Abstract
This work aims at demonstrating the benefits of integrating co-simulation and formal verification in the standard design flow of a brushless power drive system for precision robotic applications. A sufficient condition on controller gain for system stability is derived from the system’s mathematical model, including a control algorithm for the reduction of cogging torque. Then, using co-simulation and design space exploration, fine tuning of the controller gain parameters has been executed, exploiting the results from the formal verification.
Work partially supported by the Italian Ministry of Education and Research (MIUR) in the framework of the CrossLab project (Departments of Excellence), and by the PRA 2018_81 project entitled “Wearable sensor systems: personalized analysis and data security in healthcare” funded by the University of Pisa.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994)
Behrmann, G., et al.: UPPAAL 4.0. In: Third International Conference on Quantitative Evaluation of Systems (QEST 2006), pp. 125–126, September 2006
Bernardeschi, C., Domenici, A.: Verifying safety properties of a nonlinear control by interactive theorem proving with the Prototype Verification System. Inf. Process. Lett. 116(6), 409–415 (2016)
Bernardeschi, C., Domenici, A., Masci, P.: A PVS-simulink integrated environment for model-based analysis of cyber-physical systems. IEEE Trans. Software Eng. 44(6), 512–533 (2018)
Bernardeschi, C., Domenici, A., Saponara, S.: Formal verification in the loop to enhance verification of safety-critical cyber-physical systems. In: Proceedings of Interactive Workshop on the Industrial Application of Verification and Testing, InterAVT 2019 (ETAPS 2019), Electronic Communications of the EASST (2019)
Blochwitz, T., et al.: Functional mockup interface 2.0: the standard for tool independent exchange of simulation models. In: Proceedings of the 9th International MODELICA Conference, Munich, Germany, 3–5 September 2012, pp. 173–184. No. 76 in Linköping Electronic Conference Proceedings, Linköping University Electronic Press (2012)
Dini, P., Saponara, S.: Cogging torque reduction in brushless motors by a nonlinear control technique. Energies 12(11), 2224 (2019)
Domenici, A., Fagiolini, A., Palmieri, M.: Integrated simulation and formal verification of a simple autonomous vehicle. In: Cerone, A., Roveri, M. (eds.) SEFM 2017. LNCS, vol. 10729, pp. 300–314. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-74781-1_21
Dutertre, B.: Elements of mathematical analysis in PVS. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 141–156. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0105402
Fitzgerald, J.S., Larsen, P.G., Verhoef, M.: Vienna development method. In: Wah, B. (ed.) Wiley Encyclopedia of Computer Science and Engineering. Wiley (2007)
Fulton, N., Mitsch, S., Quesel, J.-D., Völp, M., Platzer, A.: KeYmaera X: an axiomatic tactical theorem prover for hybrid systems. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS (LNAI), vol. 9195, pp. 527–538. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_36
Gamble, C.: DSE in the INTO-CPS platform. Technical report, D5.3e, INTO-CPS Deliverable (2017)
Gomes, C., Thule, C., Broman, D., Larsen, P.G., Vangheluwe, H.: Co-simulation: State of the art. CoRR abs/1702.00686 (2017)
Henzinger, T.A.: The theory of hybrid automata. In: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, LICS 1996, pp. 278–292. IEEE Computer Society, Washington (1996)
Isidori, A.: Nonlinear Control System. Communications and Control Engineering. Springer, London (1995). https://doi.org/10.1007/978-1-84628-615-5
Larsen, P.G., et al.: Integrated tool chain for model-based design of Cyber-Physical Systems: the INTO-CPS project. In: 2016 2nd International Workshop on Modelling, Analysis, and Control of Complex CPS (CPS Data), pp. 1–6, April 2016
Larsen, P.G., Gamble, C., Pierce, K., Ribeiro, A., Lausdahl, K.: Support for co-modelling and co-simulation: the Crescendo tool. In: Fitzgerald, J., Larsen, P.G., Verhoef, M. (eds.) Collaborative Design for Embedded Systems. LNCS, pp. 97–114. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54118-6_5
Leivant, D.: Higher order logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 229–321. Oxford University Press Inc., New York (1994)
Lotov, A.V., Miettinen, K.: Visualizing the Pareto frontier. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 213–243. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88908-3_9
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive Systems: Safety. Springer, New York (1995). https://doi.org/10.1007/978-1-4612-4222-2
Muñoz, C.: Rapid prototyping in PVS. Technical report, NIA 2003–03, NASA/CR-2003-212418, National Institute of Aerospace, Hampton, VA, USA (2003)
Nibert, J., Herniter, M.E., Chambers, Z.: Model-based system design for MIL, SIL, and HIL. World Electr. Veh. J. 5(4), 1121–1130 (2012)
Owre, S., Rushby, J.M., Shankar, N.: PVS: a prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55602-8_217
Palensky, P., van der Meer, A., Lopez, C., Joseph, A., Pan, K.: Applied cosimulation of intelligent power systems: implementing hybrid simulators for complex power systems. IEEE Ind. Electron. Mag. 11(2), 6–21 (2017)
Palensky, P., Meer, A.A.V.D., Lopez, C.D., Joseph, A., Pan, K.: Cosimulation of intelligent power systems: fundamentals, software architecture, numerics, and coupling. IEEE Ind. Electron. Mag. 11(1), 34–50 (2017)
Palmieri, M., Bernardeschi, C., Masci, P.: A flexible framework for FMI-based co-simulation of human-centred cyber-physical systems. In: Software Technologies: Applications and Foundations - STAF 2018 Collocated Workshops, Toulouse, June 25–29 France 2018, Revised Selected Papers, pp. 21–33 (2018)
Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science (sfcs 1977), pp. 46–57, October 1977
Pulle, D., Darnell, P., Veltman, A.: Applied Control of Electrical Drives: Real Time Embedded and Sensorless Control Using VisSimTM and PLECSTM. Power Systems. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20043-9
Tudorache, T., Trifu, I., Ghita, C., Bostan, V.: Improved mathematical model of PMSM taking into account cogging torque oscillations. Adv. Electr. Comput. Eng. 12(3), 59–64 (2012)
Acknowledgments
The authors wish to thank the anonymous referees for their valuable suggestions. The authors also thank the INTO-CPS project for providing the co-simulation environment.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Bernardeschi, C., Dini, P., Domenici, A., Saponara, S. (2020). Co-simulation and Verification of a Non-linear Control System for Cogging Torque Reduction in Brushless Motors. In: Camara, J., Steffen, M. (eds) Software Engineering and Formal Methods. SEFM 2019. Lecture Notes in Computer Science(), vol 12226. Springer, Cham. https://doi.org/10.1007/978-3-030-57506-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-57506-9_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57505-2
Online ISBN: 978-3-030-57506-9
eBook Packages: Computer ScienceComputer Science (R0)