damp(sys) displays
a table of the damping ratio (also called damping factor),
natural frequency, and time constant of the poles of the linear model sys.
For a discrete-time model, the table also includes the magnitude of
each pole. Frequencies are expressed in units of the reciprocal of
the TimeUnit property of sys.
Time constants are expressed in the same units as the TimeUnit property
of sys.

This command requires a Control System Toolbox™ license.

[Wn,zeta]
= damp(sys) returns the natural frequencies, Wn,
and damping ratios,zeta, of the poles of sys.

Vector containing the natural frequencies of each pole of sys,
in order of increasing frequency. Frequencies are expressed in units
of the reciprocal of the TimeUnit property of sys.

If sys is a discrete-time model with specified
sampling time, Wn contains the natural frequencies
of the equivalent continuous-time poles (see Algorithms). If sys has an unspecified
sampling time (Ts = -1), then the software uses Ts
= 1 and calculates Wn accordingly.

zeta

Vector containing the damping ratios of each pole of sys,
in the same order as Wn.

If sys is a discrete-time model with specified
sampling time, zeta contains the damping ratios
of the equivalent continuous-time poles (see Algorithms). If sys has an unspecified
sampling time (Ts = -1), then the software uses Ts
= 1 and calculates zeta accordingly.

P

Vector containing the poles of sys, in
order of increasing natural frequency. P is the
same as the output of pole(sys), except for the
order.

Calculate the natural frequency, damping ratio, time constant,
and poles of a discrete-time transfer function.

H = tf([5 3 1],[1 6 4 4],0.01);

Display information about the poles of H.

damp(H)

Pole Magnitude Damping Frequency Time Constant
(rad/seconds) (seconds)
-3.02e-01 + 8.06e-01i 8.61e-01 7.74e-02 1.93e+02 6.68e-02
-3.02e-01 - 8.06e-01i 8.61e-01 7.74e-02 1.93e+02 6.68e-02
-5.40e+00 5.40e+00 -4.73e-01 3.57e+02 -5.93e-03

The Magnitude column displays the discrete-time
pole magnitudes. The Damping, Frequency,
and Time Constant columns display values calculated
using the equivalent continuous-time poles.

Obtain vectors containing the natural frequencies and
damping ratios of the poles.