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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 the following:


  • εk — QP slack variable used for constraint softening (See Constraint Softening)

  • u(k+i|k) — nu MV values, in engineering units

  • y(k+i|k) — ny predicted plant outputs, in engineering units

  • v(k+i|k) — nv measured plant disturbance inputs, in engineering units

  • E, F, S, G, and V are constants

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

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.

See Also


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