19 June 2000 Analytical solution technique for multiple-patch piezoelectric sensor-actuator vibration control problems
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An analytical method is given for the determination of the eigenfunctions and eigenfrequencies for one-dimensional structural vibration problems in the presence of patch sensors and patch actuators. The method is based on converting the differential equation formulation of the problem to an integral equation formulation. The conversion is accomplished by introducing an explicit Green's function. The Green's function consists of two parts, one taking account of the stiffness and the other taking account of the control moments induced by the distributed actuators. The control moments involve piezoelectric constants and feedback voltages made up of gains times the sensor signals. Obtaining the eigenvalues and eigenfunctions of this integral equation gives the solution to the piezo-control problem.
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James M. Sloss, John C. Bruch, Ibrahim S. Sadek, Sarp Adali, "Analytical solution technique for multiple-patch piezoelectric sensor-actuator vibration control problems", Proc. SPIE 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures, (19 June 2000); doi: 10.1117/12.388793; https://doi.org/10.1117/12.388793



Differential equations

Vibration control



Feedback control

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