User`s guide

5 ODE P ara meter Estimation (Grey-Box Modeling)
Supported Grey-Box Models
If you understand the physics of your system and can represent the system
using ordinary differential or difference equations (ODEs) with unknown
parameters, then you can use System Identification Toolbox commands to
perform linear or nonlinear grey-box modeling. Grey-box model ODEs specify
the mathematical structure of the mod el explicitly, including couplings
between parameters and known parameter values. Grey-box m odeling is
useful when you know the relationships between variables, constraints on
model behavior, or explicit equations representing system dynamics.
The toolbox suppo rts both continuous-time and discrete -time models.
However, because most laws of physics are expressed in continuous time, it is
easier to construct models with physical insight in continuous time, rather
than in discrete time.
In addition to dynamic input-output models, you can also create time-series
models that have no inp uts and s ta tic models that have no states.
If it is too difficult to describe your system usingknownphysicallaws,youcan
perform black-box modeling.
You can also use the
idss model o bject to perform structured model
estimation by using structure matrices
As, Bs, Cs, Ds, X0s, Ks to fixorfree
specific parameters. However, you cannot use this approach to estim ate
arbitrary structures (arbitrary parameterization). For more information
about structure matrices, see “How to Estimate State-Space Models with
Structured Parameterization” on page 3-93.
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