A hybrid integrator-gain system is discussed that aims for improved low-frequency disturbance rejection, while, at the same time, does not deteriorate overshoot and settling times when compared with a linear integrator. The hybrid integrator has similar phase advantages as the well-known Clegg integrator but without inducing the discontinuous behavior resulting from resetting system state values. Optimal tuning of the controller parameters of the hybrid integrator is strongly influenced by machine-specific properties and therefore favors a data-driven optimization approach. However, as a time-domain optimization algorithm can easily lead to nonrobust solutions in the sense of large peaking of the closed-loop frequency response functions, frequency-domain robustness constraints will be imposed. By means of an adaptive weighting filter design, the parameter updates are penalized upon violation of said robustness constraints. Posed in an unconstrained problem formulation, this is subsequently solved by applying a Gauss-Newton-based parameter update scheme.Closed-loop stability of the linear time-invariant plant and controller in feedback connection with a hybrid integrator-gain system element follows from a circle-criterion-like analysis, which is based on evaluating (measured) frequency response data. Measurement results obtained from an industrial wafer scanner demonstrate the effectiveness of the approach.