linmod
Extract continuoustime linear statespace model around operating point
Syntax
argout
= linmod('sys
')argout
= linmod('sys
',x,u)argout
= linmod('sys
',x,u,para)argout
= linmod('sys
',x,u,'v5')argout
= linmod('sys
',x,u,para,'v5')argout
= linmod('sys
',x,u,para,xpert,upert,'v5')
Arguments
 Name of the Simulink^{®} system from which the linear model is extracted. 
State ( x = Simulink.BlockDiagram.getInitialState('sys'); You
can then change the operating point values within this structure by
editing If the state
contains different data types (for example,  
 Sample time of the discretetime 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 threeelement 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) + 1e3*para(1)*abs(x) upert = para(1) + 1e3*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'); You
can then change the perturbation values within this structure by editing The
perturbation input arguments are only available when invoking the
perturbation algorithm created prior to MATLAB 5.3, either by
calling 


Description
Note
linmod
provides only basic linearization functionality. For full
linearization functionality, use Simulink
Control Design™ software. For more information, see Choose Linearization Tools (Simulink Control Design).
linmod
compute a linear statespace 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 blockbyblock analytic algorithm for linearization.
The default algorithm also allows for special treatment of problematic blocks such as the Transport Delay and the Quantizer. See the mask dialog of these blocks for more information and options.
Notes
By default, the system time is set to zero. For systems that
are dependent on time, you can set the variable para
to
a twoelement vector, where the second element is used to set the
value of 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
where xstring
is a vector of strings whose ith
row is the block name associated with the i
th state.
Inputs and outputs are numbered sequentially on the diagram.
For singleinput multioutput systems, you
can convert to transfer function form using the routine ss2tf
or
to zeropole form using ss2zp
. You can also convert
the linearized models to LTI objects using ss
.
This function produces an LTI object in statespace form that can
be further converted to transfer function or zeropolegain form using tf
or zpk
.
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.
Linearization is not supported when the model contains model blocks where Use
local solver when referencing model
is enabled in the Solver Pane.
Examples
Linearization with Referenced Models
You can use linmod
to extract a linear model from a Simulink® environment that contains Model blocks. For example, open the referenced model mdlref_dynamics
and the top model mdlref_f14
.
open_system('mdlref_dynamics'); open_system('mdlref_f14');
In the mdlref_f14
model, the Aircraft Dynamics Model block references the mdlref_dynamics
model.
To linearize the mdlref_f14
model, use the linmod
command.
[A,B,C,D] = linmod('mdlref_f14');
### Starting serial model reference simulation build. ### Successfully updated the model reference simulation target for: mdlref_dynamics Build Summary Simulation targets built: Model Action Rebuild Reason =========================================================================================== mdlref_dynamics Code generated and compiled. mdlref_dynamics_msf.mexa64 does not exist. 1 of 1 models built (0 models already up to date) Build duration: 0h 0m 17.956s
The resulting statespace model corresponds to the complete mdlref_f14
model, including the referenced model.
You can call linmod
with a state and input operating point for models that contain Model blocks. When using operating points, the state vector x
refers to the total state vector for the top model and any referenced models. You must enter the state vector using the structure format. To get the complete state vector, use getInitialState
.
x = Simulink.BlockDiagram.getInitialState(
topModelName
)
Tip
In Normal mode, the linmod
command applies the blockbyblock linearization algorithm on blocks inside the referenced model. If the Model block is in Accelerator mode, the linmod
command uses numerical perturbation to linearize the referenced model. Due to limitations on linearizing multirate Model blocks in Accelerator mode, you should use Normal mode simulation for all models referenced by Model blocks when linearizing with referenced models.
Linearization Using the 'v5' Algorithm
Calling the linmod
command with the 'v5'
argument
invokes the perturbation algorithm created prior to MATLAB software version 5.3. This algorithm also allows you to specify the
perturbation values used to perform the perturbation of all the states and inputs of the
model.
[A,B,C,D]=linmod('sys',x,u,para,xpert,upert,'v5')
linmod
with the 'v5'
option to linearize a model
that contains Derivative or Transport Delay blocks can be troublesome. Before linearizing,
replace these blocks with specially designed blocks that avoid the problems. These blocks
are in the Simulink Extras library in the Linearization sublibrary.You access the Extras library by opening the Blocksets & Toolboxes icon:
For the Derivative block, use the Switched derivative for linearization.
When using a Derivative block, you can also try to incorporate the derivative term in other blocks. For example, if you have a Derivative block in series with a Transfer Fcn block, it is better implemented (although this is not always possible) with a single Transfer Fcn block of the form
$$\frac{s}{s+a}.$$
In this example, the blocks on the left of this figure can be replaced by the block on the right.
Version History
Introduced in R2007a
See Also
Functions
dlinmod
linmod2
linmodv5
linearize
(Simulink Control Design) slLinearizer
(Simulink Control Design)
Apps
 Model Linearizer (Simulink Control Design)
Topics
 Choose Linearization Tools (Simulink Control Design)
 Linearize Nonlinear Models (Simulink Control Design)
 Exact Linearization Algorithm (Simulink Control Design)