Tracking Control of Fully-actuated port-Hamiltonian Mechanical Systems via Sliding Manifolds and Contraction Analysis

Authors

Rodolfo Reyes-Báez, Arjan van der Schaft, Bayu Jayawardhana

Abstract

In this paper, we propose a trajectory tracking controller for fully-actuated port-Hamiltonian (pH) mechanical systems, which is based on recent advances in contraction analysis and differential Lyapunov theory. The tracking problem is solved by defining a suitable invariant sliding manifold which provides a desired steady state behavior. The manifold is then made attractive via contraction techniques. Finally, we present numerical simulation results where a SCARA robot is commanded by the proposed tracking control law.

Keywords

Trajectory tracking control; port-Hamiltonian systems; sliding manifold; differential Lyapunov theory; contraction analysis

Citation

• Journal: IFAC-PapersOnLine
• Year: 2017
• Volume: 50
• Issue: 1
• Pages: 8256–8261
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2017.08.1395
• Note: 20th IFAC World Congress

BibTeX

@article{Reyes_B_ez_2017,
  title={{Tracking Control of Fully-actuated port-Hamiltonian Mechanical Systems via Sliding Manifolds and Contraction Analysis}},
  volume={50},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2017.08.1395},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Reyes-Báez, Rodolfo and van der Schaft, Arjan and Jayawardhana, Bayu},
  year={2017},
  pages={8256--8261}
}

Download the bib file

References

• Andrieu, V., Jayawardhana, B. & Praly, L. Transverse Exponential Stability and Applications. IEEE Transactions on Automatic Control vol. 61 3396–3411 (2016) – 10.1109/tac.2016.2528050
• Arimoto, (1996)
• Crouch, (1987)
• Dirksz, Adaptive tracking control of fully actuated port-hamiltonian mechanical systems. In CCA (2010)
• DUAN, G.-R. & PATTON, R. J. A Note on Hurwitz Stability of Matrices. Automatica vol. 34 509–511 (1998) – 10.1016/s0005-1098(97)00217-3
• Forni, (2014)
• Fujimoto, Trajectory tracking control of port-controlled hamiltonian systems via generalized canonical transformations. Au-tomatica (2003)
• Ghorbel, F. & Spong, M. W. Integral manifolds of singularly perturbed systems with application to rigid-link flexible-joint multibody systems. International Journal of Non-Linear Mechanics vol. 35 133–155 (2000) – 10.1016/s0020-7462(98)00092-4
• Jayawardhana, B., Ortega, R., García-Canseco, E. & Castaños, F. Passivity of nonlinear incremental systems: Application to PI stabilization of nonlinear RLC circuits. Systems & Control Letters vol. 56 618–622 (2007) – 10.1016/j.sysconle.2007.03.011
• Jayawardhana, B. & Weiss, G. Tracking and disturbance rejection for fully actuated mechanical systems. Automatica vol. 44 2863–2868 (2008) – 10.1016/j.automatica.2008.03.030
• Jouffroy, J. & Fossen, T. I. Tutorial on Incremental Stability Analysis using Contraction Theory. Modeling, Identification and Control: A Norwegian Research Bulletin vol. 31 93–106 (2010) – 10.4173/mic.2010.3.2
• Kelly, (2006)
• Lohmiller, (1998)
• Ortega, (2013)
• Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 53 2527–2542 (2008) – 10.1109/tac.2008.2006930
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Pavlov, A. & Marconi, L. Incremental passivity and output regulation. Proceedings of the 45th IEEE Conference on Decision and Control (2006) doi:10.1109/cdc.2006.377803 – 10.1109/cdc.2006.377803
• Romero, J. G., Donaire, A., Navarro-Alarcon, D. & Ramirez, V. Passivity-Based Tracking Controllers for Mechanical Systems with Active Disturbance Rejection. IFAC-PapersOnLine vol. 48 129–134 (2015) – 10.1016/j.ifacol.2015.10.226
• Sanfelice, (2015)
• Sira-Ramrez, (2015)
• Slotine, J.-J. E. & Weiping Li. On the Adaptive Control of Robot Manipulators. The International Journal of Robotics Research vol. 6 49–59 (1987) – 10.1177/027836498700600303
• van der Schaft, The hamilto-nian formulation of energy conserving physical systems with external ports. Archiv fr Elektronik und bertra-gungstechnik (1995)
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• Venkatraman, (2010)
• Wang, W. & Slotine, J.-J. E. On partial contraction analysis for coupled nonlinear oscillators. Biological Cybernetics vol. 92 38–53 (2004) – 10.1007/s00422-004-0527-x
• Yaghmaei, (2015)
• Zada, V. & Belda, K. Mathematical modeling of industrial robots based on Hamiltonian mechanics. 2016 17th International Carpathian Control Conference (ICCC) 813–818 (2016) doi:10.1109/carpathiancc.2016.7501208 – 10.1109/carpathiancc.2016.7501208