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Online Frequency Domain Identification Method for Stable Systems

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Part of the Lecture Notes in Electrical Engineering book series (LNEE,volume 327)


An online estimation method for single-input single-output (SISO)-type stable systems is discussed based on frequency transformation technique. Reported method based on fast Fourier transform (FFT) is an off-line identification method means the controller is required to remove from the closed loop at the time of autotuning test. So the modified method is suggested for online identification and has been tested on several systems to show the effectiveness of the method. A relay with hysteresis in parallel with proportional–integral (PI) controller induces stationary oscillation cycle whose frequency and amplitude are used for system identification. We consider the development of a non-iterative approach with less computational efforts and a reasonable amount of data. A simulation study is given to illustrate the potential advantage of the presented method.


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  1. Atherton DP (2006) Relay autotuning: an overview and alternative approach. Ind Eng Chem Res 45:4075–4080

    Article  Google Scholar 

  2. Tan KK, Lee TH, Jiang X (2000) Robust on-line relay automatic tuning of PID control system. ISA Trans 39(2):219–232

    Article  Google Scholar 

  3. Wang QG, Lee TH, Lin C (2003) Relay feedback: analysis, identification and control. Springer, London

    Book  Google Scholar 

  4. Wang QG, Hang CC, Bi Q (1997) A technique for frequency response identification from relay feedback. IEEE Trans Control Syst Technol 7(1):122–128

    Article  Google Scholar 

  5. Kano M, Ogawa M (2009) The state of the art in advanced chemical process control in Japan. In: IFAC symposium ADCHEM2009

    Google Scholar 

  6. Udaykumar YR, Sreenivasappa VB (2009) Design and implementation of FPGA based low power digital PID controllers. In: Fourth international conference on industrial and information systems, ICIIS 2009, 28–31 Dec 2009

    Google Scholar 

  7. Schei TS (1992) A method for closed loop automatic tuning of PID controllers. Automatica 28(3)

    Google Scholar 

  8. Tan KK, Ferdous R, Huang S (2002) Closed-loop automatic tuning of PID controller for nonlinear systems. Chem Eng Sci 57:3005–3011

    Article  Google Scholar 

  9. Ho WK, Honga Y, Hanssonb A, Hjalmarssonc H, Denga JW (2003) Relay auto-tuning of PID controllers using iterative feedback tuning. Automatica 39:149–157

    Article  MATH  Google Scholar 

  10. Arruda GHM, Barros PR (2003) Relay-based gain and phase margins PI controller design. IEEE Trans Instrum Measur 52(5):1548–1553

    Google Scholar 

  11. Majhi S (2005) On-line PI control of stable processes. J Process Control 15:859–867

    Article  Google Scholar 

  12. Tsay TS (2009) On-line computing of PI/lead compensators for industry processes with gain and phase specifications. Comp Chem Eng 33:1468–1474

    Article  Google Scholar 

  13. Mehta U, Majhi S (2012) On-line relay test for automatic tuning of PI controllers for stable processes. Trans Inst Measur Control 34(7):903–913

    Article  Google Scholar 

  14. Wang QG, Bi Q, Zou B (1997) Use of FFT in relay feedback systems. IET Elect Lett 33(12):1099–1100

    Article  MathSciNet  Google Scholar 

  15. Kuhfittig PKF (1978) Introduction to the Laplace transform. Plenum, New York

    Book  MATH  Google Scholar 

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Correspondence to Priti Kshatriy .

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Kshatriy, P., Mehta, U. (2015). Online Frequency Domain Identification Method for Stable Systems. In: Vijay, V., Yadav, S., Adhikari, B., Seshadri, H., Fulwani, D. (eds) Systems Thinking Approach for Social Problems. Lecture Notes in Electrical Engineering, vol 327. Springer, New Delhi.

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2140-1

  • Online ISBN: 978-81-322-2141-8

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