Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments

Authors

Nahla Khraief Haddad, Ahmed Chemori, Safya Belghith

Abstract

Improving the robustness, vis-à-vis matched input disturbances of interconnection and damping assignment, passivity based control (IDA-PBC) for a class of underactuated mechanical systems is addressed in this paper. The characterised class of systems is described by a Port Controlled Hamiltonian (PCH) model which represents another alternative to the classical Euler–Lagrange models for which IDA–PBC yields a smooth stabilising controller. Our main contribution consists of combining the so-called IDA-PBC controller with an adaptive control technique. Some sufficient stability conditions on matched input disturbances are given. In order to estimate the stability and performance robustness of both controllers, a stochastic robustness analysis was used. Indeed, we used the Monte Carlo simulation (MCS) based on uncertainties to analyse the behaviour of the closed-loop system. The comparison of the stability robustness between the classical IDA-PBC controller and the proposed one is then provided. As an illustration, we proposed to revisit the application of IDA-PBC controller to the inertia wheel inverted pendulum in the presence of matched disturbances. Simulation and real-time experimental results mirror the theoretical results and prove the efficiency of the proposed controller.

Citation

• Journal: International Journal of Control
• Year: 2018
• Volume: 91
• Issue: 12
• Pages: 2657–2672
• Publisher: Informa UK Limited
• DOI: 10.1080/00207179.2017.1331378

BibTeX

@article{Haddad_2017,
  title={{Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments}},
  volume={91},
  ISSN={1366-5820},
  DOI={10.1080/00207179.2017.1331378},
  number={12},
  journal={International Journal of Control},
  publisher={Informa UK Limited},
  author={Haddad, Nahla Khraief and Chemori, Ahmed and Belghith, Safya},
  year={2017},
  pages={2657--2672}
}

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References

• Acosta J. A., Proceedings American control conference, (2004)
• Andary, S., Chemori, A. & Krut, S. Estimation-based disturbance rejection in control for limit cycle generation on inertia wheel inverted pendulum testbed. 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems 1302–1307 (2009) doi:10.1109/iros.2009.5354120 – 10.1109/iros.2009.5354120
• Andary, S., Chemori, A. & Krut, S. Control of the Underactuated Inertia Wheel Inverted Pendulum for Stable Limit Cycle Generation. Advanced Robotics 23, 1999–2014 (2009) – 10.1163/016918609x12529279062438
• Batlle, C., Dòria-Cerezo, A. & Ortega, R. Power Flow Control of a Doubly-Fed Induction Machine Coupled to a Flywheel. European Journal of Control 11, 209–221 (2005) – 10.3166/ejc.11.209-221
• Becherif, M. & Mendes, E. STABILITY AND ROBUSTNESS OF DISTURBED-PORT CONTROLLED HAMILTONIAN SYSTEMS WITH DISSIPATION. IFAC Proceedings Volumes 38, 574–579 (2005) – 10.3182/20050703-6-cz-1902.00751
• Choukchou-Braham, A., Cherki, B., Djemaï, M. & Busawon, K. Analysis and Control of Underactuated Mechanical Systems. (Springer International Publishing, 2014). doi:10.1007/978-3-319-02636-7 – 10.1007/978-3-319-02636-7
• Dirksz, D. A. & Scherpen, J. M. A. Structure Preserving Adaptive Control of Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 57, 2880–2885 (2012) – 10.1109/tac.2012.2192359
• Dirksz D. A., Proceeding mtns (2010)
• Donaire, A., Romero, J. G., Ortega, R., Siciliano, B. & Crespo, M. Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances. Int. J. Robust. Nonlinear Control 27, 1000–1016 (2016) – 10.1002/rnc.3615
• D‘oria-Cerezo A., Modeling, simulation and control of a doubly-fed induction machine controlled by a back-to-back converter (2006)
• Gómez-Estern, F. & Van der Schaft, A. J. Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control 10, 451–468 (2004) – 10.3166/ejc.10.451-468
• Fujimoto, K. & Sugie, T. Canonical Transformation and Stabilization of Generalized Hamiltonian Systems. IFAC Proceedings Volumes 31, 523–528 (1998) – 10.1016/s1474-6670(17)40390-9
• Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
• Fujimoto K., American control (2000)
• Gentili, L. & van der Schaft, A. Regulation and Input Disturbance Suppression for Port-Controlled Hamiltonian Systems 1. IFAC Proceedings Volumes 36, 205–210 (2003) – 10.1016/s1474-6670(17)38892-4
• Khraief N., IEEE multi-conference on systems and control - msc’14 (2014)
• Khraief-Haddad N., 3rd international conference on control, engineering and information technology - ceit’15 (2015)
• Ortega R., Proceedings of the american control conference (2000)
• Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control 10, 432–450 (2004) – 10.3166/ejc.10.432-450
• Wang, Q. & Stengel, R. F. Robust control of nonlinear systems with parametric uncertainty. Automatica 38, 1591–1599 (2002) – 10.1016/s0005-1098(02)00046-8
• Romero, J. G., Donaire, A. & Ortega, R. Robust energy shaping control of mechanical systems. Systems & Control Letters 62, 770–780 (2013) – 10.1016/j.sysconle.2013.05.011
• Reddy C. K., Proceedings of the american control conference (2004)
• Rodriguez, H., Ortega, R., Escobar, G. & Barabanov, N. A robustly stable output feedback saturated controller for the boost DC-to-DC converter. Systems & Control Letters 40, 1–8 (2000) – 10.1016/s0167-6911(99)00113-9
• Rodriguez, H., Ortega, R. & Mareels, I. A novel passivity-based controller for an active magnetic bearing benchmark experiment. Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334) 2144–2148 vol.3 (2000) doi:10.1109/acc.2000.879580 – 10.1109/acc.2000.879580
• Rodriguez, H., Siguerdidjane, H. & Ortega, R. Experimental comparison of linear and nonlinear controllers for a magnetic suspension. Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162) 715–719 doi:10.1109/cca.2000.897518 – 10.1109/cca.2000.897518
• Santibanez, V., Kelly, R. & Sandoval, J. Control of the Inertia Wheel Pendulum by Bounded Torques. Proceedings of the 44th IEEE Conference on Decision and Control 8266–8270 doi:10.1109/cdc.2005.1583500 – 10.1109/cdc.2005.1583500
• Touati, N. & Chemori, A. Predictive control for the stabilization of a fast mechatronic system : from simulation to real-time experiments. IFAC Proceedings Volumes 46, 237–242 (2013) – 10.3182/20130410-3-cn-2034.00031
• van der Schaft A., Proceedings of the international congress of mathematicians, (2006)