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

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

Enhanced Event-Based Identification Procedure for Process Control

“…The second solution is to insert a nonlinear block composed of an integrator plus a relay in parallel with the original relay; ,− the phase lag of the integrator produces the orthogonal displacement of the lower frequencies. The third solution is to introduce filters in the loop; , by designing the filter adequately, it is possible to introduce lag and arbitrarily displace a point of the loop transfer function to a desired point.…”

A speed loop autotuning method based on signal injection for electrical drives

“…Many variations have been proposed for better autotuning, including a saturation relay [13], relay with a P control preload [11] and a two-level relay [10]. Relay methods have anyway some disadvantages [2]. First, in noisy environments, pure relay feedback methods can suffer from chattering, which is not allowed in some processes.…”