ACTIVE ATTENUATION OF PERIODIC VIBRATION IN NONLINEAR-SYSTEMS USING AN ADAPTIVE HARMONIC CONTROLLER

The article describes a nonlinear adaptive controller for the attenuat ion of harmonic disturbances in. nonlinear systems. The steepest desce nt algorithm is used to adapt the controller coefficients and synthesi ze the optimum periodic waveform at the input of the nonlinear system, giving the best attenuation of the disturbance. A simple frequency-do main model of the system is required to implement the steepest descent approach. The scheme is particularly applicable where the secondary a ctuator used for active vibration control is a nonlinear device such a s a magnetostrictive actuator. Simulation studies show that an adaptiv e scheme of this type is robust to the choice of frequency-domain mode l when the nonlinearity is hysteretic, but much more sensitive when th e nonlinearity is a saturation function. A real-time adaptive harmonic controller has been built and used to control the motion of a magneto strictive actuator. With de and 7 harmonics under control the system w as able to overcome the inherent nonlinearity of the actuator at funda mental frequencies in excess of 3 kHz.