Control System Toolbox™

damp - Natural frequency and damping of system poles

Syntax

[Wn,Z] = damp(sys)
[Wn,Z,P] = damp(sys)

Description

damp calculates the damping factor and natural frequencies of the poles of an LTI model sys. When invoked without lefthand arguments, a table of the eigenvalues in increasing frequency, along with their damping factors and natural frequencies, is displayed on the screen.

[Wn,Z] = damp(sys) returns column vectors Wn and Z containing the natural frequencies and damping factors of the poles of sys. For discrete-time systems with poles and sample time , damp computes "equivalent" continuous-time poles by solving

The values Wn and Z are then relative to the continuous-time poles . Both Wn and Z are empty if the sample time is unspecified.

[Wn,Z,P] = damp(sys) returns an additional vector P containing the (true) poles of sys. Note that P returns the same values as pole(sys) (up to reordering).

Example

Compute and display the eigenvalues, natural frequencies, and damping factors of the continuous transfer function

Type

H = tf([2 5 1],[1 2 3])
Transfer function:
2 s^2 + 5 s + 1
---------------
 s^2 + 2 s + 3

Type

damp(H)

This command returns the following result.

Eigenvalue            Damping     Freq. (rad/s)  
                                                         
-1.00e+000 + 1.41e+000i     5.77e-001      1.73e+000    
-1.00e+000 - 1.41e+000i     5.77e-001      1.73e+000 

See Also

eig, esort, dsort, pole, pzmap, zero

d2d

dare