High-dimensional nonsquare systems, with more outputs than inputs, are common in industrial chemical processes. For such systems, it is impossible to control all the outputs at specific set-points. Interval control is needed for, at least, some of the output variables. An operability-based methodology, formulated in a Linear Programming framework, systematically determines the feasible set of the steady-state output constraints of high-dimensional nonsquare linear Model Predictive Controllers. These controllers are related to several industrial-scale chemical processes provided by Air Products and Chemicals and DuPont. It is shown that, for the operable cases, the constrained region of operation can be reduced, without causing infeasibilities, by a factor of 103–107 for systems that have an output dimensionality of 6–15. For the inoperable examples, the amount of constraint relaxation necessary to make the control problem feasible at the steady-state is also calculated. © 2009 American Institute of Chemical Engineers AIChE J, 2010
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