Stabilization of cart pendulum system by using fractional order PD controller
Abstract
This paper deals with stability problem of cart inverted pendulum controlled by a fractional
order PD controller. Inverted pendulum is an underactuated mechanical system because it has one
control input and two degrees of freedom. Detailed mathematical model of pendulum is derived
using the Rodriguez method and fractional order PD controller is introduced in order to stabilize
it. Control strategy consists of two parts, a swing up controller and stabilizing controller. Problem
of asymptotic stability of closed loop system is solved using the D-decomposition approach.
Stability regions in control parameters space are calculated using this method, and tuning of the
fractional order controller can be carried out.
Keywords:
inverted pendulum / fractional order PID / D-decomposition / asymptotic stabilitySource:
Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, C2c, 2015, 1-8Publisher:
- Belgrade : Serbian Society of Mechanics
- Novi Sad : Faculty of Technical Sciences
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 - Djurović, Nikola AU - Šekara, Tomislav PY - 2015 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4250 AB - This paper deals with stability problem of cart inverted pendulum controlled by a fractional order PD controller. Inverted pendulum is an underactuated mechanical system because it has one control input and two degrees of freedom. Detailed mathematical model of pendulum is derived using the Rodriguez method and fractional order PD controller is introduced in order to stabilize it. Control strategy consists of two parts, a swing up controller and stabilizing controller. Problem of asymptotic stability of closed loop system is solved using the D-decomposition approach. Stability regions in control parameters space are calculated using this method, and tuning of the fractional order controller can be carried out. PB - Belgrade : Serbian Society of Mechanics PB - Novi Sad : Faculty of Technical Sciences C3 - Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, C2c T1 - Stabilization of cart pendulum system by using fractional order PD controller EP - 8 SP - 1 UR - https://hdl.handle.net/21.15107/rcub_machinery_4250 ER -
@conference{ author = "Mandić, Petar and Lazarević, Mihailo and Djurović, Nikola and Šekara, Tomislav", year = "2015", abstract = "This paper deals with stability problem of cart inverted pendulum controlled by a fractional order PD controller. Inverted pendulum is an underactuated mechanical system because it has one control input and two degrees of freedom. Detailed mathematical model of pendulum is derived using the Rodriguez method and fractional order PD controller is introduced in order to stabilize it. Control strategy consists of two parts, a swing up controller and stabilizing controller. Problem of asymptotic stability of closed loop system is solved using the D-decomposition approach. Stability regions in control parameters space are calculated using this method, and tuning of the fractional order controller can be carried out.", publisher = "Belgrade : Serbian Society of Mechanics, Novi Sad : Faculty of Technical Sciences", journal = "Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, C2c", title = "Stabilization of cart pendulum system by using fractional order PD controller", pages = "8-1", url = "https://hdl.handle.net/21.15107/rcub_machinery_4250" }
Mandić, P., Lazarević, M., Djurović, N.,& Šekara, T.. (2015). Stabilization of cart pendulum system by using fractional order PD controller. in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, C2c Belgrade : Serbian Society of Mechanics., 1-8. https://hdl.handle.net/21.15107/rcub_machinery_4250
Mandić P, Lazarević M, Djurović N, Šekara T. Stabilization of cart pendulum system by using fractional order PD controller. in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, C2c. 2015;:1-8. https://hdl.handle.net/21.15107/rcub_machinery_4250 .
Mandić, Petar, Lazarević, Mihailo, Djurović, Nikola, Šekara, Tomislav, "Stabilization of cart pendulum system by using fractional order PD controller" in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, C2c (2015):1-8, https://hdl.handle.net/21.15107/rcub_machinery_4250 .