A method of robust multi-rate state estimation

Zambare, N.; Soroush, Masoud; Ogunnaike, Babatunde A.

doi:10.1016/s0959-1524(02)00027-6

Cited by 22 publications

(16 citation statements)

References 29 publications

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“…On the basis of the developed reduced-order model, a reduced-order multi-rate state estimator is designed using the method described in References [12,18]. The estimator is in the forṁ Figure 6.…”

Section: Reduced-order Multi-rate State Estimator Designmentioning

confidence: 99%

“…The non-zero terms in effect indicate which slow measurement is used to correct a state variable estimate. A more thorough discussion on how the estimation error (between the estimates and their true values) depends on the estimator gain matrix entries is given in Reference [18].…”

Section: Reduced-order Multi-rate State Estimator Designmentioning

confidence: 99%

“…The method-of-moments model presented in Reference [4] is able to successfully predict monomer conversion and number-average molecular weight (Figure 1), however it over-predicts the polymer polydispersity index and under-predicts the concentration of terminal double bonds ( Figure 2). In view of these predictive deficiencies, this study aims to (i) develop a simplified reducedorder polymerization reactor model for high-temperature polymerization of n-butyl acrylate, (ii) develop a multi-rate state estimator using the method described in Reference [18] and the reduced order model and (iii) evaluate the performance of the state estimator in predicting numberand weight-average molecular weights (chromatographic properties) and polymer chain microstructures (spectroscopic properties). The approach of modeling macromolecular kinetics as small-molecular kinetics [19] is adopted as a Figure 2.…”

Section: Introductionmentioning

confidence: 99%

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Reduced‐order model for monitoring spectroscopic and chromatographic polymer properties

Rantow

Soroush

Grady

2007

Journal of Chemometrics

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A reduced-order mechanistic polymerization model and its application in the design of a lowdimension multi-rate state estimator (soft sensor) for monitoring spectroscopic and chromatographic polymer properties are presented. A model reduction approach is used to simplify a method-ofmoments mechanistic model. Using this approach, the order (number of the state variables) of the model is reduced from 20 to 7. The soft sensor estimates spectroscopic and chromatographic polymer properties from (a) frequent measurements of the reactor temperature and the flow rates of monomer (n-butyl acrylate), initiator (t-butyl peroxy acetate) solution and solvent (xylene) feed streams, and (b) infrequent and delayed measurements of polymer number-and weight-average molecular weights and the concentrations of terminal solvent groups, terminal double bonds and short chain branches. The benefits of using the infrequent measurements in the estimation are shown. The soft sensor is implemented in real-time, and the calculated continuous estimates of polymer number-and weightaverage molecular weights and the concentrations of solvent, terminal double bonds and short chain branches are compared to the corresponding chromatographic and spectroscopic measurements.

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Section: Reduced-order Multi-rate State Estimator Designmentioning

confidence: 99%

Section: Reduced-order Multi-rate State Estimator Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reduced‐order model for monitoring spectroscopic and chromatographic polymer properties

Rantow

Soroush

Grady

2007

Journal of Chemometrics

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“…This approach has been given various names over the decades such as bias estimation [13,17,18], garbage collector [10], or integral observer [3,22]. Note that, with integral observers, unbiased estimation of all states typically requires the measurement of all states [24,28], or of at least as many independent outputs as there are independent sources of disturbance [25], which is rather impractical.…”

mentioning

confidence: 99%

“…One way of handling two-time-scale systems is to extrapolate the slow measurements for the fast time scale by using some kind of approximations, e.g. zero-order hold or polynomial approximations, and then use a single-rate estimation technique [27,28]. Another approach is to update the estimates only when the slow measurements become available and, in-between, use the predictions given by the process model corrected using the available fast measurements [2,23,5].…”

mentioning

confidence: 99%

On the design of integral observers for unbiased output estimation in the presence of uncertainty

Bodizs

Srinivasan

Bonvin

2011

Journal of Process Control

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Integral observers are useful tools for estimating the plant states in the presence of non-vanishing disturbances resulting from plant-model mismatch and exogenous disturbances. It is well known that these observers can eliminate bias in all states, given that as many independent measurements are available as there are independent sources of disturbance. In the most general case, the dimensionality of the disturbance vector affecting the plant states corresponds to the order of the system and thus all states need to be measured. This condition, which is termed integral observability in the literature, represents a fairly restrictive situation. This study focuses on the more realistic case, where only the output variables are measured. Accordingly, the objective reduces to the unbiased estimation of the output variables. It is shown that both stability and asymptotically unbiased output estimation can be achieved if the system is observable, regardless of the dimensionality of the disturbance vector. Furthermore, a condition is provided under which, using output measurements, the errors in all states can be pushed to zero. It is also proposed to use off-line output measurements to tune the observer using a calibration-like approach. Integral observers and integral Kalman filters are evaluated via the simulation of a fourth-order linear system perturbed by unknown non-vanishing disturbances.

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A dead time compensation approach for multirate observer design with large measurement delays

Ling¹,

Kravaris

2018

AIChE Journal

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In our previous work, we developed a multirate observer design method in linear systems with asynchronous sampling based on a Luenberger observer design coupled with inter‐sample predictors. In this article, the problem of multirate multidelay observer design is addressed where both asynchronous sampling and possible measurement delays are accounted for. The proposed observer adopts an available multirate observer design in the time interval between two consecutive delayed measurements. A dead time compensation approach is developed to compensate for the effect of delay and update past estimates when a delayed measurement arrives. The stability and robustness properties of the multirate observer will be preserved under nonconstant, arbitrarily large measurement delays. A mathematical example and a gas‐phase polyethylene reactor example demonstrate good performance of the proposed observer in the presence of nonuniform sampling and nonconstant measurement delays. © 2018 American Institute of Chemical Engineers AIChE J, 65: 562–570, 2019

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A method of robust multi-rate state estimation

Cited by 22 publications

References 29 publications

Reduced‐order model for monitoring spectroscopic and chromatographic polymer properties

Reduced‐order model for monitoring spectroscopic and chromatographic polymer properties

On the design of integral observers for unbiased output estimation in the presence of uncertainty

A dead time compensation approach for multirate observer design with large measurement delays

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