395
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Control via interconnection and damping assignment of linear time-invariant systems: a tutorial

, &
Pages 603-611 | Received 27 Sep 2011, Accepted 22 Jan 2012, Published online: 14 Feb 2012

References

  • Acosta , JA and Astolfi , A . 2009 . On the PDEs Arising in IDA . IEEE Conference on Decision and Control, (CDC'09) . 2009 . pp. 2132 – 2137 .
  • Acosta , JA , Ortega , R and Astolfi , A . 2005 . Interconnection and Damping Assignment Passivity-based Control of Mechanical Systems with Underactuation Degree One . IEEE Transactions on Automatic Control , 50 : 1936 – 1955 .
  • Auckly , D , Kapitanski , L and White , W . 2000 . Control of Nonlinear Underactuated Systems . Communication on Pure and Applied Mathematics , 3 : 354 – 369 .
  • Blankenstein , G , Ortega , R and van der Schaft , A . 2002 . The Matching Conditions of Controlled Lagrangians and Interconnection and Damping Passivity-based Control . International Journal of Control , 75 : 645 – 665 .
  • Bloch , A , Leonard , N and Marsden , J . 2000 . Controlled Lagrangians and the Stabilisation of Mechanical Systems: Part I. The First Matching Theorem . IEEE Transactions on Automatic Control , 45 : 2253 – 2270 .
  • Boyd , S , El Ghaoui , L , Feron , E and Balakrishnan , V . 1994 . Linear Matrix Inequalities in System and Control Theory, SIAM (Studies in Applied Mathematics) , Philadelphia , PA : SIAM .
  • Chang , DE . 2010a . Generalization of the IDA–PBC Method for Stabilisation of Mechanical Systems . Proceedings of the 18th Mediterranean Conference Control and Automation . 2010a . pp. 226 – 230 .
  • Chang , DE . 2010b . The Method of Controlled Lagrangians: Energy Plus Force Shaping . SIAM Journal on Control and Optimisation , 48 : 4821 – 4845 .
  • Chang , DE , Bloch , AM , Leonard , NE , Marsden , JE and Woolsey , CA . 2002 . The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems . ESAIM: Control, Optimisation, and Calculus of Variations , 8 : 393 – 422 .
  • Consortium , G . 2009 . Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach, Communications and Control Engineering , Berlin : Springer-Verlag .
  • Doerfler , F , Johnsen , JK and Allgower , F . 2009 . An Introduction to Interconnection and Damping Assignment Passivity-based Control in Process Engineering . Journal of Process Control , 19 : 1413 – 1426 .
  • Favach , A , Dochain , D and Winkin , J . 2011 . Power-shaping Control: Writing the System Dynamics Into the Brayton–Moser Form . Systems & Control Letters , 60 : 618 – 624 .
  • Fujimoto , K and Sugie , T . 2001 . Canonical Transformations and Stabilisation of Generalised Hamiltonian Systems . Systems & Control Letters , 42 : 217 – 227 .
  • Hamberg , J . 2000 . Controlled Lagrangians, Symmetries and Conditions for Strong Matching . in Proceedings of the IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Systems , : 62 – 67 .
  • Hoeffner , K . 2011 . “ Geometric Aspects of Interconnection and Damping Assignment Passivity-based Control ” . In Ph.D. Dissertation , Kingston, ON , , Canada : Queen's University .
  • Horn , R and Johnson , C . 1985 . Matrix Analysis , New York : Cambridge University Press .
  • Lewis , AD . 2006 . Potential Energy Shaping After Kinetic Energy Shaping . Proceedings of the 45th IEEE Conference on Decision and Control . 2006 . pp. 3339 – 3344 .
  • Liu , Z , Ortega , R and Su , H . 2011 . Control Via Interconnection and Damping Assignment of Linear Time-invariant Systems is Equivalent to Stabilisability . in 18th IFAC World Congress , : 7358 – 7362 .
  • Ortega , R and Garcia-Canseco , E . 2004 . Interconnection and Damping Assignment Passivity-based Control: A Survey . European Journal of Control , 10 : 432 – 450 .
  • Ortega , R , Loria , A , Nichlasson , PJ and Sira-Ramirez , H . 1998 . “ Passivity-based Control of Euler–Lagrange Systems ” . In Communications and Control Engineering , Berlin : Springer .
  • Ortega , R and Spong , M . 1989 . Adaptive Motion Control of Rigid Robots: A Tutorial . Automatica , 25 : 877 – 888 .
  • Ortega , R , Spong , M , Gomez , F and Blankenstein , G . 2002a . Stabilization of Underactuated Mechanical Systems via Interconnection and Damping Assignment . IEEE Transactions on Automatic Control , 47 : 1218 – 1233 .
  • Ortega , R , van der Schaft , A , Mareels , I and Maschke , B . 2001 . Putting Energy Back in Control . IEEE Control Systems Magazine , 21 : 18 – 33 .
  • Ortega , R , van der Schaft , A , Maschke , B and Escobar , G . 2002b . Interconnection and Damping Assignment Passivity-based Control of Port-controlled Hamiltonian Systems . Automatica , 38 : 585 – 596 .
  • Prajna , S , van der Schaft , A and Meinsma , G . 2002 . An LMI Approach to Stabilisation of Linear Port-controlled Hamiltonian Systems . Systems & Control Letters , 45 : 371 – 385 .
  • van der Schaft , A . 1999 . L2–Gain and Passivity Techniques in Nonlinear Control , Berlin : Springer .
  • Zenkov , D . 2002 . Matching and Stabilisation of Linear Mechanical Systems . in Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems (MTNS), South Bend ,

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.