15 July 2002 Feedback control of an active material adaptive-tuned vibration absorber using relative phase
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Adaptive tuned vibration absorbers for attenuation of harmonic vibration may be realized through the use of active materials in absorber designs. For example, the variable elastic modulus of shape memory alloy may be used to incorporate variable springs in an absorber, such that the absorber natural frequency may be on-line tuned. The difficulty then becomes the control of the tuned condition of the absorber. One method for controlling the tuned condition of the absorber is to drive the relative phase between the primary system and the absorber to a desired value. The classical phase-locked loop is one method that might be used to achieve this control goal. An alternative method is to utilize a simple PI controller that uses the relative phase as an error signal. The map between the control input to the active material elements and the resulting relative phase can be modeled as a first-order linear system in series with a static nonlinearity with certain characteristics. This paper presents an analysis of the stability of the phase tracking of an adaptive tuned vibration absorber made of active material. The necessary characteristics for the map between the control signal and the resulting relative phase are presented. A control algorithm is developed that results in asymptotic stability of the system in the presence of an uncertain fixed excitation frequency. Results of implementation of an experimental ATVA on a primary system are presented.
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Keith A. Williams, Keith A. Williams, George T.C. Chiu, George T.C. Chiu, Robert J. Bernhard, Robert J. Bernhard, } "Feedback control of an active material adaptive-tuned vibration absorber using relative phase", Proc. SPIE 4701, Smart Structures and Materials 2002: Smart Structures and Integrated Systems, (15 July 2002); doi: 10.1117/12.474659; https://doi.org/10.1117/12.474659

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