A dynamic model for the soft dielectric elastomer actuator (SDEA) is developed in this paper to describe its intricately nonlinear behaviors considering different input frequencies and external loads. Firstly, the characteristics of the SDEA are observed by several groups of experiments. A phenomenological model is proposed to describe the asymmetric hysteresis behavior of the SDEA, which consists of a Prandtl-Ishlinskii model with one-side play operator and a dead-zone model with one-side dead-zone operator. Meanwhile, a mathematical model is built to depict the creep behavior of the SDEA. The dynamic model including a module and a linear system is proposed to further handle the rate-dependent and the stress-dependent hysteresis behaviors of the SDEA, in which the module is the superposition of the asymmetric hysteresis model and the creep model. To ensure that the inverse solution of the module is existing, as well as the linear system is controllable and observable, the constraint conditions of parameter values of the dynamic model are constructed. Next, the parameter identification is divided into two steps, and the differential evolution algorithm is employed in each step. Finally, the generalization of the proposed dynamics model is demonstrated by comparing the model output with the experimental data.

本文开发了软介电弹性体执行器 (SDEA) 的动态模型，以描述其在考虑不同输入频率和外部负载的情况下的复杂非线性行为。首先，通过几组实验观察了SDEA的特性。提出了一种现象学模型来描述 SDEA 的非对称滞后行为，该模型由具有单侧游动算子的 Prandtl-Ishlinskii 模型和具有单侧死区算子的死区模型组成。同时，建立了一个数学模型来描述SDEA的蠕变行为。提出了包括模块和线性系统的动力学模型，以进一步处理SDEA的速率相关和应力相关滞后行为，其中模块是非对称滞后模型和蠕变模型的叠加。为保证模的逆解存在，以及线性系统可控可观，构造了动力学模型参数值的约束条件。接下来，参数识别分为两步，每一步都采用差分进化算法。最后，通过将模型输出与实验数据进行比较，证明了所提出的动力学模型的泛化。