A nonparametric approach to design robust controllers for uncertain systems

Application to an air flow heating system

Sofiane Khadraoui, Hazem Nounou, Mohamed Nounou, Aniruddha Datta, Shankar P. Bhattacharyya

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalJournal of Process Control
Volume36
DOIs
Publication statusPublished - 1 Dec 2015

Fingerprint

Uncertain systems
Robust Design
Uncertain Systems
Heating
Controller
Controllers
Air
Uncertainty
Frequency Response
Frequency response
Frequency Domain
Identification (control systems)
Interval Analysis
Control System Design
Model Identification
Nonparametric Methods
Control Design
Closed loop systems
Envelope
Closed-loop System

Keywords

  • Frequency response template
  • Interval analysis
  • Measurement-based control
  • Robust control design
  • Uncertain system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

Cite this

A nonparametric approach to design robust controllers for uncertain systems : Application to an air flow heating system. / Khadraoui, Sofiane; Nounou, Hazem; Nounou, Mohamed; Datta, Aniruddha; Bhattacharyya, Shankar P.

In: Journal of Process Control, Vol. 36, 01.12.2015, p. 1-10.

Research output: Contribution to journalArticle

@article{c9667ea56e5147fdaecc6752bee03cde,
title = "A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system",
abstract = "This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.",
keywords = "Frequency response template, Interval analysis, Measurement-based control, Robust control design, Uncertain system",
author = "Sofiane Khadraoui and Hazem Nounou and Mohamed Nounou and Aniruddha Datta and Bhattacharyya, {Shankar P.}",
year = "2015",
month = "12",
day = "1",
doi = "10.1016/j.jprocont.2015.08.012",
language = "English",
volume = "36",
pages = "1--10",
journal = "Journal of Process Control",
issn = "0959-1524",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - A nonparametric approach to design robust controllers for uncertain systems

T2 - Application to an air flow heating system

AU - Khadraoui, Sofiane

AU - Nounou, Hazem

AU - Nounou, Mohamed

AU - Datta, Aniruddha

AU - Bhattacharyya, Shankar P.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.

AB - This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.

KW - Frequency response template

KW - Interval analysis

KW - Measurement-based control

KW - Robust control design

KW - Uncertain system

UR - http://www.scopus.com/inward/record.url?scp=84952328172&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952328172&partnerID=8YFLogxK

U2 - 10.1016/j.jprocont.2015.08.012

DO - 10.1016/j.jprocont.2015.08.012

M3 - Article

VL - 36

SP - 1

EP - 10

JO - Journal of Process Control

JF - Journal of Process Control

SN - 0959-1524

ER -