Modeling of a walking piezo actuator

Piezoelectric actuators are often used in positioning devices that require (sub)nano-meter resolution. In this paper, wedevelop an electro-mechanical dynamic model of a walking piezo actuator. The derived model structure can be used forthe dynamic modeling of bimorph piezo motors in general. Furthermore, the physical nature enables the model to beused in design optimizations to derive new motors with di erent properties and for a dynamic analysis to investigatethe maximum allowable driving frequency in relation to the dynamic e ects of the motor. The walking piezo actuatorcontains four legs, each with two electrically separated piezo stacks. The legs are modeled as a connection of coupledmass-spring-damper systems. Using a Lagrange approach, the nonlinear system dynamics are derived. The variationin the system dynamics is assessed using linearization around di erent equilibrium positions. Also a static linearizedapproximation is derived, which describes the static relation between the supply voltages and the tip trajectories ofthe legs. The dynamic analysis shows that the motor can be modeled su ciently accurate using a connection of sixlumped mass-spring-damper systems. The variation in system dynamics appears to be most signi cant in the movementperpendicular to the leg orientation. Experiments show that the static linearized model accurately describes the tiptrajectories of the legs for both sinusoidal and asymmetric waveforms.