Nonlinear microelectromechanical systems (MEMS) analysis and design via the Lyapunov stability theory

This article applies the Lyapunov stability theory to microelectromechanical systems (MEMS) analysis and design taking into account electromagnetic and electromechanical features. Due to the mathematical rigor and unique systematic capabilities, the Lyapunov theory has been widely used. However, it is important to bridge the gap with practical applications to MEMS. Multidisciplinary studies are needed to be carried out to illustrate the diverse applications of nonlinear systems theory for analysis and control of MEMS because desired level of validity and performance can be attained through synergy of nonlinear control, electromagnetics, and electromechanics. Micro-electromechanical systems; integrate microstructures and microdevices, and the component models are described by nonlinear deterministic/stochastic time-invariant/time-varying multivariable ordinary and partial differential equations as well as difference equations. Focusing our efforts on microelectromechanical motion devices, we apply Lyapunov's stability theory. These microscale motion devices, integrated with ICs, comprise MEMS. It must be emphasized that the circuitry dynamics is very fast compared with the electromechanical transients. Therefore, the motion devices behavior has the dominant effect. To address systematic analysis, it must be emphasized that the electromagnetic features and operating principles of MEMS must be thoroughly studied. Thus, analysis and design should be performed researching electromagnetic electromechanical - circuitry aspects. For example, the pulse-width-modulation technique is used to design high-performance ICs, optimal energy conversion and torque maximization problems require particular currents and voltages applied to the phase micro-windings (distinct control laws must be designed), etc. Fundamental, analytical, numerical, and experimental results are documented in this paper.