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Passivity-Based Control of Mechanical Systems

  • Romeo OrtegaEmail author
  • Alejandro Donaire
  • Jose Guadalupe Romero
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 473)

Abstract

Stabilization of mechanical systems by shaping their energy function is a well-established technique whose roots date back to the work of Lagrange and Dirichlet. Ortega and Spong in 1989 proved that passivity is the key property underlying the stabilization mechanism of energy shaping designs and the, now widely popular, term of passivity-based control (PBC) was coined. In this chapter, we briefly recall the history of PBC of mechanical systems and summarize its main recent developments. The latter includes: (i) an explicit formula for one of the free tuning gains that simplifies the computations, (ii) addition of PID controllers to robustify and make constructive the PBC design and to track ramp references, (iii) use of PBC to solve the position feedback global tracking problem, and (iv) design of robust and adaptive speed observers.

Keywords

Inertia Matrix Globally Exponentially Stable Gyroscopic Force Underactuated System Energy Shaping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

R. Ortega is supported by Government of Russian Federation (grant 074-U01, GOSZADANIE 2014/190 (project 2118)), the Ministry of Education and Science of Russian Federation (project 14.Z50.31.0031). The work of J.G. Romero is supported by a public grant overseen by the French National Research Agency (ANR) as part of the Investissement d’Avenir program, through the iCODE Institute, research project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Romeo Ortega
    • 1
    Email author
  • Alejandro Donaire
    • 2
    • 3
  • Jose Guadalupe Romero
    • 4
  1. 1.Laboratoire des Signaux et Systèmes, CNRS–SUPELECGif–sur–YvetteFrance
  2. 2.PRISMA Lab, Dipartimento di Ingegneria Elettrica e Tecnologie dell’InformazioneUniversità di Napoli Federico IINaplesItaly
  3. 3.School of EngineeringThe University of NewcastleCallaghanAustralia
  4. 4.Departamento Académico de Sistemas DigitalesInstituto Tecnológico Autónomo de México-ITAMDistrito FederalMexico

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