Hybrid Time Delay Petri Nets as a Mathematical Novel Tool to Model Dynamic System with Current Sample Time

Document Type: بنیادی - نظری


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

2 Department of Electrical and Computer Engineering,Semnan university, Semnan, Iran



The existing modeling methods using Petri Nets‎, ‎have been successfully applied to model and analyze dynamic systems‎. ‎However‎, ‎these methods are not capable of modeling all dynamic systems such as systems with the current sample time signals‎, ‎systems including various subsystems and multi-mode systems‎. ‎This paper proposes Hybrid Time Delay Petri Nets (HTDPN) to solve the problem‎. ‎In this approach‎, ‎discrete and continuous Petri Nets are combined so that the continuous PNs part and the discrete PNs are responsible for past time samples and current sample time‎, ‎respectively‎. ‎To evaluate the performance of the proposed tool‎, ‎it is employed to model a legless piezoelectric capsubot robot as a multi modes system and a $PID$ controller‎, ‎in which the gains tuned by the Genetic Algorithm are designed for the resulting model by HTDPN‎. ‎Results show that the proposed method is faster in terms of mathematical calculations which can reduce the simulation time and complexity of complicated systems‎. ‎It would be observed that the proposed approach makes the $PID$ controller design simpler as well‎. ‎In addition‎, ‎a comparative study of capsubot has been performed‎. ‎Simulation results show that the presented method is encouraging compared to the predictive control‎, ‎which is used in the literature.


Main Subjects

‎bibitem{1} Wu N‎. ‎Q.‎, ‎Zhou M‎. ‎C.‎, ‎Li Z‎. ‎W‎. ‎(2015) ``Short-Term scheduling of crude-oil operations‎: ‎Petri Net-based control-theoretic approach"‎, ‎IEEE Robotics and Automation Magazine‎, ‎22‎, ‎64-76‎.

‎bibitem{2} Hazza M‎. ‎H‎. ‎F‎. ‎A.‎, ‎Taha A‎. ‎H.‎, ‎Adesta E‎. ‎Y‎. ‎T.‎, ‎Albakri A‎. ‎(2015) ``Modelling and analysing deadlock in flexible manufacturing system using untimed Petri Net"‎, ‎4th International Conference on Advanced Computer Science Applications and Technologies (ACSAT)‎, ‎Kuala Lumpur‎, ‎261-265‎.

‎bibitem{3} Lennartson B.‎, ‎Basile F.‎, ‎Miremadi S.‎, ‎Fei Z.‎, ‎Hosseini M‎. ‎N‎. ‎(2014) ``Supervisory control for state-vector transition models-A unified approach"‎, ‎IEEE Transaction on Automation Science and Engineering‎, ‎11‎, ‎33–47‎.

‎bibitem{4} Ahanarani Farahani A.‎, ‎Dideban A.‎, ‎Najafgholi E‎. ‎(2016) ``Modeling continuous systems by Petri Nets using speed control arcs"‎, ‎The 4th International Conference on Control‎, ‎Instrumentation‎, ‎and Automation‎, ‎Iran‎, ‎75-80‎.

‎bibitem{5} Taleb M.‎, ‎Leclercq E.‎, ‎Lefebvre D‎. ‎(2014) ``Limitation of flow variation of timed continuous Petri Nets via model predictive control"‎, ‎American Control Conference (ACC) Portland Oregon USA‎, ‎4919-4924‎.

‎bibitem{6} Demongodin I.‎, ‎Giua A‎. ‎(2014) ``Dynamics and steady state analysis of controlled generalized batches Petri Nets"‎, ‎Nonlinear Analysis‎: ‎Hybrid Systems‎, ‎12‎, ‎33–49‎.

‎bibitem{7} Milinkovic S.‎, ‎Markovic M.‎, ‎Veskovic S.‎, ‎Ivic M.‎, ‎Pavlovic N‎. ‎(2013) ``A fuzzy Petri Net model to estimate train delays"‎, ‎Simulation Modelling Practice and Theory‎, ‎33‎, ‎144–157‎.

‎bibitem{8} Wang Y.‎, ‎Ding D‎. ‎(2015) ``Revealing the structure and function of P‎. ‎pastoris metabolic network using Petri Nets"‎, ‎14th International Symposium on Distributed Computing and Applications for Business Engineering and Science‎, ‎360-363‎.


‎bibitem{9} Chen C.‎, ‎Yang Y.‎, ‎Zhang X‎. ‎(2017) ``Application study on knowledge representation of emergency scenario using hybrid Petri Net"‎, ‎3rd International Conference on Information Management‎, ‎332-336‎.


‎bibitem{10} Ahangarani Farahani A.‎, ‎Dideban A‎. ‎(2015) ``Output feedback controller design and modeling of dynamics systems using Petri Nets"‎, ‎3rd Nation and First International Conference in applied research on Electrical‎, ‎Mechanical and Mechatronics Engineering Iran‎, ‎1-6‎.


