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Problem 1:

A two-phase servomotor has rated voltage applied to its excitation winding. The torque speed characteristic of the motor with Vc = 220 V, 60 Hz applied to its control phase winding is shown in Fig.1. The moment of inertia of the motor and the load is 5×10-5 kg.m2 and the resultant motor-load viscous friction coefficient is B = 0.002 N.m x s / rad .

a) Write the torque equation and draw the block diagram of the motor with and without load.

b) Find the shaft speed and position response to the step voltage Vc = 220 V applied to the control phase winding when no load is applied.

c) Find the shaft speed and position response to the step control voltage Vc = 220 V if the load is applied of TL = 0.0003ω2m.

d) Compare results obtained for operating conditions b) and c) and make comments.

629_figure.jpg

Problem 2: In Fig.2 (below) a radar antenna is controlled by the position system with two- phase induction servomotor. Let the transformer selsyn system and the potentiometer transducer give a voltage of 1V per radian of position. The transfer function of the servo amplifier is G(s)= 10(5+0.01571s)/7+s.

Assume that the initial angular position of the radar is zero. The transfer function between the motor control phase voltage Vc and radar position

θ is M(s)= 2.733/s(1+0.01571s)

a) Draw the block diagram of the system

b) For step change in the command angle of 120o find the time response of the angular position of the antenna.

c) Find step response if transfer function G(s) has changed to:

G(s)= (10(0.8+0.01571s))/(7+s)

d) Compare results obtained for operating conditions b) and c) and make comments.

1822_figure1.jpg

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