Linearize Hammerstein-Wiener model
SYS = linearize(NLSYS,U0)
SYS = linearize(NLSYS,U0,X0)
SYS = linearize(NLSYS,U0) linearizes a
Hammerstein-Wiener model around the equilibrium operating point. When
using this syntax, equilibrium state values for the linearization
are calculated automatically using
SYS = linearize(NLSYS,U0,X0) linearizes
the operating point specified by the input
X0. In this usage,
not contain equilibrium state values. For more information about the
definition of states for
idnlhw models, see Definition of idnlhw States.
The output is a linear model that is the best linear approximation for inputs that vary in a small neighborhood of a constant input u(t) = U. The linearization is based on tangent linearization.
U0: Matrix containing the constant
input values for the model.
X0: Operating point state values
for the model.
operating point specifications, use the
SYS is an
When the Control System
Toolbox™ product is installed,
an LTI object.
idnlhw model structure represents a nonlinear
system using a linear system connected in series with one or two static
nonlinear systems. For example, you can use a static nonlinearity
to simulate saturation or dead-zone behavior. The following figure
shows the nonlinear system as a linear system that is modified by
static input and output nonlinearities, where function f represents the input nonlinearity, g represents the output
nonlinearity, and [A,B,C,D]
represents a state-space parameterization of the linear model.
The following equations govern the
dynamics of an
v(t) = f(u(t))
X(t+1) = AX(t)+Bv(t)
w(t) = CX(t)+Dv(t)
y(t) = g(w(t))
u is the input signal
v and w are intermediate signals (outputs of the input nonlinearity and linear model respectively)
y is the model output
The linear approximation of the Hammerstein-Wiener model around an operating point (X*, u*) is as follows:
where y* is the output of the model corresponding to input u* and state vector X*, v* = f(u*), and w* is the response of the linear model for input v* and state X*.