Precision State Space Resonant Filter Structures for Digital Fixed-Point Converter Control Systems

Stationary frame converter control systems routinely use resonant filters because they produce infinite loop gain at resonance, which is critical to enable the elimination of steady state tracking errors at the desired AC frequency. However, digital resonant filters are susceptible to discretisation and coefficient rounding errors when implemented using fixed-point arithmetic. This paper investigates the fixed-point realisation of discrete state space resonant filters for zero-order hold (ZOH), first-order hold (FOH) and Tustin with pre-warping discrete formulations. Both shift-operator and delta-operator implementations are presented, to show how the state space structure offers significant benefits in terms of accuracy and the coefficient number range for a given bit resolution. The theoretical findings are supported by frequency domain analysis, simulation and experimental results.