Demodulation considerations in extremum seeking control loops

This paper addresses a few demodulation aspects in extremum seeking (ES) control loops and their possible use in the tuning of the algorithm. After a quick review of the basics, different situations are discussed, and loop tuning methods are derived for each case. Main contributions are on high-pass filter and demodulation signal selection, under consideration of the excitation (dither) signal frequency and the system´s dynamics. Robustness issues are addressed, along with the following loop performance indicators: convergence speed and steady-state accuracy. Results are validated in computer simulations on an ideal case study, characterized by constant open-loop dynamics and an exact parabolic nonlinearity over its entire domain of operation. These two conditions allow for constant closed-loop characteristics of the ES algorithm and are necessary to obtain to establish its ideal behavior.