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Question: 22 modeling a dc motor servo consider the de servomotor...

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2.2 Modeling a DC motor servo Consider the de servomotor system shown in Figure 2. Assume that the magnetic field is constant. 7 Ja Figure 2. DC servomotor system. In the figure, R-armature resistance, Ω; L-armature inductance, H iarmature current, A; ir- magnetic field current, A e applied armature voltage, V ebackemf, V T- torque developed by the motor, N-rm Jmoment of inertia of the motor rotor, kg-m Jmoment of inertia of the load, kg-m O- angular displacement of the motor rotor, rad 0- angular displacement of the load element, rad n 12 number of teeth of gear1 n-36, number of teeth of gear 2 1) Assume the motor torque constant is Ki, the back emf constant is K. Derive the governing equations of this system. Write the equations in the following format Im 2) Obtain the transfer function between the output 6 (speed of Ji) and the input voltage e. Identify the order of this system. If the armature inductance L can be neglected, ie, L-0, what will happen to the order of this system?
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