dlinmod
Extract discretetime linear statespace model around operating point
Syntax
argout
= dlinmod('sys
',Ts
)argout
= dlinmod('sys
',Ts
,x
,u
)argout
= dlinmod('sys
',Ts
,x
,u
,para
, 'v5')argout
= dlinmod('sys
',Ts
,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
dlinmod
provides only basic linearization functionality. For full
linearization functionality, use Simulink
Control Design™ software. For more information, see Choose Linearization Tools (Simulink Control Design).
dlinmod
computes a linear statespace model for a discretetime system 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.
DiscreteTime System Linearization
The function dlinmod
can linearize
discrete, multirate, and hybrid continuous and discrete systems at
any given sampling time. Use the same calling syntax for dlinmod
as
for linmod
, but insert the sample time at which
to perform the linearization as the second argument. For example,
[Ad,Bd,Cd,Dd] = dlinmod('sys', Ts, x, u);
produces a discrete statespace model at the sampling
time Ts
and the operating point given by the state
vector x
and input vector u
.
To obtain a continuous model approximation of a discrete system, set Ts
to 0
.
For systems composed of linear, multirate, discrete, and continuous
blocks, dlinmod
produces linear models having identical
frequency and time responses (for constant inputs) at the converted
sampling time Ts
, provided that
Ts
is an integer multiple of all the sampling times in the system.The system is stable.
For systems that do not meet the first condition, in general
the linearization is a timevarying system, which cannot be represented
with the [A,B,C,D]
statespace model that dlinmod
returns.
Computing the eigenvalues of the linearized matrix Ad
provides
an indication of the stability of the system. The system is stable
if Ts>0
and the eigenvalues are within the unit
circle, as determined by this statement:
all(abs(eig(Ad))) < 1
Likewise, the system is stable if Ts = 0
and
the eigenvalues are in the left half plane, as determined by this
statement:
all(real(eig(Ad))) < 0
When the system is unstable and the sample time is not an integer
multiple of the other sampling times, dlinmod
produces Ad
and Bd
matrices,
which can be complex. The eigenvalues of the Ad
matrix
in this case still, however, provide a good indication of stability.
You can use dlinmod
to convert the sample
times of a system to other values or to convert a linear discrete
system to a continuous system or vice versa.
You can find the frequency response of a continuous or
discrete system by using the bode
command.
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
and dlinmod
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.