Polymerization reactor control using computationally tractable input/output models
Abstract
A nonlinear model predictive control scheme based on the second-order Volterra model is presented. Formulations using successive substitution and direct solution of a nonlinear programming problem are employed in the control of single variable and multivariable polymerization reactor case studies. Closed-loop performance is compared with that of linear model predictive control, and a desired, linear reference trajectory. In the majority of the cases examined, the output obtained with the Volterra controller tracks the reference trajectory more closely. In both case studies, the model parameters are obtained analytically through Carleman linearization of the fundamental model and discretization of the continuous-time bilinear model. Equations relating the discrete-time bilinear model matrices and their continuous-time analogs using an explicit fourth-order Runge-Kutta method are also presented. It is shown that a large reduction in the number of second-order parameters does not significantly degrade closed-loop performance. Autoregressive plus Volterra models are identified from input-output data using "plant-friendly" input sequences for two case studies. Significantly improved steady-state and dynamic modeling, as compared to that obtained with a linear model, is shown using open-loop simulations. Improved closed-loop performance over PI and linear model predictive control is demonstrated for both setpoint tracking and disturbance rejection using a nonlinear model predictive control scheme based on this model structure. Results for a single variable problem and an industrially motivated, multivariable case study are presented. Nominal stability analysis is performed for an autoregressive plus Volterra model-based case study. The analyzed model was identified from input-output data, rather than using a contrived model. The identified model was characterized by unstable zero dynamics which highlighted the need for a less conservative uncertainty description to analyze its p-inverse. A focused uncertainty formulation is constructed and enables closed-loop exponential stability to be guaranteed for the nominal case over a region that is 40% larger than is possible using the uncertainty description of previous researchers. An improved gain scheduling algorithm based on polynomial ARMA models is presented. Improved performance is demonstrated for the control of an isothermal polymerization reactor.
Degree
Ph.D.
Advisors
Doyle, Purdue University.
Subject Area
Chemical engineering|Operations research
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