Modeling of a walking piezo actuator

Piezo actuators are often used in positioning devices that require (sub)nanometer resolution. For the purpose of control design a model is needed. In this paper, we develop an electromechanical dynamic model of a walking piezo actuator. The walking piezo actuator contains four legs, each with two electrically separated piezo stacks. The legs are modeled as a connection of coupled mass-spring-damper systems. Using a Lagrange approach, the nonlinear system dynamics are derived. The variation in the system dynamics is assessed using linearization around different equilibrium positions. Also a static linearized approximation is derived, which describes the static relation between the supply voltages and the tip trajectories of the legs. The model is based on the physical properties of the actuator. The variation in system dynamics appears to be most significant in the movement perpendicular to the leg orientation. Experimental validation shows that the static linearized model accurately describes the tip trajectories of the legs for sinusoidal waveforms.