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

Active Cancellation of Acoustical Resonances with an FPGA FIR Filter