  Nanobeam optomechanical crystals, in which localized GHz frequency mechanical
modes are coupled to wavelength-scale optical modes, are being employed in a
variety of experiments across different material platforms. Here, we
demonstrate the electrostatic tuning and stabilization of such devices, by
integrating a Si$_3$N$_4$ slot-mode optomechanical crystal cavity with a
nanoelectromechanical systems (NEMS) element, which controls the displacement
of an additional "tuning" beam within the optical near-field of the
optomechanical cavity. Under DC operation, tuning of the optical cavity
wavelength across several optical linewidths with little degradation of the
optical quality factor ($Q\approx10^5$) is observed. The AC response of the
tuning mechanism is measured, revealing actuator resonance frequencies in the
10 MHz to 20 MHz range, consistent with the predictions from simulations.
Feedback control of the optical mode resonance frequency is demonstrated, and
alternative actuator geometries are presented.
