Nyquist Plots d1y7

UMY KALSOOM

• What is a Nyquist Plot?

Nyquist plot is a plot used mostly in control and signal processing and can be used to predict the stability and performance of a closed-loop system.

• a polar plot of the frequency response function of a system • Bode' plots use frequency as the horizontal axis and use two separate plots to display amplitude and phase of the frequency response • Nyquist plots display both amplitude and phase angle on a single plot, using frequency as a parameter in the plot • Nyquist plots have properties that allow you to see whether a system is stable or unstable

STEPS 1. Change Transfer Function From “s” Domain To “jw” Domain • First, If the transfer function G(s) is given in “s” domain, transfer it to “jω” domain.

2. Find The Magnitude & Phase Angle Equations • Write an equation explaining the Magnitude and Phase Angle of the transfer function (now in “jω” form) that would look like:

G( j) G( j)

3. Evaluate At Point “0+” and “+∞” points • Evaluate the magnitude and phase angle equations found above, at ω (omega) values of “0+” and “+∞” points. 4. Find The Positions of “0+” & “+∞” On The Plot, And Connect Them

EXAMPLE • Nyquist plot of G ( s) 

20 s4

G (s) 

5 0.25s  1

• Frequency responses G ( j ) 

5 1  0.0625

2

and

  tan 1 (0.25 )

and

  tan 1 (0)  0

and

 1   tan 1    tan     1 

At

 0

G( j 0) 

5 5 1 0

 

G( j) 

5 0 1 

  90

Plot Nyquist G(s)=5/(0.25s+1) 2.5 2 System: sys Real: 0.917 Imag: 1.93 Freq (rad/sec): -8.46 System: sys Real: 0.000335 Imag: -0.0409 Freq (rad/sec): 489

1.5 1

Paksi Khayali

System: sys Real: 3.64 Imag: 2.22 Freq (rad/sec): -2.45

0.5 0 -0.5

System: sys Real: 5 Imag: 0 Freq (rad/sec): 0

System: sys Real: 4.52 Imag: -1.47 Freq (rad/sec): 1.3

-1

System: sys Real: 1.24 Imag: -2.16 Freq (rad/sec): 6.98

-1.5 -2 -2.5 -1

0

1

2 Paksi Hakiki

3

4

5

6

NYQUIST STABILITY • If open loop Nyquist plot of a system encircles the point (-1, 0) as the frequency ꙍ takes any value from -∞ to +∞, the closed-loop response is unstable

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