Modelling, simulation and optimal control of dielectric elastomer actuated systems


Publication Details

Author(s): Schlögl T
Editor(s): Prof. Dr.-Ing. habil. Sigrid Leyendecker
Title edited volumes: Schriftenreihe Technische Dynamik
Publication year: 2018
Language: English


The aim of this work is to present a physically motivated simulation framework to predict and control the time dependent behaviour of multibody systems that are actuated via artificial muscles. The artificial muscles are composed of stacked dielectric elastomers that contract due to electrostatic forces when a voltage is applied. As both electrical and mechanical quantities are involved in this interrelation, a multidisciplinary modelling approach is required. Existing electromechanically coupled models for dielectric elastomers can be categorised in two groups. The first group covers general three-dimensional field theory of electromagnetic forces in deformable continua with arbitrary geometry. The second group contains so called lumped parameter models, where spatially discrete configuration variables condense the complex physical relationships by exploiting symmetries, regularities and predicted behaviour. Both approaches are usually based on different assumptions, material models and modelling procedures, resulting in different simulation results. This work tries to bridge these two groups by deriving an energy consistent lumped parameter model directly from the corresponding three dimensional field theory. As both models consequently share the same modelling approach, they can be easily compared and assessed.


The present work starts by introducing a time dependent, versatile and monolithic three-dimensional finite element formulation for the electromechanically coupled problem that serves as the artificial muscle model. A variational time integration scheme ensures structure preservation as well as a good energy behaviour. An electromechanically coupled, visco-hyperelastic material approach provides flexibility and modularity. The artificial muscle model is coupled with a multibody system that represents the actuated structure. This setting allows for exploring the complex behaviour of humanoid structures that are driven by artificial muscles instead of electrical drives. The multibody system is composed of rigid bodies that are connected via joints and based on a redundant formulation that avoids rotational degrees of freedom and singularities. As a result, a very modular coupling between the multibody system and the finite element muscle is obtained. The set-up of multibody systems and the derivation of relevant equations is supported by the C++ library MulDi that emerged from this work. In order to control artificial muscle actuated systems and possibly avoid oscillations that are inherent with the elastic structure of the actuators, optimal control theory is utilised. To reduce the computational cost that is necessary to solve optimal control problems, an energy consistent lumped parameter model for dielectric elastomers is derived, where numerical examples illustrate potential applications.


The utilised variational time integration scheme turned out to be very suitable for solving electromechanically coupled problems. Apart from the preservation characteristics and the good energy behaviour, the integrator allows to solve algebraic constraints on configuration level exactly at the discrete time nodes. This allows for a neat coupling between the artificial muscles and the actuated structure. Moreover, fully incompressible material behaviour can be obtained, avoiding volumetric locking effects. Numerical examples show that the rather small achievable maximum contraction and forces of stacked actuators compared to real muscles still limit their use in human like structures. Optimal control theory, however, has been proven to provide a suitable tool for avoiding oscillations that are inherent with the elastic nature of the actuators and yields optimised voltage control trajectories.

FAU Authors / FAU Editors

Schlögl, Tristan
Chair of Applied Dynamics

How to cite

Schlögl, T. (2018). Modelling, simulation and optimal control of dielectric elastomer actuated systems (Dissertation).

Schlögl, Tristan. Modelling, simulation and optimal control of dielectric elastomer actuated systems. Dissertation, 2018.


Last updated on 2018-06-08 at 15:08