GATE EE 2024 Set 1 — Question 58
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Control Systems → Frequency Response & Root Locus → Bode Plots
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Question
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of has a constant slope of dB/decade at least till rad/sec with the gain crossover frequency being rad/sec. The asymptotic Bode phase plot remains constant at at least till rad/sec. The steady-state error of the closed-loop system for a unit ramp input is ______________ (rounded off to 2 decimal places).
Correct answer
0.09 to 0.11
Solution
The asymptotic Bode magnitude plot has a slope of dB/decade and the phase is constant at for rad/sec. This indicates that the system is of Type 1, and in this frequency range, the transfer function can be approximated as .At the gain crossover frequency rad/sec, the magnitude is 1 (0 dB):
.The steady-state error for a unit ramp input for a Type 1 system is given by:
.Thus, the steady-state error is 0.10.
.The steady-state error for a unit ramp input for a Type 1 system is given by:
.Thus, the steady-state error is 0.10.
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