Controller Design of Hybrid-Time ‎Delay-Petri Nets Based on Lyapunov Theory by Adding Control Places

Document Type : Original Article


Department of Electrical and Computer Engineering Semnan University, Semnan, Iran


The aim of this paper is to propose a new method for controller design using control places in special hybrid Petri Nets called Hybrid-Time Delay-Petri Nets (HTDPN). Most control approaches use the control place of the supervisory control for discrete Petri Nets. However, the new approach uses the place to control the linear dynamical systems which are modeled by the HTDPN tool. This controller consists of control places, transitions, arcs connected to the control place, and weights of the arcs, which are added to the HTDPN model of the system. In this paper, there are three main steps for the controller design. In the first step, the plant is modeled using the HTDPN tool, and in the second step, a controller is designed using the novel method presented. Finally, the weights of arcs connected to the control place are computed using the Lyapunov function theory, which guarantees closed-loop stability. The main advantage of this method is the possibility of using continuous and discrete places simultaneously in nonlinear systems. Unlike most previous approaches, in the proposed method, an expert designer can create a favorite controller in the graphical environment, and then apply changes to the mathematical environment of the HTDPN model. The performance of the proposed controller is evaluated by a comparative study. The comparison criteria in this article are: error criteria (IEA), energy consumption, rise time, settling time and simulation run time. The simulation results showed that the proposed method was 45% and 600% better conditions than the Model Predictive Conrol (MPC) and optimal control methods, respectively.


