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Numerical Solution of the Controlled Harmonic Oscillator by Homotopy Perturbation Method | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 6، دوره 2، شماره 1، تیر 2017، صفحه 77-91 اصل مقاله (533.85 K) | ||
| نوع مقاله: Research Article | ||
| نویسنده | ||
| Seyed Mehdi Mirhosseini-Alizamini* | ||
| Department of Mathematics, Payame Noor University (PNU), Tehran, Iran | ||
| چکیده | ||
| The controlled harmonic oscillator with retarded damping, is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems. In this paper, to solve this problem, we presented an analytical method. This approach is based on the homotopy perturbation method. The solution procedure becomes easier, simpler and more straightforward. In order to use the proposed method, a control design algorithm with low computational complexity is presented. Through the finite iterations of the proposed algorithm, a suboptimal control law is obtained for the problems. Finally, the obtained results have been compared with the exact solution of the controlled harmonic oscillator and variational iteration method, so that the high accuracy of the results is clear. | ||
| کلیدواژه‌ها | ||
| Suboptimal control؛ Harmonic oscillator؛ Damping؛ Homotopy perturbation method | ||
| عنوان مقاله [English] | ||
| حل عددی نوسانگر هارمونیک کنترل شده با استفاده از روش اختلال هموتوپی | ||
| نویسندگان [English] | ||
| سید مهدی میرحسینی عالیزمینی | ||
| استادیار ریاضی کاربردی، تهران، گروه ریاضی، دانشگاه پیام نور | ||
| چکیده [English] | ||
| مسأله نوسانگر هارمونیک کنترل شده با دمپینگ، دسته‌ی مهمی از مسائل کنترل بهینه است، که نقش مهمی در زمینه پدیده نوسانی در سیستم‌های مهندسی غیرخطی ایفا می‌کند. در این مقاله، برای حل این مسأله، روش تحلیلی ارائه می‌شود. این رویکرد بر اساس روش اختلال هموتوپی پایه ریزی شده است. فرایند حل آسان و ساده است. برای این منظور، یک الگوریتم طراحی کنترل با پیچیدگی محاسبات کم، پیشنهاد می‌شود. هم چنین، به کمک تکرارهای متناهی از الگوریتم پیشنهادی، یک قانون کنترل زیر بهینه برای مسأله به دست می‌آید. در نهایت، نتایج به دست آمده با جواب دقیق مسأله نوسانگر هارمونیک و سایر نتایج حاصله از آثار قبلی مقایسه شده، که به وضوح، دقت بالای نتایج آشکار است. | ||
| کلیدواژه‌ها [English] | ||
| کنترل زیر بهینه, نوسانگر هارمونیک, دمپینگ, روش اختلال هموتوپی | ||
| مراجع | ||
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