Tracking Control of Join-Free Timed Continuous Petri net Systems

Abstract

Petri Nets (PNs) is a powerful mathematical tool with appealing graphical representations for the modeling, analysis and synthesis of Discrete Even Systems (DESs). In all DESs, discrete PN systems suffer from the state explosion problem. One possible way to partially tackle this problem is to fluidify the discrete PN models. The resulting continuous Petri Net (contPN) systems have the potential for the applications of more analytical techniques, which were originally developed for continuous, and hybrid systems. Furthermore, analogous to discrete PN systems, contPN systems are introduced, which leads to time contPN systems. In the proposed control approach, LQ theory is first utilized to design a low-gain controller such that the control signals satisfy the input constraints. Based on the low-gain controller, a high-gain term is further added to improve the system transient performance. In order to guarantee global tracking convergence and smoothness of control signals, in the work, a new mixed tracking trajectory (state step and ramp) is utilized instead of a pure step reference signal.