Classical extremum seeking control (ESC), when applied to systems with disturbances, can be subject to large deviations during transients caused by abrupt changes in the disturbances. In oil and gas production applications, such deviations can make ESC impractical. This paper presents a simple yet practical extension to the classical gradient-based extremum seeking control to make it robust to such disturbances, by removing the effect of the disturbance with a priori information of the disturbance model. Modelling and robustness of the disturbance models are discussed. The proposed method is demonstrated by a simulation-based study on gas lift optimization of a single well in oil and gas production.
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