### Abstract

In this paper the adaptive control of a 2 Degrees Of Freedom (DOF) Classical Mechanical System, a ball-beam system is considered. The control task has the interesting feature that only one of the DOFs of the system, i.e. the position of the ball is controlled via controlling the other axis, the tilting angle of the beam. Since the acceleration of the ball rolling on the beam depends on the gravitation and the tilting angle of the beam, and due to the phenomenology of Classical Mechanical Systems the directly controllable physical quantity is the rotational acceleration of the beam, this system is a 4 order one because it is the 4^{th} time-derivative of the ball's position that can directly be influenced by the control. Another interesting feature of this system is its "saturation" since the rotational angle of the beam must be limited within the interval (-90°, +90°) that also sets limits to the available acceleration of the ball. In the present approach a feedback control is applied in which the above limitation is achieved by the application of an angular potential and an angular velocity potential. Utilizing the fact that the partial derivative of the 4^{th} time-derivative of the ball's position according to the angular acceleration of the beam has a well defined sign, a single tuneable adaptive parameter is introduced that does not represent the parameters of the system under control. The control is illustrated via simulation results.

Original language | English |
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Title of host publication | 2006 IEEE International Conference on Mechatronics, ICM |

Pages | 513-518 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2006 |

Event | 2006 IEEE International Conference on Mechatronics, ICM - Budapest, Hungary Duration: júl. 3 2006 → júl. 5 2006 |

### Other

Other | 2006 IEEE International Conference on Mechatronics, ICM |
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Country | Hungary |

City | Budapest |

Period | 7/3/06 → 7/5/06 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Electrical and Electronic Engineering
- Mechanical Engineering

### Cite this

^{th}order system using coordinate and velocity potentials. In

*2006 IEEE International Conference on Mechatronics, ICM*(pp. 513-518). [4018415] https://doi.org/10.1109/ICMECH.2006.252580

**Stabilization of the adaptive control of a 4 ^{th} order system using coordinate and velocity potentials.** / Rudas, I.; Tar, J.; Kosuge, Kazuhiro.

Research output: Conference contribution

^{th}order system using coordinate and velocity potentials. in

*2006 IEEE International Conference on Mechatronics, ICM.*, 4018415, pp. 513-518, 2006 IEEE International Conference on Mechatronics, ICM, Budapest, Hungary, 7/3/06. https://doi.org/10.1109/ICMECH.2006.252580

^{th}order system using coordinate and velocity potentials. In 2006 IEEE International Conference on Mechatronics, ICM. 2006. p. 513-518. 4018415 https://doi.org/10.1109/ICMECH.2006.252580

}

TY - GEN

T1 - Stabilization of the adaptive control of a 4th order system using coordinate and velocity potentials

AU - Rudas, I.

AU - Tar, J.

AU - Kosuge, Kazuhiro

PY - 2006

Y1 - 2006

N2 - In this paper the adaptive control of a 2 Degrees Of Freedom (DOF) Classical Mechanical System, a ball-beam system is considered. The control task has the interesting feature that only one of the DOFs of the system, i.e. the position of the ball is controlled via controlling the other axis, the tilting angle of the beam. Since the acceleration of the ball rolling on the beam depends on the gravitation and the tilting angle of the beam, and due to the phenomenology of Classical Mechanical Systems the directly controllable physical quantity is the rotational acceleration of the beam, this system is a 4 order one because it is the 4th time-derivative of the ball's position that can directly be influenced by the control. Another interesting feature of this system is its "saturation" since the rotational angle of the beam must be limited within the interval (-90°, +90°) that also sets limits to the available acceleration of the ball. In the present approach a feedback control is applied in which the above limitation is achieved by the application of an angular potential and an angular velocity potential. Utilizing the fact that the partial derivative of the 4th time-derivative of the ball's position according to the angular acceleration of the beam has a well defined sign, a single tuneable adaptive parameter is introduced that does not represent the parameters of the system under control. The control is illustrated via simulation results.

AB - In this paper the adaptive control of a 2 Degrees Of Freedom (DOF) Classical Mechanical System, a ball-beam system is considered. The control task has the interesting feature that only one of the DOFs of the system, i.e. the position of the ball is controlled via controlling the other axis, the tilting angle of the beam. Since the acceleration of the ball rolling on the beam depends on the gravitation and the tilting angle of the beam, and due to the phenomenology of Classical Mechanical Systems the directly controllable physical quantity is the rotational acceleration of the beam, this system is a 4 order one because it is the 4th time-derivative of the ball's position that can directly be influenced by the control. Another interesting feature of this system is its "saturation" since the rotational angle of the beam must be limited within the interval (-90°, +90°) that also sets limits to the available acceleration of the ball. In the present approach a feedback control is applied in which the above limitation is achieved by the application of an angular potential and an angular velocity potential. Utilizing the fact that the partial derivative of the 4th time-derivative of the ball's position according to the angular acceleration of the beam has a well defined sign, a single tuneable adaptive parameter is introduced that does not represent the parameters of the system under control. The control is illustrated via simulation results.

UR - http://www.scopus.com/inward/record.url?scp=34250864561&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250864561&partnerID=8YFLogxK

U2 - 10.1109/ICMECH.2006.252580

DO - 10.1109/ICMECH.2006.252580

M3 - Conference contribution

AN - SCOPUS:34250864561

SN - 0780397134

SN - 9780780397132

SP - 513

EP - 518

BT - 2006 IEEE International Conference on Mechatronics, ICM

ER -