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There are a number of polar graph options for studying control systems including the nyquist,
inverse polar plot and the nichols plot. The nyquist open loop polar plot
indicates the degree of stability, and the adjustments required and provides stability information
for systems containing time delays. Polar plots are not used exclusively because,without
powerful computing facilities, they can be difficult to generate at a detailed level and they do
not directly yield frequency values.
Basic Rules for constructing Nyquist plots
In control systems a transfer function to be assessed is often of the form
This transfer function is modified for frequency response analysis by replacing the s with jω
Assuming the function is proper and n > m..he Nyquist plot will have the following characteristics. Crude plots to be may be produced relatively easily using these characteristics.
Relative stability assessments Using the Nyquist Plot
As identified in the page on frequency response Frequency response The nyquist
plots are based on using open loop performance to test for closed loop stability. The system will be unstable
if the locus has unity value at a phase crossover of 180 o ( p ).
Nyquist Stability Criterion.
In the nyquist plots below the area covered to the right of the locus(shaded) is the Right Hand Plane (RHP)
A closed loop control system is absolutely stable if the roots of the characteristic equation
have negative real parts. This means the poles of the closed loop transfer function,
or the zeros of the denominatior ( 1 + GH(s)) of the closed loop tranfer function, must lie in the (LHP).
The nyquist stability criterion establishes the number of zeros of (1 + GH(s) in the RHP directly from the
Nyquist stability plot of GH(s) as indicated below.
N = -Po ≤ 0
Nyquist Plots A number of typical nyquist plots are shown below to illustrate the various shapes.
Plot 1..... 1 /(s + 2)
Note that G(i0) = 0.5 and as ω increases to ¥ the plot approaches zero along the negative locus.
Plot 2.....1 /(s 2 + 2s + 2)
The zero-frequency behaviour is:G(j0) =0.5
Plot 3.....s(s+1) /(s 3 + 5.s 2 +3.s + 4 )
Plot 4.....(s+1) /[(s+2)(s+3)]
Plot 5.....1 /s(s-1).. an unstable regime
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Last Updated 28/01/2013