On the search speed for the Extremum Seeking Control 2D-schemes. Part I - signal processing using orthogonal dither signals

In this paper an analysis of the Extremum Seeking Control (ESC) 2D-scheme for the dual-inputs single-output (DISO) systems is presented. The ESC 2D-schemes have two loops where the output signal is obtained based on two different ESC algorithms proposed in the literature. The basic high-order ESC (bhoESC) 2D-scheme and an improved ESC variant will be analyzed here based on the two orthogonal dither signals. The proposed ESC scheme is based on a band-pass filter (BPF) instead of the series combination of high-pass (HP) and low-pass (LP) filters used in the bhoESC scheme. The processing of the output signal shows that the search speed in both bpfESC loops depends on the BPF cut-off frequencies. So, besides the gradient signals, the injected signals on the both bhoESC inputs contain the Low Frequencies (LF) components from the BPF band. Thus the dither persistence in the bpfESC loops is improved in comparison with the bhoESC scheme. The relations between the search speeds and the partial derivatives of an unknown DISO map are shown.