طراحی رؤیتگر مد لغزشی تطبیقی غیر شكننده برای دسته‌ای از سامانه‌های مرتبه كسری شبه‌خطی دارای تأخیر حالت
محورهای موضوعی : مهندسی برق و کامپیوترمجيد پرويزيان 1 , خسرو خانداني 2 , وحيد جوهري مجد 3 *
1 - دانشگاه تربيت مدرس
2 - دانشگاه اراك
3 - دانشگاه تربيت مدرس
کلید واژه: رؤیتگر تطبیقی غیر شكننده, سامانه مرتبه كسری شبه‌خطی, مد لغزشی, نابرابری‌های ماتریسی خطی,
چکیده مقاله :
سامانه‌های مرتبه كسری و سیستم‌های كنترل مرتبه كسری در سال‌های اخیر به صورت فزاینده‌ای مورد توجه پژوهشگران در حوزه‌های مختلف علوم و مهندسی بوده است. از دیگر سو، بسیاری از رویكردهای كنترلی مرتبه صحیح برای استفاده در مورد سامانه‌های مرتبه كسری توسعه داده شده‌اند. با وجود این، پژوهش‌های انگشت‌شماری در زمینه گسترش رؤیتگرهای كلاسیك به حالت كسری انجام شده است. با توجه به گسترش روزافزون كاربردهای سامانه‌های مرتبه كسری، توسعه رؤیتگرهای مرتبه كسری نیز ضروری به نظر می‌رسد. در این مقاله، مسئله طراحی یك رؤیتگر مد لغزشی تطبیقی غیر شکننده برای دسته‌ای از سامانه‌های مرتبه کسری شبه‌خطی دارای تأخیر زمانی بررسی شده است. ابتدا حالت‌های سیستم مرتبه کسری تأخیردار با قسمت غیر خطی سازگار با استفاده از روش کنترل مد لغزشی تخمین زده شده و سپس مسئله تخمین حالت برای سیستم مرتبه کسری با قسمت غیر خطی غیر سازگار بررسی شده است. پایداری مجانبی دینامیک خطای تخمین با استفاده از روش تحلیل پایداری لیاپانوف برای سامانه‌های مرتبه کسری اثبات گردیده و شرایط كافی پایداری در قالب نابرابری‌های ماتریسی خطی استخراج شده است. در نهایت عملكرد مؤثر روش ارائه‌شده در این مقاله با شبیه‌سازی بر روی یك مثال عددی و نیز مطالعه موردی بر روی یك سامانه اقتصادی مرتبه كسری نشان داده شده است.
In recent years, fractional order systems and fractional order control have increasingly attracted the attention of researchers in various fields of science and engineering. On the other hand, numerous control approaches have been extended in order to be utilized in fractional order systems. Despite this fact, few research studies have been devoted to generalizing integer order observers to fractional order ones. Since the applications of fractional order systems are increasing, developing fractional order observers seems to be essential. In this paper the problem of non-fragile adaptive sliding mode observer design for a class of fractional-order nonlinear systems with time delay is addressed. First, the states of the fractional-order pseudo-linear time-delay system with matched nonlinearity are estimated employing the sliding mode control method. Then the state estimation problem of fractional order systems with mismatched nonlinearity has been investigated. The asymptotic stability of the estimation error dynamics is proven by employing the Lyapunov stability analysis method for fractional order systems. The sufficient stability conditions are derived in the form of Linear Matrix Inequalities (LMIs). Eventually, the effective performance of the proposed approach in this paper has been corroborated through simulation of a numerical example and also a case study of a fractional order economic system.
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