getOffsetsForLPV

Extract LPV offsets from linearization results

Syntax

offsets = getOffsetsForLPV(info)

Description

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

Examples

Extract LPV Offsets from Linearization Results

Open the Simulink model.

model = 'watertank';
open_system(model)

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

info — Linearization information

structure

Linearization information returned by exact linearization commands, specified as a structure. This structure has an Offsets field that contains an N₁-by-...-by-N_m array of structures, where N₁ to N_m 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:

• linearize

• getIOTransfer

• getLoopTransfer

• getSensitivity

• getCompSensitivity

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

offsets — Linearization offsets

structure

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

Field	Description
x	State 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.
y	Output 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.
u	Input 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.
dx	Derivative 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 Approximating Nonlinear Behavior Using an Array of LTI Systems.