Flatness and quasi-static state feedback in non-linear delay systems

References

• Chelouah , A , Delaleau , E , Martin , P and Rouchon , P . 1996 . Differential flatness and control of induction motors . Proceedings Symposium on Control, Optimization and Supervision, Computational Engineering in Systems Application IMACS Multiconference . 1996 , Lille. pp. 80 – 85 . July 9–12 1996 (CESA’96)
   Google Scholar
• Chiasson , J . “A new approach to dynamic feedback linearization control of an induction motor” . Proceedings 34th IEEE Conference on Decision and Control . December 1995 , New Orleans, LA. pp. 2173 – 2178 .
   Google Scholar
• Cohn , RM . 1965 . Difference Algebra , New York : Interscience .
   Google Scholar
• Cohn , RM . 1970 . A difference-differential basis theorem . Can. J. Math. , XXII : 1224 – 1237 .
   Google Scholar
• Delaleau , E and Fliess , M . 1992 . Algorithme de structure, filtrations et découplage . C. R. Acad. Sci. Paris Sér. I Math. , 315 : 101 – 106 .
   Google Scholar
• Delaleau , E and Pereira da Silva , PS . 1998a . Filtrations in feedback synthesis: Part I — Systems and feedbacks . Forum Math. , 10 : 147 – 174 .
   Web of Science ®Google Scholar
• Delaleau , E and Pereira da Silva , PS . 1998b . Filtrations in feedback synthesis: Part II — Input-output decoupling and disturbance decoupling . Forum Math. , 10 : 259 – 275 .
   Web of Science ®Google Scholar
• Delaleau , E and Respondek , W . 1995 . Lowering the orders of derivatives of controls in generalized state space systems . J. Math. Systems Estim. Contr. , 5 : 1 – 27 .
   Google Scholar
• Delaleau , E and Rudolph , J . 1995 . “Decoupling and linearization by quasi-static feedback of generalized states” . Proceedings 3rd European Control Conference . 1995 . pp. 1069 – 1074 .
   Google Scholar
• Delaleau , E and Rudolph , J . 1998 . Control of flat systems by quasi-static feedback of generalized states . Internat. J. Contr. , 71 : 745 – 765 .
   Web of Science ®Google Scholar
• Fliess , M . 1989a . Automatique et corps différentiels . Forum Math. , 1 : 227 – 238 .
   Google Scholar
• Fliess , M . 1989b . “Some remarks on nonlinear input-output systems with delays” . In New Trends in Nonlinear Control Theory, vol. 122 of Lecture Notes in Control and Inform. Sci , Edited by: Descusse , J , Fliess , M , Isidori , A and Leborgne , D . 172 – 181 . Berlin : Springer-Verlag .
   Google Scholar
• Fliess , M . 1990 . Generalized controller canonical forms for linear and nonlinear dynamics . IEEE Trans. Automat. Contr. , AC-35 : 994 – 1001 .
   Web of Science ®Google Scholar
• Fliess , M and Glad , ST . 1993 . “An algebraic approach to linear and nonlinear control”, in Essays on Control: ” . In Perspectives in the Theory and its Applications, volume 14 of Progr. Systems Control Theory , Edited by: Trentelman , HL and Willems , JC . 223 – 267 . Boston : Birkhäuser .
   Google Scholar
• Fliess , M , Lévine , J , Martin , P and Rouchon , P . 1992 . Sur les systèmes non linéaires différentiellement plats . C. R. Acad. Sci. Paris Sér. I Math. , 315 : 619 – 624 .
   Google Scholar
• Fliess , M , Lévine , J , Martin , P and Rouchon , P . 1995 . Flatness and defect of non-linear systems: introductory theory and examples . Inter. J. Contr. , 61 : 1327 – 1361 .
   Web of Science ®Google Scholar
• Fliess , M and Mounier , H . 1998 . Controllability and observability of linear delay systems: an algebraic approach . ESAIM: Control, Optimisation and Calculus of Variations , 3 : 301 – 314 .
   Google Scholar
• Fliess , M and Rudolph , J . 1997 . Corps de Hardy et observateurs asymptotiques locaux pour systèmes différentiellement plats . C.R. Acad. Sci. Paris Sér. IIb , 324 : 513 – 519 .
