Stability and Vibration Control of Electrostatically Excited Functionally Graded Microresonator using Nonlinear Observer based Sliding Mode Controller

Abstract The dynamic stability analysis of microsystems is an important aspect in understanding the critical operating regions under different excitations. Present study proposes an observer-based adaptive back-stepping sliding mode controller (ABSMC) model to control and stabilize an electrostatically excited functionally graded microresonator. The dynamic model of a microsystem subjected to random disturbances is derived using modified couple stress theory and Euler–Bernoulli’s beam model. The effective material properties are obtained from Mori-Tanaka scheme and the equations of motion are derived using Hamilton principle and solved by Galerkin’s method. A trained neural network estimator predicts the disturbances and the adaptive back-stepping sliding mode controller is designed for improving the system stability. The results of the proposed controller are compared with conventional sliding mode control (SMC) and proportional-derivative (PD) control solutions and it is found that ABSMC reduces settling time and input control force by 52.42% and 88.40%, respectively, with minimal chattering. The proposed control methodology effectively extends the travelling range of FG microsystems within and beyond the pull-in voltage.