SavedAdd your journal

Journals / Eskişehir Osmangazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi / 2005 / Cilt: 18 - Sayı: 2

SABİT GERİBESLEMELİ TERS SARKAÇ SİSTEMİNİN YAPISAL GÜRBÜZ KARARLILIK ANALİZİ

STRUCTURED ROBUST STABILITY ANALYSIS OF AN INVERTED PENDULUM SYSTEM WITH A FIXEDFEEDBACK

AHMET YAZICI
ABDURRAHMAN KARAMANCIOĞLU
Pages
55–70
DOI
—
🏛️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)

A simulation test for validity of the results is provided.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Robust stability analysis of inverted pendulum system with a fixed linear quadratic feedback is carried out using µ analysis tools.
📊
Key Findings & Data:A mathematical model of inverted pendulum system is presented and linearized about the desired equilibrium point.
💡
Conclusion & Impact:A simulation test for validity of the results is provided.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Robust stability analysis of inverted pendulum system with a fixed linear quadratic feedback is carried out using µ analysis tools. A mathematical model of inverted pendulum system is presented and linearized about the desired equilibrium point. A linear quadratic control feedback matrix is used in the configuration of the nominal inverted pendulum system for its stabilization. After this, uncertainties in the inverted pendulum with a fixed feedback, is modeled in linear fractional transformation form , which is suitable for structured singular value computation. Both parametric and modeling uncertainties are considered in the inverted pendulum system. After deriving out uncertain system model, mixed µ analysis method which is a structured uncertainty analysis method, is used to compute the uncertainty bound that does not cause instability of the inverted pendulum under feedback. A simulation test for validity of the results is provided.

Özet

Sabit doğrusal-kuadratik kontrol altındaki ters sarkaç sistemindeki belirsizliklere karşı gürbüzlük analizi, µ analiz araçları kullanılarak yapılmıştır. Ters sarkaç sisteminin matematiksel modeli verilip, çalışma noktası etrafında doğrusallaştırılmaktadır. Nominal ters sarkaç sisteminin kararlaştırılması için doğrusal-kuadratik kontrol geri besleme matrisi kullanılmaktadır. Yapısal tekil değer hesaplanmasında kullanılmak üzere, sabit doğrusal-kuadratik kontrol altında olan ters sarkaç sistemindeki belirsizlikler doğrusal kesirli dönüşümler kullanılarak modellenmektedir. Ters sarkaç sistemindeki parametrik ve modellemeden kaynaklanan belirsizlikler dikkate alınmıştır. Belirsizlik modeli oluşturulduktan sonra, karışık µ analizi (bir yapısal belirsizlik analiz yöntemi) yöntemi kullanılarak, geri belsem altındaki ters sarkaç sisteminde kararsızlığa neden olmayan belirsizlik sınırı bulunmaktadır. Bulunan sonuçları doğrulayan simülasyonlar da verilmektedir.

🔖

Cite This Article

YAZICI, A., KARAMANCIOĞLU, A. (2005). SABİT GERİBESLEMELİ TERS SARKAÇ SİSTEMİNİN YAPISAL GÜRBÜZ KARARLILIK ANALİZİ. Eskişehir Osmangazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, Cilt: 18 - Sayı: 2, 55–70. https://ajindex.com/articles/287542

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. P. Gaspar, I. Szaszi, and J. Bokor, ”Robust control design for mechanical systems using the mixed µ synthesis,” Periodica Polytechnica Ser. Transp. Eng., v. 30, pp. 37- 52, 2002
  2. S. Dussy and L. El-Ghaoui, “Multiobjective bounded control of uncertain nonlinear systems: An inverted pendulum example”, European Control Conference, Brussels, July 1997
  3. S. Cheang and W. J. Chen, “Stabilizing control of an inverted pendulum system based on H∞ loop shaping design procedure”, Proceedings of the 3rd World Congress on Intelligent Control and Automation, v. 5, pp. 3385 – 3388, 2000
  4. G.A. Medrano-Cerda, “Robust computer control of an inverted pendulum”, IEEE Control Systems Magazine, v.19, pp.58 – 67, 1999
  5. K. Ogata, “Modern Control Engineering”, Prentice-Hall Inc. 1990
  6. A. Yazıcı, “ Application of sliding mode control on an inverted pendulum system”,Masters thesis, Osmangazi University, December 2000 (in Turkish)
  7. R. P. Braatz, P. M Young, J. C. Doyle, and M. Morari, “Computational-Complexity Of Mu-Calculation”, IEEE Transactions on Automatic Control, v. 39, pp.1000-1002,1994
  8. A. Nemirovskii, “Several NP-hard problems arising in robust stability analysis”,Mathematics of Control, Signals, and Systems, v. 6, pp. 99–105, 1993
  9. M. K. H Fan, A. L Tits, and J. C. Doyle, “Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics”, IEEE Transactions on Automatic Control, v.36, pp. 25-38, 1991
  10. P. M. Young, “Structured singular value approach for systems with parametric uncertainty”, Int. Journal of Robust and Nonlinear Control, v.11, pp.653-680, 2001
  11. M. Fu and N. E. Barabanov, “Improved Upper Bounds for the Mixed Structured Singular Value”, IEEE Transactions on Automatic Control, v. 42, pp.1447-1452, 1997
  12. P. M. Young, M. P. Newlin, and J. C. Doyle, “Computing Bounds For The MixedMu-Problem”, Int. Journal of Robust and Nonlinear Control, v.5, pp. 573-590, 1995
  13. K. Zhou and J. C. Doyle, “Essentials of Robust Control", Prentice-Hall, Inc, 1998
  14. G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith, “µ-Analysis and Synthesis Toolbox: User’s Guide, MUSYN Inc. and The MathWorks, Inc.”, 2001.