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Extract LPV offsets from linearization results



offsets = getOffsetsForLPV(info) extracts linearization offsets from info and converts them to the array format supported by the LPV System block.


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Open the Simulink model.

model = 'watertank';

Specify linearization I/Os.

io(1) = linio('watertank/Desired  Water Level',1,'input');
io(2) = linio('watertank/Water-Tank System',1,'output');

Vary plant parameters A and b, and create a 3-by-4 parameter grid.

[A_grid,b_grid] = ndgrid(linspace(0.9*A,1.1*A,3),linspace(0.9*b,1.1*b,4));
params(1).Name = 'A';
params(1).Value = A_grid;
params(2).Name = 'b';
params(2).Value = b_grid;

Create a linearization option set, setting the StoreOffsets option to true.

opt = linearizeOptions('StoreOffsets',true);

Linearize the model using the specified parameter grid, and return the linearization offsets in the info structure.

[sys,op,info] = linearize('watertank',io,params,opt);

Extract the linearization offsets.

offsets = getOffsetsForLPV(info)
offsets = 

  struct with fields:

     x: [2x1x3x4 double]
     y: [1x1x3x4 double]
     u: [1x1x3x4 double]
    dx: [2x1x3x4 double]

To configure an LPV System block, use the fields from offsets directly.

Input Arguments

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Linearization information returned by exact linearization commands, specified as a structure. This structure has an Offsets field that contains an N1-by-...-by-Nm array of structures, where N1 to Nm are the dimensions of the operating point array or parameter grid used for linearization. Each structure in info.Offsets contains offset information that corresponds to a specific operating point.

You can store and obtain linearization offsets when you linearize your model using one of the following commands:

For example:

opt = linearizeOptions('StoreOffsets',true);
[sys,op,info] = linearize(mdl,io,params,opt);

You can then extract the offset information using getOffsetsForLPV.

offsets = getOffsetsForLPV(info);

Output Arguments

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Linearization offsets corresponding to the operating points at which the model was linearized, returned as a structure with the following fields:

xState offsets used for linearization, returned as an nx-by-1-by-N1-by-...-by-Nm array, where nx is the number of states in the linearized system.
yOutput offsets used for linearization, returned as an ny-by-1-by-N1-by-...-by-Nm array, where ny is the number of outputs in the linearized system.
uInput offsets used for linearization, returned as an nu-by-1-by-N1-by-...-by-Nm array, where nu is the number of inputs in the linearized system.
dxDerivative offsets for continuous time systems, or updated state values for discrete-time systems, returned as an nx-by-1-by-N1-by-...-by-Nm array.

For instance, suppose that your model has three inputs, two outputs, and four states. If you linearize your model using a 5-by-6 array of operating points, offsets contains arrays with the following dimensions:

  • offsets.x — 4-by-1-by-5-by-6

  • offsets.y — 2-by-1-by-5-by-6

  • offsets.u — 3-by-1-by-5-by-6

  • offsets.dx — 4-by-1-by-5-by-6

To configure an LPV System block, you can use the fields of offsets directly. For an example, see Approximate Nonlinear Behavior Using Array of LTI Systems.

Version History

Introduced in R2016b