Synthesis of feedback control elements for discrete event systems using Petri net models and theory of regions

This paper describes a method for constructing a Petri-net-based controller for a discrete event system (DES) modelled by a Petri net. Assuming that an uncontrolled Petri net model of the DES and a set of forbidden state specifications are given, feedback control elements, i.e. a set of places and related transitions, with initial marking, are computed using the theory of regions, which is a formal synthesis technique for deriving Petri nets from automaton-based models. When feedback control elements are added to the uncontrolled Petri net model, the controlled (closed-loop) Petri net model of the system is obtained. The controlled Petri net model obtained is maximally permissive while guaranteeing that forbidden states do not occur. The proposed method is computationally efficient and does not suffer from the state explosion problem. Two examples are provided to show the applicability of the proposed method.     

Discrete event control system design using automation Petri nets and their ladder diagram implementation

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.     

A hybrid approach to supervisory control of discrete event systems coupling RW supervisors to Petri nets

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.     

Binary logic diagrams imply nonunique functionality

Binary logic diagrams (BLDs) are widely used to document the functionality of logic-based control systems. The ambiguous functionality implied by certain BLDs is highlighted by drawing analogies with asynchronous sequential logic systems. Non-deterministic state transitions in these BLDs occur due to the existence of hazard and race conditions or, equivalently, non-unique feedback cut sets. The need for additional specifications to remove this ambiguity is discussed, and recommendations are made to aid in the specification of BLDs with unique functionality.     

A systematic approach for the sequence controller design in manufacturing systems

This paper presents a systematic approach for the design and implementation of the sequence controller in manufacturing systems. By employing the IDEF0, we construct the simplified Petri net controller (SPNC) through the material flow diagram and the information flow diagram. Then, the ladder logic diagram (LLD) can be transformed from the SPNC through the token passing logic (TPL). The proposed approach, including the IDEF0, SPNC, and TPL tools, leads to the standard IEC1131-3 LLD for PLC implementation. Finally, an application of a stamping process is provided to illustrate the design procedure of the developed approach .     

Asynchronous implementation of discrete event controllers based on safe automation Petri nets

In this paper, a new method is proposed for digital hardware implementation of Petri net-based specifications. The purpose of this paper is to introduce a new discrete event control system paradigm, where the control system is modeled with extended Petri nets and implemented as an asynchronous controller using circuit elements. The applicability of the proposed method is demonstrated by an asynchronous implementation of a Petri net-based discrete event control system (DECS) for an experimental manufacturing system using a Xilinx field programmable gate array (FPGA). Unlike microprocessor, microcontroller or programmable logic controller (PLC)-based software implementations or hardware-based synchronous implementations, the implementation method used in this paper is asynchronous and based on hardware offering very high speed to control fast plants at low cost. This paper is expected to serve as a guideline to show how to obtain very high speed, concurrent and asynchronous Petri net-based controllers.     

Material flow and control sequence specification of flexible production systems using coloured Petri nets

Starting with the specification of each resource and the whole structure of a flexible production system, in this approach a special kind of coloured Petri nets is used for performing the modelling and the validation of the coordination control structure of the systems. In a second phase, it is proposed to modify the first models to synchronised Petri net schemas to facilitate the supervision and the interaction of the coordination model with the physical components of the system as well as the development and maintainability of the discrete-event control structures. The final result is a formal specification of coloured Petri net based coordination control of resources of the system, and logic control structures for control sequencing based on the use of synchronised subPetri net structures derived from the first one by refining transitions, i.e., their occurrence. Based on the proposed approach, the coordination control model of resources and a first skeleton of the logic control structures of a flexible assembly cell located at the Institute of Manufacturing Automation and Production Systems at the University of Erlangen-Nuremberg, Germany is elaborated and then the correctness of the obtained models with regard to material flow and control sequence specifications is validated by means of the structural analysis of the coloured Petri net-based models.     

Robust observer-based absolute stabilization for Lur’e singularly perturbed systems with state delay

This paper is concerned with the problem of robust observer-based absolute stabilization for Lur’e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods.     

