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A servomechanism is required to position a load having moment of inertia J and viscous damping C. the property of the amplifier motor combination

A servomechanism is required to position a load having moment of inertia J and viscous damping C. the

A servomechanism is required to position a load having moment of inertia J and viscous damping C. the property of the amplifier motor combination is that it produces a torque on the load which is K times the angular error, where K is a constant. Show that, if the input shaft of the servomechanism is rotated at constant angular velocity @, rad/s, the steady state velocity lag is 25 Wp C where and an are the @n K damping ratio and natural frequency of the system respectively. If = 0.5 s, determine the value of (@n) such that the velocity lag shall not exceed 1 at an angular speed of 1.26 rad/s. C In order to increase the damping ratio & to a value of 0.5 without increasing the velocity lag, derivative controller is used, that is a transfer function in the form (1+Ta s) is introduced in the forward path. Find the value of Ta and under these conditions derive an expression for the angular error when the input is in the form 0.54r, where A is a constant acceleration in rad/s. If C is now considered to be zero, find the steady state acceleration error for 4 = 12 rad/s.

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