  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.
