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.
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.
Keywords
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Electrical Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | August 31, 2020 |
| Acceptance Date | August 24, 2020 |
| Published in Issue | Year 2020 Volume: 28 Issue: 2 |
