Control of the cart pendulum system by using a 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. Mathematical model
of cart pendulum system is derived 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 : 12th International conference on accomplishments in Electrical and Mechanical Engineering and Information Technology (DEMI 2015) Banja Luka, 2015, 2015, 557-562Publisher:
- Faculty of Mechanical Engineering University of Banja Luka
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)
- 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 - Šekara, Tomislav PY - 2015 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4179 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. Mathematical model of cart pendulum system is derived 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 - Faculty of Mechanical Engineering University of Banja Luka C3 - Proceedings : 12th International conference on accomplishments in Electrical and Mechanical Engineering and Information Technology (DEMI 2015) Banja Luka, 2015 T1 - Control of the cart pendulum system by using a fractional order PD controller EP - 562 SP - 557 UR - https://hdl.handle.net/21.15107/rcub_machinery_4179 ER -
@conference{ author = "Mandić, Petar and Lazarević, Mihailo 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. Mathematical model of cart pendulum system is derived 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 = "Faculty of Mechanical Engineering University of Banja Luka", journal = "Proceedings : 12th International conference on accomplishments in Electrical and Mechanical Engineering and Information Technology (DEMI 2015) Banja Luka, 2015", title = "Control of the cart pendulum system by using a fractional order PD controller", pages = "562-557", url = "https://hdl.handle.net/21.15107/rcub_machinery_4179" }
Mandić, P., Lazarević, M.,& Šekara, T.. (2015). Control of the cart pendulum system by using a fractional order PD controller. in Proceedings : 12th International conference on accomplishments in Electrical and Mechanical Engineering and Information Technology (DEMI 2015) Banja Luka, 2015 Faculty of Mechanical Engineering University of Banja Luka., 557-562. https://hdl.handle.net/21.15107/rcub_machinery_4179
Mandić P, Lazarević M, Šekara T. Control of the cart pendulum system by using a fractional order PD controller. in Proceedings : 12th International conference on accomplishments in Electrical and Mechanical Engineering and Information Technology (DEMI 2015) Banja Luka, 2015. 2015;:557-562. https://hdl.handle.net/21.15107/rcub_machinery_4179 .
Mandić, Petar, Lazarević, Mihailo, Šekara, Tomislav, "Control of the cart pendulum system by using a fractional order PD controller" in Proceedings : 12th International conference on accomplishments in Electrical and Mechanical Engineering and Information Technology (DEMI 2015) Banja Luka, 2015 (2015):557-562, https://hdl.handle.net/21.15107/rcub_machinery_4179 .