Complex dynamics in classical control systems

Joaquín Alvarez*, Esteban Curiel, Fernando Verduzco

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


An analysis of the complex dynamical behavior of second-order linear plants controlled with conventional controllers is presented. The control signal is passed through a classical nonlinearity before being applied to the plant. Existence of periodic and homoclinic orbits is discussed. Using the Melnikov/Smale and Genesio/Tesi methods some conditions about the existence of invariant strange sets are also established. It is shown that simple classical control schemes with typical nonlinearities can exhibit chaotic dynamics in a certain range of the controller parameters. Numerical and experimental results support the analysis presented.

Original languageEnglish
Pages (from-to)277-285
Number of pages9
JournalSystems and Control Letters
Issue number5
StatePublished - 10 Oct 1997
Externally publishedYes


  • Bifurcations
  • Chaos
  • Harmonic balance method
  • Melnikov theory
  • PI control


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