Active Attenuation of Periodic Vibration in Nonlinear Systems Using an Adaptive Harmonic Controller

Abstract

The article describes a nonlinear adaptive controller for the attenuation of harmonic disturbances in nonlinear systems. The steepest descent algorithm is used to adapt the controller coefficients and synthesize the optimum periodic waveform at the input of the nonlinear system, giving the best attenuation of the disturbance. A simple frequencydomain model of the system is required to implement the steepest descent approach. The scheme is particularly applicable where the secondary actuator used for active vibration control is a nonlinear device such as a magnetostrictive actuator. Simulation studies show that an adaptive scheme of this type is robust to the choice of frequency-domain model when the nonlinearity is hysteretic, but much more sensitive when the nonlinearity is a saturation function. A real-time adaptive harmonic controller has been built and used to control the motion of a magnetostrictive actuator. With dc and 7 harmonics under control the system was able to overcome the inherent nonlinearity of the actuator at fundamental frequencies in excess of 3 kHz.