Independent estimation of input and measurement delays for a hybrid vertical spring-mass-damper via harmonic transfer functions

Ismail Uyamk, M. Mert Ankarali, Noah J. Cowan, Uluç Saranli, Ömer Morgül, Hitay Özbay

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations


System identification of rhythmic locomotor systems is challenging due to the time-varying nature of their dynamics. Even though important aspects of these systems can be captured via explicit mechanics-based models, it is unclear how accurate such models can be while still being analytically tractable. An alternative approach for rhythmic locomotor systems is the use of data-driven system identification in the frequency domain via harmonic transfer functions (HTFs). To this end, the input-output dynamics of a locomotor behavior can be linearized around a stable limit cycle, yielding a linear, time-periodic system. However, few if any model-based or data-driven identification methods for time-periodic systems address the problem of input and measurement delays in the system. In this paper, we focus on data-driven system identification for a simple mechanical system and analyze its dynamics in the presence of input and measurement delays using HTFs. By exploiting the way input delays are modulated by the periodic dynamics, our results enable the separate, independent estimation of input and measurement delays, which would be indistinguishable were the system linear and time invariant.

Original languageEnglish (US)
Pages (from-to)298-303
Number of pages6
Issue number12
StatePublished - Jul 1 2015
Externally publishedYes
Event12th IFAC Workshop on Time Delay Systems, TDS 2015 - Ann Arbor, United States
Duration: Jun 28 2015Jun 30 2015

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


  • Harmonic transfer functions
  • Legged locomotion
  • System identification
  • Time-delay estimation
  • Time-periodic systems


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