Resonance seeking control

An adaptive control method that seeks the unknown resonant frequency of a load and drives it at its resonant frequency to achieve optimal performance is proposed and investigated. The method is based on estimating the derivative of the average power delivered to the load with respect to the driving frequency and using this estimate to adaptively control the driving frequency. The estimate of the derivative of the average power is obtained by sinusoidally perturbing the driving frequency and synchronously demodulating the average power delivered to the load. Assuming that the driving frequency is sufficiently large compared to the amplitude of sinusoidal perturbation, a nonlinear model that accurately predicts the performance of the resonance seeking control 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 seeking control system. Based on the developed linear time-invariant model, guidelines for designing the resonance seeking control system are also provided. The results are illustrated by several examples