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Polynomial controller design based on flatness. (English) Zbl 1265.93118
Summary: 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 parameter design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.

93B55 Pole and zero placement problems
93C05 Linear systems in control theory
93B52 Feedback control
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[1] Aström K. J., Bernardson B., Ringdhal A.: Solution using robust adaptive pole placement. 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. Proc. European Control Conference (ECC’97), Bruxelles 1997
[4] Fliess M.: Sur des pensers nouveaux faisons des vers anciens. 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 · Zbl 0776.93038
[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 · Zbl 0796.93042
[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 · Zbl 0838.93022
[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 · Zbl 0964.93028
[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 · Zbl 0908.93013
[10] Fliess M., Sira-Ramirez, H., Marquez R.: Regulation of non minimum phase outputs: a flatness approach. Perspectives in Control Theory & Applications, Colloquim in Honor of I. D. Landau, Paris, Springer-Verlag, Berlin 1998 · Zbl 0967.93021
[11] Franklin G. F., Powell J. D., Workman M.: Digital Control of Dynamic Systems. Addison-Wesley, Reading 1998 · Zbl 0697.93002
[12] Isidori A.: Nonlinear Control Systems. Springer-Verlag, Berlin 1989 · Zbl 0931.93005
[13] Horowitz I. M.: Synthesis of Feedback Systems. Wiley, New York 1963 · Zbl 0515.93023
[14] Kailath T.: Linear Systems. Prentice-Hall, Englewood Cliffs, N.J. 1980 · Zbl 0870.93013
[15] Kučera V.: Analysis and Design of Discrete Linear Control Systems. Prentice Hall, Englewood Cliffs, N.J. 1991 · Zbl 0762.93060
[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 · Zbl 1234.93002
[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
[19] Lévine J.: Are there new industrial perspectives in the control of mechanical systems? In: Advances in Control (P. M. Frank, 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. Proc. CIFA 2000, Lille 2000, pp. 453-458
[21] Nijmeijer H., Schaft, Van Der: Nonlinear Dynamical Control Systems. Springer-Verlag, Berlin 1990 · Zbl 0701.93001
[22] Rotella F., Carrillo F. J.: Flatness based control of a turning process. 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. 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. 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 · Zbl 0865.93046
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