A position control system may be constructed by using an AC motor and AC components, as shown in Figure P8.13.The syncro and control transformer may be considered to be a transformer with a rotating winding. The syncro position detector rotor turns with the load through an angle 80. The syncro motor is energized with an AC reference voltage, for example, 115 volts, 60 Hz. The input signal or command is R(s) = θin (s) ana" is applied by turning the rotor of the control transformer. The AC two-phase motor operates as a result of the amplified error signal. The advantages of an AC control system are (1) freedom from DC drift effects and (2) the simplicity and accuracy of AC components. To measure the open-loop frequency response, we simply disconnect X from Y and X' from Y' and then apply a sinusoidal modulation signal generator to the Y - Y' terminals and measure the response at X - X'. (The error (θ0- θi,) will be adjusted to zero before applying the AC generator.) The resulting frequency response of the loop transfer function LQGO) = Gc(j(ω)G(jω)H(jω)) is shown in Figure P8.13(b). Determine the transfer function L(;'w). Assume that the system has a minimum phase transfer function

FIGURE P8.13
(a) AC motor control.
(b) Frequency response

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40 -20 dB/dec 09 -90 p(n)180 -270 -360 n 20 -40 dB/dec -80 dB/ded 100 ω (rad/s) 10 1000 -40 L 10 1000 100 ω (radis)