Adaptive resonance tuning through feedback

An adaptive control method that tunes the resonant frequency of a lightly damped second order system to its excitation frequency is investigated. The resonance tuning is achieved by using proportional feedback around the second order system and adaptively controlling the feedback gain using the error between the excitation and resonant frequencies. This error is obtained by a phase detector. Assuming that the parameters of the lightly damped second order system are slowly time-varying, a nonlinear time-varying model that accurately predicts the performance of the resonance tuning system is developed. This developed model is subsequently linearized to obtain a linear time-invariant model that facilitates both analysis and design of the resonance tuning system. Based on the developed linear time-invariant model, guidelines for designing the resonance tuning system are also provided. The results are illustrated by examples.