Accelerated adaptive stability control of the fractional-order MEMS resonator

In this paper, an accelerated adaptive stability controller based on the Chebyshev neural network (CNN) is devised to restrain chaotic oscillation and improve the dynamic performance of the fractional-order (FO) MEMS resonators. Firstly, the dynamic equation of the FO MEMS resonator is established. Secondly, the phase diagrams are presented to reveal the dynamic behaviors of the FO MEMS resonator. Then, an analog circuit of the MEMS resonator is constructed. During the design of the acceleration adaptive stability controller, the speed function, tracking differential (TD) and CNN are integrated into the technical framework of backstepping to realize the acceleration convergence, suppression of complex item explosion and unknown term approximation. In the last, simulation results illustrate that the designed controller can suppress chaotic oscillation and accelerated convergence.