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

Abstract

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(jω_osc), … , G(jnω_osc), being ω_osc the oscillation frequency, and where G(jω_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(jω’_osc) with 0 < ω’_osc < ω_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.

KEYWORDS:

• Asymmetric relay
• estimation
• system identification
• oscillation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by MINECO: [grant number DPI2017-84259-C2-2-R, RTI2018-094665-B-I00]; Ministerio de Ciencia e Innovación: [grant number TEC2015-69155-R]; CEIE, Generalitat Valenciana: [grant number ACIF/2018/244]; Universitat Jaume I: [grant number 18I411-Uji-b2018-39].