H_∞ active minimization of acoustic energy in a sound field through common acoustical pole and zero modeling

A method of feedback control that minimizes the total acoustic potential energy in a sound field excited by an unknown disturbance is introduced. A state-space description of an acoustic plant is derived using common acoustical pole and zero modeling of room transfer functions, which we consider an effective scheme for experimental system identification. The feedback controller was designed using H_∞ control theory to achieve both robust performance and high stability. Computer simulations verified that the resonant peaks in the frequency spectrum of the total acoustic potential energy could be attenuated in the low-frequency range involved in the nominal model of the plant without exciting the residual dynamics in the high-frequency range. A practical control system was built for experimental verification of the theory. Experimental results showed that the proposed control method provided the desired performance in real-time.