Asymmetric delayed relay feedback identification based on the n-shifting approach

The paper presents an improvement of the n-shifting technique to identify the frequency response of an industrial process using a fully asymmetric and delaying relay. The n-shifting approach allows the calculation of n + 1 points of G(s) by an asymmetric relay experiment. This set of n points is composed of G(0), G(j omega(osc)), horizontal ellipsis , G(jn omega(osc)), being omega(osc) the oscillation frequency, and where G(j omega(osc)) is in most cases located in the third quadrant of the Nyquist map. By delaying the relay output and repeating a similar experiment it can be generated n additional points of G(s) where the first point is G(j omega'(osc)) with 0 < omega'(osc) < omega(osc). In this way, it is possible to depict the full output spectrum of G(s) from zero to very high frequencies by a short relay experiment. An example of identification and tuning of a PID controller with data from the n-shifting are presented to show the validity of the approach.