PD-Based Active Control Approach for Vibration Mitigation in Nonlinear MEMS Resonators

This research proposes a novel approach to controlling the nonlinear vibrational behavior of micro-electro-mechanical systems (MEMS) subjected to harmonic excitation. A proportional–derivative (PD) controller is integrated into a simplified single-degree-of-freedom (SDOF) nonlinear model representing the MEMS dynamics. The multiple time scales perturbation method (MTSPM) is applied to the linearized system to derive approximate analytical solutions for the controlled autonomous model. The primary objective is to suppress vibration amplitudes, particularly under primary resonance conditions. The Routh–Hurwitz criterion is employed to assess the system’s stability. Furthermore, the frequency response curves (FRCs) exhibit symmetrical behavior across different parameter values. Compared with other control strategies, the findings highlight a direct relationship between the PD control action and the effectiveness of vibration suppression. The amplitude response of the system is examined, and the analytical predictions are validated through numerical simulations using the fourth-order Runge–Kutta method. The strong agreement between analytical and numerical results confirms the accuracy and robustness of the proposed control framework.