Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

Mohammad Mehdi Mardani*, Navid Vafamand, Mohammad Hassan Khooban, Tomislav Dragicevic, Frede Blaabjerg

*Corresponding author

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)

Abstract

This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.
Original languageEnglish
JournalTransactions of the Institute of Measurement and Control
Volume41
Issue number3
Pages (from-to)842-858
Number of pages17
ISSN0142-3312
DOIs
Publication statusPublished - Feb 2019

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fuzzy systems
Fuzzy systems
controllers
polynomials
disturbances
Polynomials
Controllers
hardware-in-the-loop simulation
approach control
systems stability
arts
Asymptotic stability
feedback control
System stability
Closed loop systems
MATLAB
balls
Decomposition
saturation
Hardware

Keywords

  • Sum-of-squares
  • uncertain polynomial fuzzy models
  • non-fragile controller
  • L1 performance
  • robust controller
  • input saturation

Cite this

@article{33078f7761534102a1b7ea34ffcb41c1,
title = "Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance",
abstract = "This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.",
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Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance. / Mardani, Mohammad Mehdi; Vafamand, Navid; Khooban, Mohammad Hassan; Dragicevic, Tomislav; Blaabjerg, Frede.

In: Transactions of the Institute of Measurement and Control, Vol. 41, No. 3, 02.2019, p. 842-858.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Blaabjerg, Frede

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AB - This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.

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