In this paper, we present a modification of the fast phasor extremum-seeking control for the fast optimization of a class of Wiener-Hammerstein nonlinear dynamical systems. The proposed technique provides a significant improvement of the closed-loop system's performance. This study introduces a new adaptive amplitude technique that is used to adaptively adjust the perturbation amplitude to a small predetermined value in a neighbourhood of the system's unknown optimal equilibrium. An analysis of the system demonstrates that semi-global practical stability analysis of the overall system to the unknown optimum is achieved. The effectiveness of the proposed approach is illustrated using numerical examples. The approach is also implemented for the optimal operation of a lean burn combustion system.