Two-cascaded gradient extremum closed loop with seeking self-oscillations

This paper presents further development of the cascaded gradient extremum seeking control loop design. Such closed loop consists of two cascades. The inner cascade includes the dynamical part of a plant, while the outer cascade works with an extremum characteristic. The frequently used synchronous detector method is applied as gradient evaluation mechanism, but its technical realization is nonstandard. Structure of the inner cascade allows to obtain the self-oscillation signal. These oscillations can be further used as seeking oscillations for extremum characteristic gradient evaluation. This paper provides calculations of seeking oscillations parameters and recommendations for the correct choice of these parameter values.