FEEDBACK CONTROL LOGIC FOR BACKWARD CONFLICT FREE CHOICE NETS

An approach for enforcing a class of GMECs on time Petri nets with uncontrollable transitions

This paper describes a synthesis method of forbidden state controller for a class of discrete-event systems (DES) with generalized mutual exclusion constraints (GMEC). The system models are a class of restricted Petri nets named forward-synchronization and backward-conflict free (FSBCF) nets. The properties of FSBCF nets, in which each place has at most one output transition and each transition has at most one input place, is studied and used to analyze the reachable state space of the system. An efficient controller synthesis algorithm that is able to deal with the so-called precedence path condition is then proposed to avoid the forbidden state represented by GMEC. One example is provided for illustration.

In this paper we deal with the problem of controlling a Petri net whose marking cannot be measured but is estimated using an observer. The control objective is that of enforcing a set of generalized mutual exclusion constraints (GMEC) and all the transitions are assumed to be controllable. Clearly, the use of marking estimates may significantly reduce the performance of the closed-loop system and may lead to a deadlock. If the net times out, i.e., if no transition firing occurs within a reasonable amount of time in the controlled system, an efficient procedure may be invoked to recover the net from a controller induced deadlock. The novel contribution of this paper is that of exploring in detail the characterization of those cases in which the proposed recovery procedure works.

Deadlocks in automated flexible manufacturing systems (FMS)is a crucial problem in production process. This paper presents an effective deadlock prevention policy for a special class of Petri nets, S3PR. Based on siphon method, a set of generalized mutual exclusion constraints (GMEC) expressed by the marking vector can be found. Then monitors based on the GMEC are added to the plant model such that the siphons in the resultant net are all invariant-controlled and no emptiable siphon is generated due to the addition of the monitors. This novel deadlock prevention policy can usually lead to a maximally permissive supervisor by adding a number of monitors and arcs, the number of monitors is decided by the number of emptiable siphon in the net system, the proposed policy can work excellently in proper size petri net system. Finally two manufacturing examples are utilized to illustrate the proposed method.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

This paper addresses the enforcement of a class of generalized mutual exclusion constraints (GMECs) within time constraints on time-colored Petri nets by adjusting the time restrictions of transitions with soft time intervals. Colored GMECs are defined to represent a set of markings that are determined by a subset of colors. Then, time constraints are imposed on the proposed colored GMECs to further refine the representation of state specifications in real-time systems. To enhance the modeling accuracy of real-world systems, we formally define time-colored Petri nets, based on which the extended GMECs are enforced. In this research, two types of time-constrained colored GMECs are proposed, with the main idea being to adjust the time boundaries of soft transitions, such that the system's specifications represented by time-constrained colored GMECs are satisfied. A structure called a parameterized modified state class graph is designed to describe the possible behaviors of the time-colored Petri net, where the time intervals of soft transitions are parameterized by variables. Based on the proposed graph, the enforcement of time-constrained colored GMECs is achieved by solving a linear programming problem.

This paper deals with the problem of forbidden states in Discrete Event Systems modelled by non‐safe Petri Nets. To avoid these states, some Generalized Mutual Exclusion Constraints can be assigned to them. These constraints limit the weight sum of tokens in some places and can be enforced on the system using control places. When the number of these constraints is large, a large number of control places should be added to the system. In this paper, a method is presented to assign the small number of constraints to forbidden states using some states which cover the forbidden states. So, a small number of control places are added to the system leading to obtaining a maximally permissive controller.

In this paper, we propose an analytical solution to the problem of Generalized Mutual Exclusion Constraints (GMECs) in a Network of Timed Event Graphs (NTEGs). The contribution of the paper lies in the development of a method to design control laws that satisfy these constraints across different place paths in the graphs. Using Min-Plus dioid algebra, we employ algebraic techniques to express GMECs as weighted inequalities. The solution involves translating the constraints into Min-Plus linear equations that describe the behavior of NTEGs. We provide sufficient conditions for the existence of causal control laws, considering both the initial marking of the NTEGs and the parameters of the GMECs. To demonstrate the practical application of the approach, we include a case study that illustrates the effectiveness of the proposed control strategy.

