Notch Filters for Port-Hamiltonian Systems
Authors
D. A. Dirksz, J. M. A. Scherpen, A. J. van der Schaft, M. Steinbuch
Abstract
Many powerful tools exist for control design in the frequency domain, but are theoretically only justified for linear systems. On the other hand, nonlinear control deals with control design methodologies that are theoretically justified for a larger and more realistic class of systems, but primarily dealing with stability and to a lesser extent with performance. In this technical note a standard linear notch filter is modeled in the port-Hamiltonian (PH) framework, thereby proving that the notch filter is a passive system. The notch filter can then be interconnected with any other (nonlinear) PH system, while preserving the overall passivity property. By doing so, we can combine a frequency-based control method to improve performance, the notch filter, with the nonlinear control methodology of passivity-based control.
Citation
- Journal: IEEE Transactions on Automatic Control
- Year: 2015
- Volume: 60
- Issue: 9
- Pages: 2440–2445
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/tac.2015.2390552
BibTeX
@article{Dirksz_2015,
title={{Notch Filters for Port-Hamiltonian Systems}},
volume={60},
ISSN={1558-2523},
DOI={10.1109/tac.2015.2390552},
number={9},
journal={IEEE Transactions on Automatic Control},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Dirksz, D. A. and Scherpen, J. M. A. and van der Schaft, A. J. and Steinbuch, M.},
year={2015},
pages={2440--2445}
}
References
- Isidori, A. & Byrnes, C. I. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control vol. 35 131–140 (1990) – 10.1109/9.45168
- Isidori, A., Marconi, L. & Praly, L. Robust design of nonlinear internal models without adaptation. Automatica vol. 48 2409–2419 (2012) – 10.1016/j.automatica.2012.06.076
- Jacobson, C. A., Stankovic, A. M., Tadmor, G. & Stevens, M. A. Towards a dissipativity framework for power system stabilizer design. IEEE Transactions on Power Systems vol. 11 1963–1968 (1996) – 10.1109/59.544671
- Koopman, J., Jeltsema, D. & Verhaegen, M. Port-Hamiltonian formulation and analysis of the LuGre friction model. 2008 47th IEEE Conference on Decision and Control 3181–3186 (2008) doi:10.1109/cdc.2008.4739351 – 10.1109/cdc.2008.4739351
- 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
- maschke, Port-controlled Hamiltonian systems: modeling origins and system-theoretic properties. IFAC Symp Nonlinear Control Systems (0)
- maschke, Port controlled Hamiltonian representation of distributed parameter systems. Proc IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (0)
- 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
- Rijlaarsdam, D., Nuij, P., Schoukens, J. & Steinbuch, M. Frequency domain based nonlinear feed forward control design for friction compensation. Mechanical Systems and Signal Processing vol. 27 551–562 (2012) – 10.1016/j.ymssp.2011.08.008
- Francis, B. A. & Wonham, W. M. The internal model principle for linear multivariable regulators. Applied Mathematics & Optimization vol. 2 170–194 (1975) – 10.1007/bf01447855
- 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
- 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
- franklin, Feedback Control of Dynamic Systems (2006)
- 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
- gerritsen, On switched Hamiltonian systems. Proc 15th Int Symp Mathematical Theory of Networks and Systems (0)
- Celani, F., Isidori, A. & Marconi, L. A reduction paradigm for output regulation. International Journal of Robust and Nonlinear Control vol. 18 756–781 (2007) – 10.1002/rnc.1262
- Isidori, A. & Astolfi, A. Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control vol. 37 1283–1293 (1992) – 10.1109/9.159566
- Byrnes, C. I. & Isidori, A. Nonlinear Internal Models for Output Regulation. IEEE Transactions on Automatic Control vol. 49 2244–2247 (2004) – 10.1109/tac.2004.838492
- 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
- Serrani, A., Isidori, A. & Marconi, L. Semi-global nonlinear output regulation with adaptive internal model. IEEE Transactions on Automatic Control vol. 46 1178–1194 (2001) – 10.1109/9.940923
- Serrani, A. & Isidori, A. Global robust output regulation for a class of nonlinear systems. Systems & Control Letters vol. 39 133–139 (2000) – 10.1016/s0167-6911(99)00099-7
- Steinbuch, M. & Norg, M. L. Advanced Motion Control: An Industrial Perspective. European Journal of Control vol. 4 278–293 (1998) – 10.1016/s0947-3580(98)70121-9
- slotine, Applied nonlinear control (1991)
- Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493