Data-driven tuning of a hybrid integrator-gain system

In an attempt to surpass Bode's gain-phase relationship, a hybrid integrator-gain system is studied that has significantly less phase lag in its describing function description when compared to a linear integrator. The hybrid integrator is designed to obtain improved low-frequency disturbance rejection properties under double-integrator (PI²D-like) control, but without the unwanted increase of overshoot otherwise resulting from adding an extra linear integrator. Closed-loop stability of the hybrid control design is guaranteed on the basis of a circle-criterion-like argument and checked through (measured) frequency response data. Closed-loop performance is obtained by data-driven optimization using gradients derived from a state-space description of the hybrid integrator, frequency response data from the linear part of the control system, and data obtained from machine-in-the-loop measurement.