Forced Oscillations in Second Order SISO Systems

  • Jun Fu
  • A. P. Loh
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 99)


In the relay feedback system shown in Figure ?, when the magnitude of the forcing signal is larger enough, the phenomenon of forced oscillation occurs, that is, the system synchronizes itself automatically with the frequency of the external signal. Forced oscillation behaviors in First Order plus Time Delay system (FOPTD) has been discussed in many papers. But those behaviors in second order plus time delay system (SOPTD) is under discussed. In this paper, with analysis of the conditions of forced oscillation, the minimum magnitude of the external forcing signal for SOPTD system is obtained. Overdamped, underdamped, critically damped systems are discussed separately. Simulation results are given.


Forced Oscillation Second Order plus Dead Time system relay feedback auto-tuning 


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  1. 1.
    Lim, L.H., Loh, A.P., Fu, J.: Estimation of minimum conditions for forced oscillations in relay feedback systems. In: Proceedings of the 5th International Conference on Control and Automation, ICCA 2005, pp. 1262–1267 (2005)Google Scholar
  2. 2.
    Loh, A.P., Fu, J.: Forced oscillations in First Order Systems. In: Europe Control Conference, UK (September 2003)Google Scholar
  3. 3.
    Fu, J., Loh, A.P., Wei, Y.Y.: Forced Oscillations Conditions in Relay Feedback Control Systems. In: The Chinese Symposium on Information Science and Technology, CSIST 2010 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jun Fu
    • 1
  • A. P. Loh
    • 1
  1. 1.Mechanical and Electrical EngineeringWuhan Textile UniversityWuhanP. R. China

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