| Creating and Manipulating Models | |
Model Dynamics
The Control System Toolbox offers commands to determine the system poles, zeros, DC gain, norms, etc. You can apply these commands to single LTI models or LTI arrays. The following table gives an overview of these commands.
| Model Dynamics | |
|
Covariance of response to white noise. |
|
Natural frequency and damping of system poles. |
|
Low-frequency (DC) gain. |
|
Sort discrete-time poles by magnitude. |
|
Sort continuous-time poles by real part. |
|
Norms of LTI systems ( and  ). |
|
System poles. |
|
Pole/zero map. |
|
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
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