Improving the comb drive actuator transient response using Digital Compensation Technique M. S. Mahmoud (1) , D. Khalil (2,3) , M. T. El -Hagry (1) and M. A. Badr (2) (1) Electronics Research Institute: National Research Center, El-Tahrer St. Dokki, Cairo12622 , Egypt. mostafa_mahmoud74@yahoo.com (2) Ain Shams University, faculty of engineering, 1 El-srayat St., Abbsia, Cairo, Egypt. (3) MEMScAP Egypt: 9, Ibn Battouta St. Heliopolis, Cairo11341, Egypt Fax: (+202) 4146492. diaa.khalil@memscap.com ABSTRACT In this work we propose a new technique to improve the transient response of the comb drive actuator using a digital compensation technique. This technique is mainly based on the use of a specific digital pulse train that satisfies the equal area criterion on the force displacement diagram of the actuator. Applying this technique to a specific actuator design, we show that it enables to increase the forward displacement without sticking, reduce the overshoot, and improve the speed of response. INTRODUCTION Linear comb drive actuators (CDA) are very important MEMS structures that are widely used in many applications [1,2]. They are currently used in force-balanced accelerometers, resonant accelerometers, opto-mechanical subsystems and others [4-7]. Current CDA step response is characterized by limited forward displacements and strong overshoot [8]. Many techniques have been proposed to improve the step response to minimize the overshoot and/or the settling time of the actuator by adding extra network controllers or series resistances as electrically damping elements or by optimizing the comb finger structure [9-10]. The basic idea in the digital compensation depends on the fact that, the overshoot in the comb drive response is mainly due to the excess energy stored in the actuator during its acceleration by the applied voltage. In our technique, the energy supplied to the CDA is just enough to enable the shuttle to reach the designed destination. COMB DRIVE ANALYSIS Fig.1. a- Schematic representation of the CDA. , b- Geometrical details of the drive fingers. A schematic representation of the analyzed CDA is shown in Fig. 1-a with geometrical details of on of its fingers in Fig. 1-b. When a potential deference V is applied between moving and fixed fingers an electrostatic driving force F e is generated and the shuttle is displaced in the x-direction [6,9] against a restoring spring force F s . Fe = Fp+F f , where, F f = 1.12nε tV 2 /g , F p = nε tbV 2 /(d-x) 2 (1) Where n is the number of moving fingers and ε is the dielectric constant of air and the other geometrical parameters are defined in Fig. 1-b. It is clear that F p is the main reason of the front sticking. The dynamic response of the CDA could be expressed by the simple equation of motion (2), where m eff is the effective mass, b f is the damping coefficient and k is the restoring spring force, F p can be ignored in calculating the response. In this case the CDA is simply a second order system, whose response to a step voltage is exponentially damped sinusoidal wave. f e f eff F F t kx t t x b t t x m 2245 = + ∂ ∂ + ∂ ∂ ) ( ) ( ) ( 2 2 (2) Stability equal area criterion Considering the Force-Displacement diagram of Fig. 2 we have two intersection points B and G at two different displacements x 1 (stable position) and x 3 (unstable position). The dynamic behavior of the CDA can be thus described, shuttle d L g g b b y x Direction of motion