Constraints on Linear Combinations of Inputs and Outputs

You can constrain linear combinations of plant input and output variables. For example, you can constrain a particular manipulated variable (MV) to be greater than a linear combination of two other MVs.

The general form of such constraints is:


  • is the QP slack variable used for constraint softening. For more information, see Constraint Softening.

  • are the manipulated variable values, in engineering units.

  • are the predicted plant outputs, in engineering units.

  • are the measured plant disturbance inputs, in engineering units.

  • , , , , and are constant matrices and vectors. For more information, see setconstraint.

As with the QP cost function, output prediction using the state observer makes these constraints a function of the QP decision variables.

To set the mixed input/output constraints of an MPC controller, use the setconstraint function. To obtain the existing constraints from a controller, use getconstraint.

When using mixed input/output constraints, consider the following:

  • Mixed input/output constraints are dimensional by default.

  • Run-time updating of mixed input/output constraints is supported at the command line and in Simulink®. For more information, see Update Constraints at Run Time.

  • Using mixed input/output constraints is not supported in MPC Designer.

As an example, consider an MPC controller for a double-integrator plant with mixed input/output constraints.

Create Initial MPC Controller

The basic setup of the MPC controller includes:

  • A double integrator as the prediction model

  • Prediction horizon of 20

  • Control horizon of 20

  • Input constraints:

plant = tf(1,[1 0 0]);
Ts = 0.1;
p = 20;
m = 20;
mpcobj = mpc(plant,Ts,p,m);
mpcobj.MV = struct('Min',-1,'Max',1);
-->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.

Define Mixed Input/Output Constraints

Constrain the sum of the input u(t) and output y(t) must be nonnegative and smaller than 1.2:

To impose this combined (mixed) I/O constraint, formulate it as a set of inequality constraints involving and .

To define these constraints using the setconstraint function, set the constraint constants as follows:


Simulate Controller

Simulate closed-loop control of the linear plant model in Simulink. The controller mpcobj is specified in the MPC Controller block.

mdl = 'mpc_mixedconstraints';
-->Converting the "Model.Plant" property of "mpc" object to state-space.
-->Converting model to discrete time.
   Assuming no disturbance added to measured output channel #1.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

The MPC controller keeps the sum between 0 and 1.2 while tracking the reference signal, .


See Also


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