TY - GEN

T1 - Fractional robust control of a ball-beam system

AU - Rudas, Imre J.

AU - Tar, József K.

AU - Kosuge, Kazuhiro

PY - 2006/12/1

Y1 - 2006/12/1

N2 - In this paper the robust 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 linear position of the ball along the beam 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 on this tilting angle, and that the directly controllable physical quantity is the rotational acceleration of the beam, this system is a 4th order one because only the 4th time-derivative of the ball's position can directly be influenced by the torque rotationally accelerating the beam. This system has a "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 taken into account by the application of angular and angular velocity potentials. The method is based on a standard error metrics that has to converge to zero during finite time according to a fractional order differential equation in discrete time approximation. It is shown that little reduction of the order of differentiation from 1 improves the robustness of the control against the measurement noises. The control is illustrated via simulation.

AB - In this paper the robust 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 linear position of the ball along the beam 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 on this tilting angle, and that the directly controllable physical quantity is the rotational acceleration of the beam, this system is a 4th order one because only the 4th time-derivative of the ball's position can directly be influenced by the torque rotationally accelerating the beam. This system has a "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 taken into account by the application of angular and angular velocity potentials. The method is based on a standard error metrics that has to converge to zero during finite time according to a fractional order differential equation in discrete time approximation. It is shown that little reduction of the order of differentiation from 1 improves the robustness of the control against the measurement noises. The control is illustrated via simulation.

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U2 - 10.1109/IECON.2006.347707

DO - 10.1109/IECON.2006.347707

M3 - Conference contribution

AN - SCOPUS:50249189466

SN - 1424401364

SN - 9781424401369

T3 - IECON Proceedings (Industrial Electronics Conference)

SP - 5408

EP - 5413

BT - IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics

T2 - IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics

Y2 - 6 November 2006 through 10 November 2006

ER -