Soizick Calvez

P-Time Petri Nets for Manufacturing Systems with Staying Time Constraints

Abstract This work shows that P-time Petri Nets are convenient tools to model and evaluate performances of manufacturing systems with staying time constraints. When the model of such a system including its control is a Strongly Connected Event Graph, two linear programs can be expressed to obtain the minimum and the maximum average cycle time. As this kind of Petri Nets requires a control of the firing dates of each transition, we proof that the admissible solutions of these programs can be used to built a periodic schedule. So, the performances of the periodic functioning mode are the same as the ones obtained for the average cycle time.

Towards the control of time-critical systems

Petri nets are a powerful formalism for the specification and analysis of concurrent systems, such as sequential systems, manufacturing systems etc. Adapted to time-critical systems (systems whose time issues become essential), different time Petri nets have been developed in the literature: Merlins model, p-time Petri-net, Time ER nets etc. The presented approach allows us to determine transitions firing instants in order to ensure functional timing correctness of the modeled system. It uses a p-time Petri-net as the modeling tool. It is based on an enumerative procedure and on the evaluation of transitions firing conditions successively at the first, the second and the q/sup th/ firing instant. Moreover, it provides a performance evaluation and control component.

Using P-Time Petri Nets for Robust Control of Manufacturing Systems

Abstract Constraints such as zero stock and/or just in time require a robust control in order to maintain specified properties (sequence, throughput rate, …) although disturbances appear in the manufacturing system. In this paper, a method to determine a robust schedule of a manufacturing cell with staying time constraints, in regard of disturbances on the input rate of the parts is proposed. This method uses P-time Petri net as model and the periodic control functioning mode. The schedule for a definite throughput rate is obtained by solving a linear program which constraints are all stemming from the model.

Using firing instants approach and partial order to control time critical systems

Time-critical systems are characterized by operation times included between a minimum and a maximum value. A transgression of these specifications acts again the quality of service. In this paper, a dynamic robust control is proposed to cancel as quickly as possible the effects of a delay or an advance on a planned task. P-time Petri Net is used as modeling tool and the control is based on an extension of the firing instant approach permitting negative instants to update the tasks scheduling. The illustration of the method is made on a graphite ceramic cell.

Using Robustness Properties for Multi-Products Processing

Abstract In this paper, we propose to use the robustness properties to build a temporal control when the manufacturing system processes several kinds of parts. The approach presented amounts to consider a multi-products functioning as a mono-product disturbed one (the control structure is the same whatever the type of parts). No supposition is made on the ratios of the different products as well as on the processing order of the parts. Consequently, this approach is interesting when the lots size is unknown or when a part of an other type must be inserted in a large lot in order to satisfy a pressing order. The illustration of the method is made on an electroplating line with two types of products.

Proactive/reactive approach for maintenance tasks in time critical systems

The maintenance of systems involved in production processes must be carried out with maximum efficiency and minimum downtime, especially on time-critical systems (operation times are included between a minimum and a maximum value). This paper presents a proactive/reactive control to fit preventive maintenance into a busy production schedule. As preventive maintenance is regarded as a non-preemptive task, p-time Petri net is used as modelling tool to generate temporal and logical constraints to be considered. To update the tasks scheduling, flexibility on time and on task order is obtained by permitting negative instants in the used firing instant approach. The illustration of the method is made on a graphite ceramic cell

Verification technique for time Petri nets

Petri nets are a powerful formalism for the specification and verification of concurrent systems, such as sequential systems, 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. A verification technique for time Petri nets (Merlins model) is proposed. It is based on the determination of an inequalities system generated by a possible evolution (in terms of a feasible firing sequence) of the model considered. This system can be used to check reachability problems as well as evaluating the performances of the model considered and determining the associated control for a definite functioning mode.

Hierarchical control of time Petri nets by means of transformations

Usually, reduction techniques are proposed to transform the original model of the system into a simpler one, while preserving some properties of interest to be analyzed. In this paper, it is proposed to take advantage of the reduction of complexity provided by the application of transformations rules to ease the determination of a feasible control for the system considered. The proposed technique consists of building the reduced model and its constraints graph representing a set of timing constraints. Thus, checking the existence of feasible controls is performed by verifying admissibility conditions on the reduced model constraints graph. Then, if feasible controls exist, their associated controls for the original model are made possible in a hierarchical way.

Firing instant approach to control time critical systems in multi-product processing

Time-critical systems are characterized by operation times between a minimum and a maximum value. Any transgression of these specifications acts against production quality. In this paper, we propose to use a firing instant approach to build temporal control when the systems process several kinds of parts. The formalism presented refers to lot switching when the cyclic scheduling is the same whatever the type of part. Under the same assumption, it can be applied to interlaced production leading to a steady state. The P-time Petri net is used as a modeling tool. The method is illustrated for an electroplating line with two types of products.

A control model for multi-products processing

Time-critical systems are characterized by operation times included between a minimum and a maximum value. An acceptable behaviour depends not only on the logical correctness of the task sequence but also on the time at which the operations are performed. So, a specific control is required. In this paper, the robustness property is used to build a time schedule of when the manufacturing system is to process several kinds of parts. This approach uses a p-time Petri net as its modeling tool and considers the multi-processing case as a disturbed mono-processing one. To make a more succinct and manageable description of the obtained control, p-time coloured Petri nets are defined. A typical illustration of an electroplating line is given.