Application of frequency-domain neural networks to the active control of harmonic vibrations in nonlinear structural systems

The authors show how a nonlinear adaptive controller of quasi-neural architecture can be used to control harmonic vibrations even when it has to act through a nonlinear actuator element. The controller comprises a fixed nonlinearity to generate harmonics of the sinusoidal reference signal and a linear adaptive combiner. The coefficients in the adaptive combiner are adjusted using a steepest descent algorithm in which harmonic generation in the nonlinear system under control is taken into account. A neural model for this frequency domain description of a nonlinear system is discussed, and it is shown that using information derived from this model in the steepest descent algorithm amounts to backpropagating the error signal through the plant model