P8.13 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 rotat

ing winding. The syncro position detector rotor turns with the load through an angle θ0. The syncro motor is energized with an AC reference voltage, for exam

ple, 115 volts, 60 Hz. The input signal or command is

R s( ) = θin ( )s and 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 ac

curacy 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 modu

lation signal generator to the Y Y − ′ terminals and measure the response at X X − ′. (The error ( ) θ θ 0 − i 

will be adjusted to zero before applying the AC gen

erator.) The resulting frequency response of the loop transfer function L j ( ) ω is shown in Figure P8.13(b).

Determine the loop transfer function. Assume that the system has a minimum phase transfer function.

AC amplifier X Y Control winding Rotor Ka X' Y' Control transformer Stator Reference winding AC two-phase motor Load Rotor m ------ Syncro generator