Learn more about Control System Toolbox

Model Dynamics

You can use functions to determine the system poles, zeros, DC gain, norms, etc. You can apply these functions to single LTI models or LTI arrays. The following table gives an overview of these commands.

Model Dynamics
covar	Covariance of response to white noise.
damp	Natural frequency and damping of system poles.
dcgain	Low-frequency (DC) gain.
dsort	Sort discrete-time poles by magnitude.
esort	Sort continuous-time poles by real part.
norm	Norms of LTI systems ( and ).
pole, eig	System poles.
pzmap	Pole/zero map.
zero	System transmission zeros.

With the exception of norm, these commands are not supported for FRD models.

Here is an example of model analysis using some of these commands.

h = tf([4 8.4 30.8 60],[1 4.12 17.4 30.8 60])

Transfer function:
     4 s^3 + 8.4 s^2 + 30.8 s + 60
---------------------------------------
s^4 + 4.12 s^3 + 17.4 s^2 + 30.8 s + 60

pole(h)

ans =
  -1.7971 + 2.2137i
  -1.7971 - 2.2137i
  -0.2629 + 2.7039i
  -0.2629 - 2.7039i
zero(h)
ans =
  -0.0500 + 2.7382i
  -0.0500 - 2.7382i
  -2.0000 
dcgain(h)

ans =
   1

[ninf,fpeak] = norm(h,inf)			% peak gain of freq. response

ninf =
1.3402			% peak gain
fpeak =
1.8537			% frequency where gain peaks

These functions also operate on LTI arrays and return arrays. For example, the poles of a three dimensional LTI array sysarray are obtained as follows.

sysarray = tf(rss(2,1,1,3))
Model sysarray(:,:,1,1)
=======================
Transfer function:
    -0.6201 s - 1.905
  ---------------------
  s^2 + 5.672 s + 7.405
 
Model sysarray(:,:,2,1)
=======================
Transfer function:
  0.4282 s^2 + 0.3706 s + 0.04264
  -------------------------------
      s^2 + 1.056 s + 0.1719
 
Model sysarray(:,:,3,1)
=======================
Transfer function:
    0.621 s + 0.7567
  ---------------------
  s^2 + 2.942 s + 2.113

3x1 array of continuous-time transfer functions.
pole(sysarray)
ans(:,:,1) =
   -3.6337
   -2.0379
ans(:,:,2) =
   -0.8549
   -0.2011
ans(:,:,3) =
   -1.6968
   -1.2452

General Model Characteristics

State-Space Realizations

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