User`s guide

Computing Linear Approximations of Nonlinear Black-Box Models
Computing Linear Approximations of Nonlinear Black-Box
Models
In this section...
“Why Compute a Linearize Approximation of a Nonlinear M odel?” on page
4-33
“Choosing Your Linear Appro xi mation Approach” on page 4-33
“Linear Approximation of Nonlinear Black-Box Models for a Given Input”
on page 4-34
“Tangent Linearization of Nonlinear Black-Box Models” on page 4-35
“Computing Operating Points for Nonlinear Black-Box Model s” on page 4-35
Why Compute a Linearize Approximation of a
Nonlinear M odel?
Linearizing a nonlinear model is required for linear control design and
linear analysis. After you linearize your model, you can use C ontrol System
Toolbox software t o design a co ntro ller and perform linear analysis. For more
information, see “U sing Models with Control Syste m Toolbox Software” on
page 10-2.
Choosing Your Linear Approximation Approach
System Identification Toolbox software provides two approaches for computing
a linear a pproxim ation of No nline ar ARX and Hammers te in-Wiener models.
To generate a linear approximation of a nonlinear m odel for a given input
signal, use the
linapp command. The resulting model is only valid for
the s ame input you u se to generate the linear approximation. For more
information, see “Linear Approx imation o f Non line ar Black- Box M od els for a
Given Input” on page 4-34.
Ifyouwantatangentapproximationof the nonlinear dynamics that is
accurate near the system operating point, use the
linearize command. The
resulting model is a fi rst-orderTaylorseriesapproximationforthesystem
about this operating point,whichisdefined by a constant input and model
4-33