Modeling requirements for process control

Abstract

Modeling and control system design have traditionally been viewed as distinct, independent problems. Not all model characteristics, however, are relevant to the control system design problem. One can expect, then, that parsimonious, more effective controllers are possible if control considerations are incorporated in the modeling stage. The synergism of dynamic modeling and process control, as pertaining to the fields of low-order controller design, model reduction, and model identification, is investigated in this thesis. The guiding theoretical framework is the robust control paradigm using the Structured Singular Value, which addresses controller design in the presence of model uncertainty. The main contribution of this thesis is the development of a control-relevant model reduction methodology. The effectiveness of reduction is increased by incorporating the closed-loop performance/robustness specifications, plant uncertainties, and setpoint/disturbance characteristics explicitly as weights in the reduction procedure. The efficient computation of the control-relevant reduction problem is indicated and illustrated with examples taken from the control of a methanation reactor and a binary distillation column. A low-order controller design methodology for single-input, single-output plants is also presented. The basis for this methodology is the combination of the control-relevant reduction problem with the Internal Model Control (IMC) design procedure. The relationship between low-order IMC controllers and classical feeback compensators is examined. It is shown that for many models common to the process industries, the controllers obtained from the low-order compensator design technique are of the PID type. Finally, a model identification methodology is established using spectral time series analysis to obtain plant transfer function and uncertainty estimates directly from experiments. The control-relevant model reduction procedure can then be used to fit the full-order frequency response to a reduced-order parametric model. Model validation for control purposes is achieved by insuring that the robustness condition is satisfied.