Dynamics analysis, integrated circuit implementation, and prescribed performance backstepping control of a coupled network of 5-DOF Duffing-type MEMS resonators

This paper investigates the nonlinear dynamics of a coupled network of 5-DOF (Degree of Freedom) Duffing-type micro-electro-mechanical systems (MEMS) resonators, develops an integrated circuit-based equivalent circuit system, and proposes a prescribed-performance adaptive neural network backstepping controller. Initially, to improve the modal frequency and dynamic range of traditional single or multiple resonators (up to four DOFs), we propose a coupled network consisting of 5 MEMS resonators which mutually couples in a specified layout, and accurately establish the relevant mathematical model. The dynamic analysis reveals how coupling stiffness and excitation amplitude influence the system transitions be-tween periodic and chaotic states. Subsequently, to mitigate risks in the fabrication-stage development of the MEMS chips, a PCB-based platform is constructed to validate the model and define the design boundaries. Furthermore, a prescribed-performance adaptive backstepping control scheme is proposed to simultaneously suppress chaos, guarantee fast preset performance convergence, and achieve high-precision tracking under constraints. In this scheme, an accelerated tracking differentiator not only mitigates the complexity explosion of conventional backstepping but also enhances convergence speed, while an interval type-2 fuzzy neural network (IT2FNN) and an improved cubic prescribed performance function (CPPF) are adopted to approximate unknown nonlinearities and constrain tracking errors within predefined bounds, respectively. Finally, comprehensive simulation results demonstrate the scheme's feasibility, robustness, and superior performance.