Dielectric elastomers (DEs) deform and change shape when an electric field is applied across them. They are flexible, resilient, lightweight, and durable and as such are suitable for use as soft actuators. In this paper a physics-based and control-oriented model is developed for a DE tubular actuator using a physics-lumped parameter modeling approach. The model derives from the nonlinear partial differential equations (PDE) which govern the nonlinear elasticity of the DE actuator and the ordinary differential equation (ODE) that governs the electrical dynamics of the DE actuator. With the boundary conditions for the tubular actuator, the nonlinear PDEs are numerically solved and a quasi-static nonlinear model is obtained and validated by experiments. The full nonlinear model is then linearized around an operating point with an analytically derived Hessian matrix. The analytically linearized model is validated by experiments. Proportional–Integral–Derivative (PID) and \(H_{\infty }\) control are developed and implemented to perform position reference tracking of the DEA and the controllers’ performances are evaluated according to control energy and tracking error.

当电场施加在介电弹性体 (DE) 上时，介电弹性体 (DE) 会变形和改变形状。它们灵活、有弹性、重量轻且耐用，因此适合用作软致动器。在本文中，使用物理集总参数建模方法为 DE 管状执行器开发了基于物理和面向控制的模型。该模型源自控制 DE 执行器非线性弹性的非线性偏微分方程 (PDE) 和控制 DE 执行器电气动力学的常微分方程 (ODE)。利用管状致动器的边界条件，非线性偏微分方程被数值求解，并获得准静态非线性模型并通过实验验证。然后使用解析导出的 Hessian 矩阵围绕工作点对完整的非线性模型进行线性化。通过实验验证了分析线性化模型。比例-积分-微分 (PID) 和\(H_{\infty }\)控制被开发和实施以执行 DEA 的位置参考跟踪，并根据控制能量和跟踪误差评估控制器的性能。