User`s guide

Computing Linear Approximations of Nonlinear Black-Box Models
Tangent Linearization of Nonlinear Black-Box Models
linearize computes a first-order Taylor series approximation for n onlinear
system dynamics about and operating point,whichisdefined by a constant
input and model state values.
To compute a tangent linear approximation of a nonlinear black-box model,
you must h ave the fo llowing varia bles in th e MATLAB wor kspace:
• Nonlinear ARX (
idnlarx)orHammerstein-Weiner(idnlhw)model.
• Operating point
The resulting linear model is accurate in the local neighbo rho od of the
operating conditions you used to compute the linear approximation.
To specify a known the operating point for your system, you must specify the
constant input and the states. For more information about state definitions
for each type of p ara m e tric model, see the corresponding reference pages:
•
idnlarx (nonlinear ARX models)
•
idnlhw (nonlinear Hammerstein-Wiener models)
If you do not know the operating point v alues for your sy stem, see “Computing
Operating Points for Nonlinear B lack-B ox Models” on page 4-35. For more
information, see the
linearize(idnlarx) or linea rize(idnlhw) reference
page.
Computing Operating Points for Nonlinear Black-Box
Models
The line arize command for computing a first-order Taylor s eries
approximation for the system requires that you specify an ope rating po int. An
operating point is defined by a constant input and model state values.
If you do not know the operating conditions of your system, you can use the
findop command to compute the operating point from specifications, as
follows:
• “Computing Operating Point from Steady-State Specifications” on page 4-36
4-35