Generate z-plane grid of constant damping factors and natural frequencies
zgrid generates a grid of constant damping factors from 0 to 1 in
steps of 0.1 and natural frequencies from 0 to
π/T in steps of
0.1*π/T for root locus and pole-zero maps. The default steps of
0.1*π/T represent fractions of the Nyquist frequencies.
zgrid then plots the grid over the current axis.
zgrid creates the grid over the plot without altering the current
axis limits if the current axis contains a discrete z-plane root locus diagram or
pole-zero map. Use this syntax to plot multiple systems with different sample
Alternatively, you can select Grid from the context menu in the plot window to generate the same z-plane grid.
zgrid( generates the z-plane grid by using
default values for damping factor and natural frequency relative to the sample time
zgrid( plots a
grid of constant damping factor and natural frequency lines for the damping factors and
normalized natural frequencies in the vectors
wn, respectively. When the sample time is not specified, the
frequency values in
wn are interpreted as normalized values, that is,
plots a grid of constant damping factor and natural frequency lines for the damping
factors and natural frequencies in the vectors
wn, relative to sample time
zeta lines are independent for
T but the
wn lines depend on the sample time value. Use this syntax to create
the z-plane grid with specific values of
zgrid(___,'new') clears the current axes first and
zgrid( plots the z-plane
grid on the
UIAxes object in the current
figure with the handle
AX. Use this syntax when creating apps with
zgrid in the App Designer.
Plot z-plane Grid Lines on the Root Locus
To see the z-plane grid on the root locus plot, type
H = tf([2 -3.4 1.5],[1 -1.6 0.8],-1)
H = 2 z^2 - 3.4 z + 1.5 ------------------- z^2 - 1.6 z + 0.8 Sample time: unspecified Discrete-time transfer function.
rlocus(H) zgrid axis equal
Normalized and True z-plane Grid Lines on the Pole-Zero Map
For this example, consider a discrete-time transfer function
sys with a sample time of 0.1s. Now plot the pole-zero map of
sys and visualize the default z-plane grid without specifying the sample time.
sys = tf([2 -3.4 1.5],[1 -1.6 0.8],0.1); Ts = 0.1; figure() pzmap(sys) zgrid() axis equal
Observe that the frequencies on the z-plane grid are normalized in terms of . To obtain the true frequency values on the grid, specify the sample time with the
figure() pzmap(sys) zgrid(Ts) axis equal
Now, observe that the frequency values on the plot are true values, that is, they are non-normalized.
wn — Natural frequency values
Natural frequency values, specified as a vector. Natural frequencies are plotted as
true values when
T is specified. When the sample time is not
zgrid normalizes the values as
T — Sample time
positive scalar |
Sample time, specified as:
A positive scalar representing the sampling period of a discrete-time system. The actual frequency values are displayed on the frequency grid.
-1for a discrete-time system with an unspecified sample time. The frequency values are displayed as normalized values
f*π/Tfor the default grid.
zeta lines are independent of
wn lines are dependent on the sample time. You must specify
T to plot specific values of
wn. When the
T is not specified, the required
values are interpreted as normalized values, that is,
AX — Object handle
Axes object |
Object handle, specified as an
AX to create apps with
zgrid in the