New Results on Stabilization of Port-Hamiltonian Systems via PID Passivity-Based Control

Pablo Borja*, Romeo Ortega, Jacquelien M. A. Scherpen

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)


In this article, we present some new results for the design of PID passivity-based controllers (PBCs) for the regulation of port-Hamiltonian (pH) systems. The main contributions of this article are: (i) new algebraic conditions for the explicit solution of the partial differential equation required in this design; (ii) revealing the deleterious impact of the dissipation obstacle that limits the application of the standard PID-PBC to systems without pervasive dissipation; (iii) the proposal of a new PID-PBC which is generated by two passive outputs, one with relative degree zero and the other with relative degree one. The first output ensures that the PID-PBC is not hindered by the dissipation obstacle, while the relative degree of the second passive output allows the inclusion of a derivative term. Making the procedure more constructive and removing the requirement on the dissipation significantly extends the realm of application of PID-PBC. Moreover, allowing the possibility of adding a derivative term to the control, enhances its transient performance.

Original languageEnglish
Article number9064945
Pages (from-to)625-636
Number of pages12
JournalIEEE Transactions on Automatic Control
Issue number2
Publication statusPublished - Feb-2021


  • Energy shaping
  • nonlinear systems
  • passive output
  • stabilization

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