Dynamic modeling and residual vibration suppression of electrostatically driven soft dielectric elastomer minimum energy structures

Dielectric elastomers (DEs), a special class of soft electro-active polymers that undergo finite deformation under external electrical stimuli, offer a wide range of applications that include but are not limited to soft actuators, soft robots, and energy harvesters. Among the various configurations of dielectric elastomer-based soft mechanisms, DE-based minimum energy structures (DEMES) are elite due to their several advantageous characteristics, such as lightweight, an easy fabrication process, the ability to achieve a desirable complex 3-D shape, the capability of undergoing large out-of-plane actuation despite planar fabrication, fast response, and controllability. However, when a DEMES actuator is driven by an input voltage signal consisting of different Heaviside steps, the intrinsic residual vibrations exhibited by the actuator may restrict the motion precision required in real-world applications. In this work, a nonlinear dynamic model of the DEMES actuator is devised using the Euler–Lagrange equation of motion, and the neo-Hookean material model is utilized to describe the material behavior of the DE membrane. A feedforward control technique is developed to suppress the inherent residual vibrations exhibited by the DEMES actuator. The control technique relies on the balance of the electro-mechanical forces at the minimum point, characterized by zero velocity and minimum bending angle in an oscillation cycle. The capability of the proposed feedforward control technique is demonstrated by controlling the DEMES actuator to different desired positions without residual vibrations. A parametric study is performed to explore the dependence of the proposed control technique on several parameters, such as frame bending stiffness, pre-stretch of the membrane, and membrane damping. The feedforward control technique and the inferences obtained from the current research can be implemented effectively in the design and development of open loop controllers for electrostatically driven soft electro-active devices.