Model life extension for continuous process: Non-invasive correction of model-plant mismatch with regularization

TL;DR

The paper addresses MPC performance degradation in continuous processes caused by aging-induced model-plant mismatch (MPM). It introduces Model Life Extension (MLE), a non-invasive approach that continually updates MPM estimates using routine operating data by solving an $L_1$ regularized regression problem and selecting the regularization parameter via cross-validation. Applying MLE to a pilot-scale distillation column, the authors demonstrate that a suitable $\lambda$ exists and can be found, enabling correction of static-gain and transport-delay mismatches without exciting inputs. This method offers a safer, maintenance-friendly alternative to traditional closed-loop re-identification and has potential applicability to a wide range of time-varying processes where aging occurs on a slow timescale.

Abstract

In continuous process plants controlled by model predictive control, model-plant mismatch (MPM), due to the aging of processes, causes degradation of control performance. We propose a concept called Model Life Extension (MLE) and its implementation to mitigate this degradation in a non-invasive manner. The purpose of MLE is to continually update (re-identify) process models by using routine operating data on the assumption that the timescale of aging is much larger than the interval of excitation of reference signals. We implemented MLE by estimating MPM via $\mathcal{L}_1$ regularized regression and by finding an optimal regularization parameter via cross-validation and showed through numerical experiments that an optimal parameter can exist and be found by cross-validation for a pilot-scale distillation column. We then constructed the updated model based on the found parameter to demonstrate the possibility of correcting static-gain mismatch and transport-delay mismatch without injecting excitation signals to process inputs.

Figures (6)

• Figure 1: Conceptual diagram of MLE.
• Figure 2: Pilot-scale distillation column.
• Figure 3: Step-response benchmarks for (a) ${\sf G}_{\hbox{\scriptsizegain}}$ and (b) ${\sf G}_{\hbox{\scriptsizedelay}}$. Blue curves denote (a) $E({\sf G}_{\hbox{\scriptsizegain}}, \hat{\sf R}_\lambda)$ and (b) $E({\sf G}_{\hbox{\scriptsizedelay}}, \hat{\sf R}_\lambda)$, black lines (a) $E({\sf G}_{\hbox{\scriptsizegain}}, {\sf G}_0)$ and (b) $E({\sf G}_{\hbox{\scriptsizedelay}}, {\sf G}_0)$, and red cross regularization parameter $\lambda^*$ found by cross-validation. In the panel (a), the domain encompassed by the broken lines is enlarged in the top subfigure.
• Figure 4: Step-response curves derived in experiment for ${\sf G}_{\hbox{\scriptsizegain}}$. Dashed lines represent response of initial dynamics ${\sf G}_0$, dotted lines true dynamics ${\sf G}_{\hbox{\scriptsizegain}}$, blue lines ${\sf R}_{\lambda^*}$ estimated using MLE, and red lines ${\sf R}_0$ estimated without regularization.
• Figure 5: Step-response curves derived in experiment for ${\sf G}_{\hbox{\scriptsizedelay}}$. Dashed line represents response of initial dynamics ${\sf G}_0$, dotted line true dynamics ${\sf G}_{\hbox{\scriptsizedelay}}$, blue line ${\sf R}_{\lambda^*}$ estimated using MLE, and red line ${\sf R}_0$ estimated without regularization.