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Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received April 26, 2010
Accepted July 27, 2010

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Third quadrant Nyquist point for the relay feedback autotuning of PI controllers

Jeonguk Byeon Jin-Su Kim Su Whan Sung Won Ryoo¹ Jietae Lee^†

Department of Chemical Engineering, Kyungpook National University, Daegu 702-701, Korea ¹Department of Chemical Engineering, Hongik University, 72-1 Sangsu-dong, Seoul 121-791, Korea

jtlee@knu.ac.kr

Korean Journal of Chemical Engineering, February 2011, 28(2), 342-347(6), 10.1007/s11814-010-0391-4

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Abstract

The original relay feedback autotuning method of Astrom and Hagglund [1] is based on the Nyquist point at the phase angle of -π (the critical frequency). Recently, Friman and Waller [8] showed that the critical frequency is too high to tune PI controllers and proposed an autotuning method that finds a Nyquist point at the third quadrant through the two-channel relay. Here, the method to find Nyquist points in the third quadrant is revisited and adaptive relay feedback method which can be applied to noisy processes is proposed. It is shown that the bandwidths of PI control systems and the first-order plus time delay model identifications support the Nyquist point at the third quadrant. Nyquist points at the third quadrant can be obtained by introducing a filter and hysteresis to the relay feedback loop. However, the filter time constant and the size of hysteresis should be adjusted iteratively because their phase shifts are dependent on the resulting relay oscillation frequency. Simulations show that this adaptive relay feedback method_x000D_ finds a given Nyquist point at the third quadrant accurately under noisy environments and provides excellent PI control systems.

Keywords

Nyquist Points Third Quadrant PI Controller Tuning Filters Hysteresis

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