Asymptotic stabilisation of the ball and beam system: design of energy-based control law and experimental results. (English) Zbl 1222.93197
Summary: We present a new nonlinear control law to stabilise the ball and beam system at a desired operating point. The control law is based on the Interconnection and Damping Assignment-Passivity-Based Control (IDA-PBC) methodology developed in [R. Ortega, M. Spong, F. Gomez-Estern and G. Blankenstien, ‘Stabilization of underactuated mechanical systems via interconnection and damping assignment’, IEEE Transactions Automatic Control 47, 1218–1233 (2002)] that guarantees stability in the sense of Lyapunov. We present a novel proof of the asymptotic stability of the desired operating point. The validity of the proposed control law is demonstrated through the experimental results.
MSC:
| 93D20 | Asymptotic stability in control theory |
| 93B35 | Sensitivity (robustness) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
References:
| [1] | DOI: 10.1007/s11071-009-9534-8 · Zbl 1183.70066 · doi:10.1007/s11071-009-9534-8 |
| [2] | DOI: 10.1016/S0005-1098(02)00145-0 · Zbl 1018.93014 · doi:10.1016/S0005-1098(02)00145-0 |
| [3] | DOI: 10.1137/S0363012901393304 · Zbl 1036.93031 · doi:10.1137/S0363012901393304 |
| [4] | Chang, BC, Kwtany, H and Hu, SS. An Application of Robust Feedback Linearisation to a Ball and Beam Control Problem. Proceedings of the IEEE International Conference on Control Applications, September. 1998. Trieste, Italy |
| [5] | Gordillo, F, Aracil, J and Gomez-Estern, F. Stabilization of Autonomous Oscillations and the Hopf Bifurcation in the Ball and Beam System. Proceedings of the 41st IEEE Conference on Decision and Control, December. 2002. Las Vegas, Nevada, USA |
| [6] | DOI: 10.1109/9.119645 · doi:10.1109/9.119645 |
| [7] | Huang, J and Lin, CF. Robust Nonlinear Control of the Ball and Beam System. Proceedings of the American Control Conference, June. 1995. Seattle, Washington, USA |
| [8] | Laukanen, E and Yurkovich, S. A Ball and Beam Testbed for Fuzzy Identification and Control Design. Proceedings of the American Control Conference, June. 1993. San Francisco, California, USA |
| [9] | DOI: 10.1080/00207170802061269 · Zbl 1168.93398 · doi:10.1080/00207170802061269 |
| [10] | Mazenc, F, Astolfi, A and Lozano, R. Lyapunov Function for the Ball and Beam: Robustness Property. Proceedings of the 38th IEEE Conference on Decision and Control, December. 1999. Phoenix, Arizona, USA |
| [11] | DOI: 10.1109/TAC.2002.800770 · Zbl 1364.93662 · doi:10.1109/TAC.2002.800770 |
| [12] | Tack, HH, Choo, YG, Kim, CG and Jung, MW. The Stabilisation Control of a Ball-beam using Self Recurrent Neural Networks. Proceedings of the 3rd International Conference on Knowledge-based Intelligent Information Engineering Systems, August. 1999. Adelaide, Australia |
| [13] | Teel, AR. Semi-global Stabilisation of the Ball and Beam using Output Feedback. Proceedings of the American Control Conference, June. 1993. San Francisco, California, USA |
| [14] | Yu, W and Ortiz, F. Stability Analysis of PD Regulation for the Ball and Beam System. Proceedings of the 2005 IEEE Conference on Control Applications, August. 2005. Toronto, Canada |
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