A control system that tunes the resonant frequency of a lightly damped resonator to its excitation frequency in the face of detuning disturbances is investigated. The resonance tuning is achieved by adaptively controlling the resonant frequency of the resonator using the error between the excitation frequency and resonant frequency. Assuming that the parameters of the resonator are slowly time-varying, a nonlinear time-varying model that accurately predicts the tuning performance of the 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 provided. The results are illustrated by examples.
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.
A method that enhances the performance of a phase locked loop is proposed. The method is based on integrating an adaptive frequency estimator into a standard phase locked loop. This integration significantly improves the performance of the resulting phase locked loop and eliminates some design tradeoffs that are inherent in a standard phase locked loop. The proposed enhanced phase locked loop is analyzed and a nonlinear model that accurately predicts its performance is developed. This developed model is subsequently linearized to obtain a linear time-invariant model that facilitates both analysis and design of the enhanced phase locked loop. Based on the developed linear time-invariant model, guidelines for designing the enhanced phase locked loop are also provided. The results are illustrated by several examples.Index Terms-Phase lacked loops, adaptive frequency estimators, phase detectors.
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