GATE EC 2014 Set 2 — Question 57
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Control Systems → Frequency-Domain Analysis → Bode Plots
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Question
The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is_________.
Correct answer
0.49 to 0.51
Solution
1.Identify the system type: The initial slope of the Bode magnitude plot is dB/decade. This indicates that the system is a Type-1 system.
2.Determine the velocity error constant (): For a Type-1 system, the low-frequency asymptote is defined by the equation:
From the given plot, at rad/s, the magnitude is dB. Substituting these values into the equation:3.Calculate the steady-state error (): For a unity negative feedback system of Type-1, the steady-state error for a unit ramp input is given by:
The steady-state error is .Continue learning with Success Tracker
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