Main Subjects

  1. Yin, L., Fang, H. and Shao, H., "Design and implementation of petri net for brain-computer interface system", in 2019 Chinese Automation Congress (CAC), IEEE. (2019), 5810-5814.
  2. Du, N., Hu, H. and Zhou, M., "Robust deadlock avoidance and control of automated manufacturing systems with assembly operations using petri nets", IEEE Transactions on Automation Science and Engineering, Vol. 17, No. 4, (2020), 1961-1975. doi: 10.1109/TASE.2020.2983672.
  3. YadollahzadehTabari, M. and Mohammadizad, P., "Modeling and performance evaluation of energy consumption in s-mac protocol using generalized stochastic petri nets", International Journal of Engineering, Transactions C: Aspects, Vol. 33, No. 6, (2020), 1114-1121. doi: 10.5829/IJE.2020.33.06C.08.
  4. Liu, F., Chen, S., Heiner, M. and Song, H., "Modeling biological systems with uncertain kinetic data using fuzzy continuous petri nets", BMC Systems Biology, Vol. 12, (2018), 63-74. doi: 10.1186/s12918.018.0568.8.
  5. Feng, Y., Xing, K., Zhou, M., Wang, X. and Liu, H., "Robust deadlock prevention for automated manufacturing systems with unreliable resources by using general petri nets", IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 50, No. 10, (2018), 3515-3527. doi: 10.1109/TSMC.2018.2884316.
  6. Li, J., Yu, X. and Zhou, M., "Analysis of unbounded petri net with lean reachability trees", IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 50, No. 6, (2018), 2007-2016. doi: 10.1109/TSMC.2018.2791527.
  7. Gao, X. and Hu, X., "A petri net neural network robust control for new paste backfill process model", IEEE Access, Vol. 8, No., (2020), 18420-18425. doi: 10.1109/ACCESS.2020.2968510.
  8. Demongodin, I. and Koussoulas, N.T., "Differential petri net models for industrial automation and supervisory control", IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), Vol. 36, No. 4, (2006), 543-553. doi: 10.1109/TSMCC.2005.848154.
  9. Demongodin, I. and Koussoulas, N.T., "Differential petri nets: Representing continuous systems in a discrete-event world", IEEE transactions on Automatic Control, Vol. 43, No. 4, (1998), 573-579. doi: 10.1109/9.665073.
  10. Demongodin, I. and Koussoulas, N.T., "Modeling of mixed continuous/discrete-event systems via differential petri nets", in Proceedings of Third International Conference on Electronics, Circuits, and Systems, IEEE. Vol. 1, (1996), 475-478.
  11. Saleh, A., Chiachío, M., Salas, J.F. and Kolios, A., "Self-adaptive optimized maintenance of offshore wind turbines by intelligent petri nets", Reliability Engineering & System Safety, Vol. 231, (2023), 109013. doi: 10.1016/j.ress.2022.109013.
  12. Ruan, K. and Li, L., "Traffic network modeling and volume control using labeled petri nets", in 2021 IEEE International Intelligent Transportation Systems Conference (ITSC), IEEE. (2021), 3578-3583.
  13. Taleb, M., Leclercq, E. and Lefebvre, D., "Model predictive control for discrete and continuous timed petri nets", International Journal of Automation and Computing, Vol. 15, (2018), 25-38. doi: 10.1007/s11633-016-1046-7.
  14. Caligola, S., Carlucci, T., Fummi, F., Laudanna, C., Constantin, G., Bombieri, N. and Giugno, R., "Efficient simulation and parametrization of stochastic petri nets in systemc: A case study from systems biology", in 2019 Forum for Specification and Design Languages (FDL), IEEE. (2019), 1-7.
  15. Ding, Z., Xiao, L. and Hu, J., "Performance analysis of service composition using ordinary differential equations", in 2008 12th IEEE International Workshop on Future Trends of Distributed Computing Systems, IEEE. (2008), 30-36.
  16. Dideban, A. and Ahangarani Farahani, A., "A new adaptive controller for the three‎ axis satellite simulator based on continuous‎ time delay petri nets tool", Space Science and Technology, (2022). doi: 10.22034/jsst.2022.314634.1376.
  17. Dideban, A., Farahani, A.A. and Razavi, M., "Modeling continuous systems using modified petri nets model", Modeling and Simulation in Electrical and Electronics Engineering (MSEEE), Semnan, Iran, Vol. 1, No. 2, (2015), 75-79. doi: 10.22075/MSEEE.2015.247.
  18. Dideban, A. and Sabouri Rad, M., "Electrical circuit modelling with petri net by using of control arcs", Journal of Modeling in Engineering, Vol. 11, No. 35, (2014), 39-47. doi: 10.22075/JME.2017.1657.
  19. Farahani, A.A., Dideban, A. and Najafgholi, E., "Modeling continuous systems by petri nets using speed control arcs", in 2016 4th International Conference on Control, Instrumentation, and Automation (ICCIA), IEEE. (2016), 75-80.
  20. Ahangarani, A. and Dideban, A., "Continuous-time delay-petri nets as a new tool to design state space controller", Information Technology and Control, Vol. 45, No. 4, (2016), 401-411. doi: 10.5755/j01.itc.45.4.13665.
  21. Ahangarani Farahani, A. and Dideban, A., "Hybrid time delay petri nets as a mathematical novel tool to model dynamic system with current sample time", Control and Optimization in Applied Mathematics, Vol. 3, No. 1, (2018), 45-64. doi: 10.30473/coam.2019.41925.1090.
  22. Ma, Z., Zou, M., Zhang, J. and Li, Z., "Design of optimal control sequences in petri nets using basis marking analysis", IEEE transactions on Automatic Control, Vol. 67, No. 7, (2021), 3685-3692. doi: 10.1109/TAC.2021.3106883.
  23. Othman, S., Alali, M.A., Sbita, L., Barbot, J.-P. and Ghanes, M., "Modeling and control design based on petri nets tool for a serial three-phase five-level multicellular inverter used as a shunt active power filter", Energies, Vol. 14, No. 17, (2021), 5335. doi: 10.3390/en14175335.
  24. Bashir, M., Zhou, J. and Muhammad, B.B., "Optimal supervisory control for flexible manufacturing systems model with petri nets: A place-transition control", IEEE Access, Vol. 9, (2021), 58566-58578. doi: 10.1109/ACCESS.2021.3072892.
  25. Chen, C. and Hu, H., "Extended place-invariant control in automated manufacturing systems using petri nets", IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 52, No. 3, (2020), 1807-1822. doi: 10.1109/TSMC.2020.3035668.
  26. Baniardalani, S., "Fault diagnosis of discrete-time linear systems using continuous time delay petri nets", International Journal of Industrial Electronics Control and Optimization, Vol. 3, No. 1, (2020), 81-90. doi: 10.22111/ieco.2019.28395.1130.
  27. Qiu, Z., Duan, C., Yao, W., Zeng, P. and Jiang, L., "Adaptive lyapunov function method for power system transient stability analysis", IEEE Transactions on Power Systems, (2022). doi: 10.1109/TPWRS.2022.3199448.
  28. Ashjaee, M. and Tavazoei, M. S., "Optimal tuning of implementable fractional order PI controllers based on ISE performance index", Sharif Journal of Mechanical Engineering, Vol. 35, No. 1, (2019), 133-141. doi: 10.24200/J40.2018.10795.1431.