استفاده از حاشیه‌های بهره و فاز برای طراحی کنترل‌کننده‌های مقاوم به وسیله تئوری بازخورد کمی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشگاه گیلان، رشت، ایران

چکیده

مدلسازی عدم‌قطعیت در قالب بهره و فاز اضافی و محاسبه حاشیه‌های مقاومت بر اساس آن‌ها یکی از روش‌های متداول طراحی مقاوم سیستم‌های کنترلی و مقایسه مقاومت آن‌هاست. از طرفی یک روش‌ مرسوم کنترل مقاوم در حوزه‌ی فرکانس، تئوری بازخورد کمی است که به علت مدلسازی عدم‌قطعیت در قالب نامعینی پارامتری با محدوده‌ی مشخص، با چالش‌هایی از جمله عدم امکان مقایسه‌ی کنترل‌کننده‌ها و طراحی غیر خودکار همراه است. همچنین شرایط سیستم به ازای مقادیر نامعینی پارامتری خارج از بازه طراحی مشخص نیست. در این پژوهش با استفاده از مدلسازی عدم‌قطعیت در قالب بهره و فاز در روش تئوری بازخورد کمی این مشکلات مرتفع شده است. به این منظور حاشیه‌ای ترکیبی، متشکل از بهره و فاز، معرفی شده که با استفاده از نمودار نیکولز اصلاح‌شده و نامعادلات مرتبط با معیارهای تئوری بازخورد کمی، محاسبه می‌شود. کنترل موقعیت یک موتور جریان مستقیم به عنوان نمونه‌ی مطالعاتی انتخاب شده و برای آن کنترل‌کننده‌ی تناسبی-مشتق‌گیر بهینه و مقاومی طراحی شده است. بررسی نتایج به دو شیوه عددی و تجربی صورت پذیرفته است. نتایج نشان می‌دهد روش پیشنهادی توانسته است به خوبی نواقص روش تئوری بازخورد کمی را رفع نماید. کنترل‌کننده‌ی طراحی شده در این حالت نسبت به کنترل‌کننده‌ طراحی شده به روش مرسوم تئوری بازخورد کمی نتایج مطلوب‌تری داشته و حتی به ازای مقادیر نامعینی پارامتری بالاتر از محدوده‌ی طراحی، توانسته است عملکرد خود را به نحو بهتری حفظ نماید.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Application of Gain and Phase Margins for Designing Robust Controllers within Quantitative Feedback Theory

نویسندگان [English]

  • Mohammadreza Hadipour
  • Ali Jamali
  • Nader Nariman-zadeh
  • Behnam Miripour Fard
Faculty of Mechanical Engineering, Guilan University, Rasht, Iran
چکیده [English]

Modeling uncertainty in the form of additional gain and phase and calculating robustness margins based on them is one of the standard methods in designing robust control systems and comparing their robustness. On the other hand, one of the prevalent methods of robust control in the frequency domain is “Quantitative Feedback Theory”, which, due to modeling uncertainty in the form of parametric uncertainty with a specified range, faces challenges such as the inability to compare controllers and non-automated design. Additionally, the system's conditions for parametric uncertainty values outside the design range are unknown. This research addresses these issues using uncertainty modeling in the form of gain and phase within the quantitative feedback theory method. To this end, a combined margin consisting of gain and phase is introduced and calculated using a modified Nichols chart and inequalities related to design criteria in the quantitative feedback theory method. The position control of a DC motor is selected as a case study, and an optimal and robust proportional-derivative controller is designed for it. The results are examined both numerically and experimentally which show that the proposed method effectively overcomes the shortcomings of the quantitative feedback theory method. The controller designed in this manner gains more favorable results than the controller designed using the conventional quantitative feedback theory method and even maintains its performance better for parametric uncertainty values higher than the design range.

کلیدواژه‌ها [English]

  • Robust Control
  • Uncertainty
  • Gain Margin
  • Phase Margin
  • Quantitative Feedback Theory
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