Methods of measuring the size and complexity of PLC programs in different logic control design methodologies

Currently there is a wide variety of logic control design methodologies used in industrial logic design. These methodologies include ladder diagrams, function block diagrams, sequential function charts, and flow charts, but driven by a desire for verifiability, academics are developing additional logic control design methodologies, such as modular finite state machines and Petri nets. Using these, important properties of programs can be verified and some logic can be generated automatically from a part plan. The main contribution of this paper is to define methods for measuring programs written in different methodologies, so that the performance of the methodologies can be compared.We demonstrate these methods of measurement using four program samples that perform similar functions on the same machine, written in four logic control design methodologies: ladder diagrams, Petri nets, signal interpreted Petri nets and modular finite state machines.     

On a deadlock prevention policy for a class of Petri nets S3PMR

In Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009), a deadlock prevention policy is proposed for a subclass of Petri nets, S³PMR, that can well model a large class of flexible manufacturing systems (FMS) where deadlocks are caused by unmarked siphons in their Petri net models. To validate the effectiveness and efficiency of the proposed approach, two examples were demonstrated in Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009). This paper shows that there is a problem with one of the control places computed for one of the examples. In Yan et al. (J Inf Sci Eng 25(1): 167–183, 2009), for another example, two different deadlock prevention supervisors were proposed. It is also shown in this paper that, for these two supervisors, it is possible to obtain two subsets of control places. Thus, the structures of the two supervisors are further simplified with the same permissive system behaviours.     

An implementation methodology for supervisory control theory

In this study, a methodology for PLC implementation of Supervisory Control Theory is introduced and realized on a pneumatic manufacturing system. The implementation methodology resolves the problem of avalanche effect and enhances program readability. We use local modular approach, which exploits modular structure of the plant and of the specifications. Local modular approach, together with the implementation methodology presented in this study provides an effective way for synthesizing and realizing supervisors for Discrete Event Systems (DES) control problems. The resulting PLC program is also modular in structure, making it handable for modification and error detection.     

Identification and elimination of redundant control places in petri net based liveness enforcing supervisors of FMS

In the past two decades, a number of Petri-net-based approaches were proposed for deadlock prevention in flexible manufacturing systems (FMS). An FMS is modeled as a Petri net, and then the controller or the liveness enforcing supervisor (LES) is computed as a Petri net. A live Petri net (LPN) guarantees deadlock-free operations of the modeled FMS. An LES consists of a number of control places (CPs) and their related arcs. To-date most of the attention has been paid to make the underlying Petri net models live without questioning whether or not all of the computed CPs are necessary. It is often the case that the number of CPs determined by these approaches is not minimal. Reducing it in order to reduce the complexity of the controlled system is an important issue that was not tackled before. To address this problem, this paper proposes a redundancy test for an LES of an FMS. The proposed approach takes an LPN model, controlled by n CPs, as input and in the existence of any redundant CPs it produces redundant and necessary CPs. The proposed approach is applicable to any LPN consisting of a Petri net model (PNM), controlled by means of a set of CPs.     

面向仓储物流的建模及控制系统设计方法

为提高现代企业仓储物流的设计质量和效率,提出了一种基于资源颜色时序信号的扩展Petri网建模及控制系统设计方法.该方法首先采用资源颜色时序信号的扩展Petri网建立了仓储系统的动态模型,清晰地描述了各种物流活动的顺序、并发,冲突等关系,并结合关联矩阵,阐述了判断死锁和陷阱的方法.该方法建立的模型可根据Petri网运算规则进行保性化简,便于仿真分析和验证,且可直接用于系统可编程逻辑控制器的控制程序设计.最后,以仓储物流控制系统为例,阐述了系统建模及控制设计过程.     

