# getconstraint

Obtain mixed input/output constraints from model predictive controller

## Syntax

``````[E,F,G,V,S] = getconstraint(MPCobj)``````

## Description

example

``````[E,F,G,V,S] = getconstraint(MPCobj)``` returns the mixed-input/output constraints previously defined for the MPC controller, `MPCobj`. For more information, see Mixed Input/Output Constraints.```

## Examples

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Create a third-order plant model with two manipulated variables, one measured disturbance, and two measured outputs.

```plant = rss(3,2,3); plant.D = 0; plant = setmpcsignals(plant,'mv',[1 2],'md',3);```

Create an MPC controller for this plant.

`MPCobj = mpc(plant,0.1);`
```-->The "PredictionHorizon" property is empty. Assuming default 10. -->The "ControlHorizon" property is empty. Assuming default 2. -->The "Weights.ManipulatedVariables" property is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property is empty. Assuming default 1.00000. ```

Assume that you have two soft constraints.

`$\begin{array}{l}{u}_{1}+{u}_{2}\le 5\\ {y}_{2}+v\le 10\end{array}$`

Set the constraints for the MPC controller.

```E = [1 1; 0 0]; F = [0 0; 0 1]; G = [5;10]; V = [1;1]; S = [0;1]; setconstraint(MPCobj,E,F,G,V,S)```

Retrieve the constraints from the controller.

`[E,F,G,V,S] = getconstraint(MPCobj)`
```E = 2×2 1 1 0 0 ```
```F = 2×2 0 0 0 1 ```
```G = 2×1 5 10 ```
```V = 2×1 1 1 ```
```S = 2×1 0 1 ```

## Input Arguments

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Model predictive controller, specified as an MPC controller object. To create an MPC controller, use `mpc`.

## Output Arguments

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Manipulated variable constraint constant, returned as an Nc-by-Nmv array, where Nc is the number of constraints, and Nmv is the number of manipulated variables.

If `MPCobj` has no mixed input/output constraints, then `E` is `[]`.

Controlled output constraint constant, returned as an Nc-by-Ny array, where Ny is the number of controlled outputs (measured and unmeasured).

If `MPCobj` has no mixed input/output constraints, then `F` is `[]`.

Mixed input/output constraint constant, returned as a column vector of length Nc., where Nc is the number of constraints.

If `MPCobj` has no mixed input/output constraints, then `G` is `[]`.

Constraint softening constant representing the equal concern for the relaxation (ECR), returned as a column vector of length Nc, where Nc is the number of constraints. If `MPCobj` has no mixed input/output constraints, then `V` is `[]`.

If `V` is not specified, a default value of `1` is applied to all constraint inequalities and all constraints are soft. This behavior is the same as the default behavior for output bounds, as described in Standard Cost Function.

To make the ith constraint hard, specify V(i) = 0.

To make the ith constraint soft, specify V(i) > 0 in keeping with the constraint violation magnitude you can tolerate. The magnitude violation depends on the numerical scale of the variables involved in the constraint.

In general, as V(i) decreases, the controller hardens the constraints by decreasing the constraint violation that is allowed.

Measured disturbance constraint constant, returned as an Nc-by-Nv array, where Nv is the number of measured disturbances.

If there are no measured disturbances in the mixed input/output constraints, or `MPCobj` has no mixed input/output constraints, then `S` is `[]`.

## Algorithms

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### Mixed Input/Output Constraints

The general form of the mixed input/output constraints is:

Eu(k + j) + Fy(k + j) + Sv(k + j) ≤ G + εV

Here, j = 0,...,p, and:

• p is the prediction horizon.

• k is the current time index.

• u is a column vector manipulated variables.

• y is a column vector of all plant output variables.

• v is a column vector of measured disturbance variables.

• ε is a scalar slack variable used for constraint softening (as in Standard Cost Function).

• E, F, G, V, and S are constant matrices.

Since the MPC controller does not optimize u(k+p), `getconstraint` calculates the last constraint at time `k+p` assuming that u(k+p) = u(k+p-1).

## Version History

Introduced in R2011a