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Periodic operation and optimal control of chemical processes
Periodic operation has proven to be a viable mechanism for improving the system peformance of many chemical processes beyond their optimal steady-state. It has been determined through numerous theoretical and experimental studies when periodic control can be successively employed. Few results are available, however, that predict the magnitude of improvement and none of the results indicate how periodic control should be implemented.^ To analyze the feasibility of periodic control, the $\Pi$-criterion, an expression developed by Guardabassi et. al., is used as a basis for the research. This criterion can be applied to periodic perturbations spanning the entire frequency range and it is shown that this criterion can be used to describe perturbations around any given steady-state. From this criterion expressions reflecting the percentage improvement are developed and applied to periodically forced CSTR's, polymerization reactions, gas-liquid reactions and a case study of a plant. All of these systems show an increase in performance when using periodic control, with the greatest increase occurring in processes which are not at the optimal steady-state. The derived expressions, which are applicable to both the single-input and multi-input case, are also used to show that multiple control variables should be implemented either completely in- or out-of-phase, depending upon the sign of the diagonal elements of the $\Pi$-matrix.^ Furthermore, analytic expressions are derived from the $\Pi$-criterion for a few simple reaction mechanisms to determine regions in a parametric space that can improve system performance by periodic perturbations. Thus, the type of systems that have the most potential for improvement are specified. To operate these systems periodically with a feedback control law, relay controllers with hysteresis and an integrator are used.^ A method is then discussed that enables the $\Pi$-criterion and the derived expressions to be applied to systems with uncertainties. Least-squares estimation, an on-line estimation technique, is incorporated into the system model. Thus, the scope of the $\Pi$-criterion is further broadened. Even with model mismatch, it is possible to determine the type of periodic input that should be employed, its operating frequency and the feedback control strategy to implement the desired perturbations. ^
Leah Ellen Sterman,
"Periodic operation and optimal control of chemical processes"
(January 1, 1987).
Electronic Doctoral Dissertations for UMass Amherst.