomotor system. e(s) E(s). R all ww Jm Figure 3-42 Armature-controlled dc servomotor system. 1. Derive the differential equations of the system. 2. Build the block diagram of the system showing all variables relations e (s) 3. Simplify the block diagram to get the transfer function E(s)' 4. What is the transfer function if the output is the sped instead of angular displacement, i.e. w (s) 2 E (s) 5. If the inductance of the motor is very small such that it can be ignored, What is the new w (S), transfer function E (s)