Geodesic
Polynomial controller design based on flatness
Kybernetika, Tome 38 (2002) no. 5, pp. 571-584 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.
By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.
Classification : 93B50, 93B52, 93B55, 93C05, 93C10
Keywords: polynomial controller; linear system; parameters design 
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Rotella, Frédéric; Carillo, Francisco Javier; Ayadi, Mounir. Polynomial controller design based on flatness. Kybernetika, Tome 38 (2002) no. 5, pp. 571-584. http://geodesic.mathdoc.fr/item/KYB_2002_38_5_a5/

[1] Aström K. J., Bernardson B., Ringdhal A.: Solution using robust adaptive pole placement. In: Proc. European Control Conference (ECC’91), Grenoble 1991, pp. 1341–2346

[2] Aström K. J., Wittenmark B.: Computer Controlled Systems, Theory and Design. Prentice Hall, Englewood Cliffs, N.J. 1990

[3] Bitaud L., Fliess, M., Lévine J.: A flatness based control synthesis of linear systems and application to windshield wipers. In: Proc. European Control Conference (ECC’97), Bruxelles 1997

[4] Fliess M.: Sur des pensers nouveaux faisons des vers anciens. In: Proc. CIFA2000, Lille 2000, pp. 26–36

[5] Fliess M., Lévine J., Martin,, Ph., Rouchon P.: Sur les systèmes non linéaires différentiellement plats. C. R. Acad. Sci. Paris I-315 (1992), 619–624 | MR | Zbl

[6] Fliess M., Lévine J., Martin, Ph., Rouchon P.: Linéarisation par bouclage dyna- mique et transformées de Lie–Backlund. C. R. Acad. Sci. Paris I-317 (1993), 981–986 | MR

[7] Fliess M., Lévine J., Martin, Ph., Rouchon P.: Flatness and defect of nonlinear systems: introductory theory and applications. Internat. J. Control 61 (1995), 6, 1327–1361 | DOI | MR

[8] Fliess M., Lévine J., Martin, Ph., Rouchon P.: A Lie–Bäcklund approach to equivalence and flatness of nonlinear system. IEEE Trans. Automat. Control 44 (1999), 922–937 | DOI | MR

[9] Fliess M., Mounier H.: Controllability and observability of linear delay systems: an algebraic approach. ESAIM: Control, Optimization and Calculus of Variations 3 (1998), 301–314 | DOI | MR | Zbl

[10] Fliess M., Sira-Ramirez, H., Marquez R.: Regulation of non minimum phase outputs: a flatness approach. In: Perspectives in Control Theory & Applications, Colloquim in Honor of I. D. Landau, Paris, Springer–Verlag, Berlin 1998

[11] Franklin G. F., Powell J. D., Workman M.: Digital Control of Dynamic Systems. Addison–Wesley, Reading 1998 | Zbl

[12] Isidori A.: Nonlinear Control Systems. Springer–Verlag, Berlin 1989 | Zbl

[13] Horowitz I. M.: Synthesis of Feedback Systems. Wiley, New York 1963 | Zbl

[14] Kailath T.: Linear Systems. Prentice–Hall, Englewood Cliffs, N.J. 1980 | MR | Zbl

[15] Kučera V.: Analysis and Design of Discrete Linear Control Systems. Prentice Hall, Englewood Cliffs, N.J. 1991 | MR | Zbl

[16] Landau I. D.: Identification et Commande des Processus. Hermès, Paris 1993

[17] Landau I. D., Lozano R., M’Saad M.: Adaptive Control. Springer–Verlag, New York 1998 | MR | Zbl

[18] Lévine J., Lottin J., Ponsart J. C.: A nonlinear approach to the control of magnetic bearings. IEEE Trans. Control Systems Techn. 4 (1996), 5, 524–44 | DOI

[19] Lévine J.: Are there new industrial perspectives in the control of mechanical systems? In: Advances in Control (P. M. Frank, ed.), Springer–Verlag, New York 1999, pp. 197–226

[20] Marquez R., Delaleau E., Fliess M.: Commande par PID généralisé d’un moteur électrique sans capteur mécanique. In: Proc. CIFA 2000, Lille 2000, pp. 453–458

[21] Nijmeijer H., Schaft, Van Der: Nonlinear Dynamical Control Systems. Springer–Verlag, Berlin 1990 | MR | Zbl

[22] Rotella F., Carrillo F. J.: Flatness based control of a turning process. In: Proc. CESA’98, Vol. 1, Hammamet 1998, pp. 397–402

[23] Rotella F., Carrillo F. J.: Flatness approach for the numerical control of a turning process. In: Proc. European Control Conference (ECC’99), Karlsruhe 1999

[24] Rotella F., Carrillo F. J., Ayadi M.: Digital flatness-based robust controller applied to a thermal process. In: IEEE–CCA, Mexico–City 2001, pp. 936–941

[25] Rothfuß R., Rudolph, J., Zeitz M.: Flatness based control of a nonlinear chemical reactor. Automatica 32 (1996), 10, 1433–1439 | DOI | MR | Zbl