Research Article
BibTex RIS Cite

PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES

Year 2020, , 210 - 218, 31.08.2020
https://doi.org/10.31796/ogummf.736651

Abstract

A cubic Bezier curve formulation is used for generating phase portrait of an inverted pendulum system. Assuming that the cart and pendulum masses, pendulum length, and friction coefficient values in the inverted pendulum model are unknown, its finite number of experimentally obtained trajectories are utilized as a basis for generating the experimentally unavailable trajectories. It is shown that both the experimentally obtained and the remaining computationally generated trajectories can be formulated as an overlapping sequence of cubic Bezier curves in a computationally efficient manner. In the case of having no model of system dynamics, cubic Bezier curve formulation accurately relates experimentally obtained trajectories to the computationally generated trajectories corresponding to different initial conditions. A case study presented in this manuscript verifies that the computational approach using a cubic Bezier curves formulation has far better approximation performance compared to the ones obtained by the linear interpolation.

References

  • Stefani, R.T., Shahian, B., Savant, C.J., and Hostetter, G.H. (2002). “Design of Feedback Control Systems”. 4th ed. Oxford University Press.
  • Chalupa, P., Bobal, V., (2008). “Modelling and predictive control of inverted pendulum”. 22nd European Conference on Modelling and Simulation; 3-6 June, Nicosia, Cyprus. pp. 531-537.
  • Aström, K.J., Furuta, K., (2000). “Swinging up a pendulum by energy control”. Automatica, 36, 287-295.
  • Slotine, J.J.E., Li, W., (1991), “Applied Nonlinear Control”. Prentice Hall.
  • Farouki, R.T., (2012). “The Bernstein polynomial basis: A centennial retrospective”. Comput Aided Geom D 29, 379-419.
  • Yamaguchi, F., (1988). “Curves and Surfaces in Computer Aided Geometric Design”. 5th ed. Springer Verlag.
  • Riskus, A., (2006). “Approximation of a cubic Bezier curve by a circular arcs and vice versa”. Inf Technol Control, 35, 371-378.
  • Zdesar, A., Skrjanc, I., Klanjar, G., (2013). “Visual trajectory-tracking model-based control for mobile robots”. Int J Adv Robot Syst 10, 323.

BİR TERS SARKAÇ İÇİN KÜBİK BEZİER EĞRİLERİNİN KULLANILARAK YÜKSEK DOĞRULUKLU FAZ PORTRESİ ÇIKARIMI

Year 2020, , 210 - 218, 31.08.2020
https://doi.org/10.31796/ogummf.736651

Abstract

Bir ters sarkaç sisteminin faz portresinin oluşturulmasında kübik Bezier eğrisi formülasyonu kullanılmıştır. Sonlu sayıda elde edilen deneysel yörünge verileri kullanılarak, araç ve sarkaç kütlelerinin, sarkaç boyunun ve sürtünme katsayı değerlerinin bilinmediği durumlarda deneysel olarak elde edilenlerin dışındaki yörüngelerin yüksek doğrulukla çıkarılabilmesi sağlanmıştır. Deney yapılmadan hesaplanan yörüngelerin elde edilmesinde içiçe geçmiş Bezier eğrileri kullanılarak verimli bir hesaplama yapılabildiği gösterilmiştir. Verilen keyfi başlangıç şartları için, system dinamiği modelinin bilinmemesi durumunda, deneysel verilerden kübik Bezier eğrisi formülasyonu ile elde edilen yörüngeler, model dinamiği bilgisi ile hesaplanan yörüngelerle yüksek doğrulukla uyuşmaktadır. Makalede sunulan örnek çalışma, kübik Bezier eğrileri ile hesaplama yaklaşımının doğrusal interpolasyon ile elde edilebilecek değerlere göre çok daha yüksek yaklaşıklık performansı gösterdiğini doğrulamaktadır.

References

  • Stefani, R.T., Shahian, B., Savant, C.J., and Hostetter, G.H. (2002). “Design of Feedback Control Systems”. 4th ed. Oxford University Press.
  • Chalupa, P., Bobal, V., (2008). “Modelling and predictive control of inverted pendulum”. 22nd European Conference on Modelling and Simulation; 3-6 June, Nicosia, Cyprus. pp. 531-537.
  • Aström, K.J., Furuta, K., (2000). “Swinging up a pendulum by energy control”. Automatica, 36, 287-295.
  • Slotine, J.J.E., Li, W., (1991), “Applied Nonlinear Control”. Prentice Hall.
  • Farouki, R.T., (2012). “The Bernstein polynomial basis: A centennial retrospective”. Comput Aided Geom D 29, 379-419.
  • Yamaguchi, F., (1988). “Curves and Surfaces in Computer Aided Geometric Design”. 5th ed. Springer Verlag.
  • Riskus, A., (2006). “Approximation of a cubic Bezier curve by a circular arcs and vice versa”. Inf Technol Control, 35, 371-378.
  • Zdesar, A., Skrjanc, I., Klanjar, G., (2013). “Visual trajectory-tracking model-based control for mobile robots”. Int J Adv Robot Syst 10, 323.
There are 8 citations in total.

Details

Primary Language English
Subjects Electrical Engineering
Journal Section Research Articles
Authors

Gökhan Dındış 0000-0001-5642-7212

Abdurrahman Karamancıoğlu 0000-0003-2898-186X

Publication Date August 31, 2020
Acceptance Date August 24, 2020
Published in Issue Year 2020

Cite

APA Dındış, G., & Karamancıoğlu, A. (2020). PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, 28(2), 210-218. https://doi.org/10.31796/ogummf.736651
AMA Dındış G, Karamancıoğlu A. PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES. ESOGÜ Müh Mim Fak Derg. August 2020;28(2):210-218. doi:10.31796/ogummf.736651
Chicago Dındış, Gökhan, and Abdurrahman Karamancıoğlu. “PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi 28, no. 2 (August 2020): 210-18. https://doi.org/10.31796/ogummf.736651.
EndNote Dındış G, Karamancıoğlu A (August 1, 2020) PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 28 2 210–218.
IEEE G. Dındış and A. Karamancıoğlu, “PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES”, ESOGÜ Müh Mim Fak Derg, vol. 28, no. 2, pp. 210–218, 2020, doi: 10.31796/ogummf.736651.
ISNAD Dındış, Gökhan - Karamancıoğlu, Abdurrahman. “PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 28/2 (August 2020), 210-218. https://doi.org/10.31796/ogummf.736651.
JAMA Dındış G, Karamancıoğlu A. PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES. ESOGÜ Müh Mim Fak Derg. 2020;28:210–218.
MLA Dındış, Gökhan and Abdurrahman Karamancıoğlu. “PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, vol. 28, no. 2, 2020, pp. 210-8, doi:10.31796/ogummf.736651.
Vancouver Dındış G, Karamancıoğlu A. PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES. ESOGÜ Müh Mim Fak Derg. 2020;28(2):210-8.

20873 13565 13566 15461 13568  14913