in Wiley Online Library (wileyonlinelibrary.com).Relay feedback identification methods are widely used to find the process ultimate information and tune proportional-integral-derivative controllers. The conventional relay feedback method has several disadvantages, which include poor estimates of the process ultimate information for low-order processes, chattering of relay for noisy environments, and asymmetric relay responses for constant biases or slow drifts in the process outputs. Methods to mitigate each of the above disadvantages are available. However, a systematic method to treat all of them has not been studied yet. Here, simple relay feedback methods that resolve these problems by introducing band-pass filters in the feedback loop are proposed. The high-pass filter part in band-pass filter removes a constant bias or low frequency drift, and the low-pass filter part removes high frequency noise and high-order harmonic terms in the relay feedback oscillation, resulting better estimates of the process ultimate information. Because filters used for the proposed methods are able to reject constant biases, the process steady state gains can be estimated without disturbing the relay feedback oscillations and first order plus time delay (FOPTD) models can be obtained by combining the process steady state gains with the relay oscillation information. V V C

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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 finds a given Nyquist point at the third quadrant accurately under noisy environments and provides excellent PI control systems.

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Sustained oscillations are obtained by putting relays in the feedback loop, which provide ultimate periods and gains of processes that can be used to tune PID controllers. The ultimate periods obtained by conventional relay autotuning have relative errors up to 5% for first order plus time delay processes. To improve the estimation of ultimate periods, modified relays such as a saturation relay and a relay with preload have been available. However, these modifications lose the binary (on-off) property of the conventional relay. Here relays with multiple switching which produce pulse-widthmodulation (PWM) signals are proposed. They retain the binary property and show improved identification accuracies of ultimate parameters.