Modelling and control of a class of lumped beam with distributed control

Authors

Andrea Mattioni, Yongxin Wu, Hector Ramirez, Yann Le Gorrec, Alessandro Macchelli

Abstract

A simple lumped port-Hamiltonian model for an actuated flexible beam is proposed. The flexible beam is modelled as a n-DOF actuated beam, and the port-Hamiltonian model is constructed by a systematic interconnection of the links of the beam. The proposed model is then instrumental to derive a stabilizing controller using interconnection and damping assignment - passivity based control considering an underactuated scenario. The work has been developed motivated by the practical application to a medical endoscope with distributed actuation by electro-active polymers. The lumped parameter model offers the possibility of having input/output ports in every joint between successive links, this permits to easily model the action of the actuators as an input force applied to a specific joint.

Keywords

Port-Hamiltonian system; IDA-PBC; medical endoscope; actuated beam

Citation

Journal: IFAC-PapersOnLine
Year: 2018
Volume: 51
Issue: 3
Pages: 217–222
Publisher: Elsevier BV
DOI: 10.1016/j.ifacol.2018.06.057
Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018

BibTeX

@article{Mattioni_2018,
  title={{Modelling and control of a class of lumped beam with distributed control}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.06.057},
  number={3},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Mattioni, Andrea and Wu, Yongxin and Ramirez, Hector and Gorrec, Yann Le and Macchelli, Alessandro},
  year={2018},
  pages={217--222}
}

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References

Chikhaoui, (2014)
Dòria-Cerezo, A., Batlle, C. & Espinosa-Pérez, G. Passivity-based control of a wound-rotor synchronous motor. IET Control Theory & Applications vol. 4 2049–2057 (2010) – 10.1049/iet-cta.2009.0641
Duindam, (2009)
Falaize, A. & Hélie, T. Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano. Journal of Sound and Vibration vol. 390 289–309 (2017) – 10.1016/j.jsv.2016.11.008
Jacob, (2012)
Macchelli, A., Le Gorrec, Y., Ramirez, H. & Zwart, H. On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 62 1700–1713 (2017) – 10.1109/tac.2016.2595263
Macchelli, A., Melchiorri, C. & Stramigioli, S. Port-Based Modeling and Simulation of Mechanical Systems With Rigid and Flexible Links. IEEE Transactions on Robotics vol. 25 1016–1029 (2009) – 10.1109/tro.2009.2026504
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
Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
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
Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science vol. 89 223–234 (2013) – 10.1016/j.ces.2012.12.002
Ramírez, H., Le Gorrec, Y., Maschke, B. & Couenne, F. On the passivity based control of irreversible processes: A port-Hamiltonian approach. Automatica vol. 64 105–111 (2016) – 10.1016/j.automatica.2015.07.002
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