Control Systems
Frequency Domain Analysis
Practice questions from Frequency Domain Analysis.
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IncorrectThe Nyquist plot of a strictly stable having the numerator polynomial as encircles the critical point -1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?
Given that open loop system is stable.
No. of open -loop poles in RH of s-plane
Also, No. of encirclements about critical point is once,
Assume Nyquist Contour is clockwise
N = 1
N = P-Z
P= Open Loop Poles in RHP = 0
Z = Closed Loop Poles in RHP
Hence Z = -1 which is invalid
Now assume Nyquist Contour is Anti-Clockwise
N = -1 = P – Z
Hence Z = 1, which means one closed loop pole
lies in RHP and hence closed loop system is unstable
Option (d) is correct.
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of has a constant slope of decade at least till with the gain crossover frequency being . The asymptotic Bode phase plot remains constant at at least till . The steady-state error of the closed-loop system for a unit ramp input is ________ (rounded off to 2 decimal places).
Starting slope
pole at origin
The value of frequency at which the initial line of slope -20dB/dec intersects 0dB line gives the value of velocity error constant.
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of are given in the table. The value of the gain for a phase margin is ________ (rounded off to 2 decimal places).
Based on phase angle of transfer function G, we can determine the frequency,
From table,
and
By definition of ,
In the Nyquist plot of the open-loop transfer function
Corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at
Nyquist contour:
Infinite semicircular arc: S =
θ: to –
G (s) H (s) =
=
The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is
Magnitude of gain = 8dB = 20 log K
Phase is linear & at
Or rad at ω = 1
∴ Slope of phase plot
So, transfer function can be expressed as
