Robustness properties of nonlinear process control and implications for the design and control of a packed bed reactor

Citation

Doyle, Francis Joseph, III (1991) Robustness properties of nonlinear process control and implications for the design and control of a packed bed reactor. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3n52-hk32. https://resolver.caltech.edu/CaltechETD:etd-07112007-084012

Abstract

The robustness properties of nonlinear process control are studied with particular emphasis on applications to the design and control of a catalytic fixed bed reactor. Analysis tools are developed to determine the stability and performance of nonlinear dynamical systems. The results are based upon new extensions of the structured singular value to a class of nonlinear and time-varying systems. Conic sectors are utilized in approximating the static nonlinearities present and an algorithm is developed for optimal conic sector calculation. The synthesis tools of differential geometry are studied with respect to their closed loop robust performance properties. New results in approximate linearization are contrasted with exact linearization and linear control. It is shown that the approximate linearization technique is superior with respect to disturbance handling, optimization of the resultant transformations, and range of applicability. Nonlinear approaches for the control of a packed bed reactor are investigated. In particular, the differential geometric technique of input-output linearization is found to yield superior closed-loop performance over regions of open-loop parametric sensitivity. The synthesis of a linearizing controller for this nonlinear distributed parameter system involves a two-tier approach. In the first stage, a low order nonlinear model is developed for the reactor. This is accomplished by treating the active transport mechanisms in the bed as a nonlinear wave which propagates through the bed in response to changes in the operating conditions. The resultant lumped parameter model facilitates the design of the input-output linearizing controller in the second tier of this scheme. The implementational hurdles for this approach are identified and comparisons are drawn on the strengths of this approach over robust linear control for the reactor. Practical guidelines are developed for the design of packed bed reactors. The criteria result from requirements on the radial temperature profile, temperature sensitivity, and acceptable pressure drop. The stabilizing effects of feedback control for industrial fixed bed catalytic reactors are addressed. Simulations support the result that violation of the proposed criteria leads to unacceptable closed-loop performance. In conclusion, general guidelines are constructed from a series of case studies on the proper selection of linear versus "linearizing" control. The relative performance is measured by the region of attraction, magnitude of manipulated variable action, and sensitivity to input disturbances. The work represents the first objective evaluation of the strengths and limitations of input-output linearization compared to linear control.

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