Realistic disturbance modeling using hidden markov models: applications in model-based process control

Journal of Process Control 19 (2009) 1438–1450

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Journal of Process Control
journal homepage: www.elsevier.com/locate/jprocont

Realistic disturbance modeling using Hidden Markov Models: Applications in model-based process control
Wee Chin Wong, Jay H. Lee *
School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, 311Ferst Drive NW, Atlanta, GA 30332, United States

a r t i c l e

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a b s t r a c t
Understanding and modeling disturbances play a critical part in designing effective advanced modelbased control solutions. Existing linear, stationary disturbance models are oftentimes limiting in the face of time-varying characteristics typically witnessed in process industries. These includeintermittent drifts, abrupt changes, temporary oscillations, outliers and the likes. This work proposes a Hidden Markov Model-based framework to deal with such situations that exhibit discrete, modal behavior. The usefulness of the proposed disturbance framework – from modeling to ensuring the integral action under a wide variety of scenarios – is demonstrated through several examples. Ó 2009 Elsevier Ltd.All rights reserved.

Article history: Received 10 November 2008 Received in revised form 29 April 2009 Accepted 30 April 2009

Keywords: Disturbance modeling Hidden Markov Models

1. Introduction System identification plays a vital role in model-based control. For example, Model Predictive Control (MPC) relies on an appropriate description of plant dynamics so that future behavior may bepredicted and optimized. Within this, disturbance modeling is crucial for it accounts for the effect of unmeasured signals, parameter changes, as well as other unmodeled phenomena (the residuals). Indeed, one of the main aims of control is to mitigate the impact of disturbances. Appropriate disturbance modeling leads to more accurate predictions of key variables’ behavior, and consequently, superiorcontrol [1]. It can also allow for the better capturing of cross-correlations among the various output channels, which is useful for soft-sensing and inferential control. Furthermore, offset-free control is often imparted by appending integrating disturbance states [2–4] to the process model. Eqs. (1) and (2) together form a general representation of a dynamical system. Here, xt 2 Rnx is the systemstate at discretetime index t; ut 2 Rnu , a vector of manipulated variables, xt 2 Rnx , additive state noise, v t 2 Rny , additive measurement noise, and yt 2 Rny , output measurements. f ð:Þ; gð:Þ are models of the state transition and measurement dynamics, respectively.

disturbance patterns, which, for practical purposes, is usually determined by the user. For example, the authors of [5],use h as a fault parameter vector to describe changes in process and disturbance parameters as well as actuator and sensor problems. Common deterministic signals for ht include the pulse, step changes (e.g., in Dynamic Matrix Control [6]), ramps, and sinusoids [1]. Stochastic processes lend themselves to an additional level of sophistication and generalization, given the typically-assumedprobabilistic nature of disturbances. Eq. (3) (see [7]) is capable of modeling common stochastic signals (and indeed deterministic ones), through appropriate choices of A 2 Rnc Ânc ; B 2 Rnc Ânu ; C 2 Rnh Ânc , and the mathematical forms of u 2 Rnu and e 2 Rnh .

ctþ1 ¼ Act þ Butþ1 ht ¼ Cct þ et

ð3Þ

xtþ1 ¼ f ðxt ; ut ; htþ1 Þ þ xt yt ¼ gðxt ; ht Þ þ v t
nh

ð1Þ ð2Þ

ht 2 R is a vector ofdisturbance signals. The use of h provides flexibility as it is sufficiently general to represent a variety of possible

* Corresponding author. Tel.: +1 404 385 2148; fax: +1 404 894 2866. E-mail addresses: wwong@chbe.gatech.edu (W.C. Wong), jlee@chbe.gatech.edu (J.H. Lee). 0959-1524/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jprocont.2009.04.014

In the stochastic...