Authors

Ammar Touati Brahim, Madjid Kidouche

Abstract

This paper presents an adaptive speed observer for general port‐Hamiltonian mechanical systems with non‐holonomic constraints in the presence of unknown friction forces and constant disturbances. Unlike the observers recently reported in the literature, which have been designed either under the assumptions of no friction and the absence of disturbances or for a specific class of mechanical systems with the requirement of an explicit solution of certain Partial Differential Equations (PDEs) that cannot be derived a priori, this observer proposes a design that obviates the solution of PDEs and ensures global convergence for general mechanical systems with k‐non‐holonomic constraints. The observer is totally constructive and given by explicit expressions. The simulation results testify to the effectiveness and the robust features of the developed observer.

Citation

  • Journal: Asian Journal of Control
  • Year: 2019
  • Volume: 21
  • Issue: 2
  • Pages: 965–976
  • Publisher: Wiley
  • DOI: 10.1002/asjc.1794

BibTeX

@article{Touati_Brahim_2018,
  title={{A Constructive Globally Convergent Adaptive Speed Observer For Port‐Hamiltonian Mechanical Systems with Non‐Holonomic Constraints}},
  volume={21},
  ISSN={1934-6093},
  DOI={10.1002/asjc.1794},
  number={2},
  journal={Asian Journal of Control},
  publisher={Wiley},
  author={Touati Brahim, Ammar and Kidouche, Madjid},
  year={2018},
  pages={965--976}
}

