ADAPTIVE FEEDFORWARD VIBRATION CONTROL OF A ME- CHANICAL SYSTEM WITH NONLINEAR DAMPING

This paper describes an adaptive system to control the tonal vibration of a mechanical system with cubic damping. Since the response of a system with cubic damping to a sinusoidal excitation is mainly sinusoidal, nonlinear controllers are not required for the control of a tone in such a mechanical system. The adaptation and stability of an adaptive control algorithm at the disturbance frequency, however, depends on the accuracy of the plant model. Since the tonal response of the nonlinear system changes with excitation level, conventional adaptive algorithms, with a linear model of the plant, can be slow to converge and may not achieve the desired performance. In this paper the use of an on-line observer is proposed, to estimate the describing function model of the plant, which will vary with excitation level. This allows the adaptive control algorithm to converge more quickly than using a fixed plant model, although care has to be taken to ensure that the dynamics of the observer do not interfere with the dynamics of the adaptive controller.