Adaptive Implicit Inverse Control for a Class of Butterfly-Like Hysteretic Nonlinear Systems and Its Application to Dielectric Elastomer Actuators

In this article, a butterfly-like Prandtl–Ishlinskii (PI) hysteresis model and a novel neural network based adaptive implicit inverse control scheme to describe and control the butterfly-like hysteresis are proposed. The main contributions are: 1) a butterfly-like PI model is developed for the purpose of predicting the hysteresis effects and the model is feasible for controller design; 2) an implicit inverse control scheme especially for mitigating the butterfly-like hysteresis is implemented, which avoids the construction of the direct inverse of the butterfly-like PI model; 3) an adaptive implicit inverse control approach, which integrates the neural network and the implicit inverse technique into the output-feedback control is developed for eliminating the butterfly-like hysteresis and an arbitrarily smallL∞norm of tracking error is achieved. The proposed modeling and control methods are validated experimentally via the dielectric elastomer actuator based motion control platform.