کنترل مد لغزشی سیستم ربات دوچرخ تعادلی در حضور عدم قطعیت‌های ساختاری و غیر ساختاری موجود در معادلات دینامیکی و بدون نیاز به معادلات سینماتیکی
محورهای موضوعی : مهندسی برق و کامپیوترمحمدرضا سلطانپور 1 * , رضا غلامي 2
1 - دانشگاه علوم و فنون هوایی شهید ستاری
2 - دانشگاه علوم و فنون هوایی شهید ستاری
کلید واژه: ربات دوچرخ تعادلی کنترل مد لغزشیعدم قطعیت‌های ساختاری و غیر ساختاری معادلات سینماتیک,
چکیده مقاله :
در این مقاله، راهکارهایی برای کنترل سیستم ربات دوچرخ تعادلی در حضور عدم قطعیت‌های موجود در معادلات دینامیکی و بدون نیاز به معادلات سینماتیکی پیشنهاد می‌گردد. بدین منظور در ابتدا معادلات دینامیکی این سیستم به حوزه خطا انتقال داده می‌شود و سپس این معادلات به دو زیرسیستم فروتحریک و تمام‌تحریک کاملاً مستقل تقسیم‌بندی می‌گردند. در ادامه برای کنترل زیرسیستم فروتحریک، دو کنترل‌کننده مد لغزشی کاملاً متفاوت ارائه می‌گردد که قادرند این زیرسیستم را در حضور عدم قطعیت‌های ساختاری و غیر ساختاری دارای پایداری مجانبی سراسری نمایند. پس از آن برای کنترل زیرسیستم تمام تحریک نیز کنترل مد لغزشی پیشنهاد می‌شود که این زیرسیستم را در حضور عدم قطعیت‌های موجود دارای پایداری مجانبی سراسری می‌کند. از آنجا که این دو زیرسیستم کاملاً از یکدیگر مستقل می‌باشند، بنابراین اثبات پایداری مجانبی سراسری آنها، اثبات پایداری مجانبی سراسری سیستم حلقه بسته را مهیا می‌سازد. جداسازی زیرسیستم‌های ربات دوچرخ تعادلی، نیاز به استفاده از معادلات سینماتیک را مرتفع نموده و این امر باعث می‌شود تا حضور عدم قطعیت‌های ساختاری تأثیری بر دقت ردگیری متغیرهای حالت سیستم حلقه بسته نداشته باشند. نهایتاً برای بررسی عملکرد کنترل‌کننده‌های پیشنهادی و مقایسه نتایج عملکرد آنها، شبیه‌سازی‌هایی در 3 مرحله بر روی سیستم ربات دوچرخ تعادلی پیاده‌سازی می‌شود. اثبات ریاضی و نتایج شبیه‌سازی‌ها عملکرد مطلوب راهکارهای پیشنهادی را نشان می‌دهند.
In this paper, we proposed solutions for controlling the two-wheel self-balancing robot system in the presence of uncertainties in dynamical equation and without the need for kinematic equations. For this purpose, the dynamical equations of this system are initially transmitted to the domain of error, then these equations are divided into two independent subsystems, one of which is an under-actuated system and the other is fully actuated system. In order to control the under-actuated subsystem, two completely different sliding mode controllers are proposed that are able to provide this subsystem in the presence of structured and un-structured uncertainties with global asymptotic stability. Subsequently, in order to control the fully under-actuated subsystem, a sliding mode control is proposed to provide this subsystem in the presence of existing uncertainties with global asymptotic stability. Since these two subsystems are completely independent of each other, their global asymptotic stability proofs prove the global asymptotic stability of the closed-loop system. The separation of two-wheeled self-balancing robot sub-systems eliminates the need to use the kinematic equations, and this causes the presence of structured uncertainties to have no effect on the accuracy of tracing the closed-loop system state variables. Finally, to evaluate the performance of the proposed controllers and compare their performance results, three-stage simulations are implemented on the two-wheeled self-balancing robot system. Mathematical proofs and simulation results show the desired performance of the proposed solutions.
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