Extending the piezoelectric transducer bandwidth of an optical interferometer by suppressing resonance using a high dimensional IIR filter implemented on an FPGA

This paper considers the application of Field Programmable Gate Array (FPGA)-based infinite impulse response (IIR) filtering to increase the usable bandwidth of a piezoelectric transducer used in optical phase locking. We experimentally perform system identification of the interferometer with the cross-correlation method integrated on the controller hardware. Our model is then used to implement an inverse filter designed to suppress the low frequency resonant modes of the piezoelectric transducer. This filter is realized as a 24th-order IIR filter on the FPGA, while the total input-output delay is kept at 350 ns. The combination of the inverse filter and the piezoelectric transducer works as a nearly flat response position actuator, allowing us to use a proportional-integral (PI) control in order to achieve stability of the closed-loop system with significant improvements over a non-filtered PI control. Finally, because this controller is completely digital, it is straightforward to reproduce. Our control scheme is suitable for many experiments that require highly accurate control of flexible structures.