Stability analysis of real-time dynamic substructuring using delay differential equation models

MI Wallace, J Sieber, SA Neild, DJ Wagg, B Krauskopf

Research output: Working paper

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Real-time dynamic substructuring is an experimental technique for testing the dynamic behaviour of complex structures. It involves creating a hybrid model of the entire structure by combining an experimental test piece --- the substructure --- with a numerical model describing the remainder of the system. In this paper we focus on the influence of delay in the system, which is generally due to the non-instantaneous nature of the involved transfer systems (actuators). This naturally gives rise to a delay differential equation (DDE) model of the substructured system. With the case of a substructured system consisting of a single mass-spring oscillator we demonstrate how the DDE model can be used to understand the influence of the response delay of the actuator. Specifically, we describe a number of methods for identifying the critical delay time above which the system becomes unstable, which is characterized by positive exponential growth. It is a typical situation in dynamic substructuring that the response time of the actuators exceeds the critical delay time. Therefore, additional (control) techniques need to be implemented in practice. We demonstrate with an adaptive delay compensation technique that the substructured mass-spring oscillator system can be stabilized successfully in an experiment. The approach of DDE modelling allows us to determine the dependence of the critical delay on the parameters of the delay compensation scheme. In this way it is possible to develop specific testing strategies that ensure stable operation of the substructured system. Finally, we describe an over-compensation method that is particularly suited to ensure stable testing of structures with very low damping.
Original languageEnglish
Publication statusUnpublished - 2004

Bibliographical note

Additional information: Preprint submitted to Earthquake Engineering & Structural Dynamics

Sponsorship: The research of M.I.W. is supported by an EPSRC DTA and that of J.S. by EPSRC grant
GR/R72020/01. D.J.W. and B.K. are EPSRC Advanced Research Fellows.


  • delay dfifferential equations
  • substructuring
  • delay compensation
  • hybrid testing


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