Experimental and Numerical Validation of Digital, Electromechanical, Parametrically Excited Amplifiers

Abstract

A parametric amplifier having a tunable, dualfrequency pumping signal and a controlled cubic stiffness term is realized and investigated experimentally. This device can be tuned to amplify a desired, single frequency weak signal, well below resonance. The transition between a previously described theoretical model and a working prototype requires an additional effort in several areas: modeling, design, calibration, identification, verification, and adjustment of the theoretical model. The present paper describes these necessary steps and analyzes the results. Tunability is achieved here by adding a digitally controlled feedback, driving a linear mechanical oscillator with an electromechanical actuator. The main advantage of the present approach stems from the separation of the controlled parametric and nonlinear feedback terms which are linked to the resonating element. This separation allows for the realization of feedback in an electronic form where a digital implementation adds further advantages as the feedback coefficients can be tuned in situ. This arrangement benefits from the mechanical resonance of a structure and from the ability to set the parametric excitation such that it accommodates sinusoidal input signals over a wide range of frequencies. The importance of an in situ identification phase is made clear in this work, as the precise setting of model and feedback parameters was shown to be crucial for successful application of the amplifier. A detailed modelidentification effort is described throughout this paper. It has been shown through identification that the approach is robust despite some modeling uncertainties and imperfections.