Define Plant Model

Create a state-space model of your plant, and specify the MPC signal types. For this example, use the CSTR model described in CSTR Model and used in Design Controller Using MPC Designer. For this example, assume that the second input is an unmeasured disturbance and that the second output is not measured.

A = [   -5  -0.3427;
     47.68    2.785];
B = [    0   1
       0.3   0];
C = [0 1; 1 0];
D = zeros(2,2);

plant = ss(A,B,C,D);
plant = setmpcsignals(plant,'MV',1,'UD',2,'MO',1,'UO',2);

Open MPC Designer, and import the plant model.

mpcDesigner(plant)

The app imports the specified plant to the Data Browser and creates a default controller, mpc1, and a default simulation scenario, scenario1.

Define Simulation Scenario

Configure a disturbance rejection simulation scenario.

In MPC Designer, on the MPC Designer tab, click Edit Scenario > scenario1.

In the Simulation Scenario dialog box, specify a Simulation duration of 6 seconds.

In the Reference Signals table, in the Signal drop-down lists, select Constant to hold the setpoints of both outputs at their nominal values.

In the Unmeasured Disturbances table, in the Signal drop-down list, select Step. Use the default Time and Step values.

This scenario simulates a unit step change in the unmeasured input disturbance at a time of 1 second.

Click OK.

The app runs the updated simulation scenario and updates the controller response plots. In the Output Response plots, the default controller returns the measured output, MO1, to its nominal value, however the control action causes an increase in the unmeasured output, UO1.

Create Controller with Hard Output Constraints

Suppose that the control specifications indicate that such an increase in the unmeasured disturbance is undesirable. To limit the effect of the unmeasured disturbance, create a controller with a hard output constraint.

In the Data Browser, in the Controllers section, right-click mpc1, and select Copy.

The app creates a copy of the default controller and adds it to the Controllers section.

Click each controller name and rename them as follows.

Right-click the mpcHard controller, and select Tune (select as current MPC). The app adds the mpcHard controller response to the Input Response and Output Response plots.

On the Tuning tab, in the Controller section, mpcHard is selected as the current MPC Controller being tuned.

In the Design section, click Constraints.

In the Constraints dialog box, in the Output Constraints section, in the Max column, specify a maximum output constraint of 0.15 for the unmeasured output (UO).

By default, all output constraints are soft, that is the controller can allow violations of the constraint when computing optimal control moves.

To make the unmeasured output constraint hard, click Constraint Softening Settings, and enter a MaxECR value of 0 for the UO. This setting places a strict limit on the controller output that cannot be violated.

Click OK.

The response plots update to reflect the new mpcHard configuration. In the Output Response plot, in the UO1 plot, the mpcHard response is limited to a maximum of 0.15. As a trade-off, the controller cannot return the MO1 response to its nominal value.

Create Controller with Soft Output Constraints

Suppose the deviation of MO1 from its nominal value is too large. You can soften the output constraint for a compromise between the two control objectives: MO1 output tracking and UO1 constraint satisfaction.

On the Tuning tab, in the Analysis section, click Store Controller to save a copy of mpcHard in the Data Browser.

In the Controllers section, rename mpcHard_Copy to mpcSoft.

On the Tuning tab, in the Controller section, in the MPC Controller drop-down list, select mpcSoft as the current controller.

The app adds the mpcSoft controller response to the Input Response and Output Response plots.

In the Design section, click Constraints.

In the Constraints dialog box, in the Output Constraints section, enter a MaxECR value of 10 for the UO to soften the constraint.

Click OK.

The response plots update to reflect the new mpcSoft configuration. In the Output Response plot, mpcSoft shows a compromise between the previous controller responses.

Remove Default Controller Response Plot

To compare the two constrained controllers only, you can remove the default unconstrained controller from the input and output response plots.

On the MPC Designer tab, in the Result section, click Compare Controllers > mpcNone to deselect the first controller.

The app removes the mpcNone responses from the Input Response and Output Response plots.

You can toggle the display of any controller in the Data Browser except for controller currently being tuned. Under Compare Controllers, the controllers with displayed responses are indicated with check marks.