  The possibility to apply active feedback to a single ion in a Penning trap
using a fully digital system is demonstrated. Previously realized feedback
systems rely on analog circuits that are susceptible to environmental
fluctuations and long term drifts, as well as being limited to the specific
task they were designed for. The presented system is implemented using an
FPGA-based platform (STEMlab), offering greater flexibility, higher temporal
stability and the possibility for highly dynamic variation of feedback
parameters. The system's capabilities were demonstrated by applying feedback to
the ion detection system primarily consisting of a resonant circuit. This
allowed shifts in its resonance frequency of up to several kHz and free
modification of its quality factor within two orders of magnitude, which
reduces the temperature of a single ion by a factor of 6. Furthermore, a
phase-sensitive detection technique for the axial ion oscillation was
implemented, which reduces the current measurement time by two orders of
magnitude while simultaneously eliminating model-related systematic
uncertainties. The use of FPGA technology allowed the implementation of a
fully-featured data acquisition system, making it possible to realize feedback
techniques that require constant monitoring of the ion signal. This was
successfully used to implement a single-ion self-excited oscillator.
