Direct connection between time-domain performance and frequency-domain characteristics

Matthew Franchek, Paul A. Herman

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


Presented are the relationships between the transient response characteristics of a closed-loop system due to a step input and the frequency response characteristics which influence this response. The class of transfer functions addressed include those which are RH2. The relationships developed are for the problem: Given: Y(s) = H(s)R(s) where H(s) ε RH2 and R(s) is ys. Find: The relationship ∥y(t)∥ ≤ Λy ∥H (jω)∥ where the scaling factor Λ is a function of the frequency-domain characteristics of H(s). These relationships are useful for feedback control in that hard time-domain constraints can be enforced as amplitude and phase conditions on the open-loop transfer function. Two applications using these relationships are developed. The first application demonstrates controller design for an actuator saturation constraint. The second application is the development of a performance prediction technique for minimum phase, stable regulating systems.

Original languageEnglish (US)
Pages (from-to)1021-1042
Number of pages22
JournalInternational Journal of Robust and Nonlinear Control
Issue number12
StatePublished - Jan 1 1998

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Chemical Engineering(all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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