Interval Operability: A tool to design the feasible output constraints for non-square model predictive controllers

Non-square systems with more outputs than inputs are common in industrial chemical processes. Such systems are particularly challenging because it is impossible to control all the outputs at specific set-points when there are fewer degrees of freedom available than the number of controlled variables. Thus, interval control is needed for at least some of the output variables. These intervals must be wide enough to guarantee feasible operation in the presence of process disturbances, but still achieve satisfactory tightness of control for some of the outputs.; Two Interval Operability approaches are introduced that systematically calculate, from the steady-state point of view, the tightest feasible set of output constraints that can be achieved (represented by the Achievable Output Interval Set (AOIS)). These two approaches, an Iterative and a Linear Programming (LP) based framework, differ in the algorithm used to calculate the AOIS in Rn , where n is the dimensionality of the output set. The results of each method are used in the design of high-dimensional and non-square Model Predictive Controllers (MPC). Both approaches enable the offline design of output constraints before the MPC controller is deployed. Because of its high-speed of computations, the LP approach also enables the online design of such constraints, making real-time adaptation of the control objectives possible, depending on the current state of the process.; The applicability of the developed methodologies is illustrated with 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 with an output dimensionality of 6 - 15. The calculated new limits are validated by running DMCplus(TM) (AspenTech) simulations for the extreme values of the disturbances. For the inoperable examples, the amount of relaxation necessary for each of the output constraints to make the control problem feasible was calculated for steady-state conditions.; Finally, the design of output constraints during transient operation, using the concepts of dynamic operability and output funnels, is briefly discussed at the end of this Thesis.