طراحی قانون هدایت پیش‌بین در یک مساله هدایت دو بعدی با وجود محدودیت در شتاب ورودی

نوع مقاله : مقاله پژوهشی

نویسنده

عضو هیات علمی / گروه مهندسی برق، دانشکده مهندسی، دانشگاه خلیج فارس

چکیده

در این مقاله، به منظور طراحی قانون هدایت پیش‌بین، یک روش مبتنی بر نامساوی ماتریسی خطی LMI پیشنهاد می‌گردد. برای رسیدن به این هدف، ابتدا با نوشتن معادله‌های حاکم بر حرکت جسم و هدف در دستگاه مختصات دو بعدی، مساله هدایت و قانون هدایت پیش‌بین فرموله می‌شود. در قانون هدایت پیش‌بین، با استفاده از یک مدل دینامیکی رفتار سیستم هدایت می‌تواند پیش‌بینی شود. سپس در هر لحظه دلخواه از زمان، یک سیگنال فرمان به گونه‌ای محاسبه می‌گردد تا یک تابع هزینه مینیمم شود. در این مطالعه برای طراحی قانون هدایت پیش‌بین، یک قانون هدایت متناسب با تغییرات زاویه خط دید، با بهره متغیر (نامعلوم) انتخاب می‌گردد. با استفاده از مفاهیم و تعاریف LMI، مساله طراحی قانون هدایت پیش‌بین به حل یک مساله دیگر مینیمم‌یابی تبدیل می‌گردد. در هر لحظه از زمان، چنین مساله بهینه‌یابی مبتنی بر LMI می‌تواند به صورت عددی حل شود. سپس با توجه به جواب بدست آمده، بهره قانون هدایت پیشنهادی بروز‌‌رسانی شود. الگوریتم هدایت پیشنهادی در یک سیستم هدایت دو بعدی شبیه‌سازی می‌گردد. نتایج شبیه‌سازی بیانگر اثر بخشی و کارآیی روش هدایت پیشنهادی در مقایسه با روش هدایت موجود می باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Model predictive guidance law design in a two-dimensional guidance problem in presence of Input constraint

نویسنده [English]

  • Valiollah Ghaffari
Assistant Professor / Department of Electrical Engineering, School of Enginnering, Persian Gulf University
چکیده [English]

In this paper, an LMI based algorithm is mainly addressed to design a model predictive guidance law in presence of the input acceleration constraint. For achieving this purpose, firstly, the model predictive guidance issue is mathematically formulated in a two-dimensional problem. In the proposed algorithm, the future behavior of the guidance problem can be predicted by using of a dynamical model. The commanded acceleration would be determined, at each certain time instant, while a quadratic cost function is minimized. In this study, an acceleration command proportional to the line-of-sight (LOS) rate is considered as the predictive guidance policy with unknown variable gain. Then the model predictive guidance issue would be translated into another minimization problem subjected to some linear matrix inequalities (LMI). Hence, at each known time instant, such an optimization problem can be numerically solved in the real-time applications. Then the gain of the proposed guidance algorithm can be automatically updated. The proposed method will be used in a typical two-dimensional guidance example. The simulation results will show the effectiveness of the suggested method in comparing with the existing guidance algorithms.

کلیدواژه‌ها [English]

  • Linear matrix inequality
  • model predictive guidance law
  • guidance law
  • constrained system
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