D-decomposition technique for stabilization of Furuta pendulum: fractional approach
Apstrakt
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.
Ključne reči:
inverted pendulum / fractional order PID / D-decomposition / asymptotic stabilityIzvor:
Bulletin of The Polish Academy of Sciences-Technical Sciences, 2016, 64, 1, 189-196Izdavač:
- Polska Akad Nauk, Polish Acad Sci, Div Iv Technical Sciences Pas, Warszawa
Finansiranje / projekti:
- Inteligentni sistemi upravljanja klimatizacije u cilju postizanja energetski efikasnih režima u složenim uslovima eksploatacije (RS-MESTD-Technological Development (TD or TR)-33047)
- Održivost i unapređenje mašinskih sistema u energetici i transportu primenom forenzičkog inženjerstva, eko i robust dizajna (RS-MESTD-Technological Development (TD or TR)-35006)
- Povećanje energetske efikasnosti HE i TE EPS-a razvojem tehnologije i uređaja energetske elektronike za regulaciju i automatizaciju (RS-MESTD-Technological Development (TD or TR)-33020)
DOI: 10.1515/bpasts-2016-0021
ISSN: 0239-7528
WoS: 000372945900021
Scopus: 2-s2.0-84966655510
Kolekcije
Institucija/grupa
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 . .