Showing posts with label Nyquist plots. Show all posts
Showing posts with label Nyquist plots. Show all posts

12 Jul 2018

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

In this post we will learn what are polar plots. Here we will also trace polar plots of some transfer functions also.
Here we will see the general shapes of the polar plots of some important transfer functions. You will learn in this post, how the shape of the polar plot changes on adding poles (non zero poles and poles at origin) or zeros to the transfer function.
But before this it is important to understand what we mean by polar plots-

Watch the Complete Video Here-

What is Polar Plot in Control System

A polar plot is a plot of a function that is expressed in polar coordinates, with radius as a function of angle.
Polar plots are drawn between magnitude and phase.
If we have a sinusoidal transfer function G(jw), which is a complex function.
Therefore we can write-
G(jw)= Re[G(jw)] + jIm[G(jw)]
G(jw)= lG(jw)l angle(G(jw))

Therefore we can represent the transfer function G(jw), as a phasor of magnitude M and phase angle phi. This phase angle is measured positively in the counter clockwise direction.
The magnitude and the phase angle changes as the input frequency (w), is varied from zero to infinity.
So the locus obtained in the complex plane by the tip of the phasor G(jw) is called the polar plot.
Polar plots are also known as a Nyquist Plots.

Now we will understand the effect on shape of the polar plot on adding poles or zeros to the transfer function.


Polar Plots of Transfer Functions (Adding Poles and Zeros)

There are following three rules that are followed to trace Polar Plots in control systems, on adding poles and zeros to the transfer function-