Energy-Based Modeling and Hamiltonian LQG Control of a Flexible Beam Actuated by IPMC Actuators
Authors
Weijun Zhou, Ning Liu, Yongxin Wu, Hector Ramirez, Yann Le Gorrec
Abstract
The control of a flexible beam using ionic polymer metal composites (IPMCs) is investigated in this paper. The mechanical flexible dynamics are modelled as a Timoshenko beam. The electric dynamics of the IPMCs are considered in the model. The port-Hamiltonian framework is used to propose an interconnected control model of the mechanical flexible beam and IPMC actuator. Furthermore, a passive and Hamiltonian structure-preserving linear quadratic Gaussian (LQG) controller is used to achieve the desired configuration of the system, and the asymptotic stability of the closed-loop system is shown using damping injection. An experimental setup is built using a flexible beam actuated by two IPMC patches to validate the proposed model and show the performance of the proposed control law.
Citation
- Journal: IEEE Access
- Year: 2022
- Volume: 10
- Issue:
- Pages: 12153–12163
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/access.2022.3146367
BibTeX
@article{Zhou_2022,
title={{Energy-Based Modeling and Hamiltonian LQG Control of a Flexible Beam Actuated by IPMC Actuators}},
volume={10},
ISSN={2169-3536},
DOI={10.1109/access.2022.3146367},
journal={IEEE Access},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Zhou, Weijun and Liu, Ning and Wu, Yongxin and Ramirez, Hector and Le Gorrec, Yann},
year={2022},
pages={12153--12163}
}
References
- Maschke, Port controlled Hamiltonian systems: Modeling origins and system theoretic properties. Proc. 3rd IFAC Symp. Nonlinear Control Syst., (NOLCOS)
- 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
- Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
- van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
- 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
- Macchelli, A. Energy shaping of distributed parameter port-Hamiltonian systems based on finite element approximation. Systems & Control Letters vol. 60 579–589 (2011) – 10.1016/j.sysconle.2011.04.016
- Ramirez, H., Le Gorrec, Y., Macchelli, A. & Zwart, H. Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems With Dynamic Feedback. IEEE Transactions on Automatic Control vol. 59 2849–2855 (2014) – 10.1109/tac.2014.2315754
- Vu, N. M. T., Lefèvre, L. & Maschke, B. A structured control model for the thermo-magneto-hydrodynamics of plasmas in tokamaks. Mathematical and Computer Modelling of Dynamical Systems vol. 22 181–206 (2016) – 10.1080/13873954.2016.1154874
- Calchand, Modeling and control of magnetic shape memory alloys using port Hamiltonian framework. (2014)
- Liu, N., Wu, Y. & Le Gorrec, Y. Energy-Based Modeling of Ionic Polymer–Metal Composite Actuators Dedicated to the Control of Flexible Structures. IEEE/ASME Transactions on Mechatronics vol. 26 3139–3150 (2021) – 10.1109/tmech.2021.3053609
- Shahinpoor, M. & Kim, K. J. Ionic polymer-metal composites: I. Fundamentals. Smart Materials and Structures vol. 10 819–833 (2001) – 10.1088/0964-1726/10/4/327
- Chikhaoui, M. T., Rabenorosoa, K. & Andreff, N. Kinematic Modeling of an EAP Actuated Continuum Robot for Active Micro-endoscopy. Advances in Robot Kinematics 457–465 (2014) doi:10.1007/978-3-319-06698-1_47 – 10.1007/978-3-319-06698-1_47
- He, W., Wang, T., He, X., Yang, L.-J. & Kaynak, O. Dynamical Modeling and Boundary Vibration Control of a Rigid-Flexible Wing System. IEEE/ASME Transactions on Mechatronics vol. 25 2711–2721 (2020) – 10.1109/tmech.2020.2987963
- Liu, Z., Han, Z., Zhao, Z. & He, W. Modeling and adaptive control for a spatial flexible spacecraft with unknown actuator failures. Science China Information Sciences vol. 64 (2021) – 10.1007/s11432-020-3109-x
