Cover
Vol. 15 No. 1 (2015)

Published: June 30, 2015

Pages: 20-24

Original Article

Robust PID and Fractional PI Controllers Tuning for General Plant Model

Abstract

In this paper, a design procedure which assumes general integer or noninteger order plant models ‘also can be unknown’ has been adopted to tune PID and fractional order PI (FOPI) controller. The design procedure depends on some specifications of frequency response of open loop system to ensure performance and robustness of step response of closed loop system. Firstly, the procedure is applied to integer order conventional PID (IOPID) controller, and then it has been extended to FOPI. Extensive simulation study has been made to investigate the performance of the obtained controllers, and also to compare between the two controllers. The simulation study has showed the validity and that the proposed controllers have good features in all of control demands, where it shows that these controllers have fast rise time with no overshoot and negligible steady state error. Also, it has showed that FOPI controller performs better than IOPID one.

References

  1. Lin Kong Rong, “The analyses and comparing about several kinds of different definitions of the fractional step derivative [J]”, Minjiang river college journal in October, 2003, 24(5):3-4.
  2. I. Podlubny, “Fractional-order systems and PID controllers”, IEEE Transactions on Automatic Control 44 (1999) 208–214.
  3. S.E. Hamamci, “An algorithm for stabilization of fractional-order time delay systems using fractional- order PID controllers”, IEEE Transactions on Automatic Control 52 (2007) 1964–1969.
  4. H.F. Raynaud, A. Zergainoh, “State-space representation for fractional-order controllers”, Automatica 36 (2000) 1017–1021.
  5. A. Oustaloup, “The CRONE approach: theoretical developments and major applications”, in: Proc. Second IFAC Workshop on Fractional Differentiation and its Applications, Porto, Portugal, 2006, pp. 39–69.
  6. B.M. Vinagre, V. Feliu, “Optimal fractional controllers for rational order systems: a special case of the Wiener- Hopf spectral factorization method”, IEEE Transactions on Automatic Control 52 (2007) 2385–2389.
  7. H.S. Li, Y. Luo, Y.Q. Chen, “A fractional order proportional and derivative (FOPD) motion controller: tuning rule and experiments”, IEEE Transactions on Control Systems Technology 18 (2010) 516–520.
  8. I. Podlubny, “Fractional Differential Equations”, Academic Press, San Diego, 1999.
  9. R. Hilfer (Ed.), “Applications of Fractional Calculus in Physics”, World Scientific Pub Co., NJ, 2001.
  10. Mohammad Saleh Tavazoei, “Overshoot in the step response of fractional-order control systems”, Journal of Process Control 22 (2012) 90– 94.
  11. W. K. Ho, C. C. Hang and L. S. Cao, “Tunning of PI controllers based on gain and phase margin specifications”, ELSEVIER, Automatica volume31 issue 3, (1995) 496-502.
  12. D. Wang and X. Gao "Analytical Tuning of PI ג Controllers with Phase Margin and Robustness”, IEEE the second international conference on intelligent control and information processing, 2011.