ارائه یک سیستم فوق‌آشوب جدید و تحقق فیزیکی آن از طریق طراحی و ساخت یک مدار الکترونیکی آنالوگ

نوع مقاله: مقاله پژوهشی فارسی

نویسندگان

1 بخش کنترل و الکترونیک، دانشکده مهندسی برق، دانشگاه یزد، یزد، ایران.

2 بخش مهندسی قدرت و کنترل، دانشکده مهندسی برق و کامپیوتر، دانشگاه شیراز، شیراز، ایران

چکیده

در این مقاله، سیستم فوق‌آشوبی جدیدی تنها با یک نقطه تعادل مبدا ارائه می‌گردد که بر پایه‌ی سیستم‌ آشوبی معمولی لیو ساخته شده است. به‌منظور نشان دادن وجود پدیده فوق‌آشوب در این سیستم‌، تعدادی از معیارهای محاسباتی و ترسیمی مورد بررسی و تحلیل قرار می‌گیرند. از مهمترین این معیارها و شاخص‌ها می‌توان به بررسی اتلافی بودن، اثبات ناپایداری نقطه تعادل، ترسیم صفحه‌های فاز جاذب عجیب سیستم، بررسی پاسخ‌های زمانی‌متغیرهای حالت، محاسبه نماهای لیاپانوف، محاسبه بعد کسری سیستم و آنالیز حساسیت شدید پاسخ‌های متغیرهای حالت به تغییرات اندک در شرایط اولیه اشاره کرد. در ادامه نشان داده می‌شود که سیستم فوق‌آشوب پیشنهادی دارای دو نمای لیاپانوف مثبت بسیار بزرگ در مقایسه با سیستم‌های فوق‌آشوبی دیگر است. بررسی‌ها بر روی سیستم معرفی‌شده، این نتیجه را نمایان می‌کند که تغییر هر کدام از پارامترهای سیستم، باعث ایجاد رفتارهای گوناگون دینامیکی از جمله آشوب معمولی (آشوب بعد پایین)، سیکل‌حدی، شبه‌پریودیک و فوق‌آشوبی می‌شود. برای تحقق فیزیکی سیستم فوق‌آشوبی، مدار الکترونیکی آنالوگی طراحی می‌شود که از عناصر ساده‌ای همچون مقاومت‌های خطی، خازن‌های خطی، تقویت‌کننده‌های عملیاتی و ضرب‌کننده‌های آنالوگ تشکیل شده است. در ادامه، ابتدا با استفاده از نرم‌افزار ORCAD16.6 مدار را شبیه‌سازی کرده و در مرحله بعد مدار به صورت عملی در آزمایشگاه ساخته شده و مورد تست واقعی قرار می‌گیرد. نتایج حاصل از شبیه‌سازی با نرم‌افزار ORCAD16.6 و داده‌های آزمایشگاهی نشان می‌دهند که پدیده‌ی غیرخطی فوق‌آشوب در مدار آنالوگ رخ می‌دهد.

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