طراحی یک تخمینگر بر پایه‌ی اصل دوگانی، به منظور تخمین برخط تاخیر زمانی نامعلوم و متغیر با زمان در سیستمهای LTI

نوع مقاله : مقاله برق

نویسندگان

1 دانشکده مهندسی برق وکامپیوتر، دانشگاه بیرجند، بیرجند، ایران

2 دانشکده مهندسی برق و کامپیوتر، دانشگاه بیرجند، بیرجند، ایران

10.22075/jme.2019.17315.1696

چکیده

در این مقاله یک رؤیتگر نوین، برای تخمین آنلاین تأخیر زمانی ، در سیستم های پیوسته زمان SISO-LTI ، با تأخیر متغیر با زمان و نامعلوم در ورودی کنترلی، طراحی شده است. واضح است که تابع تبدبل لاپلاس یک سیستم تأخیر دار، شامل یک عامل تأخیر زمانی است. در این مقاله فرض بر این است که، تنها پارامتر نامعلوم و متغیر با زمان در سیستم، پارامتر تأخیر زمانی سیستم است. ایده‌ی اصلی مورد استفاده در طراحی رؤیتگر پیشنهادی، بر پایه ی برقراری اصل دوگانی، بین کنترلر و رؤیتگر می‌باشد. به این صورت که، بطور غیر مستقیم، از ساختار کنترلر تطبیقی مستقیم(MRAS)، برای طراحی یک تخمینگر، استفاده‌ می‌شود. بدین منظور، قسمتهای اصلی در یک سیستم کنترلی MRAS ، به نحوی سازماندهی می‌شوند که، طراحی کنترلر، منجر به طراحی تخمینگر تأخیر، در مسئله‌ی دوگان خواهدشد. در واقع قاعده‌ی تطبیق، در مسئله‌ی طراحی کنترلر، همان مکانیزم تخمینگر، در مسئله‌ی دوگان را ، بیان خواهد نمود. همچنین در راستای محاسبه‌ی مکانیزم تخمین، از دو روش مبتنی بر تئوی لیاپانوف و مبتنی بر قاعده‌ی MIT ، استفاده می‌شود. نهایتا، نتایج شبیه سازی ها، عملکرد نسبتاً مطلوب تخمینگر پیشنهادی، در مواجهه با تأخیرهای متغیر با زمان و نامعلوم را نشان می‌دهند.

کلیدواژه‌ها


عنوان مقاله [English]

Design of an Estimator Based on Duality Principle for Unknown and Time-varying Delay Estimation in LTI Systems

نویسندگان [English]

  • hadi chahkandi nejad 1
  • mohsen farshad 1
  • ramazan havangi 2
1 Department of Electrical and Computer Engineering, University of Birjand, Birjand, Iran
2 department of electrical and computer engineering, university of birjand, birjand, iran
چکیده [English]

Abstract: In this article, a novel observer has been designed for the online estimation of time delay in SISO-LTI continuous time systems with uncertain and time variant delay in the control input. It is obvious that Laplace transfer function of a delayed system includes a time delay factor. In this paper, it is assumed that the only uncertain and time variant parameter in the system is the very system’s time delay parameter. The main idea used in designing the proposed observer is based on the establishment of duality principle between controller and observer, such that a direct adaptive controller structure (MRAS) is indirectly used for designing an estimator. For this, the main sections in an MRAS control system are organized the way that designing the controller will lead to designing the delay estimator in dual problem. In fact, adaptation rule in designing the controller will express the same estimator mechanism in the dual problem. Also, in computing the estimation mechanism, the two methods, one based on Lyapunov Theory and the other based on MIT rule, are used. Eventually, simulation results are indicative of the rather desirable performance of the proposed estimator in dealing with uncertain and time varying delays.

کلیدواژه‌ها [English]

  • Duality principle
  • LTI systems
  • Input time varying delay
  • Uncertainty
  • Delay estimator
  • Adaptation rule
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