Simulation studies on nonlinear dynamics and chaos in a MEMS cantilever control system

We discovered period doubling and chaos in a simulated MEMS cantilever system with electrostatic sensing and actuation, intended for a MEMS based mass storage chip, with and without servo control. We used a graphical interface for a Poincare map method that allowed us to simulate multiple initial conditions simultaneously. We investigated both the static and dynamic instabilities of the MEMS cantilever system subjected to weak and strong disturbances. We observed bistability and a Hopf bifurcation in the closed loop controlled cantilever system without disturbances. We simulated the loop gain and the phase margin when the system was subjected to weak disturbances. Furthermore, we have found the period doubling, chaos and strange attractors for both the open and closed loop cantilever systems subjected to strong disturbances. For one case the stable operation range is significantly reduced by 25% because of a chaotic response.

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