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(jωosc), ... , G(jnωosc), being ωosc the oscillation frequency, and where G(jωosc) 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(jω'osc) with 0 < ω'osc < ωosc. 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. [ABSTRACT FROM AUTHOR]