DERIVING TRANSFER FUNCTIONS FOR A MEMS ACTUATOR SYSTEM THROUGH THE APPLICATION OF LAGRANGE EQUATIONS

This paper delves into the derivation of transfer functions for a MEMS Actuator System by employing Lagrange Equations. The theoretical foundations are established through an exploration of Lagrange Equations in Mechanics. The modeling of the MEMS Actuator System is comprehensively discussed, followed by the application of Lagrange Equations to derive the system's transfer functions. The study also includes the simulation of the Electrical Transfer Function and Mechanical Transfer Function using MATLAB. We followed the applied mathematical method using Simulation and Analyzing with MATLAB and we found the following some results: Varying the damping coefficient b from 1e-5 to 1e-3, the system exhibits varying responses. Higher values of b lead to faster damping in the system, influencing the overshoot and settling time in the step response. Changing the resistance R affects the system dynamics. Higher resistance values result in increased damping, impacting the overall response characteristics. Modifying the spring constant k alters the stiffness of the system. Higher values of k lead to a stiffer response, affecting the system's natural frequency and settling time. Adjusting the mass m influences the inertia of the system. An increase in mass results in a slower response and affects the overshoot and settling time. Changing the capacitance C impacts the system's electrical characteristics. Higher capacitance values affect the electrical response, influencing the overall system behaviour. These observations provide insights into how specific parameters contribute to the MEMS actuator system's behaviour, aiding in the design and optimization process.