Analog circuit implementation and adaptive neural backstepping control of a network of four Duffing-type MEMS resonators with mechanical and electrostatic coupling

This paper investigates the analog circuit implementation and adaptive neural backstepping control of a network of four Duffing-type MEMS resonators with mechanical and electrostatic coupling. Firstly, the mathematical model of such network is established by using a series-parallel mode of mechanical and electrostatic coupling between MEMS resonators. Secondly, the dynamic analysis reveals that the coupled network can generate complex nonlinear behaviors which seriously affect the system performance without taking actions. Thirdly, based on the energy flow theory, its equivalent analog electronic circuit is established to further verify inherent dynamical characteristics of a network of four Duffing-type MEMS resonators. Fourthly, to suppress the mentioned harmful nonlinear behaviors above, an adaptive neural backstepping control scheme is proposed here wherein the interval type 2 fuzzy neural network (IT2FNN) is used to estimate unknown nonlinear functions along with cosine barrier function to guarantee states boundedness. Stability analysis proves that all signals of the closed-loop system are bounded and the tracking errors are limited to the pregiven boundary. Finally, the effectiveness of our scheme is testified by abundant numerical simulation results.