Energy-Based Modeling of Ionic Polymer–Metal Composite Actuators Dedicated to the Control of Flexible Structures
Authors
Ning Liu, Yongxin Wu, Yann Le Gorrec
Abstract
This article deals with the control-oriented energy-based modeling of ionic polymer–metal composite (IPMC) patches using multiscale infinite dimensional port-Hamiltonian formulations and Lagrange multipliers. Inspired by the work of Nishida et al. in 2012, but considering different assumptions, this article focuses on the constraints arising from the coupling between the polymer gel and the compliant mechanical structure of the actuator, under the quasi-static mechanical assumption for the gel, leading to a constrained port-Hamiltonian system. The geometric structure of the overall system and the associated energy balance are derived. The proposed energy-based model of the IPMC actuator allows deriving controllers via energy-based control design methods with a clear physical interpretation. The proposed actuator model is further discretized in space using a structure preserving finite difference method. The Lagrange multipliers are eliminated using coordinate projections. Simulations are compared with experimental results. With proper discretization numbers, our model is consistent with the physical system. Finally, Lagrange multipliers are exploited to connect the actuator to a 2-D flexible structure stemming from the modeling of a flexible endoscope.
Citation
- Journal: IEEE/ASME Transactions on Mechatronics
- Year: 2021
- Volume: 26
- Issue: 6
- Pages: 3139–3150
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/tmech.2021.3053609
BibTeX
@article{Liu_2021,
title={{Energy-Based Modeling of Ionic Polymer–Metal Composite Actuators Dedicated to the Control of Flexible Structures}},
volume={26},
ISSN={1941-014X},
DOI={10.1109/tmech.2021.3053609},
number={6},
journal={IEEE/ASME Transactions on Mechatronics},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Liu, Ning and Wu, Yongxin and Le Gorrec, Yann},
year={2021},
pages={3139--3150}
}
References
- sokolnikoff, Mathematical Theory of Elasticity (1956)
- kraus, Thin Elastic Shells An Introduction to the Theoretical Foundations and the Analysis of Their Static and Dynamic Behavior (1967)
- Soedel, W. On the vibration of shells with timoshenko-mindlin type shear deflections and rotatory inertia. Journal of Sound and Vibration vol. 83 67–79 (1982) – 10.1016/s0022-460x(82)80076-x
- Kristiansen, U. R., Soedel, W. & Hamilton, J. F. An investigation of scaling laws for vibrating beams and plates with special attention to the effects of shear and rotatory inertia. Journal of Sound and Vibration vol. 20 113–122 (1972) – 10.1016/0022-460x(72)90766-3
- Brugnoli, A., Alazard, D., Pommier-Budinger, V. & Matignon, D. Port-Hamiltonian formulation and symplectic discretization of plate models Part I: Mindlin model for thick plates. Applied Mathematical Modelling vol. 75 940–960 (2019) – 10.1016/j.apm.2019.04.035
- Kanno, R., Tadokoro, S., Takamori, T., Hattori, M. & Oguro, K. Modeling of ICPF (ionic conducting polymer film) actuator-modeling of electrical characteristics. Proceedings of IECON ’95 - 21st Annual Conference on IEEE Industrial Electronics vol. 2 913–918 – 10.1109/iecon.1995.483851
- Newbury, K. M. & Leo, D. J. Linear Electromechanical Model of Ionic Polymer Transducers -Part I: Model Development. Journal of Intelligent Material Systems and Structures vol. 14 333–342 (2003) – 10.1177/1045389x03034976
- Zheng Chen & Xiaobo Tan. A Control-Oriented and Physics-Based Model for Ionic Polymer–Metal Composite Actuators. IEEE/ASME Transactions on Mechatronics vol. 13 519–529 (2008) – 10.1109/tmech.2008.920021
- Nishida, G., Takagi, K., Maschke, B. & Osada, T. Multi-scale distributed parameter modeling of ionic polymer-metal composite soft actuator. Control Engineering Practice vol. 19 321–334 (2011) – 10.1016/j.conengprac.2010.10.005
- shahinpoor, Ionic Polymer–Metal Composites (IPMCs) (2016)
- Le Gorrec, Y., Zwart, H. & Maschke, B. Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM Journal on Control and Optimization vol. 44 1864–1892 (2005) – 10.1137/040611677
- villegas, A port-Hamiltonian approach to distributed parameter systems. (2007)
