Experimental and Simulation-Based Investigation of Instability Phenomena and Stability Conditions at Resonance Point in Extremum Seeking Control Systems

In order to find quantitative stability conditions at the equilibrium (i.e., extremum) point on extremum seeking control (ESC) system, this paper investigates a shape of stability region when the compensator gain and amplitude of perturbation signal are varied both in experiment and simulation. First, by applying ESC that considers integral characteristic of plant to a vibration power generator that changes its resonance frequency by changing the position of mass on the beam to track the vibration source frequency, it is experimentally shown that the stability region in the compensator-gain-and-perturbation-amplitude plane has the boundary of a curve with negative slope. Then, by applying conventional ESC to a plant of which resonance characteristic is simply modeled as a triangle shape, it is shown by simulation that the stability region in the plane has the boundary of an inverse proportional relation.