Nonlinear dynamic behaviors and PID control of viscoelastic dielectric elastomer balloons

As a type of intelligent electroactive polymer, dielectric elastomer (DE) exhibits viscoelastic properties. It’s worth pointing out that the relaxation time has great significance for studying the mechanical behavior of viscoelastic polymer. In this paper, a generalized Maxwell model is used to describe the viscoelastic property of dielectric elastomer balloon. Meanwhile, a theoretical model with multiple relaxation times is used and the natural frequency of small amplitude oscillation is derived. Subsequently, the model is validated by comparing with experimental results. The model with double relaxation times can describe the deformation of the dielectric elastomer balloon effectively. Then the effect of relaxation time and shear modulus on the dynamic response of DE balloon is studied. Furthermore, the dielectric elastomer balloons in practical application exhibit the strong nonlinearity and the viscoelastic dissipation. Therefore, it is important to precisely control the dynamic response. The proportional-integral-differential (PID) controller in the form of nonlinear combination is adopted to control the above nonlinear dynamic systems actively. The results indicate that it is feasible to achieve desired control effect.