Development of ARX models for predictive control using fractional order and orthonormal basis filter parametrization

Muddu Madakyaru, Anuj Narang, Sachin C. Patwardhan

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Among various industrial vendors of model predictive control (MPC) schemes, ARX appears to be a popular choice of model structure while models for predictive control schemes are being developed. These models are, however, nonparsimonious in the number of model parameters. As a consequence, the length of the data required to keep the variance errors low while using the conventional ARX structure is significantly large. Thus, if it is possible to reparametrize the ARX model such that fewer parameters are required at the identification stage, then it is possible to reduce the length of identification data and thereby reduce the cost involved in model identification exercise. In this work, we explore the possibility of reparametrizing ARX models using the fractional-order differential operators (FO-ARX) and orthonormal basis filters (OBF-ARX). We also propose a novel approach for identification of time delay matrix from multivariate data using ARX and OBF-ARX models. The efficacy of the proposed modeling technique is demonstrated by conducting simulation studies on the benchmark Shell control problem. Analysis of the simulation results reveals that, when compared with the conventional high-order ARX structure, the FO-ARX and the OBF-ARX are better model parametrizations when the data length is less. In particular, OBF-ARX parametrization is able to estimate the time delay matrix from multivariate data quite accurately. The experimental studies establish the feasibility of using the proposed FO-ARX and OBF-ARX models for formulating MPC schemes.

Original languageEnglish
Pages (from-to)8966-8979
Number of pages14
JournalIndustrial and Engineering Chemistry Research
Volume48
Issue number19
DOIs
Publication statusPublished - 07-10-2009

Fingerprint

Model predictive control
Time delay
Model structures
Identification (control systems)
Costs

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Chemical Engineering(all)
  • Industrial and Manufacturing Engineering

Cite this

@article{c4af0d1ecc8b42e19c0aca01e1358d30,
title = "Development of ARX models for predictive control using fractional order and orthonormal basis filter parametrization",
abstract = "Among various industrial vendors of model predictive control (MPC) schemes, ARX appears to be a popular choice of model structure while models for predictive control schemes are being developed. These models are, however, nonparsimonious in the number of model parameters. As a consequence, the length of the data required to keep the variance errors low while using the conventional ARX structure is significantly large. Thus, if it is possible to reparametrize the ARX model such that fewer parameters are required at the identification stage, then it is possible to reduce the length of identification data and thereby reduce the cost involved in model identification exercise. In this work, we explore the possibility of reparametrizing ARX models using the fractional-order differential operators (FO-ARX) and orthonormal basis filters (OBF-ARX). We also propose a novel approach for identification of time delay matrix from multivariate data using ARX and OBF-ARX models. The efficacy of the proposed modeling technique is demonstrated by conducting simulation studies on the benchmark Shell control problem. Analysis of the simulation results reveals that, when compared with the conventional high-order ARX structure, the FO-ARX and the OBF-ARX are better model parametrizations when the data length is less. In particular, OBF-ARX parametrization is able to estimate the time delay matrix from multivariate data quite accurately. The experimental studies establish the feasibility of using the proposed FO-ARX and OBF-ARX models for formulating MPC schemes.",
author = "Muddu Madakyaru and Anuj Narang and Patwardhan, {Sachin C.}",
year = "2009",
month = "10",
day = "7",
doi = "10.1021/ie8009439",
language = "English",
volume = "48",
pages = "8966--8979",
journal = "Industrial & Engineering Chemistry Product Research and Development",
issn = "0888-5885",
publisher = "American Chemical Society",
number = "19",

}

Development of ARX models for predictive control using fractional order and orthonormal basis filter parametrization. / Madakyaru, Muddu; Narang, Anuj; Patwardhan, Sachin C.

In: Industrial and Engineering Chemistry Research, Vol. 48, No. 19, 07.10.2009, p. 8966-8979.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Development of ARX models for predictive control using fractional order and orthonormal basis filter parametrization

AU - Madakyaru, Muddu

AU - Narang, Anuj

AU - Patwardhan, Sachin C.

PY - 2009/10/7

Y1 - 2009/10/7

N2 - Among various industrial vendors of model predictive control (MPC) schemes, ARX appears to be a popular choice of model structure while models for predictive control schemes are being developed. These models are, however, nonparsimonious in the number of model parameters. As a consequence, the length of the data required to keep the variance errors low while using the conventional ARX structure is significantly large. Thus, if it is possible to reparametrize the ARX model such that fewer parameters are required at the identification stage, then it is possible to reduce the length of identification data and thereby reduce the cost involved in model identification exercise. In this work, we explore the possibility of reparametrizing ARX models using the fractional-order differential operators (FO-ARX) and orthonormal basis filters (OBF-ARX). We also propose a novel approach for identification of time delay matrix from multivariate data using ARX and OBF-ARX models. The efficacy of the proposed modeling technique is demonstrated by conducting simulation studies on the benchmark Shell control problem. Analysis of the simulation results reveals that, when compared with the conventional high-order ARX structure, the FO-ARX and the OBF-ARX are better model parametrizations when the data length is less. In particular, OBF-ARX parametrization is able to estimate the time delay matrix from multivariate data quite accurately. The experimental studies establish the feasibility of using the proposed FO-ARX and OBF-ARX models for formulating MPC schemes.

AB - Among various industrial vendors of model predictive control (MPC) schemes, ARX appears to be a popular choice of model structure while models for predictive control schemes are being developed. These models are, however, nonparsimonious in the number of model parameters. As a consequence, the length of the data required to keep the variance errors low while using the conventional ARX structure is significantly large. Thus, if it is possible to reparametrize the ARX model such that fewer parameters are required at the identification stage, then it is possible to reduce the length of identification data and thereby reduce the cost involved in model identification exercise. In this work, we explore the possibility of reparametrizing ARX models using the fractional-order differential operators (FO-ARX) and orthonormal basis filters (OBF-ARX). We also propose a novel approach for identification of time delay matrix from multivariate data using ARX and OBF-ARX models. The efficacy of the proposed modeling technique is demonstrated by conducting simulation studies on the benchmark Shell control problem. Analysis of the simulation results reveals that, when compared with the conventional high-order ARX structure, the FO-ARX and the OBF-ARX are better model parametrizations when the data length is less. In particular, OBF-ARX parametrization is able to estimate the time delay matrix from multivariate data quite accurately. The experimental studies establish the feasibility of using the proposed FO-ARX and OBF-ARX models for formulating MPC schemes.

UR - http://www.scopus.com/inward/record.url?scp=70349663672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349663672&partnerID=8YFLogxK

U2 - 10.1021/ie8009439

DO - 10.1021/ie8009439

M3 - Article

VL - 48

SP - 8966

EP - 8979

JO - Industrial & Engineering Chemistry Product Research and Development

JF - Industrial & Engineering Chemistry Product Research and Development

SN - 0888-5885

IS - 19

ER -