Active Attenuation of Acoustic Noise Using Adaptive Armax Control.

An adaptive auxiliary input autoregressive moving average (ARMAX) control system using the recursive least -squares lattice for system identification is developed for active control of dynamic systems. The closed-loop adaptive ARMAX control system is applied to active acoustic noise reduction in three-dimensional spaces. The structure of the ARMAX system is compared to that for duct cancellation systems, model-reference control systems, and the general field solution and is seen as a reasonable approach for active field control in the general case. The ARMAX system is derived for multiple inputs and outputs where the measured outputs are to be driven to desired waveforms with least -squares error using a multi-channel ARMAX lattice for recursive system identification. A significant reduction in complexity is obtained by neglecting the ARMAX zeros for the special case of active attenuation of non-dispersive acoustic waves. It is shown that using the least-squares lattice requires fewer multiplies, divides, additions, and subtractions than the recursive least-squares algorithm which is based on the matrix inversion lemma. Computational complexity is seen as an important issue in the application of adaptive ARMAX systems to active field control because the system must control relatively higher numbers of modes and frequencies in real time than are seen in industrial process plants for which the adaptive ARMAX systems were first developed using recursive least squares. Convergence requirements using the lattice system identification algorithm are the same as that for the recursive least squares algorithm in adaptive ARMAX system and are verified in numerical simulations using known ARMAX parameters. A real-time simulation of active attenuation of acoustic noise is presented using the blade-excited harmonics from a small axial flow fan. The adaptive ARMAX controller provides active attenuation for correlated spectral peaks but not for uncorrelated noise from turbulence. Since the feedback control filter must predict the optimal control input to the source far enough ahead in time to compensate for the propagation delay from the source to the sensor, the adaptive ARMAX system is seen to work well when the sensor is within several wavelengths of the control source.