A Simplified Approach to Analyze Complementary Sensitivity Trade-offs in Continuous-Time and Discrete-Time Systems

Neng Wan, Dapeng Li, Naira Hovakimyan

Research output: Contribution to journalArticle

Abstract

Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by <formula><tex>$1/\omega^2$</tex></formula> is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither Cauchy integral theorem nor Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
DOIs
StatePublished - Jan 1 2019

Fingerprint

Transfer functions
Feedback

Keywords

  • Complementary sensitivity Bode integral
  • Discrete-time systems
  • Frequency-domain analysis
  • Harmonic analysis
  • Measurement uncertainty
  • Poles and zeros
  • Sensitivity
  • control trade-offs
  • linear systems
  • simplified approach

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

@article{aee657c9d6b84950b8df9fbc27c3ae2d,
title = "A Simplified Approach to Analyze Complementary Sensitivity Trade-offs in Continuous-Time and Discrete-Time Systems",
abstract = "Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by $1/\omega^2$ is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither Cauchy integral theorem nor Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.",
keywords = "Complementary sensitivity Bode integral, Discrete-time systems, Frequency-domain analysis, Harmonic analysis, Measurement uncertainty, Poles and zeros, Sensitivity, control trade-offs, linear systems, simplified approach",
author = "Neng Wan and Dapeng Li and Naira Hovakimyan",
year = "2019",
month = "1",
day = "1",
doi = "10.1109/TAC.2019.2934010",
language = "English (US)",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - JOUR

T1 - A Simplified Approach to Analyze Complementary Sensitivity Trade-offs in Continuous-Time and Discrete-Time Systems

AU - Wan, Neng

AU - Li, Dapeng

AU - Hovakimyan, Naira

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by $1/\omega^2$ is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither Cauchy integral theorem nor Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.

AB - Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by $1/\omega^2$ is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither Cauchy integral theorem nor Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.

KW - Complementary sensitivity Bode integral

KW - Discrete-time systems

KW - Frequency-domain analysis

KW - Harmonic analysis

KW - Measurement uncertainty

KW - Poles and zeros

KW - Sensitivity

KW - control trade-offs

KW - linear systems

KW - simplified approach

UR - http://www.scopus.com/inward/record.url?scp=85070671435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070671435&partnerID=8YFLogxK

U2 - 10.1109/TAC.2019.2934010

DO - 10.1109/TAC.2019.2934010

M3 - Article

AN - SCOPUS:85070671435

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

ER -