We propose a formalism for decentralized control of discrete event systems with communications. The formalism is based on PN/sup 2/, a class of agent-oriented Petri nets proposed by the author (2001). The main difference between PN/sup 2/ and Petri nets is that each token, representing an agent, is also a Petri net. The decentralized control system to be modeled has the following features: (1) the system is asynchronous and has no global clock; (2) some events may occur concurrently; (3) the system is controlled by several control agents, each of which perceives only a subset of occurring events, and can control only a subset of events; and (4) each control agent can communicate with other agents. By communications, each agent can know occurrences of events that are not observable for it, and can ask other agents to disable events that are not controllable for it. Using the formalism, we define a problem concerning control synthesis.

Petri nets have been extensively applied for specification, design, verification, performance evaluation, and simulation of discrete event control systems (DECS). The usual way to verify the dynamic behaviour of DECS design is to employ a process-based model, which proves to be impractical in application because the process-based model does not usually fully correspond to the control programming behaviour. This paper proposes a sensor-based stage Petri net (SBSPN) to represent a programmable logic controller (PLC) stage logic diagram (LD) for discrete-event control design. The new technique is able to simplify the modelling process of the complex PLC program without considering the interlocking problem within the ladder diagram. An illustrated example is used to explore the new methodology. The proposed method contains the power and flexibility of the Petri net analysis prior to the PLC implementation. It is believed that this technique is significant for industry practice.

This paper addresses the supervisor synthesis on the forbidden state problem, in which the forbidden markings cannot be easily expressed as linear inequality constraints using reported methods. The system to be controlled is modelled by bounded Petri nets with uncontrollable transitions. Through the analysis of the reverse net, we obtain the weakly forbidden markings in order to deal with uncontrollable transitions. By introducing a transformation function, which facilitates not only tracking the system state but also determining the control pattern, we propose a synthesis method to obtain the maximally permissive supervisor. The method need not analyze the reachability graph and the online computation has the complexity of polynomial times. In addition, for a special class of generalized Petri nets called the input dominant Petri nets, the synthesis method can be applied conveniently, as illustrated by an example in the reported literature.

a generalized mutual exclusion constraint (GMEC) is a linear constraint that limits the weighted sum of tokens in a subset of places of a place/transition net system. The corresponding controller takes the simple form of a monitor place that can be added to the net to obtain the closed-loop system. In this paper we extend this approach to the case of colored Petri nets, showing that a colored GMEC can express a set of linear constraints and can be enforced by a colored monitor place. We also develop a matrix representation of multisets that is useful for the design of the monitor place.

As automated manufacturing systems become more complex, the need for an effective design tool to produce both high-level discrete event control systems (DECS) and low-level implementations becomes more important. Petri nets represent the most effective method for both the design and implementation of DECSs. In this paper, automation Petri nets (APN) are introduced to provide a new method for the design and implementation of DECSs. The APN is particularly well suited to multiproduct systems and provides a more effective solution than Grafcet in this context. Since ordinary Petri nets do not deal with sensors and actuators of DECSs, the Petri net concepts are extended, by including actions and sensor readings as formal structures within the APN. Moreover, enabling and inhibitor arcs, which can enable or disable transitions through the use of leading-edge, falling-edge and level of markings, are also introduced. In this paper, the methodology is explained by considering a fundamental APN structure. The conversion of APNs into the IEC1131-3 ladder diagrams (LD) for implementation on a PLC is also explained by using the token passing logic (TPL) concept. Finally, an illustrative example of how APNs can be applied to a discrete manufacturing problem is described in detail.

The cooperation of autonomous agents is synthesized in order to satisfy demands imposed on a group of agents or on MAS (multi agent systems). Petri nets (PNs), especially place/transition PNs (P/T PNs), are used for modelling the agents. The modular approach is utilized on that way. PN-based methods of discrete event systems (DES) control and supervising are utilized in order to synthesize the cooperation of the agents. The usefulness and applicability of the approach is demonstrated by examples and case studies.KeywordsAgentsbipartite graphscontrolcooperationdiscrete-event systemsPetri netssupervisorsynthesis

Due to the introduction of uncontrollable transitions in the supervisory control of discrete event systems modeled by controlled Petri nets, a disjunction of several linear inequalities is needed to express the admissible markings. In this paper, we propose a two level hierarchical control synthesis method to deal with this kind of OR logic constraints. In the method, the constraint function plays an important role not only in the construction of the low level monitor but also in the determination of the control policy. The obtained supervisor is maximally permissive and the online computation has the complexity of polynomial times. An example is used to illustrate the proposed synthesis algorithm.