Adaptive Interconnection and Damping Assignment Passivity Based Control for Underactuated Mechanical Systems

Authors

Mutaz Ryalat, Dina Shona Laila, Hisham ElMoaqet

Abstract

In this paper, we present two adaptive control approaches to handle uncertainties caused by parametric and modeling errors in a class of nonlinear systems with uncertainties. The methods use the Port-controlled Hamiltonian (PCH) modelling framework and the interconnection and damping assignment passivity-based control (IDA-PBC) control design methodology being the most effectively applicable method to such models. The methods explore an extension on the classical IDA-PBC by adopting the state-transformation, yielding a dynamic state-feedback controller that asymptotically stabilizes a class of underactuated mechanical systems and preserves the PCH structure of the augmented closed-loop system. The results are applied to the underactuated mechanical systems that are a class of mechanical systems with broad applications and are more interesting as well as challenging control problems within this context. The results are illustrated with numerical simulations applied to two underactuated robotic systems; the Acrobot and non-prehensile planar rolling robotic (disk-on-disk) systems.

Keywords

adaptive control, hamiltonian systems, passivity-based control, underactuated mechanical systems

Citation

• Journal: International Journal of Control, Automation and Systems
• Year: 2021
• Volume: 19
• Issue: 2
• Pages: 864–877
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s12555-019-1019-z

BibTeX

@article{Ryalat_2020,
  title={{Adaptive Interconnection and Damping Assignment Passivity Based Control for Underactuated Mechanical Systems}},
  volume={19},
  ISSN={2005-4092},
  DOI={10.1007/s12555-019-1019-z},
  number={2},
  journal={International Journal of Control, Automation and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Ryalat, Mutaz and Laila, Dina Shona and ElMoaqet, Hisham},
  year={2020},
  pages={864--877}
}

Download the bib file

References

• H Khalil, Nonlinear Systems (2002)
• J Slotine, Applied Nonlinear Control (1991)
• Isidori, A. Nonlinear Control Systems. Communications and Control Engineering (Springer London, 1995). doi:10.1007/978-1-84628-615-5 – 10.1007/978-1-84628-615-5
• M Krstić, Nonlinear and Adaptive Control Design (1995)
• Astolfi, A. & Ortega, R. Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Trans. Automat. Contr. 48, 590–606 (2003) – 10.1109/tac.2003.809820
• A Astolfi, Nonlinear and Adaptive Control Design and Applications (2007)
• 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
• Pan, Y. & Yu, H. Composite learning robot control with guaranteed parameter convergence. Automatica 89, 398–406 (2018) – 10.1016/j.automatica.2017.11.032
• Huang, J., Wen, C., Wang, W. & Jiang, Z.-P. Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance. Systems & Control Letters 62, 234–241 (2013) – 10.1016/j.sysconle.2012.11.020
• van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
• 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
• Putting energy back in control. IEEE Control Syst. 21, 18–33 (2001) – 10.1109/37.915398
• 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
• Ryalat, M. & Laila, D. S. A simplified IDA-PBC design for underactuated mechanical systems with applications. European Journal of Control 27, 1–16 (2016) – 10.1016/j.ejcon.2015.12.001
• Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica 45, 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
• Ryalat, M., Laila, D. S. & Torbati, M. M. Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems. 2015 American Control Conference (ACC) 5365–5370 (2015) doi:10.1109/acc.2015.7172178 – 10.1109/acc.2015.7172178
• 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
• 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
• Haddad, N. K., Chemori, A. & Belghith, S. Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments. International Journal of Control 91, 2657–2672 (2017) – 10.1080/00207179.2017.1331378
• Dirksz, D. A. & Scherp, J. M. A. Adaptive tracking control of fully actuated port-Hamiltonian mechanical systems. 2010 IEEE International Conference on Control Applications 1678–1683 (2010) doi:10.1109/cca.2010.5611301 – 10.1109/cca.2010.5611301
• Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42, 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
• 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
• 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
• 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
• Acosta, J. A., Ortega, R., Astolfi, A. & Mahindrakar, A. D. Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Trans. Automat. Contr. 50, 1936–1955 (2005) – 10.1109/tac.2005.860292
• Olsson, H., Åström, K. J., Canudas de Wit, C., Gäfvert, M. & Lischinsky, P. Friction Models and Friction Compensation. European Journal of Control 4, 176–195 (1998) – 10.1016/s0947-3580(98)70113-x
• Zhang, Q. & Liu, G. Precise Control of Elastic Joint Robot Using an Interconnection and Damping Assignment Passivity-Based Approach. IEEE/ASME Trans. Mechatron. 21, 2728–2736 (2016) – 10.1109/tmech.2016.2578287
• Cornejo, C. & Alvarez-Icaza, L. Passivity based control of under-actuated mechanical systems with nonlinear dynamic friction. Journal of Vibration and Control 18, 1025–1042 (2011) – 10.1177/1077546311408469
• Ortega, R. & Spong, M. W. Adaptive motion control of rigid robots: A tutorial. Automatica 25, 877–888 (1989) – 10.1016/0005-1098(89)90054-x
• Panteley, E., Ortega, R. & Moya, P. Overcoming the detectability obstacle in certainty equivalence adaptive control. Automatica 38, 1125–1132 (2002) – 10.1016/s0005-1098(01)00305-3
• D. Mahindrakar, A., Astolfi, A., Ortega, R. & Viola, G. Further constructive results on interconnection and damping assignment control of mechanical systems: the Acrobot example. Int. J. Robust Nonlinear Control 16, 671–685 (2006) – 10.1002/rnc.1088
• Ryalat, M. & Laila, D. S. A Robust IDA-PBC Approach for Handling Uncertainties in Underactuated Mechanical Systems. IEEE Trans. Automat. Contr. 63, 3495–3502 (2018) – 10.1109/tac.2018.2797191