Modelling and Control of KRC Systems Using TPN and TA

Abstract

This paper models and supervises kernel railroad crossing (KRC) systems using timed Petri nets and focuses on the control synthesis method, which consists in computing new firing conditions for the timed automaton (TA) transitions so that the forbidden locations are no longer reachable. The system to be modeled and supervised using timed Petri nets is converted to a TA and is analyzed using automata so that the functioning of the system respects given specifications. The main reason of using automata is that although the timed Petri nets supervisor controls the system, it fails to define the time units needed for the undefined time of a transition. Simulation results show the soundness of KRC modeling and supervision in the sense of ensuring the safety and maximizing utility (the gate should be opened as long as possible). KEYWORDS:Automata, Timed automata, discrete event systems, Petri nets, Timed Petri nets, KRC systems I.INTRODUCTIONThe process synchronization and forbidden states avoidance are considered as the main problems in both normal and abnormal modes of automation systems [1]. These characteristics allow the system to be considered as Discrete Event System (DES) and allow the researchers to perform the analysis and control of such systems using Petri nets (PN) and automata. DES is a dynamic system with state evolution produced by the occurrence of physical events. For example, an event is opening or closing a gate in Kernel Railroad Crossing (KRC) systems [2][3]. DES can be found in domains such as manufacturing, robotic, traffic control, logistics, and communication systems, etc.Important contributions in supervisory control of DES based on the Finite Automata (FA) and Petri Nets (PNs) are found in [4][5][6][7][8]. Petri net models are normally more compact than similar automata based models and are better suited for the representation of discrete event systems. They also have a good representational power [9]. On one hand, numerous approaches to the systematic construction of Petri net models have been proposed in [10]. On the other hand, because automata detail the process to be modelled, they are also employed to analysis and avoid forbidden states with ease.Historically, the theory of DES for supervision was initiated by the research work of Ramadge and Wonham [8]. A process is considered to be a spontaneous generator of events. Its functioning is characterized by event sequences. A supervisor is a DES which can modify the functioning of the process in order to avoid forbidden states. Unfortunately, the theory of Ramadge and Wonham does not a maximally permissive in nature [11]. A maximal permissive supervisor is to ensure that the controlled behaviour of the DES must be maximally permissive within a given specifications, i.e. all events which do not contradict the given specifications are allowed to happen. Thus, the theory of Ramadge and Wonham cannot be used to control all DES. An extension of this theory to the control of DES is proposed to force the occurrence of certain events to...

Supervisory Control Systems: Theory and Industrial Applications

“…Quiz 1: With the help of our work in [14], can you model the chemical batch process shown in Figure 2 using timed Petri nets?…”

“…The kernel railroad crossing (KRC) shown in Figure 8 is a standard benchmark in real time systems [14]. When a train is sensed to approach the crossing, a signal is sent to the supervisor that sends a command to the specified gate that is closed to prevent cars crossing that survives ourselves.…”

“…The system comprises two tasks, train task and gate task. In our work [14], consider that the controllable events are the beginning of each task. However, the accomplishing of the tasks is uncontrollable.…”

“…The design of supervisory controllers for discrete event systems has received considerable attention in research centers [14][15][16]. There are methods for designing supervisors based on automata models [17], however, they need exhaustive search over the system states that makes them impractical for systems with large number of states, as the number of states increases the state space explosion problem arises [18,19].…”

“…PN models are normally more compact compared with automata-based models and are better suited for the representation of discrete event systems due to its mathematical manipulation and graphical representation [22][23][24]. Timed Petri nets are common used for industrial control systems [14].…”