Exponential Trajectory Tracking Passivity-Based Control for Permanent-Magnet Synchronous Motors

Authors

Abstract

In this paper, a novel methodology of nonlinear control is used, and a passivity-based control of contractive port-controlled Hamiltonian (PCH) systems is applied to a permanent magnet synchronous motor (PMSM). This methodology, also called “IDA-PBC” (Trajectory Injection and Damping Assignment—Passivity-Based Control), uses passivity-based control of PCH systems “IDA-PBC” and exploits the properties of contractive Hamiltonian systems, resulting in a closed loop with its contractive system desired dynamics, thus obtaining an exponential trajectory tracking without relying on the error coordinates. In this system, a few steps are proposed in order to divide and modularize the methodology so it can be redesigned or reapplied in other systems by the reader. First, we define the model and set the way to solve the “matching equation.” Then the feasible and reference trajectories are obtained. After that, the desired Dirac structure and energy function are set in order to meet the methodology requirements. Finally, the control law is obtained, and simulations were performed. The desired trajectories (which can be time varying) are arbitrarily set, and the exponential convergence to the desired trajectories is archived. The results obtained from the simulations are an initial approach to the improvement of propulsion algorithms in electrified vehicles, where linear controls are still used and have poor performance compared to the visited methodology.

Citation

Journal: SAE Technical Paper Series
Year: 2021
Volume: 1
Issue:
Pages:
Publisher: SAE International
DOI: 10.4271/2021-01-5047

BibTeX

@inproceedings{Rodr_guez_2021,
  series={WONLYAUTO},
  title={{Exponential Trajectory Tracking Passivity-Based Control for Permanent-Magnet Synchronous Motors}},
  volume={1},
  ISSN={2688-3627},
  DOI={10.4271/2021-01-5047},
  booktitle={{SAE Technical Paper Series}},
  publisher={SAE International},
  author={Rodríguez, Luis Fernando},
  year={2021}
}

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References

Brasel, M. A gain-scheduled multivariable LQR controller for permanent magnet synchronous motor. 2014 19th International Conference on Methods and Models in Automation and Robotics (MMAR) 722–725 (2014) doi:10.1109/mmar.2014.6957443 – 10.1109/mmar.2014.6957443
Zhang, X., Tian, G., Huang, Y. & Lu, Z. A Comparative Study of PMSM Sensorless Control Algorithms: Model Based vs Luenberger Observer. 2016 IEEE Vehicle Power and Propulsion Conference (VPPC) 1–6 (2016) doi:10.1109/vppc.2016.7791566 – 10.1109/vppc.2016.7791566
Ghafarri-Kashani, A. R., Yazdanpanah, M. J. & Faiz, J. ROBUST SPEED CONTROL OF PMSM USING Mixed NONLINEAR H∞/SMC Techniques. IFAC Proceedings Volumes 41, 8413–8418 (2008) – 10.3182/20080706-5-kr-1001.01422
AC Electric Motors Control. (2013) doi:10.1002/9781118574263 – 10.1002/9781118574263
Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems and its application to a magnetic levitation system. Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) 3388–3393 doi:10.1109/cdc.2001.980360 – 10.1109/cdc.2001.980360
Kotyczka, P. Local linear dynamics assignment in IDA-PBC. Automatica 49, 1037–1044 (2013) – 10.1016/j.automatica.2013.01.028
Kotyczka, P., Volf, A. & Lohmann, B. Passivity based trajectory tracking control with predefined local linear error dynamics. Proceedings of the 2010 American Control Conference 3429–3434 (2010) doi:10.1109/acc.2010.5531100 – 10.1109/acc.2010.5531100
Reyes-Báez, R., van der Schaft, A. & Jayawardhana, B. Virtual Differential Passivity based Control for Tracking of Flexible-joints Robots. IFAC-PapersOnLine 51, 169–174 (2018) – 10.1016/j.ifacol.2018.06.048
Yaghmaei, A. & Yazdanpanah, M. J. Trajectory tracking for a class of contractive port Hamiltonian systems. Automatica 83, 331–336 (2017) – 10.1016/j.automatica.2017.06.039
Yaghmaei, A. & Yazdanpanah, M. J. Trajectory tracking of a class of port Hamiltonian systems using Timed IDA-PBC technique. 2015 54th IEEE Conference on Decision and Control (CDC) 5037–5042 (2015) doi:10.1109/cdc.2015.7403007 – 10.1109/cdc.2015.7403007
LOHMILLER, W. & SLOTINE, J.-J. E. On Contraction Analysis for Non-linear Systems. Automatica 34, 683–696 (1998) – 10.1016/s0005-1098(98)00019-3
Anderson, B. D. O., Pren, J. B. & Dickerson, S. L. Linear Optimal Control. Journal of Dynamic Systems, Measurement, and Control 93, 275–275 (1971) – 10.1115/1.3426525
Shah, D., Espinosa–Pérez, G., Ortega, R. & Hilairet, M. An asymptotically stable sensorless speed controller for non‐salient permanent magnet synchronous motors. Intl J Robust & Nonlinear 24, 644–668 (2012) – 10.1002/rnc.2910