The high-precision Penning-trap mass spectrometer Pentatrap aims at measurements of mass ratios of highly charged ions with an uncertainty of a few parts in 10−12. Within the context of this thesis, the development of an active feedback system and its possible applications for the Pentatrap experiment are described. This system allows to electronically feed back the signal from the axial detection electronics to one or multiple electrodes of the Penning trap, enabling the implementation of advanced ion manipulation techniques. It was successfully used to cool the apparent temperature of the detection electronics below the 4.2 K environment of the trap setup, enabling the application of ion feedback cooling. Furthermore, the quality-factor and the center frequency of the resonator, used in the detection system, was shown to be modified by coupling the feedback signal to the resonator. The feedback system was implemented using a novel concept, making use of real-time digital processing algorithms on an FPGA. This leads to very stable feedback operation and allows for highly dynamic variation of the feedback parameters, opening the possibility for new measurement schemes. A phase-sensitive measurements technique for the axial frequency was successfully implemented and tested, which inherently has the potential to achieve better accuracy compared to the commonly used axial dip detection. Additionally, a single-ion self-excited oscillator was realized, enabling the determination of the axial frequency at very high repetition rates. As the precision of the Pentatrap experiment is currently mainly limited by the uncertainty of the axial frequency measurement, the feedback system developed in this thesis will directly contribute to improving the precision of the mass measurements
