The straight line approximated torque-speed curve of AC servo motor for rated control voltage \(115 \mathrm{~V}, 50 \mathrm{~Hz}\) is shown in Fig. P9.4. The moment of inertia of motor is \(10^{-5} \mathrm{~kg} \cdot \mathrm{m}^{2}\). Neglect the friction and determine transfer function model that relates shaft position \(\theta_{0}\) to control voltage \(V_{C}\).

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Torque (N.m) 0.2 > 3000 Fig. P 9.4 Speed (rpm) (