Position Control via Force Feedback in the Port-Hamiltonian Framework
Authors
Mauricio Muñoz-Arias, Jacquelien M. A. Scherpen, Daniel A. Dirksz
Abstract
In this chapter, position control strategies via force feedback are presented for standard mechanical systems in the port-Hamiltonian framework. The presented control strategies require a set of coordinate transformations, since force feedback in the port-Hamiltonian framework is not straightforward. With the coordinate transformations force feedback can be realized while preserving the port-Hamiltonian structure. The port-Hamiltonian formalism offers a modeling framework with a clear physical structure and other properties that can often be exploited for control design purposes, which is why we believe it is important to preserve the structure. The proposed control strategies offer an alternative solution to position control with more tuning freedom and exploit knowledge of the system dynamics.
Citation
- ISBN: 9783319303567
- Publisher: Springer International Publishing
- DOI: 10.1007/978-3-319-30357-4_9
BibTeX
@inbook{Mu_oz_Arias_2016,
title={{Position Control via Force Feedback in the Port-Hamiltonian Framework}},
ISBN={9783319303574},
ISSN={1610-7411},
DOI={10.1007/978-3-319-30357-4_9},
booktitle={{Nonlinear Systems}},
publisher={Springer International Publishing},
author={Muñoz-Arias, Mauricio and Scherpen, Jacquelien M. A. and Dirksz, Daniel A.},
year={2016},
pages={181--207}
}
References
- Andersson, S., Söderberg, A. & Björklund, S. Friction models for sliding dry, boundary and mixed lubricated contacts. Tribology International vol. 40 580–587 (2007) – 10.1016/j.triboint.2005.11.014
- M Bol. Bol, M.: Force And Position Control of the Philips Experimental Robot Arm in a Energy-Based Setting. University of Groningen, Groningen (2012) (2012)
- Theory of Robot Control. Communications and Control Engineering (Springer London, 1996). doi:10.1007/978-1-4471-1501-4 – 10.1007/978-1-4471-1501-4
- DA Dirksz. Dirksz, D.A., Scherpen, J.M.A.: Power-based control: canonical coordinate transformations. Integr. Adapt. Control Autom. 48(6), 1046–1056 (2012) (2012)
- Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica vol. 45 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
- Duindam, V., Macchelli, A., Stramigioli, S., Bruyninckx, H. (eds.): Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach. Springer, Berlin (2009) (2009)
- Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters vol. 42 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
- Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica vol. 39 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
- Gómez-Estern, F. & Van der Schaft, A. J. Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control vol. 10 451–468 (2004) – 10.3166/ejc.10.451-468
- D Gorinevsky. Gorinevsky, D., Formalsky, A., Scheiner, A.: Force Control of Robotics Systems. CRC Press LLC, Moscow (1997) (1997)
- H Khalil. Khalil, H.: Nonlinear Systems, 2nd edn. Prentice-Hall, New York (2001) (2001)
- F Koop. Koop, F.: Trajectory Tracking Control of the Philips Experimental Robot Arm in the Port-Hamiltonian Framework. University of Groningen, Groningen (2014) (2014)
- Maschke, B.M., van der Schaft, A.J.: Port-controlled hamiltonian systems: modeling origins and system-theoretic properties. IN: Procedings of the IFAC Symposium on Nonlinear Control Systems, pp. 282–288. Bordeaux, France (1992)
- Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Transactions on Automatic Control vol. 45 1498–1502 (2000) – 10.1109/9.871758
- Muñoz-Arias, M., Scherpen, J. M. A. & Dirksz, D. A. A Class of Standard Mechanical System with Force Feedback in the port-Hamiltonian Framework. IFAC Proceedings Volumes vol. 45 90–95 (2012) – 10.3182/20120829-3-it-4022.00038
- Muñoz-Arias, M., Scherpen, J. M. A. & Dirksz, D. A. A Class of Standard Mechanical System with Force Feedback in the port-Hamiltonian Framework. IFAC Proceedings Volumes vol. 45 90–95 (2012) – 10.3182/20120829-3-it-4022.00038
- Munoz-Arias, M., Scherpen, J. M. A. & Dirksz, D. A. Position control via force feedback for a class of standard mechanical systems in the port-Hamiltonian framework. 52nd IEEE Conference on Decision and Control 1622–1627 (2013) doi:10.1109/cdc.2013.6760114 – 10.1109/cdc.2013.6760114
- Murray, R., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)
- Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
- 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
- Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control vol. 47 1218–1233 (2002) – 10.1109/tac.2002.800770
- Ortega, R. & Romero, J. G. Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Systems & Control Letters vol. 61 11–17 (2012) – 10.1016/j.sysconle.2011.09.015
- Rijs, R., Beekmans, R., Izmit, S., Bemelmans, D.: Philips Experimental Robot Arm: User Instructor Manual, Version 1.1. Koninklijke Philips Electronics N.V., Eindhoven (2010)
- Springer Handbook of Robotics. (2008) doi:10.1007/978-3-540-30301-5 – 10.1007/978-3-540-30301-5
- M Spong. Spong, M., Hutchinson, S., Vidjasagar, M.: Robot Modeling and Control. Wiley, Hoboken (2006) (2006)
- AJ Schaft van der. van der Schaft, A.J.: \(L_{2}\) L 2 -Gain and Passivity Techniques in Nonlinear Control: Lecture Notes in Control and Information Sciences 218. Springer, London (1999) (1999)
- Viola, G., Ortega, R., Banavar, R., Acosta, J. A. & Astolfi, A. Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes. IEEE Transactions on Automatic Control vol. 52 1093–1099 (2007) – 10.1109/tac.2007.899064