The Automatic Voltage Regulator (AVR) system of a generator is represented by the simplified block diagram shown in Figure 12.15, in which the sensor is modeled by a simple first-order transfer function. The voltage is sensed through a voltage transformer and then rectified through a bridge rectifier. Parameters of the AVR system are given as follows.

(a) Determine the open-loop transfer function of the block diagram and the closed-loop transfer function relating the generator terminal voltage \(V_{t}(s)\) to the reference voltage \(V_{\text {ref }}(s)\).

(b) For the range of \(K_{A}\) from 0 to 12.16, comment on the stability of the system.

(c) For \(\mathrm{K}_{\mathrm{A}}=10\), evaluate the steady-state step response and steady-state error.

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Amplifier Exciter Generator Sensor Gain K = 1 K = 1 K = 1 Time Constant (seconds) T = 0.1 T = 0.4 T = 1.0 G TR = 0.05