Abstract
With the aid of the symbolic calculating language MACSYMA, a program system has been realized for analyzing and designing the nonlinear system equations x=f(x, u), y=h(x, u). The special features of the program are on one hand the examination of controllability and observability of nonlinear systems, and on the other hand the design of nonlinear state feedback systems and state estimators. A rule-based handling of the program helps the user to select and to execute suitable analysis and design procedures. For this purpose, special structures of the nonlinear system equations, e.g. bilinear or canonical forms are recognized by symbolic calculations. Moreover, several heuristic and system theoretic rules are implemented in the MACSYMA program for application of the nonlinear methods. For a numeric evaluation and simulation of the symbolic results, interfaces to the external program systems ACSL and MATLAB are available.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
AKHRIF, O.; BLANKENSHIP, G.L.: Computer algebra for analysis and design of nonlinear control systems. Proceedings American Control Conference, Minneapolis 1987, 547–554.
BÄR, M., FRITZ, H.; ZEITZ, M.: Rechnergestützter Entwurf nichtlinearer Beobachter mit Hilfe einer symbolverarbeitenden Programmiersprache. Automatisierungstechnik 35 (1987), 177–183.
BIRK, J.; ZEITZ, M.: Computer-aided design of nonlinear observers. In: Nonlinear Control Systems Design — Selected Papers from the IFAC-Symposium Capri/Italy 1989 (A. Isidori, ed.), Pergamon Press, Oxford, 1990, 1–6.
BIRK, J.; ZEITZ, M.: Anwendung eines symbolverarbeitenden Programm-systems zur Analyse und Synthese von Beobachtern für nichtlineare Systeme. messen-steuern-regeln 12 (1990), 536–543.
CESAREO, G.; MARINO, R.: On the controllability properties of elastic robots. In: BALAKRISHNAN, A.V.; THOMA, M. (Eds.): Lecture Notes in Control and Information Sciences 63. Springer-Verlag, Berlin 1984, 352–363.
CESAREO, G.; MARINO, R.: The use of symbolic computation for power system stabilization: An example of computer aided design. In: BALAKRISHNAN, A.V.; THOMA, M. (Eds.): Lecture Notes in Control and Information Sciences 63. Springer-Verlag, Berlin 1984, 598–611.
DERESE, I.; NOLDUS, E.J.: Nonlinear control of bilinear systems. IEE Proceedings Part D 127 (1980), 169–175.
ISIDORI, A.: Nonlinear Control Systems, 2. Edition. Springer-Verlag Berlin, Heidelberg, New York 1989.
KRENER, A.J.: Normal forms for linear and nonlinear systems. In M. LUKSIC, C. MARTIN, W. SHADWICK (Eds.), Differential Geometry: The Interface between Pure and Applied Mathematics. Contemporary Mathematics 68 (1987), 157–189.
KELLER, H., FRITZ, H.: Design of nonlinear observers by a two-step-transformation. In FLIESS, M., HZEWINKEL (Eds.), Algebraic and Geometric Methods in Nonlinear Control Theory, Reidel, Dordrecht (1986), 89–98.
LUNZE, J.: Wissensbasierte Beratung beim rechnergestützten Entwurf von Automatisierungssystemen. messen-steuern-regeln 32 (1989), 204–209, 258–263.
NIJMEIJER, H.: Observability of a class of nonlinear systems: a geometric approach. Ric. Automatica 12 (1981), 50–68.
PHELPS, A.R.; KRENER, A.J.: Computation of observer normal form using MACSYMA. In: BYRNES, C.; MARTIN, C.; SEAKS, R. (eds.): Analysis and Control of Nonlinear Systems. North Holland 1988, 475–482.
RIMVALL, M.; KÜNDIG, M.: Intelligent help for CACE applications. Preprints 11th IFAC-Congress, Tallinn 1990, Vol. 10, 85–90.
TAYLOR, J.H.; JAMES, J.R.; FREDERICK, D.K.: Expert-aided control engineering environment for nonlinear systems. Preprints 10th IFAC-Congress, Munich 1987, Vol. 6, 363–368.
WALCOTT, B.L.; ZAK, S.H.: State observation of nonlinear uncertain dynamical systems. IEEE Transactions on Automatic Control AC-32 (1987), 166–170.
ZEITZ, M.: Canonical forms for nonlinear systems. In: Nonlinear Control Systems Design — Selected Papers from the IFAC-Symposium Capri/Italy 1989 (A. Isidori, ed.), Pergamon Press, Oxford, 1990, 33–38.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Birk, J., Zeitz, M. (1991). Program for symbolic and rule-based analysis and design of nonlinear systems. In: Jacob, G., Lamnabhi-Lagarrigue, F. (eds) Algebraic Computing in Control. Lecture Notes in Control and Information Sciences, vol 165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006933
Download citation
DOI: https://doi.org/10.1007/BFb0006933
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54408-1
Online ISBN: 978-3-540-47603-0
eBook Packages: Springer Book Archive