Measurement System Design for Chemical Processes
Liba, Michael Joseph
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The problem of measurement system design for stochastic linear systems, a popular modeling strategy for chemical processes, is addressed. A multi-objective optimization approach is used. The design metrics are the capital cost of measurement equipment and a weighted uncertainty in terms of the Kalman filter state estimation error covariance matrix. The Pareto optimal set of measurement systems is identified by any of the following applicable techniques: an exhaustive combinatorial search, sequential sensor addition/removal, and branch-and-bound with semi-definite programs (BnB/SDP) solved at each node. The decision-making process involves the use of simulation experiments as a means to map Pareto optimal measurement systems to a dollar cost of operation. The closed-loop performance of Pareto optimal measurement systems are then simulated under a joint Kalman filter and robust profit-maximizing model predictive control strategy. The design methodology is applied to two example problems. The first involves a low dimensionality fluid handling network where a number of stream flow rates, a tank level, and a leak stream describe the dynamics. The design variables are the process outputs and the precision with which they are measured. It is observed that the sequential and BnB/SDP techniques are able to approximate the true Pareto optimal set very well, with improved performance in the latter case attainable through trial and error. The second example problem involves a high-dimensionality thermal network model of a one-floor office building. The impact of zero and nonzero state noise covariance structures on the results of the proposed design procedure is investigated. It is shown that measurement importance is placed on the disturbance variables in the deterministic case, whereas importance is placed on the controlled variables when model uncertainty is assumed. Closed-loop simulations incorporating MPC and Kalman filtering are then performed to generate expected operational cost data. The measurement system that minimizes the overall cost of capital investment and operation over the expected lifespan of the measurement is chosen as the final design. It is shown that the combination of measured variables which minimizes the overall cost is those of the three largest bodies of air that are to be controlled.