Design of a Command-Shaping Scheme for Mitigating Residual Vibrations in Dielectric Elastomer Actuators

Dielectric elastomers (DEs) are a class of highly deformable electroactive polymers (EAPs) employed for electromechanical transduction technology. When electrostatically actuated dielectric elastomer actuators (DEAs) are subjected to an input signal comprising multiple Heaviside voltage steps, the emerging inherent residual vibrations may limit their motion accuracy in practical applications. In this paper, the systematic development of a command-shaping scheme is proposed for controlling residual vibrations in an electrically driven planar DEA. The proposed scheme relies on invoking the force balance at the point of maximum lateral stretch in an oscillation cycle to bring the actuator to a stagnation state followed by the application of an additional electric input signal of predetermined magnitude at a specific time. The underlying concept of the proposed control scheme is articulated for a single Heaviside step input-driven actuator and further extended to the actuator subjected to the multistep input signal. The equation governing the dynamic motion of the actuator is derived using the principle of virtual work. The devised dynamic model of the actuator incorporates the effects of strain stiffening of elastomer and viscous energy dissipation. The nonlinear dynamic governing equation is solved using matlab ode solver for extracting the dynamic response of the actuator. The applicability of the devised command-shaping control scheme is illustrated by taking a wide range of parameters including variations in the extent of equilibrium state sequences, damping, and polymer chain extensibility. The proposed scheme is found to be adaptable in controlling the vibrations of the actuator for any desired equilibrium state. The results presented in this paper can find its potential application in the design of an open-loop control system for DEAs.