On computing flat outputs through Goursat normal form

• Jaume Franch ^[1] ; Ana Manzanera ^[1] ; Gemma Valero ^[1]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 1, Nº. 1, 2014, págs. 1-13
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen
  • català

    Aquest article estudia el càlcul de les sortides planes mitjançant la forma normal de Goursat del sistema de Pfa associat a qualsevol sistema de control en variables d'estat. L'algorisme consta de tres passos: i) transformació del sistema de control en el seu sistema de Pfa equivalent; ii) càlcul de la forma normal de Goursat; iii) reescriptura de les equacions en les noves variables d'estat. Aquí, una realimentació simplica les equacions i, per tant, les sortides planes es calculen de manera senzilla. L'algorisme s'aplica a un vehicle amb rodes extensibles. Gràcies a la propietat de planitud diferencial, s'obtenen les trajectòries entre dos punts donats.

  • English

    This paper is devoted to computation of flat outputs by means of the Goursat normal form of the Pfaffan system associated to any control system in state space form. The algorithm consists of three steps: i) transformation of the system into its Pfaffan equivalent; ii) computation of the Goursat normal form; iii) rewriting of the state space equations in the new variables. Here, a feedback law simplies the equations and, therefore, the at outputs can be easily computed. The algorithm is applied to a car with expanding wheels. Point to point trajectories are obtained thanks to the property of diferential flatness.Keywords: Feedback linearization, diferential flatness, nonlinear control.MSC (2010): 93B18, 93B29, 93C10.

• Referencias bibliográficas
  • S.K. Agrawal, J. Yan. “A three-wheel vehicle with expanding wheels: differential flatness, trajectory planning, and control”...
  • S.K. Agrawal, J. Yan, J. Rochester. “Analyticsand motion planning of a novel four-wheel vehicle with expanding wheels”,Proc....
  • R.L. Bryant, S.S. Chern, R.B. Gardner, H.L.Goldschmidt, P.A. Griffiths. Exterior Differential Systems, Springer-Verlag (1990).
  • 4] B. Charlet, J. L ́evine, R. Marino. “On dynamicfeedback linearization”,System and ControlLetters13(1989), 143–151.
  • M. Fliess, J. Levine, Ph. Martin, P. Rouchon. “Flatness and defect of nonlinear systems: introductory theory and examples”, International...
  • E. Fossas, J. Franch. “Linearization by prolongations: new bounds on the number of integrators”, European Journal of Control11(2005),...
  • J. Franch, A. Manzanera, G. Valero. “On computing flat outputs through Goursat normalform”, Proceedings of the European ...
  • L.R. Hunt, R. Su, G. Meyer. “Design for multi-input nonlinear systems”, Differential geometric control theory, R. Brockett, ...
  • A. Isidori. “Nonlinear Control Systems”, Springer-Verlag (1995).
  • B. Jacubczyk,W. Respondek. “Remarks on equivalence and linearization of nonlinear systems”, Bull. Acad. Pol. Sci., Ser. Sci....
  • Ph. Martin. “Contribution a l etude des systemes differentiellement plats”, These de Doctorat,n Ecole Nationale Superieure des Mines...
  • Ph. Martin, P. Rouchon. “Feedback linearization and driftless systems”. Mathematics of control, signal and systems 7 (1994),...
  • R. Murray, Z. Li, S.S. Sastry. “A mathematical introduction to robotic manipulation”, CRC Press (1994).
  • H. Nijmeijer, A.J. van der Schaft. “Nonlinear dynamical control systems”, Springer-Verlag (1990).[15] S. Sastry. “Nonlinear Systems....
  • S. Sastry. “Nonlinear Systems. Analysis, Stability, and Control”, Springer-Verlag (1999).