Control of an Electrostatically Actuated Micro Portal Frame with 2:1 Internal Resonance Subjected to Damping Disturbances

Micro compound structures have rich dynamics and are very promising for use in applications. Among the intriguing nonlinear phenomena exhibited by compound structures is the saturation phenomenon due to the 2:1 internal resonance. However, this phenomenon is strongly affected by damping, which is a critical factor in microelectromechanical systems (MEMS), due to variation in the operating pressure inside environmental chambers. Therefore, this work aims to electrostatically control a micro portal frame, modeled as a two-degrees-of-freedom (2DOFs) system, with 2:1 internal resonance between the second (Y-direction motion) and first (X-direction motion) modes. To avoid irregular behaviors under the saturation phenomenon within the internal resonance regime, we propose to use the Linear Quadratic Regulator (LQR) control technique to create an electrostatic force that alleviates the damping effect. A comparison between the efficiency of an ideal control and a limited voltage actuator is highlighted.