- Zhu, Z., Chen, H., Wang, Y. & Li, B. Multi-physical modeling for electro-transport and deformation of ionic polymer metal composites. SPIE Proceedings vol. 8340 83400Q (2012) – 10.1117/12.913020
- Yamaue, T., Mukai, H., Asaka, K. & Doi, M. Electrostress Diffusion Coupling Model for Polyelectrolyte Gels. Macromolecules vol. 38 1349–1356 (2005) – 10.1021/ma047944j
- Gennes, P. G. de, Okumura, K., Shahinpoor, M. & Kim, K. J. Mechanoelectric effects in ionic gels. Europhysics Letters (EPL) vol. 50 513–518 (2000) – 10.1209/epl/i2000-00299-3
- qatu, Recent research advances in the dynamic behavior of shells. Part 1 Laminated composite shells (1989)
- Xiao, Y. & Bhattacharya, K. Modeling electromechanical properties of ionic polymers. SPIE Proceedings vol. 4329 292 (2001) – 10.1117/12.432658
- leissa, Vibration of Shells Scientific and Technical Information Office (1973)
- Park, K., Yoon, M.-K., Lee, S., Choi, J. & Thubrikar, M. Effects of electrode degradation and solvent evaporation on the performance of ionic-polymer–metal composite sensors. Smart Materials and Structures vol. 19 075002 (2010) – 10.1088/0964-1726/19/7/075002
- Khawwaf, J., Zheng, J., Chai, R., Lu, R. & Man, Z. Adaptive Microtracking Control for an Underwater IPMC Actuator Using New Hyperplane-Based Sliding Mode. IEEE/ASME Transactions on Mechatronics vol. 24 2108–2117 (2019) – 10.1109/tmech.2019.2937328
- Qatu, M. S. Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: Homogeneous shells. Applied Mechanics Reviews vol. 55 415–434 (2002) – 10.1115/1.1483078
- Newbury, K. M. & Leo, D. J. Electromechanical Modeling and Characterization of Ionic Polymer Benders. Journal of Intelligent Material Systems and Structures vol. 13 51–60 (2002) – 10.1177/1045389x02013001978
- Nemat-Nasser, S. & Li, J. Y. Electromechanical response of ionic polymer-metal composites. Journal of Applied Physics vol. 87 3321–3331 (2000) – 10.1063/1.372343
- Shahinpoor, M. Micro-Electro-Mechanics of Ionic Polymeric Gels As Electrically Controllable Artificial Muscles. Journal of Intelligent Material Systems and Structures vol. 6 307–314 (1995) – 10.1177/1045389x9500600302
- Wang, J., McDaid, A. J., Lu, C. Z. & Aw, K. C. A Compact Ionic Polymer-Metal Composite (IPMC) Actuated Valveless Pump for Drug Delivery. IEEE/ASME Transactions on Mechatronics vol. 22 196–205 (2017) – 10.1109/tmech.2016.2624762
- Branco, P. J. C. & Dente, J. A. Derivation of a continuum model and its electric equivalent-circuit representation for ionic polymer–metal composite (IPMC) electromechanics. Smart Materials and Structures vol. 15 378–392 (2006) – 10.1088/0964-1726/15/2/019
- Shahinpoor, M. & Kim, K. J. Ionic polymer–metal composites: IV. Industrial and medical applications. Smart Materials and Structures vol. 14 197–214 (2004) – 10.1088/0964-1726/14/1/020
- Macchelli, A. & Melchiorri, C. Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach. SIAM Journal on Control and Optimization vol. 43 743–767 (2004) – 10.1137/s0363012903429530
- Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics vol. 34 225–233 (1994) – 10.1016/0034-4877(94)90038-8
- Trenchant, V., Ramirez, H., Le Gorrec, Y. & Kotyczka, P. Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct. Journal of Computational Physics vol. 373 673–697 (2018) – 10.1016/j.jcp.2018.06.051
- Paquette, J. W., Kim, K. J., Nam, J.-D. & Tak, Y. S. An Equivalent Circuit Model for Ionic Polymer-Metal Composites and their Performance Improvement by a Clay-Based Polymer Nano-Composite Technique. Journal of Intelligent Material Systems and Structures vol. 14 633–642 (2003) – 10.1177/104538903038024
- Wu, Y., Hamroun, B., Gorrec, Y. L. & Maschke, B. Port Hamiltonian System in Descriptor Form for Balanced Reduction: Application to a Nanotweezer. IFAC Proceedings Volumes vol. 47 11404–11409 (2014) – 10.3182/20140824-6-za-1003.01579
- Farshidianfar, A. & Oliazadeh, P. Free Vibration Analysis of Circular Cylindrical Shells: Comparison of Different Shell Theories. International Journal of Mechanics and Applications vol. 2 74–80 (2012) – 10.5923/j.mechanics.20120205.04
- Porfiri, M., Sharghi, H. & Zhang, P. Modeling back-relaxation in ionic polymer metal composites: The role of steric effects and composite layers. Journal of Applied Physics vol. 123 (2018) – 10.1063/1.5004573