
Optimal control of bending dielectric elastomer actuators via non-intrusive dimensionality reduction
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In this work, we present a non-intrusive reduced order model (ROM) for the optimal control of Dielectric Elastomer Actuators (DEA), a type of electroactive polymer (EAP). Computational representations of DEAs typically necessitate large deformation non-linear material models integrated within electromechanical frameworks, which are resource-intensive to solve approximately. The principal aim of our methodology is to expedite the computationally demanding process of determining the optimal electrical stimuli necessary to realize a predetermined shape in a dielectric elastomer medium[1], making it suitable for real-time applications. Our approach leverages model order reduction (MOR) techniques to develop a non-intrusive ROM that significantly reduces the computational burden. The ROM is constructed using a combination of kernel Principal Component Analysis (kPCA)[2] and Isometric Mapping (isomap)[3], ensuring that the reduced model retains the essential dynamics of the full system. This method allows for efficient and accurate simulations, making it feasible to perform optimal control in a timely manner. We applied our methodology to different benchmark scenarios, demonstrating the effectiveness of the ROM in capturing the complex behaviour of DEAs under various electrical stimuli for several body configurations. The results show a substantial reduction in computational time while maintaining high accuracy, highlighting the potential of our method for real-time control applications. Acknowledgements: The group acknowledge the financial support received via project POTENTIAL (PID2022-141957OB-C21) funded by MICIN/AEI/10.13039/501100011033/FEDER, UE. The first author also acknowledges the funding PREP2022-000220 provided by MCIN/AEI/10.13039/501100011033 and the FSE+. REFERENCES [1] J. Martínez-Frutos et al. In-silico design of electrode meso-architecture for shape morphing dielectric elastomers, Journal of the Mechanics and Physics of Solids, vol. 157, p. 104594, Dec. (2021) [2] B. Schölkopf, et al. Nonlinear Component Analysis as a Kernel Eigenvalue Problem, Neural Computation, vol. 10, no. 5, pp. 1299–1319, Jul. (1998) [3] Tenenbaum JB, et al. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290:2319–2323, (2000)