(302l) Disturbance Modeling Via Hidden Markov Techniques - an Extension

Disturbance modeling, as part of process identification, is imperative for the sound performance of model-based controllers. The archetypal stochastic model form used for process identification and control is a linear system with additive stationary noise [2]. The latter (the residual) is usually white noise filtered through a stable transfer function, H(q). For processes with step disturbances and drifts, integrated white noise has been used as stationary noise models leave offsets.

However, such a model does not permit adequate description of common plant behavior like intermittent drifts or jumps. Another issue is that in practice, the stochastic properties of a disturbance pattern may not stay constant with time.

In this context, we had previously [1] explored the potential use of Hidden Markov Models (HMMs) in providing a significant generalization of the current model form used for process control. There, we provided a case where the parameters of the driving noise changed according to the discrete state of an underlying Markov chain and performed disturbance modeling in the face of a known plant.

In this presentation, we provide specific examples which consider simultaneous disturbance and process identification.

As a first example, consider the scenario where the residual switches between being stationary and integrated white noise. The common way of handling these multiple phenomena is via assuming a linear combination of the both [3]. It is shown that this is oftentimes ineffective and the framework provides a way to achieve better estimation/ control performance.

Another case is where we investigate the time varying behavior of H(q) via the proposed framework.

Lastly, we propose the use of an HMM framework for assisting the user in the removal of potential outliers. These examples are provided to demonstrate the final closed-loop performance improvement possible through the use of HMMs.

[1] W.C. Wong and J.H. Lee (2005). A Hidden Markov Model Based Approach to Process Identification and Estimation. American Institute of Chemical Engineers Annual Meeting, Cincinnati, Ohio.

[2] Ljung, L. (1999) System Identification. Theory for the user.

[3] Soderstrom T., and Stoica P. (1989) System dentification