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Flatness based control of a nonlinear chemical reactor model. (English) Zbl 0865.93046
Summary: The nonlinear model of a continuous stirred tank reactor is shown to be flat. The flatness permits the design of suitable trajectories on the basis of the explicit stationary solution and the tracking of these trajectories asymptotically using quasi-static state feedback linearization. A nonlinear local observer with a time-varying gain is designed allowing the realization of the state feedback in the case of partial measurement of the state. Simulation results illustrate the tracking behavior of the closed loop with the observer.

MSC:
93C95 Application models in control theory
93C10 Nonlinear systems in control theory
93B07 Observability
Software:
Mathematica
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[1] Bestle, D.; Zeitz, M., Canonical form observer design for non-linear time-variable systems, Int. J. control, 38, 419-431, (1983) · Zbl 0521.93012
[2] Chen, H.; Kremling, A.; Allgöwer, F., Nonlinear predictive control of a CSTR benchmark problem, (), 3247-3252 · Zbl 1027.76566
[3] Delaleau, E.; Rudolph, J., Decoupling and linearization by quasi-static feedback of generalized states, (), 1069-1074
[4] Delaleau, E.; Fliess, M., Algorithme de structure, filtrations et découplage, C. R. acad. sci. Paris. Série I, 315, 101-106, (1992) · Zbl 0791.68113
[5] Fliess, M.; Rudolph, J., Corps de Hardy et observateurs asymptotiques locaux pour systèmes différentiellement plats, (1996), In preparation
[6] Fliess, M.; Lévine, J.; Rouchon, P., Generalized state variable representation for a simplified crane description, Int. J. control, 58, 277-283, (1993) · Zbl 0782.93049
[7] Fliess, M.; Lévine, J.; Martin, P.; Rouchon, P., On differentially flat nonlinear systems, (), 408-412
[8] Fliess, M.; Lévine, J.; Martin, P.; Rouchon, P., Linéarisation par bouclage dynamique et transformations de Lie-Bäcklund, C. R acad. sci. Paris, Série I, 317, 981-986, (1993) · Zbl 0796.93042
[9] Fliess, M.; Lévine, J.; Martin, P.; Rouchon, P., Flatness and defect of nonlinear systems: introductory theory andb examples, Int. J. control, 61, 1327-1361, (1995) · Zbl 0838.93022
[10] Freund, E., ()
[11] Isidori, A., ()
[12] Klatt, K.-U.; Engell, S., Kontinuierlicher rührkesselreaktor mit neben- und folgereaktion, VDI-berichte, nr. 1026, (), 101-108
[13] Klatt, K.-U.; Engell, S.; Kremling, A.; Allgöwer, F., Testbeispiel: rührkesselreaktor mit parallel- und folgereaktion, (), 425-432
[14] Martin, P., Contribution à l’étude des systèmes différentiellement plats, ()
[15] Nijmeijer, H.; van der Schaft, A.J., ()
[16] Rothfuβ, R.; Rudolph, J.; Zeitz, M., Flatness based control of a chemical reactor model, (), 637-642
[17] Rouchon, P., Necessary condition and genericity of dynamic feedback linearization, J. math. syst., estimat. control, 4, 1-14, (1994) · Zbl 0818.93012
[18] Rouchon, P.; Fliess, M.; Lévine, J.; Martin, P., Flatness and motion planning: the car with n trailers, (), 1518-1522
[19] Rudolph, J., A canonical form under quasi-static feedback, (), 445-448 · Zbl 0925.93107
[20] Rudolph, J., Well formed dynamics under quasi-static state feedback, (), 349-359 · Zbl 0838.93016
[21] Wolfram, S., ()
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