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

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.