- Braun, P., Hernández, E. & Kalise, D. Reduced-order LQG control of a Timoshenko beam model. Bulletin of the Brazilian Mathematical Society, New Series vol. 47 143–155 (2016) – 10.1007/s00574-016-0128-z
- Wu, Y., Hamroun, B., Le Gorrec, Y. & Maschke, B. Reduced order LQG control design for port Hamiltonian systems. Automatica vol. 95 86–92 (2018) – 10.1016/j.automatica.2018.05.003
- Jonckheere, E. & Silverman, L. A new set of invariants for linear systems–Application to reduced order compensator design. IEEE Transactions on Automatic Control vol. 28 953–964 (1983) – 10.1109/tac.1983.1103159
- King, B. B., Hovakimyan, N., Evans, K. A. & Buhl, M. Reduced order controllers for distributed parameter systems: LQG balanced truncation and an adaptive approach. Mathematical and Computer Modelling vol. 43 1136–1149 (2006) – 10.1016/j.mcm.2005.05.031
- Wu, Y., Hamroun, B., Le Gorrec, Y. & Maschke, B. Reduced Order LQG Control Design for Infinite Dimensional Port Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 66 865–871 (2021) – 10.1109/tac.2020.2997373
- Mattioni, A., Wu, Y., Ramirez, H., Le Gorrec, Y. & Macchelli, A. Modelling and control of an IPMC actuated flexible structure: A lumped port Hamiltonian approach. Control Engineering Practice vol. 101 104498 (2020) – 10.1016/j.conengprac.2020.104498
- Zhou, W., Wu, Y., Hu, H., Li, Y. & Wang, Y. Port-Hamiltonian Modeling and IDA-PBC Control of an IPMC-Actuated Flexible Beam. Actuators vol. 10 236 (2021) – 10.3390/act10090236
- Wu, Y., Lamoline, F., Winkin, J. & Gorrec, Y. L. Modeling and control of an IPMC actuated flexible beam under the port-Hamiltonian framework. IFAC-PapersOnLine vol. 52 108–113 (2019) – 10.1016/j.ifacol.2019.08.019
- Korayem, M. H., Shafei, A. M., Absalan, F., Kadkhodaei, B. & Azimi, A. Kinematic and dynamic modeling of viscoelastic robotic manipulators using Timoshenko beam theory: theory and experiment. The International Journal of Advanced Manufacturing Technology vol. 71 1005–1018 (2013) – 10.1007/s00170-013-5391-1
- Korayem, M. H., Nohooji, H. R. & Nikoobin, A. Path Planning of Mobile Elastic Robotic Arms by Indirect Approach of Optimal Control. International Journal of Advanced Robotic Systems vol. 8 (2011) – 10.5772/10524
- Ghariblu, H. & Korayem, M. H. Trajectory optimization of flexible mobile manipulators. Robotica vol. 24 333–335 (2005) – 10.1017/s0263574705002225
- Malatkar, Nonlinear vibrations of cantilever beams and plates. (2003)
- Gou Nishida & Yamakita, M. Distributed port hamiltonian formulation of flexible beams under large deformations. Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005. 589–594 doi:10.1109/cca.2005.1507190 – 10.1109/cca.2005.1507190
- 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
- Jacob, B. & Zwart, H. J. Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces. (Springer Basel, 2012). doi:10.1007/978-3-0348-0399-1 – 10.1007/978-3-0348-0399-1
- Gutta, S., Lee, J. S., Trabia, M. B. & Yim, W. Modeling of ionic polymer metal composite actuator dynamics using a large deflection beam model. Smart Materials and Structures vol. 18 115023 (2009) – 10.1088/0964-1726/18/11/115023
- Curtain, R. & Zwart, H. Introduction to Infinite-Dimensional Systems Theory. Texts in Applied Mathematics (Springer New York, 2020). doi:10.1007/978-1-0716-0590-5 – 10.1007/978-1-0716-0590-5
- Harkort, C. & Deutscher, J. Stability and passivity preserving Petrov–Galerkin approximation of linear infinite-dimensional systems. Automatica vol. 48 1347–1352 (2012) – 10.1016/j.automatica.2012.04.010
- van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
- Villegas, A port-Hamiltonian approach to distributed parameter systems. (2007)
- Lamoline, Analysis and LQG control of infinite dimensional stochastic port-Hamiltonian systems. (2019)
- Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica vol. 40 757–771 (2004) – 10.1016/j.automatica.2003.12.017