Stabilization of the cart pendulum system by fractional order control with experimental realization
Abstract
This paper deals with stability problem of cart inverted pendulum system controlled by a
fractional order controller. Inverted pendulum is an underactuated mechanical system
with one control input and two degrees of freedom. Detailed mathematical model of
pendulum is derived using the Rodriguez method. Stabilization of pendulum around its
unstable equilibrium point is achieved by using the fractional order PDα controller, in
combination with partial feedback linearization technique. Since fractional order control
law includes non-rational functions, an efficient method for numerical evaluation of this
type of functions is used in this paper. The performance of the proposed method is
demonstrated with experimental verification of the stabilization control of the cart
pendulum system.
Keywords:
inverted pendulum / fractional order PID control / asymptotic stability / rational approximationsSource:
Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia, 2016, 415-423Publisher:
- Belgrade: Serbian Society of Mechanics
- Faculty of Technical Sciences Novi Sad
Funding / projects:
- Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design (RS-MESTD-Technological Development (TD or TR)-35006)
- Intelligent Control Systems of the Air-conditioning for the Purpose of Achieving Energy Efficient Exploitation Regimes in the Complex Operating Conditions (RS-MESTD-Technological Development (TD or TR)-33047)
- Energy efficiency Improvement of Hydro and Thermal power plants in EPS by development and implementation of power electronics based regulation and automation equipment (RS-MESTD-Technological Development (TD or TR)-33020)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Mandić, Petar AU - Lazarević, Mihailo AU - Šekara, Tomislav AU - Jovanović, Radiša PY - 2016 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4185 AB - This paper deals with stability problem of cart inverted pendulum system controlled by a fractional order controller. Inverted pendulum is an underactuated mechanical system with one control input and two degrees of freedom. Detailed mathematical model of pendulum is derived using the Rodriguez method. Stabilization of pendulum around its unstable equilibrium point is achieved by using the fractional order PDα controller, in combination with partial feedback linearization technique. Since fractional order control law includes non-rational functions, an efficient method for numerical evaluation of this type of functions is used in this paper. The performance of the proposed method is demonstrated with experimental verification of the stabilization control of the cart pendulum system. PB - Belgrade: Serbian Society of Mechanics PB - Faculty of Technical Sciences Novi Sad C3 - Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia T1 - Stabilization of the cart pendulum system by fractional order control with experimental realization EP - 423 SP - 415 UR - https://hdl.handle.net/21.15107/rcub_machinery_4185 ER -
@conference{ author = "Mandić, Petar and Lazarević, Mihailo and Šekara, Tomislav and Jovanović, Radiša", year = "2016", abstract = "This paper deals with stability problem of cart inverted pendulum system controlled by a fractional order controller. Inverted pendulum is an underactuated mechanical system with one control input and two degrees of freedom. Detailed mathematical model of pendulum is derived using the Rodriguez method. Stabilization of pendulum around its unstable equilibrium point is achieved by using the fractional order PDα controller, in combination with partial feedback linearization technique. Since fractional order control law includes non-rational functions, an efficient method for numerical evaluation of this type of functions is used in this paper. The performance of the proposed method is demonstrated with experimental verification of the stabilization control of the cart pendulum system.", publisher = "Belgrade: Serbian Society of Mechanics, Faculty of Technical Sciences Novi Sad", journal = "Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia", title = "Stabilization of the cart pendulum system by fractional order control with experimental realization", pages = "423-415", url = "https://hdl.handle.net/21.15107/rcub_machinery_4185" }
Mandić, P., Lazarević, M., Šekara, T.,& Jovanović, R.. (2016). Stabilization of the cart pendulum system by fractional order control with experimental realization. in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia Belgrade: Serbian Society of Mechanics., 415-423. https://hdl.handle.net/21.15107/rcub_machinery_4185
Mandić P, Lazarević M, Šekara T, Jovanović R. Stabilization of the cart pendulum system by fractional order control with experimental realization. in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia. 2016;:415-423. https://hdl.handle.net/21.15107/rcub_machinery_4185 .
Mandić, Petar, Lazarević, Mihailo, Šekara, Tomislav, Jovanović, Radiša, "Stabilization of the cart pendulum system by fractional order control with experimental realization" in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia (2016):415-423, https://hdl.handle.net/21.15107/rcub_machinery_4185 .