Chaos in PID Controlled Nonlinear Systems

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Ablay G.

JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY, vol.10, no.4, pp.1843-1850, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.5370/jeet.2015.10.4.1843
  • Journal Name: JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1843-1850
  • Keywords: Chaos, Feedback systems, Linear control, Nonlinear systems, Chaotification, PID control, CONTINUOUS-TIME SYSTEMS, ANTI-CONTROL, LYAPUNOV EXPONENTS, DELAYED FEEDBACK, CHAOTIFICATION, SYNCHRONIZATION, GENERATION, DYNAMICS, BEHAVIOR
  • Abdullah Gül University Affiliated: Yes

Abstract

Controlling nonlinear systems with linear feedback control methods can lead to chaotic behaviors. Order increase in system dynamics due to integral control and control parameter variations in PID controlled nonlinear systems are studied for possible chaos regions in the closed-loop system dynamics. The Lure form of the feedback systems are analyzed with Routh's stability criterion and describing function analysis for chaos prediction. Several novel chaotic systems are generated from second-order nonlinear systems including the simplest continuous-time chaotic system. Analytical and numerical results are provided to verify the existence of the chaotic dynamics.