{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T04:01:36Z","timestamp":1787716896102,"version":"build-2784847793"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>The purpose of this paper is to show how the Timoshenko beam can be fruitfully described within the framework of distributed port Hamiltonian (dpH) systems so that rather simple and elegant considerations can be drawn regarding both the modeling and control of this mechanical system. After the dpH model of the beam is introduced, the control problem is discussed. In particular, it is shown how control approaches already presented in the literature can be unified, and a new control methodology is presented and discussed. This control methodology relies on the generalization to infinite dimensions of the concept of structural invariant (Casimir function) and on the extension to distributed systems of the so-called control by interconnection methodology. In this way, finite dimensional passive controllers can stabilize distributed parameter systems by shaping their total energy, i.e., by assigning a new minimum in the desired equilibrium configuration that can be reached if a dissipative effect is introduced.<\/jats:p>","DOI":"10.1137\/s0363012903429530","type":"journal-article","created":{"date-parts":[[2008,2,1]],"date-time":"2008-02-01T16:16:42Z","timestamp":1201882602000},"page":"743-767","source":"Crossref","is-referenced-by-count":162,"title":["Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach"],"prefix":"10.1137","volume":"43","author":[{"given":"Alessandro","family":"Macchelli","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claudio","family":"Melchiorri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/9.100932"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1990-0998124-1"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4224-6"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996312039"},{"key":"R5","unstructured":"S. Dong\u2010Hua and F. De\u2010Xing,\n                      Exponential stabilization of the Timoshenko beam with locally distributed feedback\n                      , in Proceedings of the 14th IFAC World Congress, Beijing, People\u2019s Republic of China, H. F. Chen, D.\u2010Z. Cheng, and J.\u2010F. Zhang, eds., Elsevier, New York, 1999."},{"key":"R6","unstructured":"G. Golo, V. Talasila, and A. J. van der Schaft,\n                      A Hamiltonian formulation of the Timoshenko beam model\n                      , in Proceedings of Mechatronics 2002, University of Twente, The Netherlands, 2002, pp. 544\u2013553."},{"key":"R7","unstructured":"G. Golo, A. J. van der Schaft, and S. Stramigioli,\n                      Hamiltonian formulation of planar beams\n                      , in Proceedings of the 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, A. Astolfi, A. J. van der Schaft, and F. Gordillo, eds., Sevilla, Spain, Elsevier, New York, 2003, pp. 169\u2013174."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0325078"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-0419-3"},{"key":"R10","unstructured":"A. Macchelli,\n                      Port Hamiltonian Systems. A Unified Approach for Modeling and Control Finite and Infinite Dimensional Physical Systems\n                      , Ph.D. thesis, University of Bologna \u2013 DEIS, Bologna, Italy, 2003."},{"key":"R10","unstructured":"Available at http:\/\/www\u2010lar.deis.unibo.it\/woda\/data\/deis\u2010lar\u2010publications\/e499.Document.pdf"},{"key":"R11","unstructured":"A. Macchelli and C. Melchiorri,\n                      Control by interconnection of the Timoshenko beam\n                      , in Proceedings of the 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, 2003, pp. 175\u2013182."},{"key":"R12","unstructured":"A. Macchelli and C. Melchiorri,\n                      Distributed port Hamiltonian formulation of the Timoshenko beam: Modeling and control\n                      , in Proceedings of the 4th MATHMOD, Vienna, Austria, 2003."},{"key":"R13","unstructured":"Manuelde Le\u00f3n, JorgeCort\u00e9s, Davidde Diego, SoniaMart\u00ednez, An introduction to mechanics with symmetry, Res. Exp. Math., Vol. 25, Heldermann, Lemgo, 2002, 305\u20133322003i:70019"},{"key":"R14","unstructured":"J. E. Marsden and T. S. Ratiu,\n                      Geometry of Nonlinear Systems\n                      , 2001."},{"key":"R14","unstructured":"This book is freely available at http:\/\/www.cds.caltech.edu\/\u223cmarsden."},{"key":"R15","unstructured":"B. M. Maschke and A. J. van der Schaft,\n                      Port controlled Hamiltonian systems: Modeling origins and system theoretic properties\n                      , in Proceedings of the Third Conference on Nonlinear Control Systems (NOLCOS), Bordeaux, France, 1992."},{"key":"R16","unstructured":"B. M. Maschke and A. J. van der Schaft,\n                      Interconnection of systems: The network paradigm\n                      , in Proceedings of the 35th IEEE Conference on Decision and Control, New York, 1996, pp. 207\u2013212."},{"key":"R17","unstructured":"B. M. Maschke and A. J. van der Schaft,\n                      Port controlled Hamiltonian representation of distributed parameter systems\n                      , in Workshop on Modeling and Control of Lagrangian and Hamiltonian Systems, Princeton, NJ, 2000."},{"key":"R18","unstructured":"B. M. Maschke and A. J. van der Schaft,\n                      Fluid dynamical systems as Hamiltonian boundary control systems\n                      , in Proceedings of the 40th IEEE Conference on Decision and Control, Vol. 5, Orlando, FL, 2001, pp. 4497\u20134502."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4350-2"},{"key":"R20","unstructured":"R. Ortega, A. J. van der Schaft, B. M. Maschke, and G. Escobar,\n                      Energy\u2010shaping of port\u2010controlled Hamiltonian systems by interconnection\n                      , in Proceedings of the IEEE Conference on Decision and Control, Vol. 2, Phoenix, AZ, 1999, pp. 1646\u20131651."},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00278-3"},{"key":"R22","unstructured":"H. Rodriguez, A. J. van der Schaft, and R. Ortega,\n                      On stabilization of nonlinear distributed parameter port\u2010controlled Hamiltonian systems via energy shaping\n                      , in Proceedings of the 40th IEEE Conference on Decision and Control, Vol. 1, Orlando, FL, 2001, pp. 131\u2013136."},{"key":"R23","volume-title":"Modeling and IPC control of interactive mechanical systems","author":"Stramigioli Stefano","year":"2001"},{"key":"R24","volume-title":"Introduction to Hamiltonian fluid dynamics and stability theory","author":"Swaters Gordon","year":"2000"},{"key":"R25","unstructured":"S. W. Taylor,\n                      Boundary Control of the Timoshenko Beam with Variable Physical Characteristics\n                      , Technical report, University of Auckland, New Zealand, 1997."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-0507-7"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012903429530","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:23:49Z","timestamp":1787318629000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012903429530"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1137\/S0363012903429530"],"URL":"https:\/\/doi.org\/10.1137\/s0363012903429530","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}