Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach
Abstract
This paper deals with the stability problem of two types of inverted pendulum controlled by a fractional order PD controller. Rotational inverted pendulum and cart inverted pendulum are under-actuated mechanical systems with two degrees of freedom and one control input. Detailed mathematical models of both pendulums are derived using the Rodriguez method. Fractional order PD controller is introduced for inverted pendulum stabilization. Stability regions in control parameters space are calculated using the D-decomposition approach, based on which tuning of the fractional order controller can be carried out. Numerical simulations and experimental realization are given to demonstrate the effectiveness of the proposed method.
Keywords:
Inverted pendulum / Fractional order PID / D-decomposition / Asymptotic stabilitySource:
Advances in Robot Design and Intelligent Control, 2017, 540, 29-37Publisher:
- Springer International Publishing Ag, Cham
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: 10.1007/978-3-319-49058-8_4
ISSN: 2194-5357
WoS: 000413022000004
Scopus: 2-s2.0-85007301280
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Mandić, Petar AU - Lazarević, Mihailo AU - Sekara, Tomislav B. PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2649 AB - This paper deals with the stability problem of two types of inverted pendulum controlled by a fractional order PD controller. Rotational inverted pendulum and cart inverted pendulum are under-actuated mechanical systems with two degrees of freedom and one control input. Detailed mathematical models of both pendulums are derived using the Rodriguez method. Fractional order PD controller is introduced for inverted pendulum stabilization. Stability regions in control parameters space are calculated using the D-decomposition approach, based on which tuning of the fractional order controller can be carried out. Numerical simulations and experimental realization are given to demonstrate the effectiveness of the proposed method. PB - Springer International Publishing Ag, Cham C3 - Advances in Robot Design and Intelligent Control T1 - Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach EP - 37 SP - 29 VL - 540 DO - 10.1007/978-3-319-49058-8_4 ER -
@conference{ author = "Mandić, Petar and Lazarević, Mihailo and Sekara, Tomislav B.", year = "2017", abstract = "This paper deals with the stability problem of two types of inverted pendulum controlled by a fractional order PD controller. Rotational inverted pendulum and cart inverted pendulum are under-actuated mechanical systems with two degrees of freedom and one control input. Detailed mathematical models of both pendulums are derived using the Rodriguez method. Fractional order PD controller is introduced for inverted pendulum stabilization. Stability regions in control parameters space are calculated using the D-decomposition approach, based on which tuning of the fractional order controller can be carried out. Numerical simulations and experimental realization are given to demonstrate the effectiveness of the proposed method.", publisher = "Springer International Publishing Ag, Cham", journal = "Advances in Robot Design and Intelligent Control", title = "Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach", pages = "37-29", volume = "540", doi = "10.1007/978-3-319-49058-8_4" }
Mandić, P., Lazarević, M.,& Sekara, T. B.. (2017). Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach. in Advances in Robot Design and Intelligent Control Springer International Publishing Ag, Cham., 540, 29-37. https://doi.org/10.1007/978-3-319-49058-8_4
Mandić P, Lazarević M, Sekara TB. Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach. in Advances in Robot Design and Intelligent Control. 2017;540:29-37. doi:10.1007/978-3-319-49058-8_4 .
Mandić, Petar, Lazarević, Mihailo, Sekara, Tomislav B., "Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach" in Advances in Robot Design and Intelligent Control, 540 (2017):29-37, https://doi.org/10.1007/978-3-319-49058-8_4 . .