Modeling and Controller Design of Nonlinear Dynamical Systems Using Extended-Time Delay-Petri Nets Tool

This paper proposes Extended Time Delay Petri Nets (ETDPN) as a novel tool to model nonlinear dynamic systems and design a controller based on it. In this approach, the continuous system is initially converted to a discrete system, and then by using ETDPN, the system is modeled and analyzed. To achieve a higher level of simplicity in the ETDPN, by employing an incidence matrix, a powerful graphical and mathematical tool is presented. Subsequently, an output feedback controller is described to control the system model derived by the ETDPN. To tune and optimize the controller's gains, a Genetic Algorithm (GA) is also used as an evolutionary approach. To verify the efficiency of this tool to model the nonlinear continuous system and the controller design, the step response is compared with the classical model. Simulation results show the effectiveness of the proposed approach in terms of reduction in simulation time and complexity of the system analysis compared to the state space model.