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.

[1]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[2]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[3]  Roland E. Best.  Phase-Locked Loops , 1984 .

[4]  C. Gokcek,et al.  Tracking the resonance frequency of a series RLC circuit using a phase locked loop , 2003, Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003..

[5]  Robert Patton Leland.  Adaptive mode tuning for vibrational gyroscopes , 2003, IEEE Trans. Control. Syst. Technol..

[6]  J. Stensby,et al.  Phase-Locked Loops: Theory and Applications , 1997 .

[7]  Simon Haykin,et al.  Communication Systems , 1978 .

[8]  Cevat Gokcek,et al.  Analysis and design of resonance tuning systems , 2004, SPIE Optics East.

[9]  Floyd M. Gardner,et al.  Phaselock techniques , 1984, IEEE Transactions on Systems, Man, and Cybernetics.