Studies in the synthesis of control structures for chemical processes: Part III: Optimal selection of secondary measurements within the framework of state estimation in the presence of persistent unknown disturbances

Abstract

When primary control objectives cannot be measured directly, secondary measurements have to be selected and used in conjunction with estimators to infer the value of the unmeasurable variables. Unmeasured process disturbances (state excitation noise) are assumed to be of major importance, dominating the errors caused by measurement noise. Since the white noise assumption is generally insufficient for the persistent disturbances commonly occurring in the chemical engineering environment, a nonstationary noise model has been employed, and is shown to yield superior estimations under these circumstances. New necessary and sufficient conditions have been developed for the observability of the dynamic system augmented to include the noise model.A variety of new measurement selection criteria is presented here, with the goal of minimizing estimation error. One class of criteria aims at minimizing the transient estimation error when a static estimator is used. The other class minimizes the measurement error caused by the unobservable subspace. The design of state reconstruction procedures (which are able to handle persistent unmeasured process disturbances) is explained in a stochastic and a deterministic framework. Finally, the synthesis of reduced order control schemes is discussed. The power of the selection criteria and the superiority of a Kalman filter design employing a nonstationary noise model is demonstrated in many examples. MANFRED MORARI and GEORGE STEPHANOPOULOS SCOPEFrequently, in process control, some important variables are not available for measurement. Secondary measurements have to be selected and used to infer the value of the unmeasurable variables. The proper selection of secondary measurements is a task of paramount importance for the synthesis of control structures. The measurements should be selected to minimize estimation error. The error can be caused by differences between the real system and the process model which forms the basis for the design of the estimator, or by process and measurement noise. Here, the criteria derived consider the influence of those different factors on the error separately: Selection Criterion 1 assumes a steady state model and minimizes the error caused by unmeasurable inputs with normally distributed amplitudes: Selection Criterion 2 (Joseph, Brosilow 1978) minimizes the influence of model inaccuracies.Criteria 3 and 4 minimize the error when a static estimator, which has the advantage of being very simple to implement, is used for the dynamic system. For a linear dynamic system with white state excitation and measurement noise, the Kalman filter is known to be the best estimator-in the sense of minimum variance, maximum likelihood, etc. If a step change in the inputs to the unit occurs which cannot be measured, o r if an unknown change is caused by drifting conditions upstream (so that the process will display a steady state or pseudo steady state behavior under those disturbances), this estimator performs quite poorly. The objective of this article is to prese...

Virtual Sensing Technology in Process Industries: Trends and Challenges Revealed by Recent Industrial Applications

“…Many articles have been published on this matter (Weber and Brosilow, 1972;Joseph and Brosilow, 1978;Morari and Stephanopoulos, 1980;Moore et al, 1987). However, this simple approach is not optimal, because additional measurements may improve the performance of an estimator.…”

A review of methods for input/output selection

“…E The selection of the number and placement of temperature sensors in Bequette and Edgar (1986, IO controllability), Chang and Yu (1990, IO controllability), Havre et al (1996, IO controllability), Joseph and Brosilow (1978, IO controllability, e$ciency of manipulation and estimation), Lee (1991, Section 3.5 and Appendix B.3.3, e$ciency of manipulation and estimation, IO controllability, RP), Lee and Morari (1991, RP), Lee et al (1995, RP), and Morari and Stephanopoulos (1980b, e$ciency of manipulation and estimation). E The selection of the placement and type of sensors in Moore et al (1987, IO controllability).…”

“…DEE: Double-e!ect evaporators, i.e., two evaporators in series, are considered in Heath, Perkins, and Walsh (1996, IO controllability) and Narraway and Perkins (1993, IO controllability), where both inputs and outputs are selected, and in Morari and Stephanopoulos (1980b, e$ciency of manipulation and estimation), where only outputs are selected. Govind and Powers (1982, accessibility) focus on IO selection for the combination of a mixer, a divider, and a heat exchanger.…”

“…FCC: Hovd and Skogestad (1993, RHP zeros) and Morari and Stephanopoulos (1980b, e$ciency of manipulation and estimation) select temperature sensor sets for a #uid catalytic cracker (three units).…”

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“…Over-parameterized models can fit the original data well, but they usually lead to poor predictions [1]. One simple approach for dealing with this problem is to select a subset of independent variables to be used in the model [2][3][4]. Other modeling techniques that deal with collinearity can be divided into two main categories: full rank models and reduced rank models (or latent variable regression models).…”