Beyond pull-in angle control of a dual axis torsional micro-actuator considering bending effects

Abstract

Torsional micro-actuators are fundamental elements in micro-system technologies. They've found several applications in optical cross connects, endoscopic optical coherence tomography and miniaturized projection displays. Effective angle control in these actuators is necessary for their acceptable performance. So, the objective of the current paper is to develop a novel fuzzy controller to extend the travel range of these actuators based on an accurate dynamic model. The degrees of freedom (DoF) of the system includes two rotational angles resulted from twist of the torsion micro-beams and two translational ones originating from their bending towards the electrodes. Using these four DoFs, Lagrange equations are employed to develop a novel dynamic model for the dual axis torsional micro-actuator. Comparing the response of the system obtained from 4-DoF and 2-DoF models with those resulted from nonlinear recursive finite element simulations reveals that the use of the 4-DoF model is critical for having accurate predictions of the system's behavior. Then dynamic simulations to step input voltages are used for proposing an expert fuzzy rule base which describes the dependence of the rotation angles to input voltages. Using this rule base along with a singleton fuzzifier, product inference engine and center average defuzzifier, an incremental fuzzy controller is designed for smooth control of the rotation angles of the actuator about the desired angles. To maximize the performance of the closed-loop system, the centers of the fuzzy sets of the THEN parts of the rules are adaptively tuned using a higher-level fuzzy system. Closed loop simulations shows that the presented novel fuzzy controller is capable of stabilizing the angles of the actuator even beyond their inherently unstable pull-in range. The proposed 4-DoF model can be used for design optimization of dual axis torsional micro-actuators. Additionally, the developed incremental fuzzy controller can be employed for controlling the response of other types of electrostatically actuated micro/nano-systems.