Chaotic Behavior and Adaptive Control of the Arch MEMS Resonator With State Constraint and Sector Input

This paper mainly investigates adaptive control problem of the arch micro-electro-mechanical system (MEMS) resonator. To facilitate controller design, the power spectrum and bifurcation diagram are provided to judge whether the arch MEMS resonator is in chaotic oscillation or not under distributed electrostatic actuation. In the process of creating the controller, the Nussbaum function is employed to solve the issue of unknown control direction from the sector nonlinear input, and the barrier Lyapunov function is utilized to prevent constraint violation when the arch MEMS resonator faces physical limitations. Meanwhile a first-order filter is introduced to prevent repeated computation of the virtual control signal, and a Chebyshev neural network by merging an adaptive law is adopted to learn the behavior of unknown dynamics. Furthermore, an extended state observer which lifts the constraint against physical sensors is developed to estimate immeasurable states. Then, an adaptive control scheme fused with the Nussbaum function, filter and observer is created in the framework of backstepping without imposing any conditions on state variables and control direction of sector input. It is proved that all signals in the closed-loop system are bounded by selecting parameters appropriately. Finally, simulation verifications are presented to show the feasibility of the proposed method.