This paper is concerned with the hole-tone feedback cycle problem, also known as Rayleigh's bird-call. A simulation method for analyzing the influence of non-axisymmetric perturbations of the jet on the sound generation is described. In planned experiments these perturbations will be applied at the jet nozzle via piezoelectric or electro-mechanical actuators, placed circumferentially inside the nozzle at its exit. The mathematical model is based on a three-dimensional vortex method. The nozzle and the holed end-plate are represented by quadrilateral vortex panels, while the shear layer of the jet is represented by vortex rings, composed of vortex filaments. The sound generation is described mathematically using the Powell-Howe theory of vortex sound. The aim of the work is to understand the effects of a variety of flow perturbations, in order to control the flow and the accompanying sound generation.