Active Cancellation of Acoustical Resonances with an FPGA FIR Filter

Abstract: We present a novel approach to enhancing the bandwidth of a feedback-controlled mechanical system by digitally canceling acoustical resonances (poles) and anti-resonances (zeros) in the open-loop response via an FPGA FIR filter. By performing a real-time convolution of the feedback error signal with an inverse filter, we can suppress arbitrarily many poles and zeros below 100 kHz, each with a linewidth down to 10 Hz. We demonstrate the efficacy of this technique by canceling the ten largest mechanical resonances and anti-resonances of a high-finesse optical resonator, thereby enhancing the unity gain frequency by more than an order of magnitude. This approach is applicable to a broad array of stabilization problems including optical resonators, external cavity diode lasers, and scanning tunneling microscopes, and points the way to applying modern optimal control techniques to intricate linear acoustical systems.es to intricate linear acoustical systems.