Stabilizing dynamic control design for systems with time-varying delay in control loop

Behrouz Ebrahimi, Reza Tafreshi, Javad Mohammadpour, Matthew Franchek, Karolos Grigoriadis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Synthesis of nth-order dynamic systems with time-varying delay in the control loop is considered in this paper. First-order Padé approximation is sought to solve the infinite-dimensional problem of the pure delay. Although the approximation describes the problem in a finite-dimensional state space, it poses internal dynamics instability inherited from the resulted non-minimum phase system. The unstable internal dynamics restricts the system closed-loop bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the overall system dynamics is explored in terms of unstable internal dynamics and input/output pairs. The system internal dynamics is used to design a parameter-varying dynamic compensator which stabilizes the internal dynamics based on a desired tracking error profile. The presented dynamic compensator is used to develop a dynamic controller whose parameter-varying gains are explicitly determined in a systematic and straightforward manner. The proposed approach is used to design a controller for a spark ignition lean-burn engine with large time-varying delay in the control loop. The results are demonstrated against a baseline PI controller combined with a parameter-varying Smith predictor to compensate for the time-varying delay.

Original languageEnglish
Title of host publication2014 American Control Conference, ACC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5558-5563
Number of pages6
ISBN (Print)9781479932726
DOIs
Publication statusPublished - 2014
Event2014 American Control Conference, ACC 2014 - Portland, OR, United States
Duration: 4 Jun 20146 Jun 2014

Other

Other2014 American Control Conference, ACC 2014
CountryUnited States
CityPortland, OR
Period4/6/146/6/14

Fingerprint

Controllers
Dynamical systems
Electric sparks
Closed loop systems
Ignition
Engines
Bandwidth

Keywords

  • Automotive
  • Delay systems
  • Time-varying systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Ebrahimi, B., Tafreshi, R., Mohammadpour, J., Franchek, M., & Grigoriadis, K. (2014). Stabilizing dynamic control design for systems with time-varying delay in control loop. In 2014 American Control Conference, ACC 2014 (pp. 5558-5563). [6859299] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2014.6859299

Stabilizing dynamic control design for systems with time-varying delay in control loop. / Ebrahimi, Behrouz; Tafreshi, Reza; Mohammadpour, Javad; Franchek, Matthew; Grigoriadis, Karolos.

2014 American Control Conference, ACC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 5558-5563 6859299.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ebrahimi, B, Tafreshi, R, Mohammadpour, J, Franchek, M & Grigoriadis, K 2014, Stabilizing dynamic control design for systems with time-varying delay in control loop. in 2014 American Control Conference, ACC 2014., 6859299, Institute of Electrical and Electronics Engineers Inc., pp. 5558-5563, 2014 American Control Conference, ACC 2014, Portland, OR, United States, 4/6/14. https://doi.org/10.1109/ACC.2014.6859299
Ebrahimi B, Tafreshi R, Mohammadpour J, Franchek M, Grigoriadis K. Stabilizing dynamic control design for systems with time-varying delay in control loop. In 2014 American Control Conference, ACC 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 5558-5563. 6859299 https://doi.org/10.1109/ACC.2014.6859299
Ebrahimi, Behrouz ; Tafreshi, Reza ; Mohammadpour, Javad ; Franchek, Matthew ; Grigoriadis, Karolos. / Stabilizing dynamic control design for systems with time-varying delay in control loop. 2014 American Control Conference, ACC 2014. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 5558-5563
@inproceedings{72274e6ce95649babc53eacea1f0cee1,
title = "Stabilizing dynamic control design for systems with time-varying delay in control loop",
abstract = "Synthesis of nth-order dynamic systems with time-varying delay in the control loop is considered in this paper. First-order Pad{\'e} approximation is sought to solve the infinite-dimensional problem of the pure delay. Although the approximation describes the problem in a finite-dimensional state space, it poses internal dynamics instability inherited from the resulted non-minimum phase system. The unstable internal dynamics restricts the system closed-loop bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the overall system dynamics is explored in terms of unstable internal dynamics and input/output pairs. The system internal dynamics is used to design a parameter-varying dynamic compensator which stabilizes the internal dynamics based on a desired tracking error profile. The presented dynamic compensator is used to develop a dynamic controller whose parameter-varying gains are explicitly determined in a systematic and straightforward manner. The proposed approach is used to design a controller for a spark ignition lean-burn engine with large time-varying delay in the control loop. The results are demonstrated against a baseline PI controller combined with a parameter-varying Smith predictor to compensate for the time-varying delay.",
keywords = "Automotive, Delay systems, Time-varying systems",
author = "Behrouz Ebrahimi and Reza Tafreshi and Javad Mohammadpour and Matthew Franchek and Karolos Grigoriadis",
year = "2014",
doi = "10.1109/ACC.2014.6859299",
language = "English",
isbn = "9781479932726",
pages = "5558--5563",
booktitle = "2014 American Control Conference, ACC 2014",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - GEN

T1 - Stabilizing dynamic control design for systems with time-varying delay in control loop

AU - Ebrahimi, Behrouz

AU - Tafreshi, Reza

AU - Mohammadpour, Javad

AU - Franchek, Matthew

AU - Grigoriadis, Karolos

PY - 2014

Y1 - 2014

N2 - Synthesis of nth-order dynamic systems with time-varying delay in the control loop is considered in this paper. First-order Padé approximation is sought to solve the infinite-dimensional problem of the pure delay. Although the approximation describes the problem in a finite-dimensional state space, it poses internal dynamics instability inherited from the resulted non-minimum phase system. The unstable internal dynamics restricts the system closed-loop bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the overall system dynamics is explored in terms of unstable internal dynamics and input/output pairs. The system internal dynamics is used to design a parameter-varying dynamic compensator which stabilizes the internal dynamics based on a desired tracking error profile. The presented dynamic compensator is used to develop a dynamic controller whose parameter-varying gains are explicitly determined in a systematic and straightforward manner. The proposed approach is used to design a controller for a spark ignition lean-burn engine with large time-varying delay in the control loop. The results are demonstrated against a baseline PI controller combined with a parameter-varying Smith predictor to compensate for the time-varying delay.

AB - Synthesis of nth-order dynamic systems with time-varying delay in the control loop is considered in this paper. First-order Padé approximation is sought to solve the infinite-dimensional problem of the pure delay. Although the approximation describes the problem in a finite-dimensional state space, it poses internal dynamics instability inherited from the resulted non-minimum phase system. The unstable internal dynamics restricts the system closed-loop bandwidth and leads to an imperfect tracking performance. To circumvent this problem, the overall system dynamics is explored in terms of unstable internal dynamics and input/output pairs. The system internal dynamics is used to design a parameter-varying dynamic compensator which stabilizes the internal dynamics based on a desired tracking error profile. The presented dynamic compensator is used to develop a dynamic controller whose parameter-varying gains are explicitly determined in a systematic and straightforward manner. The proposed approach is used to design a controller for a spark ignition lean-burn engine with large time-varying delay in the control loop. The results are demonstrated against a baseline PI controller combined with a parameter-varying Smith predictor to compensate for the time-varying delay.

KW - Automotive

KW - Delay systems

KW - Time-varying systems

UR - http://www.scopus.com/inward/record.url?scp=84905674369&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905674369&partnerID=8YFLogxK

U2 - 10.1109/ACC.2014.6859299

DO - 10.1109/ACC.2014.6859299

M3 - Conference contribution

AN - SCOPUS:84905674369

SN - 9781479932726

SP - 5558

EP - 5563

BT - 2014 American Control Conference, ACC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

ER -