zgrid (Control System Toolbox)

Generate a z-plane grid of constant damping factors and natural frequencies

Syntax

zgrid
zgrid(z,wn)

Description

zgrid

generates a grid of constant damping factors from zero to one in steps of 0.1 and natural frequencies from zero to

in steps of

, and plots the grid over the current axis. If the current axis contains a discrete z-plane root locus diagram or pole-zero map, zgrid draws the grid over the plot without altering the current axis limits.

zgrid(z,wn)

plots a grid of constant damping factor and natural frequency lines for the damping factors and normalized natural frequencies in the vectors z and wn, respectively. If the current axis contains a discrete z-plane root locus diagram or pole-zero map, zgrid(z,wn) draws the grid over the plot. The frequency lines for unnormalized (true) frequencies can be plotted using

zgrid(z,wn/Ts)

where Ts is the sample time.

zgrid([],[])

draws the unit circle.

Example

Plot z-plane grid lines on the root locus for the system

by typing

H = tf([2 -3.4 1.5],[1 -1.6 0.8],-1)
Transfer function:
2 z^2 - 3.4 z + 1.5
-------------------
 z^2 - 1.6 z + 0.8

Sampling time: unspecified

To see the z-plane grid on the root locus plot, type

rlocus(H)
zgrid
axis('square')

Limitations

zgrid plots the grid over the current axis regardless of whether the axis contains a root locus diagram or pole-zero map. Therefore, if the current axis contains, for example, a step response, you may superimpose a meaningless z-plane grid over the plot.