In many process applications some key variables that are to be controlled cannot be measured on-line for a number of reasons. On-line product quality analyzers are expensive, require frequent maintenance, and suffer from large delays.
A standard approach to this problem in systems theory is to use a state estimator (e.g. a Kalman filter) that given a (state-space) model of the system and a number of measurements reconstruct an estimate of all states. This approach can be rarely applied in process industry plants (e.g. distillation columns or chemical reactors) because a phenomenological dynamic model of the process is too complicated and/or because it contains a number of parameters that are unknown (and often change in time). The alternative approach, widely used in practical applications, is to develop empirical models that, given measurements of a number of auxiliary variables, "infer" the variables to be controlled. These models are identified from (real or simulated) process data, typically using multivariate regression techniques, like Principal Component Regression (PCR) Projection to Latent Structures (PLS).
In this seminar, a number of different techniques widely used in industry such as PCR, linear and nonlinear PLS are presented, emphasizing why they improve the estimator's prediction ability with respect to the traditional Multivariable Least-square Regression (MLR). Having described these methods, control issues associated to the use of an estimator in closed-loop are addressed, and particular emphasis to the steady-state offset properties is given. An appropriate "consistency" measure is introduced as a criterion to evaluate the estimator's closed-loop performance: an estimator is consistent when it provides low closed-loop steady-state offset in the unmeasured controlled variables. It is shown that "consistency" is a different concept than "accuracy" in fitting the data (often used to choose among different estimators), and estimators that appear to fit the data well may be inappropriate for closed-loop inferential control because they would lead to large offset. Finally, consistency is proposed as a criterion to choose the most appropriate auxiliary variables to be used by the estimators, and comparisons with alternative (widely used) criteria are presented. Examples of inferential applications to distillation columns are presented to emphasize the main concepts and issues.
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