   Google Scholar
• Johnson , J . 1969 . Differential dimension polynomials and a fundamental theorem on differential modules . Amer. J. Math. , 91 : 239 – 248 .
   Web of Science ®Google Scholar
• Kolchin , ER . 1973 . Differential Algebra and Algebraic Groups , New York : Academic Press .
   Google Scholar
• Krener , A . 1986 . Normal Forms for Linear and Nonlinear Systems volume 68 of Contemporary Mathematics , Providence : American Mathematical Society . pp. 157–189
   Google Scholar
• Lévine , J , Lottin , J and Ponsart , JC . 1996 . A nonlinear approach to the control of magnetic bearings . IEEE Trans. Contr. Syst. Technol. , 4 : 524 – 544 .
   Web of Science ®Google Scholar
• Martin , P , Devasia , S and Paden , B . 1996 . A different look at output tracking: Control of a VTOL aircraft . Automatica J. IFAC , 32 : 101 – 107 .
   Web of Science ®Google Scholar
• Martin , P , Murray , RM and Rouchon , P . 1997 . “Flat systems” . Plenary Lectures and Mini-Courses, 4th European Control Conference . 1997 , Belgium. Edited by: Bastin , G and Gevers , M . pp. 211 – 264 . Brussels .
   Google Scholar
• Mounier , H . 1995 . “Propriétés structurelles des systèmes linéaires à retards: aspects théoriques et pratiques” . Paris-Sud, Orsay : Thèse de Doctorat, Université .
   Google Scholar
• Mounier , H , Rouchon , P and Rudolph , J . 1997 . Some examples of linear systems with delays . RAIRO—APII—JESA , 31 : 911 – 925 .
   Google Scholar
• Mounier , H and Rudolph , J . 1997 . First steps towards flatness based control of a class of nonlinear chemical reactors with time delays . Proceedings 4th European Control Conference . 1997 , Brussels, Belgium. Paper No. 508.
   Google Scholar
• Mounier , H and Rudolph , J . 1998 . Flatness based control of nonlinear delay systems: a chemical reactor example . Inter. J. Contr. , 71 : 871 – 890 .
   Web of Science ®Google Scholar
• Mounier , H , Rudolph , J , Fliess , M and Rouchon , P . 1998 . Tracking control of a vibrating string with an interior mass viewed as delay system . ESAIM: Control, Optimisation and Calculus of Variations , 3 : 315 – 321 .
   Google Scholar
• Murray , RM . 1995 . “Nonlinear control of mechanical systems: a Lagrangian perspective” . In Proceedings Symposium Nonlinear Control Systems Design 378 – 389 .
   Google Scholar
• Petit , N , Creff , Y and Rouchon , P . 1997 . δ-freeness of a class of linear delayed systems . Proceedings 4th European Control Conference . 1997 , Brussels. Edited by: Bastin , G and Gevers , M . Paper No. 520
   Google Scholar
• Petit , N , Rouchon , P , Boueilh , J-M , Guérin , F and Pinvidic , P . 2002 . Control of an industrial polymerization reactor using flatness . J. of Process Contr. , 12 : 659 – 665 .
   Web of Science ®Google Scholar
• Ritt , JF . 1950 . Differential Algebra , New York : American Mathematical Society .
   Google Scholar
• Rothfuss , R , Rudolph , J and Zeitz , M . 1996 . Flatness based control of a nonlinear chemical reactor model . Automatica J. IFAC , 32 : 1433 – 1439 .
   Web of Science ®Google Scholar
• Rothfuß , R , Rudolph , J and Zeitz , M . 1997 . Flachheit: Ein neuer Zugang zur Steuerung und Regelung nichtlinearer Systeme . at — Automatisierungstechnik , 45 : 517 – 525 .
   Google Scholar
• Rouchon , P . 1995 . Necessary condition and genericity of dynamic feedback linearization . J. Math. Sys. Estim. Contr. , 5 : 345 – 358 .
