Saïd Amari

Genetic algorithms for delays evaluation in networked automation systems

In this paper, we present an approach to evaluate end-to-end delays in packets switching networked automation systems. Since Client-Server paradigm is considered for communication between the field devices, the existing methods of network delays evaluation are hardly applicable to assess realistic upper bounds of these delays. In an effort to enhance these delays evaluation, we propose an alternative method. Two algorithms, usually used for optimization problems, exhaustive and genetic algorithms, are then developed to achieve this purpose. While a formal proof about the capacity of the former one to ensure the worst delay overestimation is given, the latter proves to provide faster and more accurate results at the same time. This is shown on a practical case study while comparing the results of the two methods.

Control of discrete event systems with respect to strict duration: Supervision of an industrial manufacturing plant

In this paper, we propose a (max,+)-based method for the supervision of discrete event systems subject to tight time constraints. Systems under consideration are those modeled as timed event graphs and represented with linear (max,+) state equations. The supervision is addressed by looking for solutions of constrained state equations associated with timed event graph models. These constrained state equations are derived by reducing duration constraints to elementary constraints whose contributions are injected in the systems state equations. An example for supervisor synthesis is given for an industrial manufacturing plant subject to a strict temporal constraint, the thermal treatment of rubber parts for the automotive industries. Supervisors are calculated and classified according to their performance, considering their impact on the production throughput.

Client-Server Networked Automation Systems Reactivity: Deterministic and Probabilistic Analysis

In this paper, we present an analytic approach to evaluate the reactivity of client-server networked automation systems (NASs). Both deterministic and probabilistic analyses are provided while modeling the NAS using Timed Event Graphs (TEG). Since many results with regard to the deterministic approach have already been published, we recall only its main steps that prove useful, while exposing the probabilistic method. Thereby, we provide the density of probability distribution of the response time (or reactivity) using the probability densities of the local delays, experienced at the different stages of the NAS. Furthermore, a case study is presented to compare the results of the study to measures taken from a real platform.

Networked conflicting timed event graphs representation in (Max,+) algebra

Timed Event Graphs (TEGs) are a specific class of Petri nets that have been thoroughly studied given their useful linear state representation in (Max,+) algebra. Unfortunately, TEGs are generally not suitable for modeling systems displaying resources sharing (or conflicts). In this paper, we show that if a system with conflicts is modeled using a NCTEG (Networked Conflicting Timed Event Graphs), it is quite possible to obtain an equivalent (Max,+) representation. More precisely, we prove that the evolution of a NCTEG satisfies linear time-varying (Max,+) equations. In case of cyclic NCTEGs, which are a natural model of many repetitive systems, we provide a standard time-invariant (Max,+) representation. As an application of the proposed approach to exhibit its interest, we consider the case of Jobshops. We first propose a generic NCTEG-based model of these systems and subsequently apply the corresponding (Max,+) representation to evaluate some of their performances.

Supervision of an industrial plant subject to a maximal duration constraint

This paper presents a method for the supervision of an industrial plant. This supervision is aimed at guaranteeing the respect of a maximal duration constraint for some specific processing, and is addressed by considering a discrete event system model for this industrial plant. In this associated model, the time constraint is reduced to elementary constraints whose contributions are taken into account in the state equation of the system, yielding a constrained state equation for the plant. Supervisors are then synthesized by looking for solutions of this constrained state equation.

Modeling and response time evaluation of ethernet-based control architectures using timed event graphs and Max-Plus algebra

In this paper, a new approach to evaluate the response time in Ethernet-based automation systems using client server protocols, is presented. It is based on modeling the behaviour of the system using timed event graphs and the resulting state representation in max-plus algebra. First, an algorithm for tracking the frames in the architecture and giving the response time relative to any occurring event is explicated. Subsequently, analytical formulas for direct calculus of this delay are obtained. Finally, experimental measurements taken on a laboratory platform are used to check the validity of the method. Hence, the interest and effectiveness of our results become obvious. They can be used a posteriori to assess the delays in an existing architecture or a priori during the design phase to fulfill the time requirements of a control system.

Analytic evaluation of the cycle time on networked conflicting timed event graphs in the (Max,+) algebra

This work deals with performance evaluation of Conflicting Timed Event Graph (CTEG), a class of Petri net exhibiting phenomena such as synchronization, parallelism and resources sharing. It is well known that the dynamic of Timed Event Graphs (TEG) admits a linear state space representation in the (Max,+) algebra which makes the analysis and control of this class easier. There is also a possibility of associating conflicts with the TEGs by adding conflict places that are mostly considered as safe; this extended class is called CTEG. We first present an analytic evaluation of the cycle time of CTEG as a function of the cycle time of each TEG and of the timers of the conflict places. Finally, in a more general context, we look for a relaxation of the safety hypothesis on the conflict places in order to model and evaluate the cycle time on CTEGs with multiple shared resources.

Modelling and temporal performances evaluation of networked control systems using (max, +) algebra

In this paper, we address the problem of temporal performances evaluation of producer/consumer networked control systems. The aim is to develop a formal method for evaluating the response time of this type of control systems. Our approach consists on modelling, using Petri nets classes, the behaviour of the whole architecture including the switches that support multicast communications used by this protocol. (max, +) algebra formalism is then exploited to obtain analytical formulas of the response time and the maximal and minimal bounds. The main novelty is that our approach takes into account all delays experienced at the different stages of networked automation systems. Finally, we show how to apply the obtained results through an example of networked control system.

Control of time-constrained dual-armed cluster tools using (max, +) algebra

The problem studied in this paper is the control of discrete event systems subject to strict temporal constraints using (max, +) algebra. Initially we sought necessary and sufficient conditions for the existence of a causal control law guaranteeing the respect of the temporal constraints. Subsequently, a method for calculating the control law, if any, is proposed. The application which we are interested in is the control of a manufacturing semiconductor wafers process subject to strict temporal constraints.

Feedback control for a class of discrete event systems with critical time

This paper presents an algebraic approach for control laws synthesis of timed event graphs subjected to strict temporal constraints. This class of discrete event systems is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a linear equations system in Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the Min-Plus algebra. Then, a method for the synthesis of control laws ensuring the respect of constraints is described. We give explicit formulas characterising a control law, which ensures the validity of the temporal constraints. It is a causal feedback control, involving delays. The method is illustrated on an example.