D-decomposition technique for stabilization of Furuta pendulum: fractional approach
Abstract
In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out.
Keywords:
inverted pendulum / fractional order PID / D-decomposition / asymptotic stabilitySource:
Bulletin of The Polish Academy of Sciences-Technical Sciences, 2016, 64, 1, 189-196Publisher:
- Polska Akad Nauk, Polish Acad Sci, Div Iv Technical Sciences Pas, Warszawa
Funding / projects:
- 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)
- 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)
DOI: 10.1515/bpasts-2016-0021
ISSN: 0239-7528
WoS: 000372945900021
Scopus: 2-s2.0-84966655510
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Mandić, Petar AU - Lazarević, Mihailo AU - Sekara, Tomislav B. PY - 2016 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2473 AB - In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out. PB - Polska Akad Nauk, Polish Acad Sci, Div Iv Technical Sciences Pas, Warszawa T2 - Bulletin of The Polish Academy of Sciences-Technical Sciences T1 - D-decomposition technique for stabilization of Furuta pendulum: fractional approach EP - 196 IS - 1 SP - 189 VL - 64 DO - 10.1515/bpasts-2016-0021 ER -
@article{ author = "Mandić, Petar and Lazarević, Mihailo and Sekara, Tomislav B.", year = "2016", abstract = "In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out.", publisher = "Polska Akad Nauk, Polish Acad Sci, Div Iv Technical Sciences Pas, Warszawa", journal = "Bulletin of The Polish Academy of Sciences-Technical Sciences", title = "D-decomposition technique for stabilization of Furuta pendulum: fractional approach", pages = "196-189", number = "1", volume = "64", doi = "10.1515/bpasts-2016-0021" }
Mandić, P., Lazarević, M.,& Sekara, T. B.. (2016). D-decomposition technique for stabilization of Furuta pendulum: fractional approach. in Bulletin of The Polish Academy of Sciences-Technical Sciences Polska Akad Nauk, Polish Acad Sci, Div Iv Technical Sciences Pas, Warszawa., 64(1), 189-196. https://doi.org/10.1515/bpasts-2016-0021
Mandić P, Lazarević M, Sekara TB. D-decomposition technique for stabilization of Furuta pendulum: fractional approach. in Bulletin of The Polish Academy of Sciences-Technical Sciences. 2016;64(1):189-196. doi:10.1515/bpasts-2016-0021 .
Mandić, Petar, Lazarević, Mihailo, Sekara, Tomislav B., "D-decomposition technique for stabilization of Furuta pendulum: fractional approach" in Bulletin of The Polish Academy of Sciences-Technical Sciences, 64, no. 1 (2016):189-196, https://doi.org/10.1515/bpasts-2016-0021 . .