Saudi Cultural Missions Theses & Dissertations
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Item Restricted Modeling and Experimental Validation of Time Delay Effects in Nonlinear Digital Feedback-based Resonators(Saudi Digital Library, 2025) Koshak, Amro; Bajaj, NikhilThis work demonstrates the use of nonlinear digital feedback on a microelectromechanical system (MEMS) resonator to create dynamical bifurcation behavior, and through modeling and experiment, considers the significant effect of inherent and controlled feedback delays on the resulting dynamical system. The resonator used to experimentally validate the theoretical predictions is a piezoelectric microcantilever fabricated through the PiezoMUMPS process. Two equations of motion were studied and solved using two different perturbation methods. The first method was the Krylov-Bogolyubov (KB) averaging method, while the second equation of motion used the method of multiple time scales. The KB method focused on studying the effects of a delayed cubic stiffness feedback on system dynamics. The multiple time scales approach was also considered, and applied to a linear delayed feedback as an addition to the delayed cubic stiffness in the feedback. The experimental results were attained through the use of the Moku:Pro's Field programmable gate array (FPGA), which digitally implemented a tunable feedback to the resonator. Frequency sweeps were conducted under varying feedback parameters that demonstrated strong agreement between the analytical and experimental results. The results validated the flexibility of employing the FPGA and the effects of varying the feedback parameters digitally, and point towards a flexible means of implementing nonlinear sensing schemes with resonators in the future.20 0