Design of deadlock prevention supervisors using Petri nets

This paper proposes a methodology to synthesize supervisors for a class of sequential resource allocation system for flexible manufacturing systems. The type of Petri nets are called S3PR, where deadlocks are related to emptied siphons. In a former paper (Huang et al., IEEE Trans Syst Man Cybern, 2007), a deadlock prevention policy was proposed based on Petri nets siphons for the type of Petri nets. Since all minimal siphons should be controlled, the deadlock prevention policy is very time-consuming when the system is large. In this research, a concept of the elementary siphon is used to reduce the number of control places. A new siphon-based policy of deadlock prevention for the type of Petri nets is presented. This policy consists of two main stages: The first stage, called elementary siphons control, adds control places to the original net model to prevent elementary siphons from being emptied. The second stage, called generalized siphons control, adds control places that adopt a conservative policy of controlling only the release of parts into the system are used. Compared to the existing approaches, the new deadlock prevention policy can obtain a structurally compact deadlock prevention supervisor by adding only a few control places. Finally, numerical experiments under reachable states illustrate that the proposed algorithm appears to be more permissive than the closely related approaches.     

Constraint graph-based approach for the analysis and the control of time critical systems

The increasing complexity of manufacturing systems gives rise to the development of new formal methods allowing to handle their particularities. Petri nets are a powerful formalism for the specification and verification of concurrent systems including sequential systems and manufacturing systems. To deal with systems whose time issues become fundamental, different time Petri nets extensions have been developed in the literature, each one being dependent on the application considered. For the time critical systems, their correctness depends not only on the logic correctness but also on the time constraints. Timing issues are essential. In this paper, a new method of analysis and control for P-time Petri nets is proposed. It is based on the firing instant notion and exploits a constraint graph approach.     

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations.     

Matrix Controller Design and Deadlock Analysis of Automated Manufacturing Systems. Part 1. Designing the Matrix-Based Controller

A system theory approach is used to design rule-based discrete-event controllers for the sequencing of jobs in manufacturing systems. The controller is described in terms of matrix equations that are easy to implement on a personal computer. Industrial engineering (IE) techniques and the concepts of Petri nets (PN) are included. A standard bill of materials (BOM) is used in the first design step to make a "task sequencing matrix". Then a resource requirement matrix is constructed to add non-shared resources and shared resources (e.g. pallets, transport robots, and material handling machines). Non-shared resources are controlled using inner decision loops. However, shared resources require outer decision loops for dispatching and routeing that resolve conflicts, taking into account the specified performance measures to be optimised (e.g. percentage of idle time, throughput, etc.). Failures are simply represented as disturbance inputs, allowing design for failure recovery. The rule-based controller design algorithm is a step-by-step procedure with repeatability and guaranteed conflict/deadlock resolution. It shows that the closed-loop system, once designed, is equivalent to a Petri net (PN); this gives, as a by-product, an algorithm for PN design. Furthermore, the matrix formulation allows a rigorous analysis of deadlocks in terms of circular wait and blocking, and the resources available.     

Construction and performance analysis of a Petri net model based on a functional model in a CIM system

The so-called functional models, such as IDEF0, are useful tools for describing, designing and analysing the functional aspects of a complex manufacturing system, for example a CIM (computer integrated manufacturing) System. Though it involves considerable time and cost to build a sound functional model, the model usually cannot be used directly in further systems analysis procedures, such as quantitative performance analyses, due to its informal nature. To overcome this problem, we suggest a Petri net based procedure. First, we build a Petri net model from the IDEF0 and IDEF3 models, both of which are functional modelling tools widely used in real applications. Then, employing steady-state analysis for the Petri net, we propose a method to obtain performance measures such as the production rate. Since the analytical ability of a Petri net diminishes with increasing manufacturing system size, we develop a technique to aggregate and consolidate the Petri net to alleviate this problem that is associated with increasing complexity. An example problem is included to show the viability of our method for constructing a Petri net from a functional model and to evaluate the performance of the Petri net in an analytic manner.     

A general technique for the PLC-Based implementation of RW supervisors with time delay functions

The Supervisory Control Theory (SCT) introduced by Ramadge–Wonham (RW) is a general theory to design supervisors (controllers) for discrete event systems. Although over the two decades SCT has received wide attention in academia, industrial applications are very few, due to the fact that there is a discrepancy between the abstract RW supervisor and its physical implementation. In this paper, an easy to use, general and practical technique is proposed for the PLC-based implementation of RW supervisors with time delay functions. The applicability of the proposed method is demonstrated by means of a PLC-based real-time control of an experimental manufacturing system.