Obtain mixed input/output constraints from model predictive controller

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 of "mpc" object is empty. Trying PredictionHorizon = 10. -->The "ControlHorizon" property of the "mpc" object is empty. Assuming 2. -->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property of "mpc" object 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

`MPCobj`

— Model predictive controllerMPC controller object

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

.

`E`

— Manipulated variable constraint constant`[]`

Manipulated variable constraint constant, returned as an
*N _{c}*-by-

If `MPCobj`

has no mixed input/output constraints, then
`E`

is `[]`

.

`F`

— Controlled output constraint constant`[]`

Controlled output constraint constant, returned as an
*N _{c}*-by-

If `MPCobj`

has no mixed input/output constraints, then
`F`

is `[]`

.

`G`

— Mixed input/output constraint constantcolumn vector of length

`[]`

Mixed input/output constraint constant, returned as a column vector of
length *N _{c}*., where

If `MPCobj`

has no mixed input/output constraints, then
`G`

is `[]`

.

`V`

— Constraint softening constantcolumn vector of length

`[]`

Constraint softening constant representing the equal concern for the relaxation (ECR),
returned as a column vector of length
*N _{c}*, where

`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 *i*^{th} constraint
hard, specify *V*(*i*)
= 0.

To make the *i*^{th} 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.

`S`

— Measured disturbance constraint constant`[]`

Measured disturbance constraint constant, returned as an
*N _{c}*-by-

If there are no measured disturbances in the mixed input/output constraints, or
`MPCobj`

has no mixed input/output constraints, then
`S`

is `[]`

.

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

*E**u*(*k* +
*j*) +
*F**y*(*k* +
*j*) + *S**v*(*k* +
*j*) ≤ *G* +
*ε**V*

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

assuming that *k*+*p**u*(*k*+*p*) =
*u*(*k*+*p*-1).

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