A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study

Abstract

a b s t r a c tModel-based control strategies are widely used for optimal operation of chemical processes to respond to the increasing performance demands in the chemical industry. Yet, obtaining accurate models to describe the inherently nonlinear, time-varying dynamics of chemical processes remains a challenge in most model-based control applications. This paper reviews data-driven, Linear Parameter-Varying (LPV) modeling approaches for process systems by exploring and comparing various identification methods on a high-purity distillation column case study. Several LPV identification methods that utilize input-output and series expansion model structures are explored. Two LPV identification perspectives are adopted: (i) the local approach, which corresponds to the interpolation of Linear Time-Invariant (LTI) models identified at different steady-state operating points of the system and (ii) the global approach, where a parametrized LPV model structure is identified directly using a global data set with varying operating points. For the local approach, various model interpolation schemes are studied under an Output Error (OE) noise setting, whereas in the global case, a polynomial parametrization based OE prediction error minimization approach, an Orthonormal Basis Functions (OBFs) based model estimator and a LeastSquare Support Vector Machine (LS-SVM) based non-parametric approach are investigated. Through extensive simulation studies, the aforementioned LPV identification approaches are analyzed in terms of the attainable model accuracy and local frequency response behavior of the obtained models. Recommendations are provided to achieve adequate choice between the methods for a particular process system at hand.

System Behavior and Predictive Controller Performance Near the Azeotropic Region

“…Since the azeotropic point for the ethanol‐water system under atmospheric pressure is around 88 mol % of ethanol, observations can be made for the controller performance of operating regimes as they approach the azeotropic point. It is expected that the system behavior near the azeotropic region will be similar to that of a high‐purity distillation column, which can be summarized as follows: High‐purity distillation systems are highly nonlinear. The order of the model is among the main causes of performance deterioration of high‐purity distillation columns . Directionality of the system results in the response swayed in the high‐gain direction, therefore, the top and bottom composition cannot be controlled independently . High‐purity distillation systems are usually ill‐conditioned and interacting, therefore, a small error in the identified models can impair the controllability of the system . …”

The pre-processing technique and parameter adjustment influences on NARX-based BPSO structure for time-varying water temperature modelling

“…The nonlinear dynamic behaviour has been displayed by a broad application of the distillation column in chemical operations [1][2]. Auto-Regressive with eXogenous input (ARX) [3][4] has been used for distillation column as well as Auto-Regressive Moving Average with eXogenous input (ARMAX) [5] and Nonlinear Auto-Regressive with eXogenous input (NARX) [6][7].…”

An improved robust model predictive control for linear parameter‐varying input‐output models

“…Identifying LPV models in the input‐output (IO) form from data has become well supported as powerful identification approaches have been recently developed in the literature, eg, work of Laurain et al, with several successful applications specially for process systems. () The main feature of the model identification in the IO framework is its capability to capture low‐complexity and yet highly accurate LPV models for nonlinear/time‐varying systems by solving, generally, a low‐complexity estimation problem based on the extension of the well‐developed linear time‐invariant (LTI) approaches. The LPV‐IO identification offers powerful tools to estimate models under real‐world assumptions on the disturbances and measurement noise affecting the captured data.…”