Novel Formulation and Application of Model Predictive Control.

Abstract

Model predictive control (MPC) has been extensively studied in academia and widely accepted in industry. This research has focused on the novel formulation of model predictive controllers for systems that can be decomposed according to their nonlinearity properties and several novel MPC applications including bioreactors modeled by population balance equations (PBE), gas pipeline networks, and cryogenic distillation columns. Two applications from air separation industries are studied. A representative gas pipeline network is modeled based on first principles. The full-order model is ill-conditioned, and reduced-order models are constructed using time-scale decomposition arguments. A linear model predictive control (LMPC) strategy is then developed based on the reduced-order model. The second application is a cryogenic distillation column. A low-order dynamic model based on nonlinear wave theory is developed by tracking the movement of the wave front. The low-order model is compared to a first-principles model developed with the commercial simulator HYSYS.Plant. On-line model adaptation is proposed to overcome the most restrictive modeling assumption. Extensions for multiple column modeling and nonlinear model predictive control (NMPC) also are discussed. The third application is a continuous yeast bioreactor. The autonomous oscillations phenomenon is modeled by coupling PBE model of the cell mass distribution to the rate limiting substrate mass balance. A controller design model is obtained by linearizing and temporally discretizing the ODES derived from spatial discretization of the PBE model. The MPC controller regulate the discretized cell number distribution by manipulating the dilution rate and the feed substrate concentration. A novel plant-wide control strategy is developed based on integration of LMPC and NMPC. It is motivated by the fact that most plants that can be decomposed into approximately linear subsystems and highly nonlinear subsystems. LMPCs and NMPCs are applied to the respective subsystems. A sequential solution algorithm is developed to minimize the amount of unknown information in the MPC design. Three coordination approaches are developed to reduce the amount of information unavailable due to the sequential MPC solution of the coupled subsystems and applied to a reaction/separation process. Furthermore, a multi-rate approach is developed to exploit time-scale differences in the subsystems.