Control System Toolbox™

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

Syntax

zgrid
zgrid(z,wn)
zgrid([],[])

Description

zgrid generates, for root locus and pole-zero maps, 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.

Alternatively, you can select Grid from the right-click menu to generate the same z-plane grid.

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')

See Also

pzmap, rlocus, sgrid

zero

zpk