33 rd International Electronics Manufacturing Technology Conference 2008 1 Nonlinear Modeling of a Capacitive MEMS Accelerometer Using Neural Network A. R. BAHADORIMEHR, M. Nizar B. Hamidon, Y. HEZARJARIBI Electrical and Electronic Department, Faculty of Engineering, University Putra Malaysia, 43300 Serdang, Selangor, Malaysia bahadori1018@gmail.com Abstract This paper presents a nonlinear model for a capacitive Microelectromechanical accelerometer (MEMA). System parameters of the accelerometer are developed using the effect of cubic term of the folded-flexure spring. To solving this equation we use FEA method. The neural network (NN) uses Levenberg-Marquardt (LM) method for training the system to have more accurate response. The designed NN can identify and predict the displacement of movable mass of accelerometer. The simulation results are very promising. 1. Introduction Nonlinearities in Microelectromechanical systems (MEMS) can arise from various sources such as spring and damping mechanisms [1-3], capacitive circuit elements [4], nonlinear coupling between the electrostatic force and the displacement of the MEM structure [5], therefore electrostatic MEMS has nonlinear regions [6]. Several researchers have developed various capacitive MEMS accelerometer [7- 10], however, the circuitry design after the sensing plate of all those accelerometers is based on buffers and demodulators (with low frequency sampling), which is not suitable response for high accuracy applications. This paper presents a new method to sensing the motion of movable plate to have a high accuracy and prevent from damaging the device at high accelerations using neural network. First, a nonlinear dynamic equation with mechanical nonlinearities is obtained. Solving this nonlinear equation can help to determine the displacement of movable plate with high accuracy, then the applied acceleration at the specific time sent to NN to identify and predict the displacement of movable plate. For training Neural Network we select Levenberg-Marquardt algorithm. Accelerometer sensor is a combination of springs, masses and motion sensing and actuation cells as shown in Fig.1 (a). It consists of a variable differential air capacitor whose plates are etched into the suspended polysilicon layer. The moving plate of the capacitor is formed by a large number of fingers extending from the beam, a proof mass supported by tethers anchored to the substrate. When responding to an applied acceleration (Fig.1 (b)), the proof mass’s inertia causes it to move along a predetermined axis. As the fingers extending from the beam move between the fixed fingers, capacitance change is being sensed and used to measure the amplitude of the force that led to the displacement of the beam. In section 2 analytical model of a MEM accelerometer (MEMA) is obtained. Section 3 proposed a nonlinear model using N.N.. Simulation results are given in section 4. Finally section 5 includes conclusions. (a) (b) Fig. 1 schematic diagram of accelerometer model 2. Analytical Modeling of MEMA An accelerometer can modeled as a spring- mass-damper system in the x-direction. Physics-based models for the effective spring stiffness of the folded-flexure suspensions, the effective masses of the proof mass and viscous air damping are used in the synthesis tool. Approximations to the nonlinear rod theory provide formulas for the coefficients of linear and cubic stiffening, which enable predictions of spring hardening behavior [11]. Considering folded-flexure spring and lumped element modeling, the following expression for the spring is obtained as [12,13]: