Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator
Abstract
In this paper stability problem of double inverted pendulum controlled by a fractional differential compensator is investigated. Pendubot is an underactuated mechanical system, i.e. it has only one control input and two degrees of freedom. Detailed mathematical model of Pendubot is derived using the Rodriguez method and then fractional order lead compensator is introduced in order to stabilize it around unstable upright position. D-decomposition method is used to solve the problem of asymptotic stability of closed loop system. Stability regions in control parameters space are calculated using this technique, which allows tuning of the fractional differential compensator to be carried out.
Keywords:
robust control / Pendubot / inverted pendulum / fractional control / D-decomposition / asymptotic stabilitySource:
Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017, 2017, 1911-1916Publisher:
- Institute of Electrical and Electronics Engineers Inc.
Funding / projects:
- Serbia-China bilateral project [3-12
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
- 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)
- 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)
- 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)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Mandić, Petar AU - Lazarević, Mihailo AU - Sekara, Tomislav B. AU - Cajić, Milan AU - Bučanović, Ljubiša PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2693 AB - In this paper stability problem of double inverted pendulum controlled by a fractional differential compensator is investigated. Pendubot is an underactuated mechanical system, i.e. it has only one control input and two degrees of freedom. Detailed mathematical model of Pendubot is derived using the Rodriguez method and then fractional order lead compensator is introduced in order to stabilize it around unstable upright position. D-decomposition method is used to solve the problem of asymptotic stability of closed loop system. Stability regions in control parameters space are calculated using this technique, which allows tuning of the fractional differential compensator to be carried out. PB - Institute of Electrical and Electronics Engineers Inc. C3 - Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017 T1 - Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator EP - 1916 SP - 1911 DO - 10.1109/CCDC.2017.7978829 ER -
@conference{ author = "Mandić, Petar and Lazarević, Mihailo and Sekara, Tomislav B. and Cajić, Milan and Bučanović, Ljubiša", year = "2017", abstract = "In this paper stability problem of double inverted pendulum controlled by a fractional differential compensator is investigated. Pendubot is an underactuated mechanical system, i.e. it has only one control input and two degrees of freedom. Detailed mathematical model of Pendubot is derived using the Rodriguez method and then fractional order lead compensator is introduced in order to stabilize it around unstable upright position. D-decomposition method is used to solve the problem of asymptotic stability of closed loop system. Stability regions in control parameters space are calculated using this technique, which allows tuning of the fractional differential compensator to be carried out.", publisher = "Institute of Electrical and Electronics Engineers Inc.", journal = "Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017", title = "Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator", pages = "1916-1911", doi = "10.1109/CCDC.2017.7978829" }
Mandić, P., Lazarević, M., Sekara, T. B., Cajić, M.,& Bučanović, L.. (2017). Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017 Institute of Electrical and Electronics Engineers Inc.., 1911-1916. https://doi.org/10.1109/CCDC.2017.7978829
Mandić P, Lazarević M, Sekara TB, Cajić M, Bučanović L. Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017. 2017;:1911-1916. doi:10.1109/CCDC.2017.7978829 .
Mandić, Petar, Lazarević, Mihailo, Sekara, Tomislav B., Cajić, Milan, Bučanović, Ljubiša, "Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator" in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017 (2017):1911-1916, https://doi.org/10.1109/CCDC.2017.7978829 . .