Function File: damp(sys)

Function File: [Wn, zeta] = damp(sys)

Function File: [Wn, zeta, P] = damp(sys)

Calculate natural frequencies, damping ratios and poles.

If no output is specified, display overview table containing poles, magnitude (if sys is a discrete-time model), damping ratios, natural frequencies and time constants.

Inputs

sys

LTI model.

Outputs

Wn

Natural frequencies of each pole of sys (in increasing order). The frequency unit is rad/s (radians per second). If sys is a discrete-time model with specified sample time, Wn contains the natural frequencies of the equivalent continuous-time poles (see Algorithms). If sys has an unspecified sample time (tsam = -1), tsam = 1 is used to calculate Wn.

zeta

Damping ratios of each pole of sys (in the same order as Wn). If sys is a discrete-time model with specified sample time, zeta contains the damping ratios of the equivalent continuous-time poles (see Algorithms). If sys has an unspecified sample time (tsam = -1), tsam = 1 is used to calculate zeta.

P

Poles of sys (in the same order as Wn).

Algorithm

Pole

Poles s (or z for discrete-time models) are calculated via pole and resorted in order of increasing natural frequency.

Equivalent continuous-time pole

s = log (z) / sys.tsam (discrete-time models only)

Magnitude

mag = abs (z) (discrete-time models only)

Natural Frequency

Wn = abs (s)

Damping ratio

zeta = -cos (arg (s))

Time constant

tau = 1 / (Wn * zeta)

See also: dsort, eig, esort, pole, pzmap, zero.

Package: control