User`s guide

5 ODE P ara meter Estimation (Grey-Box Modeling)
Estimating Linear Grey-Box Models
In this section...
“Specifying the Linear Grey-Box Model Structure” on page 5-6
“Example – Representing a Gr ey-BoxModelinanM-File”onpage5-7
“Example – Estima t in g a Con tinuous-Tim e Grey-Box Model for Hea t
Diffusion” on page 5-9
“Example – Estimating a Discrete-Tim e Grey-Box Model with
Parameterized Disturbance” on page 5-12
Specifying the Linear Grey-Box Model Structure
You can estimate linear discrete-time and continuous-time grey-box models
for arbitrary ordinary differential or difference equations using single-output
and multiple-output time-dom ain data, o r output-only time-serie s data.
You must represent your system equations in state-space form. State-space
models use state variables x(t) to describe a system as a set of first-order
differential e quations, rather than by one or more nth-orde r di ff erential
equations.
In continuous-time, the state-space description has the following form:


xt Fxt Gut Kwt
yt Hxt Dut wt
xx
() () () ()
() () () ()
()
=++
=++
=00
The discre
te-time state-space model structure is often written in the
innovatio
ns form :
x kT T Ax kT Bu kT Ke kT
ykT CxkT DukT ekT
x
( ) () () ()
() () () ()
()
+= + +
=+ +
=0 xx0
5-6