Extract continuous-time linear state-space model around operating point
argout = linmodv5('sys'); argout = linmodv5('sys',x,u); argout = linmodv5('sys', x, u, para); argout = linmodv5('sys', x, u, para, xpert, upert);
Name of the Simulink® system from which the linear model is extracted.
State (x) and the input (u) vectors. If specified, they set the operating point at which the linear model is extracted. When a model has model references using the Model block, you must use the Simulink structure format to specify x. To extract the x structure from the model, use the following command:
x = Simulink.BlockDiagram.getInitialState('sys');
You can then change the operating point values within this structure by editing x.signals.values.
If the state contains different data types (for example, 'double' and 'uint8'), then you cannot use a vector to specify this state. You must use a structure instead. In addition, you can only specify the state as a vector if the state data type is 'double'.
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. To extract the xpert structure, use the following command:
xpert = Simulink.BlockDiagram.getInitialState('sys');
You can then change the perturbation values within this structure by editing xpert.signals.values.
The perturbation input arguments are only available when invoking the perturbation algorithm created prior to MATLAB® 5.3, either by calling linmodv5 or specifying the 'v5' input argument to linmod.
linmod, dlinmod, and linmod2 return state-space representations if you specify the output (left-hand) side of the equation as follows:
linmodv5 computes a linear state space model using the full model perturbation algorithm created prior to MATLAB 5.3.
linmodv5 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.
By default, the system time is set to zero. For systems that are dependent on time, you can set the variable para to a two-element 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 string 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 ith state. 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 ss2tf or to zero-pole form using ss2zp. You can also convert the linearized models to LTI objects using ss. This function produces an LTI object in state-space form that can be further converted to transfer function or zero-pole-gain 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.