getconstraint

Obtain mixed input/output constraints from model predictive controller

Syntax

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

Description

[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

Retrieve Custom Constraints from MPC 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

Input Arguments

MPCobj — Model predictive controller

MPC controller object

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

Output Arguments

E — Manipulated variable constraint constant

N_c-by-N_mv array | []

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

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

F — Controlled output constraint constant

N_c-by-N_y array | []

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

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

G — Mixed input/output constraint constant

column vector of length N_c | []

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

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

V — Constraint softening constant

column vector of length N_c | []

Constraint softening constant representing the equal concern for the relaxation (ECR), returned as a column vector of length N_c, where N_c 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 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

N_c-by-N_v array | []

Measured disturbance constraint constant, returned as an N_c-by-N_v array, where N_v 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

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).