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43321-AC9
Improved Chemical Process Operations through Data-Based Disturbance Models

James B. Rawlings, University of Wisconsin

1. Estimating disturbance structures from data.

We consider the following linear, discrete time state space model:

x+ = Ax + B u + Gw

y = Cx + v

in which x is the state, u is the manipulated control input, and y is

the measurement. The state at the next sample time is x+. The random

variables w and v are the process and measurement noises,

respectively. The noises w and v are assumed to be identically and

independently distributed as normals with mean zero and covariances Q

and R, respectively. The goal of state estimation is to determine the

most likely value of the state x given the model (A, B, C, G, Q, R)

and past and current measurements of y.

There are two challenges. For typical chemical processes, we do not

know Q and R and must determine them from process operating data.

Secondly, we often do not know the G matrix, and must determine that

also from process operating data. The G matrix shapes the disturbance

w entering the state. It is unlikely to have more than a few

independent disturbances that affect the states. This would imply a

tall G matrix with more rows than columns. In previous work in our

group, the estimation of the covariances Q, R was presented. The

estimation technique was based on the correlations between the

measurements at different times. This technique and other previous

techniques in the literature assume that the disturbance structure as

given by the G matrix is known. In the absence of any knowledge about

G the incorrect assumption that G is an identity matrix is often made,

which implies that an independent disturbance enters each of the

states.

Knowledge about the G matrix then helps improve the state estimator

tuning and as a result the closed loop control performance. We

developed a technique to find the structure of the G matrix from data

and ensure that it represents the minimum number of independent

disturbances entering the state. In addition we formulated the

problem as a convex semidefinite optimization to enforce positive

definite constraints on the estimated covariances. The estimated G

matrix then provides both the smallest number of independent

disturbances required to explain the operating data, and the structure

of the disturbance. This work has been accepted for publication in

Automatica.

2. Industrial Implementation

Industrial collaborations with ExxonMobil Chemicals and Eastman

Chemicals have been established to implement the techniques developed

in this grant.

ExxonMobil Chemicals provided industrial operating data on a nonlinear

blending drum that was being controlled for level and concentrations.

The techniques in Section 1 was extended to nonlinear models and

implemented on the blending tank data. Using a first principles based

model for the blending tank, the covariances of the noises affecting

the state and measurements were estimated. The estimated covariances

were used to improve the state estimation part of the controller of

this application and to obtain information about the structure of the

G matrix. This work has been submitted for publication.

In the collaboration with Eastman Chemicals, a set of industrial data

from a process was provided. By applying the techniques developed in

Section 1, the optimal state estimator for the process estimated.

Simulations showed the new estimator gain to perform significantly

better in closed loop than the one in current use at Eastman

Chemicals. The benefits of using the new updated estimator gain will

be further evaluated by a plant implementation of the new data-based

estimator tuning.

3. Nonlinear State Estimation

Nonlinear state estimation is a challenging systems theory problem.

One approach to this problem receiving attention recently is particle

filtering, which is a nonlinear state estimation technique based on

Monte-Carlo type sampling. The drawback of particle filtering is the

lack of robustness in the presence of unmodelled disturbances or poor

initial guesses. Another option is moving horizon estimation, which

is a robust optimization based state estimation technique. The

nonlinear optimization may be prohibitively expensive, however, for

online use in state estimation. As part of this research, the

combination of a particle filter with moving horizon estimation was

evaluated as a better alternative than either method alone. This

combination of methods showed good results for both unmodelled

disturbances and for poor guesses for the initial state.

This work has been presented at scientific meetings and will be

submitted this year for publication.

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