Design of output constraints for model-based non-square controllers using interval operability

A steady-state interval operability methodology is introduced here for multivariable non-square systems with fewer inputs than output variables to be used in the design of model-based constrained controllers (MPC, DMC). For such systems, set-point control is not possible for all the outputs and interval control is needed. The proposed iterative approach enables the selection of the needed interval constraints systematically, so that the tightest possible control is achieved without rendering the control problem infeasible. The application of this methodology to high-dimensional industrial problems characterizing processes of Air Products and Chemicals and DuPont shows that very significant reduction of the constrained region can be achieved from the steady-state point of view. Ratios of the initial to the calculated volume of the constrained regions examined range between 10⁴ and 10⁸.