SavedAdd your journal

Journals / Avrupa Bilim ve Teknoloji Dergisi / 2026 / Sayı: 25

Diffusivity Control of Heat Transfer Process Using Optimality Conditions

Optimallik Koşulları Kullanılarak Isı Transferi İşleminin Yayılım Kontrolü

Seda Göktepe(YILDIZ TEKNİK ÜNİVERSİTESİ)0000-0001-7146-0846
Pages
341–346
Publication Date
2021-08-31
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The feasibility and applicability of the proposed solution is demonstrated by numerical simulations generated in MATLAB.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a distributed parameter system expressed as a parabolic partial differential equation governed by a diffusivity control is considered.
📊
Key Findings & Data:A modal space expansion approach is used to convert the distributed parameter system into a lumped parameter system.
💡
Conclusion & Impact:The feasibility and applicability of the proposed solution is demonstrated by numerical simulations generated in MATLAB.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:yayılım kontrolü · maksimum prensibi · parabolik KDD

Abstract

In this paper, a distributed parameter system expressed as a parabolic partial differential equation governed by a diffusivity control is considered. A modal space expansion approach is used to convert the distributed parameter system into a lumped parameter system. Thereafter, Pontryagin’s maximum principle is used to compute the optimal control function that leads to a nonlinear two-point boundary value problem (TPBVP). An iterative numerical technique, variation of extremals is used to solve the nonlinear TPBVP. The feasibility and applicability of the proposed solution is demonstrated by numerical simulations generated in MATLAB.

Özet

Bu çalışmada, yayılım kontrolü ile yönetilen parabolik kısmi diferansiyel denklem olarak ifade edilen dağıtılmış bir parametre sistemi ele alınmıştır. Dağıtılmış parametre sistemini toplu bir parametre sistemine dönüştürmek için bir özfonksiyon genişletme yaklaşımı kullanılmıştır. Bundan sonra, Pontryagin'in maksimum prensibi, doğrusal olmayan iki noktalı sınır değeri problemine yol açan optimum kontrol fonksiyonunu hesaplamak için kullanılmıştır. Doğrusal olmayan iki noktalı sınır değer problemini çözmek için, yinelemeli sayısal bir teknik, variation of extremals, kullanılmıştır. Önerilen çözümün fizibilitesi ve uygulanabilirliği, MATLAB'da oluşturulan sayısal simülasyonlarla gösterilmiştir.

🔖

Cite This Article

Göktepe, S. (2021). Diffusivity Control of Heat Transfer Process Using Optimality Conditions. Avrupa Bilim ve Teknoloji Dergisi, Sayı: 25, 341–346. https://doi.org/10.31590/ejosat.909910

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. Guliyev, H. F., & Jabbarova, K. S. (2010). The exact controllability problem for the second order linear hyperbolic equation. Differential Equations and Control Processes, 3, 10-19.
  2. Khapalov, A. Y. (2003). Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: A qualitative approach. SIAM journal on control and optimization, 41(6), 1886-1900.
  3. Kirk, D. E. (2004). Optimal control theory: an introduction. New York: Dover Publications.
  4. Korpeoglu, S. G., & Kucuk, I. (2018, August). Optimal control of a bilinear system with a quadratic cost functional. In Fourth International Conference on Computing Communication Control and Automation (ICCUBEA) (pp. 1-6).
  5. Lin, P., Leid, P., & Gao, H. (2007). Bilinear control system with the reaction‐diffusion term satisfying Newton's law. ZAMM‐Journal of Applied Mathematics and Mechanics, 87(1), 14-23.
  6. Lin, P., Gao, H., & Liu, X. (2007). Some results on controllability of a nonlinear degenerate parabolic system by bilinear control. Journal of mathematical analysis and applications, 326(2), 1149-1160.
  7. Pedersen, M. (1999). Functional analysis in applied mathematics and engineering. USA: CRC press.
  8. Pontryagin, L. S. (1959). Optimal regulation processes. Uspekhi Matematicheskikh Nauk, 14(1), 3-20.
  9. Xu, C., Ou, Y., & Schuster, E. (2007, December). POD-based reduced order optimal control of parabolic PDE systems via diffusivity-interior-boundary actuation. In 46th IEEE Conference on Decision and Control (pp. 3519-3524).
  10. Xu, C., Ou, Y., & Schuster, E. (2011). Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction. Automatica, 47(2), 418-426.