   Google Scholar
• Rudolph , J . 1994a . A canonical form under quasi-static feedback . Systems and Networks: Mathematical Theory and Applications, (MTNS’93, Invited and Contributed Papers) . 1994a , Berlin: Akademie Verlag. pp. 445 – 448 . U. Helmke, R. Mennicken and J. Saurer, Eds, Vol. 2
   Google Scholar
• Rudolph , J . 1994b . Viewing input-output system equivalence from differential algebra . J. Math. Systems Estim. Contr. , 4 : 353 – 383 .
   Google Scholar
• Rudolph , J . 1995 . “Well-formed dynamics under quasi-static state feedback” . In Geometry in Nonlinear Control and Differential Inclusions, Volume 32 of Banach Center Publ , Edited by: Jakubczyk , B , Respondek , W and Rzeżuchowski , T . 349 – 360 . Warszawa : Banach Center .
   Google Scholar
• Rudolph , J . 1996 . Flatness of some examples of coupled chemical reactors . Proceeding Symposium on Control, Optimization and Supervision; Computational Engineering in Systems Application IMACS Multiconference . 1996 , Lille. pp. 206 – 210 . July 9–12 1996 (CESA’96)
   Google Scholar
• Rudolph , J . 2000 . Flatness-based control by quasi-static feedback illustrated on a cascade of two chemical reactors . Inter. J. Contr. , 73 : 115 – 131 .
   Web of Science ®Google Scholar
• Rudolph , J . 2003a . Beiträge zur flachheitsbasierten Folgeregelung linearer und nichtlinearer Systeme endlicher und unendlicher Dimension , Shaker Verlag .
   Google Scholar
• Rudolph , J . 2003b . Flatness Based Control of Distributed Parameter Systems, Berichte aus der Steuerungs-und Regelungstechnik Shaker Verlag, Aachen
   Google Scholar
• Rudolph , J . 2005 . Flachheit: Eine nützliche Eigenschaft auch für Systeme mit Totzeiten . at — Automatisierungstechnik , 53 : 178 – 188 .
   Google Scholar
• Rudolph , J and Delaleau , E . 1994 . “Some remarks on quasi-static feedback of generalized states” . In 1st IFAC Workshop on New Trends in Design of Control Systems , 47 – 52 . Smolenice : Slovak Republic .
   Google Scholar
• Rudolph , J and Mounier , H . 2000 . “Trajectory tracking for π-flat nonlinear delay systems with a motor example” . In Nonlinear Control in the Year 2000 (Vol. 2), Vol. 259 of Lecture Notes in Control and Inform Sci , Edited by: Isidori , A , Lamnabhi-Lagarrique , F and Respondek , W . 339 – 351 . Berlin : Springer-Verlag .
   Google Scholar
• Rudolph , J , Rothfuß , R and Pomet , JB . 1995 . A generalized controller form for linearization by quasi-static state feedback . Proceedings IFAC Conference System Structure and Control . 1995 , Nantes/France. pp. 143 – 148 .
   Google Scholar
• Rudolph , J and Winkler , J . 2003 . A generalized flatness concept for nonlinear delay systems: motivation by chemical reactor models with constant or input-dependent delays . Inter. J. Sys. Sci. , 34 : 529 – 541 .
   Web of Science ®Google Scholar
• Rudolph , J and Winkler , J . 2004 . Difference-differential flatness of nonlinear delay systems with a chemical reactor example . Proceedings 6th IFAC-Symposium on Nonlinear Control Systems, NOLCOS 2004 . 2004 , Stuttgart, Germany. pp. 189 – 194 .
   Google Scholar
• Rudolph , J , Winkler , J and Woittennek , F . 2003 . “ Flatness Based Control of Distributed Parameter Systems: Examples and Computer Exercises from Various Technological Domains, Berichte aus der Steuerungs-und Regelungstechnik ” . Aachen : Shaker Verlag .
   Google Scholar
• Zeitz , M . 1990 . Canonical forms for nonlinear systems . Nonlinear Control Systems Design 1992, Selected papers from the 1st IFAC Symposium . 1990 . Edited by: Isidori , A . pp. 33 – 38 . Oxford : Pergamon Press .
   Google Scholar