User`s guide

3 Linear Model Identification
Definition of a Continuous-Time Polynomial Model
In continuous time, the general frequency-domain equation is written in terms
of the Laplace transform variable s, which corresponds to a differen tiation
operation:
AsY s
Bs
Fs
Us
Cs
Ds
Es() ()
()
()
()
()
()
()=+
In the continuous-tim e case, the underlying t ime-dom ain model is a
differential equation and the model order integers represent the number of
estimated numerator and denominator coefcients. For example, n
a
=3 and
n
b
=2 correspond to the following model:
Assasasa
Bs bs b
()
()
=+ + +
=+
4
1
3
2
2
3
12
The simplest way to estimate continuous-time poly n omial models of
arbitrary structure is to rst estimate a discrete-time model of arbitrary
order and then use
d2c to convert this model to continuous time. For more
information, see “Transforming Between Discrete-Time and Continuous-Time
Representations” on page 3-112.
You can also estimate continuous-time polynomial models directly using
continuous-time frequency-domain data. In this case, you must set the
Ts data
property to 0 to indicate that you have continuous-time frequency-domain
data.
Definition of Multiple-Output ARX Models
You can use a m ultiple-output ARX model to model a multiple-output dynamic
system. The ARX model structure is given by the follow ing equation:
Aqyt Bqut nk et()() () ()=−
()
+
3-46