Adaptive vibration control of a mechanical system with nonlinear damping excited by a tonal disturbance

In this study, an adaptive control system to reduce the tonal vibration of a mechanical system characterized by nonlinear damping is considered. Since the response of the system to a sinusoidal excitation is however 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, 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 fix linear model of the plant, can be slow to converge and may not achieve the desired performance. The use of an online 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.