User`s guide

3 Linear Model Identification
B(q) can also be represented as a matrix:
Bq
bq bq b q
bq bq b q
bqb
nu
nu
ny n
()
() () ()
() () ()
()
=
11 12 1
21 22 2
1
…
…
…………
yynynuq
qb
2
()
()
…
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
where the matrix element b
kj
is a polynomial in the shift operator q
-1
:
bq aq a q
kj kj
nb
kj
nk
nb nb
kj
kj
kj kj
()=++
−−−+
1
1
…
nk
kj
is the delay from the jth input to the kth output. B(q) represents the
contributions of inputs to predicting all outpu t values.
Data Supported by Polynomial Models
• “Types of Supported Data” on page 3-48
• “Designating Data for Estimating Continuous-Time Models” on page 3-49
• “Designating Data for Estimating Discrete-Time M odels” on page 3-49
Ty pes of Supported Data
You can estimate linear, black-box polynomial models from data with the
following characteristics:
• Time- or frequency-domain data (
iddata or idfrd data objects).
Note For frequency-domain data, you can only estimate ARX and OE
models.
To estimate black-box polynomial models for time-series data, see Chapter
6, “Time Series Model Identifi cation”.
• Real data or complex data in any domain.
3-48