Polar Plot

This presentation explains about the introduction of Polar Plot, advantages and disadvantages of polar plot and also steps to draw polar plot. and also explains about how to draw polar plot with an examples. It also explains how to draw polar plot with numerous examples and stability analysis by using polar plot.

1. Control System:
Polar Plot
By
Dr.K.Hussain
Associate Professor & Head
Dept. of EE, SITCOE

2. Polar Plot
•The Polar plot is a plot, which can be drawn between the
magnitude and the phase angle of G(jω)H(jω) by varying ω from
zero to ∞.

•The polar graph sheet consists of concentric circles and radial
lines.

•Polar plot is a plot of magnitude versus phase angle in complex
plane .
(i.e., locus of magnitude traced by the phasor by varying frequency from 0 to ∞)

3. Advantages of Polar plots
•It depicts the frequency response characteristics over the entire
frequency range in a single plot.

•Much easier to determine both w
pc and w
gc.

•Here we will have to work with open loop transfer function G(s)H(s)
(and not with closed loop transfer function and unlike Bode plot we
need not required to convert G(s)H(s) to the time constant form).

Disadvantage of Polar plots:
•The plot does not clearly indicate the contribution of each
individual factor of the open loop transfer function.

4. Polar Plot
Basics of Polar Plot:
•The polar plot of a sinusoidal transfer function G(jω) is a plot
of the magnitude of G(jω) Vs the phase of G(jω) on polar co-
ordinates as ω is varied from 0 to ∞.
i.e., |G(jω)| Vs angle G(jω) as ω → 0 to ∞.
• Polar graph sheet has concentric circles and radial lines.
•Concentric circles represents the magnitude.
• Radial lines represents the phase angles.
•In polar sheet:
•+ve phase angle is measured in ACW from 0
0

•-ve phase angle is measured in CW from 0
0.

5. Polar Plot
•To sketch the polar plot of G(jω) for the entire
range of frequency ω, i.e., from 0 to infinity,
there are four key points that usually need to
be known:
(1) the start of plot where ω = 0,
(2) the end of plot where ω = ∞,
(3) where the plot crosses the real axis, i.e.,
Im(G(jω)) = 0, and
(4) where the plot crosses the imaginary axis, i.e.,
Re(G(jω)) = 0.

6. Polar Plot
PROCEDURE:
• Express the given expression of OLTF in (1+sT) form.
• Substitute s = jω in the expression for G(s)H(s) and get G(jω)H(jω).
• Get the expressions for |G(jω)H(jω)| & G(jω)H(jω).
• Tabulate various values of magnitude and phase angles for different
values of ω ranging from 0 to ∞.
• Usually the choice of frequencies will be the corner frequency and
around corner frequencies.
• Choose proper scale for the magnitude circles.
• Fix all the points in the polar graph sheet and join the points by a
smooth curve.
• Write the frequency corresponding to each of the point of the plot.

7. Example-1
Q. Sketch the Polar Plot of a 1
st
Order Pole of 10/(s+2)





Step 2: We now find the magnitude and phase.





The given transfer function is
Step 1: The first step would be convert this transfer
function to the frequency domain. This can be done by
converting ‘s’ by ‘jω’.
Sol:
Step 3: Vary ‘ω’ from 0 to ∞.
Now instead of taking different
values of ω, we simply take two
extreme values of ω. i.e., ω = 0
and ω = ∞
Now these two points are sufficient to draw the polar plot. At ω = 0 since the magnitude is +5 and
angle is 0, we draw it on the right side horizontal axis. At ω = ∞, the magnitude is 0 while angle is -90
0
,
hence we draw it as dot (zero magnitude) on the -90
0
.
Polar Plot

8. Example-2 (Effect of adding more Simple Poles)
Q. Sketch the Polar Plot for the given transfer function
10/(s+2)(s+4)




Step 2: We now find the magnitude and phase.





The given transfer function is
Step 1: The first step would be convert this transfer
function to the frequency domain. This can be done by
converting ‘s’ by ‘jω’.
Sol:
Step 3: Vary ‘ω’ from 0 to ∞.
Now instead of taking different values of ω,
we simply take two extreme values of ω
i.e., ω = 0 and ω = ∞
Now these two points are sufficient to draw the
polar plot. At ω = 0 since the magnitude is +5
and angle is 0, we draw it on the right side
horizontal axis. At ω = ∞, the magnitude is 0
while angle is -90
0
, hence we draw it as dot
(zero magnitude) on the -90.
Polar Plot

9. Polar Plots-Examples

10. Polar Plot

11. Polar Plot

12. Stability on Polar plots
•Polar plots are simple method to check the stability of the system.

13. THANK YOU