Numerically Efficient Discrete-Time Dielectric Elastomer Actuators Models for Optimal Control

Abstract

Dielectric elastomers can be used to develop innovative mechatronic actuators (called DEA). In this paper, we consider the optimal control problem (OCP) of transitioning between an actuator's operating states. Following a model-based approach, a set of discrete-time state equations is derived for the DEA, which satisfy accuracy demands and, at the same time, can be solved efficiently by numerical methods. Due to numerical stiffness, the implicit midpoint rule is chosen as an integration method. Then, we discuss different classes of input signals to be considered in the OCP. In particular, zero-order-hold and first-order-hold parametrizations are compared within the OCP formulation. While we show equivalence of two OCP formulations from the theoretical point of view, numerical investigations show benefits of our proposed OCP model regarding the quality of computed solutions and the robustness w.r.t. initial guesses. Altogether, we derive a numerically treatable DEA optimal control set-up, which can be used for various control tasks.