Download the bib file

References

  • Nicosia, S. & Tomei, P. Robot control by using only joint position measurements. IEEE Transactions on Automatic Control vol. 35 1058–1061 (1990) – 10.1109/9.58537
  • Astolfi, A., Ortega, R. & Venkatraman, A. A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica vol. 46 182–189 (2010) – 10.1016/j.automatica.2009.10.027
  • Bhasin, S., Kamalapurkar, R., Dinh, H. T. & Dixon, W. E. Robust Identification-Based State Derivative Estimation for Nonlinear Systems. IEEE Transactions on Automatic Control vol. 58 187–192 (2013) – 10.1109/tac.2012.2203452
  • New Directions in Nonlinear Observer Design. Lecture Notes in Control and Information Sciences (Springer London, 1999). doi:10.1007/bfb0109917 – 10.1007/bfb0109917
  • Yin, C. et al. Fractional-order exponential switching technique to enhance sliding mode control. Applied Mathematical Modelling vol. 44 705–726 (2017) – 10.1016/j.apm.2017.02.034
  • Xian, B., de Queiroz, M. S., Dawson, D. M. & McIntyre, M. L. A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems. Automatica vol. 40 695–700 (2004) – 10.1016/j.automatica.2003.12.007
  • Dadras, S. & Momeni, H. R. Fractional sliding mode observer design for a class of uncertain fractional order nonlinear systems. IEEE Conference on Decision and Control and European Control Conference 6925–6930 (2011) doi:10.1109/cdc.2011.6161100 – 10.1109/cdc.2011.6161100
  • Astolfi A., Nonlinear and Adaptive Control Design with Applications (2007)
  • Besançon, G. Parameter/Fault Estimation in Nonlinear Systems and Adaptive Observers. Lecture Notes in Control and Information Sciences 211–222 doi:10.1007/978-3-540-73503-8_7 – 10.1007/978-3-540-73503-8_7
  • Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
  • Aghannan, N. & Rouchon, P. An intrinsic observer for a class of lagrangian systems. IEEE Transactions on Automatic Control vol. 48 936–945 (2003) – 10.1109/tac.2003.812778
  • Anisi, D. A. & Hamberg, J. RIEMANNIAN OBSERVERS FOR EULER-LAGRANGE SYSTEMS. IFAC Proceedings Volumes vol. 38 115–120 (2005) – 10.3182/20050703-6-cz-1902.00673
  • Bonnabel, S., Martin, P. & Rouchon, P. Symmetry-Preserving Observers. IEEE Transactions on Automatic Control vol. 53 2514–2526 (2008) – 10.1109/tac.2008.2006929
  • Yuxin Su, Muller, P. C. & Chunhong Zheng. A Simple Nonlinear Observer for a Class of Uncertain Mechanical Systems. IEEE Transactions on Automatic Control vol. 52 1340–1345 (2007) – 10.1109/tac.2007.900851
  • Berghuis, H. & Nijmeijer, H. Robust control of robots via linear estimated state feedback. IEEE Transactions on Automatic Control vol. 39 2159–2162 (1994) – 10.1109/9.328807
  • Canudas de Wit, C. & Slotine, J.-J. E. Sliding observers for robot manipulators. Automatica vol. 27 859–864 (1991) – 10.1016/0005-1098(91)90041-y
  • Ahmed-Ali, T. & Lamnabhi-Lagarrigue, F. Sliding observer-controller design for uncertain triangular nonlinear systems. IEEE Transactions on Automatic Control vol. 44 1244–1249 (1999) – 10.1109/9.769383
  • Choi, J.-H., Misawa, E. A. & Young, G. E. A Study on Sliding Mode State Estimation. Journal of Dynamic Systems, Measurement, and Control vol. 121 255–260 (1999) – 10.1115/1.2802463
  • Bartolini, G., Pisano, A., Punta, E. & Usai, E. A survey of applications of second-order sliding mode control to mechanical systems. International Journal of Control vol. 76 875–892 (2003) – 10.1080/0020717031000099010
  • Davila, J., Fridman, L. & Levant, A. Second-order sliding-mode observer for mechanical systems. IEEE Transactions on Automatic Control vol. 50 1785–1789 (2005) – 10.1109/tac.2005.858636
  • Yuxin Su, Muller, P. C. & Chunhong Zheng. A Simple Nonlinear Observer for a Class of Uncertain Mechanical Systems. IEEE Transactions on Automatic Control vol. 52 1340–1345 (2007) – 10.1109/tac.2007.900851
  • Su Y., A simple global asymptotic convergent observer for uncertain mechanical systems. Int. J. Syst. Sci (2014)
  • Zhang, H., Shi, Y. & Saadat Mehr, A. On ${\cal H}_{\infty }$ Filtering for Discrete-Time Takagi–Sugeno Fuzzy Systems. IEEE Transactions on Fuzzy Systems vol. 20 396–401 (2012) – 10.1109/tfuzz.2011.2175933
  • Rigatos, G. G. A derivative-free distributed filtering approach for sensorless control of nonlinear systems. International Journal of Systems Science vol. 43 1699–1712 (2012) – 10.1080/00207721.2010.549594
  • Gauthier, J.-P. & Kupka, I. Deterministic Observation Theory and Applications. (2001) doi:10.1017/cbo9780511546648 – 10.1017/cbo9780511546648
  • Besançon, G. Global output feedback tracking control for a class of Lagrangian systems. Automatica vol. 36 1915–1921 (2000) – 10.1016/s0005-1098(00)00111-4
  • Venkatraman, A., Ortega, R., Sarras, I. & van der Schaft, A. Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems. IEEE Transactions on Automatic Control vol. 55 1059–1074 (2010) – 10.1109/tac.2010.2042010
  • Karagiannis, D., Carnevale, D. & Astolfi, A. Invariant Manifold Based Reduced-Order Observer Design for Nonlinear Systems. IEEE Transactions on Automatic Control vol. 53 2602–2614 (2008) – 10.1109/tac.2008.2007045
  • Astolfi, A. & Ortega, R. Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control vol. 48 590–606 (2003) – 10.1109/tac.2003.809820
  • Yang, B., Li, H. G., Sha, X. P. & Shao, N. An immersion and invariance-based speed observer for visual servoing. International Journal of Modelling, Identification and Control vol. 17 212 (2012) – 10.1504/ijmic.2012.049688
  • Luo, H., Xu, H. & Liu, X. Immersion and Invariance Based Robust Adaptive Control of High‐Speed Train with Guaranteed Prescribed Performance Bounds. Asian Journal of Control vol. 17 2263–2276 (2015) – 10.1002/asjc.1136
  • Liu, Z., Su, H. & Pan, S. A New Robust Adaptive Control of Uncertain Nonlinear Systems and Pendulum Application. Asian Journal of Control vol. 16 1576–1582 (2014) – 10.1002/asjc.917
  • Langarica Córdoba, D. & Ortega, R. An Observer–Based Scheme for Decentralized Stabilization of Large‐Scale Systems With Application to Power Systems. Asian Journal of Control vol. 17 124–132 (2014) – 10.1002/asjc.872
  • Astolfi A., A globally exponentially convergent immersion and invariance speed observer for n‐degrees of freedom mechanical systems. 48th IEEE Conf. Decision and Control (2009)
  • Praly, L. Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate. IEEE Transactions on Automatic Control vol. 48 1103–1108 (2003) – 10.1109/tac.2003.812819
  • Karagiannis, D., Sassano, M. & Astolfi, A. Dynamic scaling and observer design with application to adaptive control. Automatica vol. 45 2883–2889 (2009) – 10.1016/j.automatica.2009.09.013
  • Romero J. G., A globally exponentially stable tracking controller for mechanical systems using position feedback. Amer. Control Conf. (2013)
  • Ishikawa M., State estimation of non‐holonomic mobile robots using nonlinear observers. Proc. IEEE Int. Conf. Robot. & Autom (1995)
  • Astolfi, A. & Schaufelberger, W. State and output feedback stabilization of multiple chained systems with discontinuous control. Systems & Control Letters vol. 32 49–56 (1997) – 10.1016/s0167-6911(97)00053-4
  • Yuqiang Wu, Wang, B. & Zong, G. D. Finite-time tracking controller design for nonholonomic systems with extended chained form. IEEE Transactions on Circuits and Systems II: Express Briefs vol. 52 798–802 (2005) – 10.1109/tcsii.2005.852528
  • Stamnes, Ø. N., Aamo, O. M. & Kaasa, G.-O. A constructive speed observer design for general Euler–Lagrange systems. Automatica vol. 47 2233–2238 (2011) – 10.1016/j.automatica.2011.08.006
  • Romero, J. G. & Ortega, R. Two globally convergent adaptive speed observers for mechanical systems. Automatica vol. 60 7–11 (2015) – 10.1016/j.automatica.2015.06.032
  • Nijmeijer, H. & van der Schaft, A. Nonlinear Dynamical Control Systems. (Springer New York, 1990). doi:10.1007/978-1-4757-2101-0 – 10.1007/978-1-4757-2101-0
  • Spivak M., A Comprehensive Introduction to Differential Geometry (1999)
  • Van der Schaft A. J., L2‐Gain and Passivity Techniques in Nonlinear Control (1999)
  • Krstić M., Nonlinear and Adaptive Control Design (1995)
  • Bloch A. M., Nonholonomic Mechanics and Control (2007)
  • Sun, W., Wu, Y.-Q. & Sun, Z.-Y. Tracking Control Design for Nonholonomic Mechanical Systems with Affine Constraints. International Journal of Automation and Computing vol. 11 328–333 (2014) – 10.1007/s11633-014-0796-3