The purpose of an Automatic Voltage Regulator is to maintain constant the voltage generated in an electrical power system, despite load and line variations, in an electrical power distribution system (Gozde, 2011). Figure P5.42 shows the block

diagram of such a system. Assuming K_a = 10, T_a = 0.1, K_e = 1, T_e = 0.4, Kg = 1, T_g = 1, K_s = 1, T_s = 0.001, and the controller, G_PID(s) = 1.6 + 0.4/s + 0.3s, find the closed-loop transfer function, T(s) = ΔV_t(s)/ΔV_ref (s), of the system, expressing it as a rational function.

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Controller Plant K,K, Kg T.T,T AVef (s)+ AV(s) u(s) AV,(s) Gpip(s) PID Compensator Amplifier, Exciter, Generator AV,(s) Feedback K, T, (+.) Sensor FIGURE P5.42