GATE EE 2019 Set 1 — Question 39
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Control Systems → Frequency Response & Root Locus → Bode Plots
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Question
The asymptotic Bode magnitude plot of a minimum phase transfer function is shown below.
Consider the following two statements.
Statement I: Transfer function has three poles and one zero.
Statement II: At very high frequency , the phase angle .
Which one of the following options is correct?
Consider the following two statements.
Statement I: Transfer function has three poles and one zero.
Statement II: At very high frequency , the phase angle .
Which one of the following options is correct?
Correct answer
(B) Statement I is false and statement II is true.
Solution
Read the asymptotic plot from left to right.
1.Initial slope dB/decade (up to ): one pole at the origin, .
2.At the slope changes from to dB/decade: one real pole at rad/s.
3.At the line simply crosses dB; the slope stays dB/decade from to , so there is no corner (and no zero) at . (Check: dB.)
4.At the slope changes from to dB/decade: one more real pole at rad/s.
Sowhich has three poles and no zero. Statement I (three poles and one zero) is therefore false.For a minimum-phase system, as each pole contributes and each zero :(consistent with the final slope of dB/decade ). Statement II is true.Hence Statement I is false and Statement II is true: option (B).Continue learning with Success Tracker
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