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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 5, Pages 556–575
DOI: https://doi.org/10.1134/S1560354714050049
(Mi rcd182)
 

This article is cited in 21 scientific papers (total in 21 papers)

On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems

Dong Eui Chang

Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
Citations (21)
References:
Abstract: Interconnection and damping assignment passivity-based control (IDA-PBC) is an excellent method to stabilize mechanical systems in the Hamiltonian formalism. In this paper, several improvements are made on the IDA-PBC method. The skew-symmetric interconnection submatrix in the conventional form of IDA-PBC is shown to have some redundancy for systems with the number of degrees of freedom greater than two, containing unnecessary components that do not contribute to the dynamics. To completely remove this redundancy, the use of quadratic gyroscopic forces is proposed in place of the skew-symmetric interconnection submatrix. Reduction of the number of matching partial differential equations in IDA-PBC and simplification of the structure of the matching partial differential equations are achieved by eliminating the gyroscopic force from the matching partial differential equations. In addition, easily verifiable criteria are provided for Lyapunov/exponential stabilizability by IDA-PBC for all linear controlled Hamiltonian systems with arbitrary degrees of underactuation and for all nonlinear controlled Hamiltonian systems with one degree of underactuation. A general design procedure for IDA-PBC is given and illustrated with examples. The duality of the new IDAPBC method to the method of controlled Lagrangians is discussed. This paper renders the IDA-PBC method as powerful as the controlled Lagrangian method.
Keywords: feedback control, stabilization, energy shaping, mechanical system.
Received: 14.12.2012
Accepted: 04.06.2014
Bibliographic databases:
Document Type: Article
MSC: 70Q05, 93C10, 93D15
Language: English
Citation: Dong Eui Chang, “On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems”, Regul. Chaotic Dyn., 19:5 (2014), 556–575
Citation in format AMSBIB
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\by Dong~Eui~Chang
\paper On the Method of Interconnection and Damping Assignment Passivity-Based Control for the Stabilization of Mechanical Systems
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 5
\pages 556--575
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\crossref{https://doi.org/10.1134/S1560354714050049}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3266827}
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Linking options:
  • https://www.mathnet.ru/eng/rcd182
  • https://www.mathnet.ru/eng/rcd/v19/i5/p556
  • This publication is cited in the following 21 articles:
    1. Mattia Mattioni, Pablo Borja, “Digital passivity-based control of underactuated mechanical systems”, Automatica, 173 (2025), 112096  crossref
    2. Ainoor Teimoorzadeh, Alejandro Donaire, Pierluigi Arpenti, Fabio Ruggiero, 2022 European Control Conference (ECC), 2022, 1409  crossref
    3. Pablo Borja, Cosimo Della Santina, Azita Dabiri, “On the Role of Coupled Damping and Gyroscopic Forces in the Stability and Performance of Mechanical Systems”, IEEE Control Syst. Lett., 6 (2022), 3433  crossref
    4. Sergio Grillo, Leandro Salomone, Marcela Zuccalli, “Explicit solutions of the kinetic and potential matching conditions of the energy shaping method”, JGM, 13:4 (2021), 629  crossref
    5. Gheibi A., Ghiasi A.R., Ghaemi S., Badamchizadeh M.A., “Designing of Robust Adaptive Passivity-Based Controller Based on Reinforcement Learning For Nonlinear Port-Hamiltonian Model With Disturbance”, Int. J. Control, 93:8 (2020), 1754–1764  crossref  mathscinet  zmath  isi  scopus
    6. Gheibi A., Ghiasi A.R., Ghaemi S., Badamchizadeh M.A., “Interconnection and Damping Assignment Control Based on Modified Actor-Critic Algorithm With Wavelet Function Approximation”, ISA Trans., 101 (2020), 116–129  crossref  isi  scopus
    7. S. D. Grillo, L. M. Salomone, M. Zuccalli, “Asymptotic Stabilizability of Underactuated Hamiltonian Systems With Two Degrees of Freedom”, Rus. J. Nonlin. Dyn., 15:3 (2019), 309–326  mathnet  crossref  mathscinet
    8. J. Chi, “Hybrid control of 2-DOF joint robot based on port-controlled Hamiltonian and PD algorithm”, Cluster Comput., 22:4 (2019), S7983–S7989  crossref  isi  scopus
    9. Yang Bai, Mikhail Svinin, 2019 12th International Conference on Developments in eSystems Engineering (DeSE), 2019, 855  crossref
    10. G. Cordero, V. Santibanez, A. Dzul, J. Sandoval, “Interconnection and damping assignment passivity-based control of an underactuated 2-DOF gyroscope”, Int. J. Appl. Math. Comput. Sci., 28:4 (2018), 661–677  crossref  mathscinet  isi  scopus
    11. Yang Bai, Mikhail Svinin, Motoji Yamamoto, “Function Approximation Based Control for Non-Square Systems”, SICE Journal of Control, Measurement, and System Integration, 11:6 (2018), 477  crossref
    12. R. Ortega, A. Donaire, J. Guadalupe Romero, “Passivity-based control of mechanical systems”, Feedback Stabilization of Controlled Dynamical Systems: in Honor of Laurent Praly, Lecture Notes in Control and Information Sciences, 473, ed. N. Petit, Springler, 2017, 167–199  crossref  mathscinet  isi  scopus
    13. S. Grillo, L. Salomone, M. Zuccalli, “On the relationship between the energy shaping and the Lyapunov constraint based methods”, J. Geom. Mech., 9:4 (2017), 459–486  crossref  mathscinet  zmath  isi  scopus
    14. H. Parks, M. Leok, “Variational integrators for interconnected Lagrange-Dirac systems”, J. Nonlinear Sci., 27:5 (2017), 1399–1434  crossref  mathscinet  zmath  isi  scopus
    15. A. Donaire, R. Ortega, J. G. Romero, “Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces”, Syst. Control Lett., 94 (2016), 118–126  crossref  mathscinet  zmath  isi  scopus
    16. N. Wei, S. Jeon, “On the gyroscopic force in mechanical manipulators and its artificial shaping for taskspace movement coordination”, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2016), IEEE, 2016, 3030–3035  crossref  isi
    17. Ya. Bai, M. Svinin, M. Yamamoto, “Motion planning for a hoop-pendulum type of underactuated systems”, 2016 IEEE International Conference on Robotics and Automation (ICRA), eds. A. Okamura, A. Menciassi, A. Ude, D. Burschka, D. Lee, F. Arrichiello, H. Liu, H. Moon, J. Neira, et, IEEE, 2016, 2739–2744  isi
    18. N. Wei, S. Jeon, “Gyroscopic forces for mechanical manipulators”, 2016 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), IEEE, 2016, 935–940  isi
    19. Yang Bai, Mikhail Svinin, Motoji Yamamoto, 2016 IEEE International Conference on Robotics and Automation (ICRA), 2016, 2739  crossref
    20. Nan Wei, Soo Jeon, 2016 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), 2016, 935  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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