GATE EC 2015 Set 3 — Question 56
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Digital Circuits → Sequential Logic → Shift Registers
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Question
The position control of a DC servo-motor is given in the figure. The values of the parameters are N-m/A, , H, kg-m, N-m/(rad/sec) and V/(rad/sec). The steady-state position response (in radians) due to unit impulse disturbance torque is ________.
📷 Figure: Block diagram: V_a(s) to summer (+, - from K_b feedback), block K_T/(R_a+L_a s), summer with T_d(s) entering negative, block 1/(Js+B) whose output feeds back through K_b, then block 1/s giving theta(s)
Correct answer
-0.51 to -0.49
Solution
Set and let be the output of the block (motor speed), so .Motor torque with back-emf feedback: .At the disturbance summing point (the disturbance enters with a minus sign):Solving,For a unit impulse, . The closed-loop poles of are in the left half plane, so the final value theorem applies:Answer: rad (accepted range to )
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