Extract continuous-time linear state-space model around operating point
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 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 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.
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.
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.
Linearization is not supported for models that contain one or more referenced models configured to use a local solver. For more information, see Use Local Solvers in Referenced Models.
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 model, the Aircraft Dynamics Model block references the m
To linearize the
mdlref_f14 model, use the
[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 32.473s
The resulting state-space 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
x = Simulink.BlockDiagram.getInitialState(
In Normal mode, the
linmod command applies the block-by-block 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
linmod command with the
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
'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
In this example, the blocks on the left of this figure can be replaced by the block on the right.
Introduced in R2007a
linearize(Simulink Control Design) |
slLinearizer(Simulink Control Design)
- Model Linearizer (Simulink Control Design)
- Choose Linearization Tools (Simulink Control Design)
- Linearize Nonlinear Models (Simulink Control Design)
- Exact Linearization Algorithm (Simulink Control Design)