An experimental evaluation of state estimation in multivariable control systems

Seborg, Dale E.; Fisher, D. Grant; Hamilton, James C.

doi:10.1016/0005-1098(75)90084-9

Cited by 14 publications

(1 citation statement)

References 23 publications

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“…The existence conditions are quite stringent however, are not statisfied in many practical situations, and other approaches have to be chosen in most cases. Seborg et al (1975) proceed in the deterministic case in the same fashion as in the stochastic one: They reduce the bias error by increasing the gain of the observer. For multivariable systems, there are different ways to increase the "overall gain" and by trial and error the most efficient way can be found.…”

Section: State Reconstruction-deterministic Approachmentioning

confidence: 98%

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

Morari

Stephanopoulos

1980

AIChE Journal

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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...

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Section: State Reconstruction-deterministic Approachmentioning

confidence: 98%

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

Morari

Stephanopoulos

1980

AIChE Journal

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Model reference identification of state space models for a double effect evaporator

1977

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A model reference identification technique is used to develop state space models of a double effect evaporator from experimental and simulated data. The model reference technique is based on a Liapunov design approach and is successfully used to estimate coefficient matrices containing 18 parameters in a third order model and 40 parameters in a fifth order model. However, in this application the success of the model reference technique required low measurement noise levels and a judicious choice of design parameters.

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Experience with Experimental Applications of Multivariable Computer Control

Seborg

Fisher

1977

Automatisierungstechnik Im Wandel Durch Mikroprozessoren

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An experimental evaluation of state estimation in multivariable control systems

Cited by 14 publications

References 23 publications

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

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

Model reference identification of state space models for a double effect evaporator

Experience with Experimental Applications of Multivariable Computer Control

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