Tuning Rules for Passivity-Based Integral Control for a Class of Mechanical Systems
Authors
Carmen Chan-Zheng, Mauricio Munoz-Arias, Jacquelien M.A. Scherpen
Abstract
This manuscript introduces a passivity-based integral control approach for fully-actuated mechanical systems. The novelty of our methodology is that we exploit the gyroscopic forces of the mechanical systems to exponentially stabilize the mechanical system at the desired equilibrium even in the presence of matched disturbances; additionally, we show that our approach is robust against unmatched disturbances. Furthermore, we provide tuning rules to prescribe the performance of the closed-loop system. We conclude this manuscript with experimental results obtained from a robotic arm.
Citation
- Journal: IEEE Control Systems Letters
- Year: 2023
- Volume: 7
- Issue:
- Pages: 37–42
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/lcsys.2022.3186618
BibTeX
@article{Chan_Zheng_2023,
title={{Tuning Rules for Passivity-Based Integral Control for a Class of Mechanical Systems}},
volume={7},
ISSN={2475-1456},
DOI={10.1109/lcsys.2022.3186618},
journal={IEEE Control Systems Letters},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Chan-Zheng, Carmen and Munoz-Arias, Mauricio and Scherpen, Jacquelien M.A.},
year={2023},
pages={37--42}
}References
- van der Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer International Publishing, 2017). doi:10.1007/978-3-319-49992-5 – 10.1007/978-3-319-49992-5
- 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
- Brogliato, B., Maschke, B., Lozano, R. & Egeland, O. Dissipative Systems Analysis and Control. Communications and Control Engineering (Springer London, 2007). doi:10.1007/978-1-84628-517-2 – 10.1007/978-1-84628-517-2
- Borja, P., Ortega, R. & Scherpen, J. M. A. New Results on Stabilization of Port-Hamiltonian Systems via PID Passivity-Based Control. IEEE Transactions on Automatic Control vol. 66 625–636 (2021) – 10.1109/tac.2020.2986731
- Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control vol. 10 432–450 (2004) – 10.3166/ejc.10.432-450
- 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
- Dirksz, D. A. & Scherpen, J. M. A. Power-based adaptive and integral control of standard mechanical systems. 49th IEEE Conference on Decision and Control (CDC) 4612–4617 (2010) doi:10.1109/cdc.2010.5717079 – 10.1109/cdc.2010.5717079
- Dirksz, D. A. & Scherpen, J. M. A. Port-Hamiltonian and power-based integral type control of a manipulator system. IFAC Proceedings Volumes vol. 44 13450–13455 (2011) – 10.3182/20110828-6-it-1002.01030
- 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
- 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
- Romero, J. G., Donaire, A. & Ortega, R. Robust energy shaping control of mechanical systems. Systems & Control Letters vol. 62 770–780 (2013) – 10.1016/j.sysconle.2013.05.011
- Ferguson, J., Donaire, A. & Middleton, R. H. Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation. IEEE Transactions on Automatic Control vol. 62 5947–5953 (2017) – 10.1109/tac.2017.2700995
- Ferguson, J., Donaire, A., Ortega, R. & Middleton, R. H. Matched Disturbance Rejection for a Class of Nonlinear Systems. IEEE Transactions on Automatic Control vol. 65 1710–1715 (2020) – 10.1109/tac.2019.2933398
- Reyes Báez, R. Virtual contraction and passivity based control of nonlinear mechanical systems: trajectory tracking and group coordination. doi:10.33612/diss.96171118 – 10.33612/diss.96171118
- Reyes-Báez, R., van der Schaft, A. & Jayawardhana, B. Virtual contractivity-based control of fully-actuated mechanical systems in the port-Hamiltonian framework. Automatica vol. 141 110275 (2022) – 10.1016/j.automatica.2022.110275
- Stadlmayr, R. & Schlacher, K. Tracking Control for Port-Hamiltonian Systems using Feedforward and Feedback Control and a State Observer. IFAC Proceedings Volumes vol. 41 1833–1838 (2008) – 10.3182/20080706-5-kr-1001.00313
- Sarras, I., Ortega, R. & van der Schaft, A. On the Modeling, Linearization and Energy Shaping Control of Mechanical Systems. IFAC Proceedings Volumes vol. 45 161–166 (2012) – 10.3182/20120829-3-it-4022.00040
- Khalil, Nonlinear Systems (2002)
- Sontag, E. D. & Wang, Y. On characterizations of the input-to-state stability property. Systems & Control Letters vol. 24 351–359 (1995) – 10.1016/0167-6911(94)00050-6
- Chan-Zheng, C., Borja, P., Monshizadeh, N. & Scherpen, J. M. A. Exponential Stability and Tuning for a Class of Mechanical Systems. 2021 European Control Conference (ECC) 1875–1880 (2021) doi:10.23919/ecc54610.2021.9655218 – 10.23919/ecc54610.2021.9655218
- Chan-Zheng, C., Borja, P. & Scherpen, J. M. A. Tuning of Passivity-Based Controllers for Mechanical Systems. IEEE Transactions on Control Systems Technology vol. 31 2515–2530 (2023) – 10.1109/tcst.2023.3260995
- Rijs, Philips Experimental Robot Arm: User Instructor Manual (2010)
- Chan Zheng, C. Tuning rules for energy-based control methods for mechanical systems. doi:10.33612/diss.581245883 – 10.33612/diss.581245883
- Bol, Model Generator for Philips Experimental Robotics Arm (2021)
- 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