Abstract:

The performance of multichannel feedforward LMS-type control algorithms is improved if control is implemented in noninteracting coordinates. A decoupling matrix can be applied to sensor inputs and actuator outputs to transform the harmonic feedforward control problem into an orthogonal (i.e., principal component) coordinate system. Convergence of the adaptive algorithm is faster in the principal coordinate system, and sensitivity to sensor noise can be reduced by eliminating components associated with ill-conditioning. One question that arises is how quickly the decoupling matrix changes with frequency. This is important for control systems where the excitation frequency might wander about a nominal value. Results of a numerical study of this frequency dependence show that the decoupling matrix is stationary around a resonance, and has the highest rate of change between resonances. However, in some cases the matrix remains stationary between resonances. The frequency dependence of the decoupling matrix will be discussed for three control systems: a simply supported plate, a plate radiating into a half-space, and an enclosed cavity. [Work supported by NASA Langley Research Center.]