‎bibitem{11} Ahangarani Farahani A.‎, ‎Dideban A‎. ‎(2016) ``Continuous-time delay-Petri Nets as a new tool to design state space controller"‎, ‎Information Technology and Control‎, ‎45‎, ‎401-412‎.


‎bibitem{12} Dideban A.‎, ‎Ahangarani Farahani A.‎, ‎Razavi M‎. ‎(2015) ``Modeling continuous systems using modified Petri Nets model"‎, ‎Modeling and Simulation in Electrical and Electronics Engineering (MSEEE)‎, ‎1‎, ‎75-79‎.


‎bibitem{13} Dideban A.‎, ‎Sabouri Rad M‎. ‎(2014) ``Electrical circuit modelling with Petri Nets by using of control arcs"‎, ‎Journal of Modeling in Engineering‎, ‎11‎, ‎39-47‎.


‎bibitem{14} Pettersson S.‎, ‎Lennarston B‎. ‎(1995) ``Hybrid modelling focused on hybrid Petri Nets"‎, ‎2nd European Workshop on Real-Time and Hybrid Systems‎, ‎303-309‎.


‎bibitem{15} Bibi Z.‎, ‎Ahmad J.‎, ‎Paracha R‎. ‎Z.‎, ‎Siddiqa A‎. ‎(2017) ``Modeling and analysis of the signaling crosstalk of PI3K‎, ‎AMPK and MAPK with timed hybrid Petri Nets approach"‎, ‎17th International Conference on Computational Science & Its Applications (ICCSA)‎, ‎1-7‎.


‎bibitem{16} Lu X.‎, ‎Zhou M‎. ‎C.‎, ‎Ammari A‎. ‎C.‎, ‎Ji J‎. ‎(2016) ``Hybrid Petri Nets for modeling and analysis of microgrid systems"‎, ‎IEEE/CAA Journal of Automatica Sinica‎, ‎3‎, ‎349-356‎.

‎bibitem{17} Nivznansk'a M.‎, ‎Kuvcera E.‎, ‎Haffner O.‎, ‎Koz'{a}kov'a A‎. ‎(2016) ``Modeling of hybrid systems by hybrid Petri Nets using open modelica and PNlib"‎, ‎Proceedings of the 28th International Conference Cybernetics and Informatics Slovakia‎, ‎1-6‎.

‎bibitem{18} Fraca E.‎, ‎J'{u}lvez J.‎, ‎Silva M‎. ‎(2016) ``Hybrid and hybrid adaptive Petri Nets‎: ‎on the computation of a reachability graph"‎, ‎Nonlinear Analysis‎: ‎Hybrid Systems‎, ‎16‎, ‎24–39‎.

‎bibitem{19} Ogata K‎. ‎H.‎, ‎(1987)‎ "‎Discrete-time control systems"‎, ‎Prentice Hall‎, ‎2nd Edition‎.

‎bibitem{20} Ibrahim D‎. ‎(2006) ``Microcontroller based applied digital control"‎, ‎John Wiley & Sons Inc.‎, ‎English‎.

‎bibitem{21} Mahmoudzadeh S.‎, ‎Mojallali H‎. ‎(2013) ``An optimized PID for legless capsubots using modified imperialist competitive algorithm"‎, ‎First RSI/ISM International Conference on Robotics and Mechatronics (ICRoM)‎, ‎Iran‎, ‎194-199‎.

‎bibitem{22} Farahani A‎. ‎A.‎, ‎Suratgar A‎. ‎A.‎, ‎Talebi H‎. ‎A‎. ‎(2012) ``Optimal controller design of Legless piezo capsubot movement"‎, ‎International Journal of Advanced Robotic Systems‎, ‎9‎, ‎1-7‎.

‎bibitem{23} Liu Y.‎, ‎Yu H.‎, ‎Yang T‎. ‎C‎. ‎(2008) ``Analysis and control of a capsubot"‎, ‎Proceedings of the Word Congress Korea‎, ‎756-761‎.

‎bibitem{24} Behmardi Kalantari S.‎, ‎Farahani A‎. ‎A.‎, ‎Doustmohammadi A.‎, ‎Menhaj M‎. ‎B.‎, ‎Suratgar A‎. ‎A.‎, ‎Talebi H‎. ‎A‎. ‎(2011) ``Hybrid model predictive control of legless piezo capsubot"‎, ‎2nd International Conference on Control‎, ‎Instrumentation and Automation (ICCIA)‎, ‎Iran‎, ‎941-945‎.

‎bibitem{25} Pareek S.‎, ‎Kishani M.‎, ‎Gupta R‎. ‎(2014) ``Optimal tuning of PID controller using genetic algorithm and swarm techniques"‎, ‎International Journal of Electronic and Electrical Engineering‎, ‎7‎, ‎189-194‎.

‎bibitem{26} Dorf R‎. ‎C.‎, ‎Bishop R‎. ‎H‎. ‎(2011) ``Modern control system‎" ‎Prentice Hall‎, ‎9th Edition‎.