Nonlinear modeling, estimation and predictive control of cryogenic air separation columns
Cryogenic air separation columns produce high-purity air components for various industries. The need to operate these very high-purity columns over a wide range of production rates in response to time-varying electrical costs motivates the development of nonlinear control strategies. First-principles models of distillation columns are too complicated to be used on-line for optimization-based nonlinear control. The goal of this dissertation is to develop reduced-order nonlinear models for cryogenic air separation columns and to use these models to develop nonlinear model predictive controllers that allow operation over a wide range of production rates.
An approach for selecting stage composition/temperature measurements for on-line estimation of wave model parameters is presented. The focus is on high-purity distillation columns, which are particularly challenging due to the presence of highly pinched composition profiles. The proposed method provides a compromise between two competing effects, the sensitivity of stage composition predictions to model parameters and collinearities between these sensitivities. An iterative calculation procedure based on a scaled sensitivity matrix yields a ranking of the stage compositions according to their usefulness for parameter estimation. The proposed method offers several important advantages over existing techniques including the capability to rank more measurements than the number of estimated variables and to allow the inclusion of existing plant measurements. Two high-purity column simulators are used to illustrate the measurement selection procedure and the subsequent design of nonlinear state/parameter estimators using the extended Kalman filtering approach. The simulation results suggest that the proposed method is more powerful than conventional measurement selection techniques based on singular value decomposition.
A simplified nonlinear wave model is used to design a nonlinear model predictive controller for a simulated nitrogen purification column. A first-principles model constructed in Aspen Dynamics (Aspen Technology) is used as a surrogate plant in the simulation studies. Estimates of the unmeasured wave position and key wave model parameters are generated with an extended Kalman filter using a combination of composition and temperature measurements determined with the measurement selection procedure. The nonlinear model predictive controller manipulates the vapor nitrogen production rate to achieve the target nitrogen purity. The estimator and controller are combined through a state disturbance model that provides feedback and eliminates offset due to modeling errors. The proposed control strategy is compared to a classical control system consisting of a ratio controller and a PID controller. The proposed controller is shown to outperform the classical control system for large measured disturbances in the feed air flow rate.
The single-column work is extended by exploring the feasibility of nonlinear model-based control for the double-column process used to produce purified nitrogen and oxygen. A reduced-order dynamic model for the upper column is developed by applying time-scale arguments to a detailed stage-by-stage model that includes mass and energy balances and that accounts for non-ideal vapor-liquid equilibrium. The column is divided into compartments according to the locations of liquid distributors as well as feed and withdrawal streams. The differential equations describing each compartment are placed in singularly perturbed form through the application of a physically based coordinate transformation. Application of singular perturbation theory yields a differential-algebraic equation model with significantly fewer differential variables than the original stage-by-stage model. A rigorous column simulator constructed using Aspen Dynamics (Aspen Technology) is used to assess the tradeoff between reduced-order model complexity and accuracy as the number of compartments is varied. The reduced-order model is shown to provide good agreement with the Aspen simulator over a wide range of operating conditions.