Block diagram of a servo control system is given below. As shown, there is a position controller with the gain of Kr. and a velocity controller with the gain of K. An external torque T, is applied to the motor to rotate it. In order to make the system resist against the external torque, and not to move x,=0 is commanded. How much does the motor move from its position when a step external torque with a magnitude of T. is applied? Derive the symbolic expression using the variables of the system. Reference Position X, Position Control T K, T₁S+1 Velocity Control Loop Velocity h Position Position Feedback

Fig: 1