Indirect Measurement of Nonlinear Effects by State Observers

  • P. C. Müller
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


Vibration and control systems are often influenced by troublesome nonlinear effects such as Coulomb friction, backlash, or hysteresis. In this contribution an indirect measuring technique of the actual values of those nonlinearities is presented. Based on a fictitious model of the time behaviour of the nonlinearities a state observer of an extended dynamical system is designed resulting in estimates of the nonlinear effects. In the paper the theory of this approach, an illustrative example, and a practical application in the position control of robots are considered. The proposed method is a successful tool to register indirectly the nonlinear effects of vibration and control systems.


Nonlinear Effect State Observer Coulomb Friction Vibration System Identity Observer 
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  1. 1.
    Müller P.C.; Lückel, J.: Zur Theorie der Störgrößenaufschaltung in linearen Mehrgrößenregelungssystemen. Regelungstechnik 25 (1977) 54–59.MATHGoogle Scholar
  2. 2.
    Müller P.C.; Lückel, J.: Optimal multivariable feedback system design with disturbance rejection. J. Problems of Control and Information Theory 6 (1977) 211–227.MATHGoogle Scholar
  3. 3.
    Luenberger, D.G.: An introduction to observers. IEEE Transact. Automatic Control AC-16 (1971) 596–602.Google Scholar
  4. 4.
    Ackermann J.: Einführung in die Theorie der Beobachter. Regelungstechnik 24 (1976) 217–226.MathSciNetGoogle Scholar
  5. 5.
    Müller, P.C.; Truckenbrodt, A.: Entwurf eines optimalen Beobachters. Regelungstechnik 25 (1977) 381–387.MATHGoogle Scholar
  6. 6.
    Müller, P.C.: Design of optimal state-observers and its application to maglev vehicle suspension control. Proc. 4the Int. IFAC Symposium on Mulitvariable Technological Systems, Fredericton/Canada, 4–8 July 1977, Paper No. 25 (revised version).Google Scholar
  7. 7.
    Cesari, L.: Asymptotic behavior and stability problems in ordinary differential equations, 2nd ed. Berlin, Heidelberg, New York: Springer-Verlag 1963.MATHGoogle Scholar
  8. 8.
    Ackermann, J.; Müller, P.C.: Dynamical behaviour of nonlinear multibody systems due to Coulomb friction and backlash. Preprints IFAC/IFIP/IMACS Int. Symp. Theory of Robots. Wien, Austria, 3–5 Dec. 1986, Austrian Center for Productivity and Efficiency, Wien 1986, 289–294.Google Scholar
  9. 9.
    Müller. P.C.: Compensation of Coulomb friction in the position control of industrial robots. In: Hiller, M; Sorg, H. (eds.): Proc. 3rd German-Japanese Seminar on Nonlinear Problems in Dynamical Systems–Theory and Applications; University of Stuttgart 1987, 130–1311.Google Scholar
  10. 10.
    Ackermann, J.: Positionsregelung reibungsbehafteter elastischer Industrieroboter. VDI-Fortschr: Ber. Reihe 8, Nr. 180, Düsseldorf 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • P. C. Müller
    • 1
  1. 1.Safety Control EngineeringUniversity of WuppertalWuppertal 1Germany

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