An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system

doi:10.1007/s11705-021-2058-6

Front. Chem. Sci. Eng.

2022, Vol. 16

Issue (2) : 237-250 https://doi.org/10.1007/s11705-021-2058-6

RESEARCH ARTICLE

An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system

Ewan Chee¹, Wee Chin Wong², Xiaonan Wang¹(

)

¹. Department of Chemical & Biomolecular Engineering, Faculty of Engineering, National University of Singapore, Singapore 117585, Singapore
². Chemical Engineering & Food Technology Cluster, Singapore Institute of Technology, Singapore 138683, Singapore

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Abstract

Advanced model-based control strategies, e.g., model predictive control, can offer superior control of key process variables for multiple-input multiple-output systems. The quality of the system model is critical to controller performance and should adequately describe the process dynamics across its operating range while remaining amenable to fast optimization. This work articulates an integrated system identification procedure for deriving black-box nonlinear continuous-time multiple-input multiple-output system models for nonlinear model predictive control. To showcase this approach, five candidate models for polynomial and interaction features of both output and manipulated variables were trained on simulated data and integrated into a nonlinear model predictive controller for a highly nonlinear continuous stirred tank reactor system. This procedure successfully identified system models that enabled effective control in both servo and regulator problems across wider operating ranges. These controllers also had reasonable per-iteration times of ca. 0.1 s. This demonstration of how such system models could be identified for nonlinear model predictive control without prior knowledge of system dynamics opens further possibilities for direct data-driven methodologies for model-based control which, in the face of process uncertainties or modelling limitations, allow rapid and stable control over wider operating ranges.

Keywords nonlinear model predictive control black-box modeling continuous-time system identification machine learning industrial applications of process control

Corresponding Author(s): Xiaonan Wang

Online First Date: 21 June 2021 Issue Date: 10 January 2022

Cite this article:

Ewan Chee,Wee Chin Wong,Xiaonan Wang. An integrated approach for machine-learning-based system identification of dynamical systems under control: application towards the model predictive control of a highly nonlinear reactor system[J]. Front. Chem. Sci. Eng., 2022, 16(2): 237-250.

URL:

https://academic.hep.com.cn/fcse/EN/10.1007/s11705-021-2058-6
https://academic.hep.com.cn/fcse/EN/Y2022/V16/I2/237

Fig.1 Integrated data-driven approach for identification of continuous-time NMPC system models.

Fig.2 Example input signal (green) and system response (red), where

t = 10000

l min = 10

l max = 100

u min = 0

u max = 1

Fig.3 (a) Schematic diagram of CSTR plant, where

q *

and

T *

represent set-points for

q

and

T

respectively; (b) system steady-state conditions for

q = 0.8

(“Reactor startup” and “Upset recovery” refer to start points for the control problems in Section 3.2).

Fig.4 Example system response (top) to an input signal (bottom) for the CSTR case study.

Fig.5 (a) WIAE for exact NMPC with

p = 5

; (b) exact NMPC solution times with

p = 5

Fig.6 Exact NMPC performance for

p = 5

and

m = 1

: (a) servo problem, (b) startup problem, and (c) upset recovery problem.

Fig.7 Exact NMPC performance for

m = 1, ? 3, ? 5

for the servo problem: (a) output profiles, and (b) control profiles.

Fig.8 (a) Validation and test

R 2

scores for each candidate model; (b) test MSE score for each candidate model (“Poly” refers to the polynomial regression model).

Fig.9 (a) Optimization history for BO of SVR; (b) slice plot for

?

hyperparameter for SVR (objective value is validation

R 2

Fig.10 ML-NMPC performance for

p = 5

and

: (a) WIAE, and (b) solution times.

Fig.11 Exact, polynomial- and SVR- NMPC performance for the servo problem: (a) output profiles, and (b) control profiles.

Fig.12 Exact, polynomial- and SVR- NMPC performance for the startup problem: (a) output profiles, and (b) control profiles.

Fig.13 Exact, polynomial- and SVR- NMPC performance for the upset recovery problem: (a) output profiles, and (b) control profiles.

Fig.14 GB-NMPC performance for

p = 5

and

m = 1

: (a) servo problem, (b) startup proble, and (c) upset recovery problem.

Tab.1 Comparison of WIAEs for polynomial- and SVR- NMPCs against exact NMPC for

p = 5

and

m = 1

Tab.2 Comparison of solution times for Polynomial- and SVR- NMPCs against exact NMPC for

p = 5

and

m = 1

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