Extract continuous-time linear state-space model around operating point
sys', x, u);
sys', x, u, para);
sys', x, u, 'v5');
sys', x, u, para, 'v5');
sys', x, u, para, xpert, upert, 'v5');
Name of the Simulink® system from which the linear model is extracted.
x = Simulink.BlockDiagram.getInitialState('sys');
can then change the operating point values within this structure by
If the state
contains different data types (for example,
Sample time of the discrete-time linearized model
An optional argument that invokes the perturbation algorithm
created prior to MATLAB® 5.3. Invoking this optional argument
is equivalent to calling
A three-element vector of optional arguments:
The perturbation values used to perform the perturbation of all the states and inputs of the model. The default values are
xpert = para(1) + 1e-3*para(1)*abs(x) upert = para(1) + 1e-3*para(1)*abs(u)
When a model has model references using the Model block, you must use the Simulink structure
format to specify
xpert = Simulink.BlockDiagram.getInitialState('sys');
can then change the perturbation values within this structure by editing
perturbation input arguments are only available when invoking the
perturbation algorithm created prior to MATLAB 5.3, either by
linmod compute a linear state-space model
by linearizing each block in a model individually.
linmod obtains linear models from systems
of ordinary differential equations described as Simulink models.
Inputs and outputs are denoted in Simulink block diagrams using
Inport and Outport blocks.
The default algorithm uses preprogrammed analytic block Jacobians for most blocks which should result in more accurate linearization than numerical perturbation of block inputs and states. A list of blocks that have preprogrammed analytic Jacobians is available in the Simulink Control Design™ documentation along with a discussion of the block-by-block analytic algorithm for linearization.
By default, the system time is set to zero. For systems that
are dependent on time, you can set the variable
a two-element vector, where the second element is used to set the
t at which to obtain the linear model.
The ordering of the states from the nonlinear model to the linear model is maintained. For Simulink systems, a character vector variable that contains the block name associated with each state can be obtained using
[sizes,x0,xstring] = sys
xstring is a vector of strings whose ith
row is the block name associated with the
Inputs and outputs are numbered sequentially on the diagram.
For single-input multi-output systems, you
can convert to transfer function form using the routine
to zero-pole form using
ss2zp. You can also convert
the linearized models to LTI objects using
This function produces an LTI object in state-space form that can
be further converted to transfer function or zero-pole-gain form using
The default algorithms in
linmod handle Transport
Delay blocks by replacing the linearization of the blocks with a Pade
approximation. For the
'v5' algorithm, linearization
of a model that contains Derivative or Transport Delay blocks can
be troublesome. For more information, see Linearizing Models.