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Specify D-Matrix System for Block Linearization Using Function

This example shows how to specify custom linearization for a saturation block using a function.

Open the Simulink model.

mdl = 'configSatBlockFcn';
open_system(mdl)

In this model, the limits of the saturation block are –satlimit and satlimit.

Define the saturation limit, which is a parameter required by the linearization function of the Saturation block.

satlimit = 10;

Linearize the model at the model operating point using the linear analysis points defined in the model. Doing so returns the linearization of the saturation block.

io = getlinio(mdl);
linsys = linearize(mdl,io)
linsys =
 
  D = 
               Constant
   Saturation       0.5
 
Static gain.

At the model operating point, the input to the saturation block is 10. This value is on the saturation boundary. At this value, the saturation block linearizes to 1.

Suppose that you want the block to linearize to a transitional value of 0.5 when the input falls on the saturation boundary. Write a function that defines the saturation block linearization to behave this way. For this example, use the configuration function in mySaturationLinearizationFcn.m.

function blocklin = mySaturationLinearizationFcn(BlockData)
% This function customizes the linearization of a saturation block. The
% linearization of the block is as follows
% BLOCKLIN = 0 when |U| > saturation limit
% BLOCKLIN = 1 when |U| < saturation limit
% BLOCKLIN = 0.5 when U = saturation limit

% Get the saturation limit specified in the parameters of the block.
satlimit = BlockData.Parameters.Value;

% Compute the linearization based on the input signal level to the block.
if abs(BlockData.Inputs.Values) > satlimit
    blocklin = 0;
elseif abs(BlockData.Inputs.Values) < satlimit
    blocklin = 1;
else
    blocklin = 0.5;
end

This configuration function defines the saturation block linearization based on the level of the block input signal. For input values outside the saturation limits, the block linearizes to zero. Inside the limits, the block linearizes to 1. For boundary values, the block linearizes to the interpolated value of 0.5. The input to the function, BlockData, is a structure that the software creates automatically when you configure the linearization of the Saturation block to use the function. The configuration function reads the saturation limits from that data structure.

The input to the function, BlockData, is a structure that the software creates automatically each time it linearizes the block. When you specify a block linearization configuration function, the software automatically passes BlockData to the function. If your configuration function requires additional parameters, you can configure the block to set those parameters in the BlockData.Parameters field.

Specify mySaturationLinearizationFcn as the linearization for the Controller block.

  1. In the Simulink model, right-click the Saturation block, and select Linear Analysis > Specify Selected Block Linearization.

  2. In the Block Linearization Specification dialog box, select Specify block linearization using one of the following.

  3. In the drop-down list, select Configuration Function.

  4. In the text box, enter the function name mySaturationLinearizationFcn.

  5. Specify the saturation limit as a parameter for the function. In the Parameter Value column, enter the variable name satlimit.

  6. In the Parameter Name column, enter the corresponding descriptive name SaturationLimit.

  7. Click OK.

Alternatively, you can define the configuration function programmatically.

satblk = 'configSatBlockFcn/Saturation';
set_param(satblk,'SCDEnableBlockLinearizationSpecification','on')
rep = struct('Specification','mySaturationLinearizationFcn',...
             'Type','Function',...
             'ParameterNames','SaturationLimit',...
	         'ParameterValues','satlimit');
set_param(satblk,'SCDBlockLinearizationSpecification',rep)

Linearize the model again. Now, the linearization uses the custom linearization of the saturation block.

linsys_cust = linearize(mdl,io)
linsys_cust =
 
  D = 
               Constant
   Saturation       0.5
 
Static gain.

At the model operating point, the input to the saturation block is 10. Therefore, the block linearizes to 0.5, the linearization value specified in the configuration function.

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