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

Abstract

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.