On stability and application of extremum seeking control without steady-state oscillation

To enhance the dynamic and static performance of the extremum seeking control (ESC) scheme, a novel fast ESC scheme without steady-state oscillation is proposed, in which the structure of the classic ESC scheme is adjusted to make the sinusoidal excitation signal amplitude locally exponentially converge to zero. The improved ESC scheme can speed up the convergence to shorten the seeking time dramatically, and enlarge the search area to avoid falling to local extrema effectively. It can also reduce the sinusoidal excitation signal amplitude to eliminate the adverse effects of the steady-state oscillation eventually. The rigorous stability analysis and proof of the improved ESC scheme are provided in detail, and the simulation results are presented to illustrate its effectiveness and superiority. Finally, the application of the improved ESC scheme to antilock braking systems (ABS) has been discussed through comparing with classical perturbation-based ESC scheme and sliding-mode-based ESC scheme to illustrate the practicability of the improved scheme.