N. Zerhouni

Neural networks implementation for modeling and control design of manufacturing systems

This paper presents a dynamic neural network implementation for the modeling and control design of a class of manufacturing systems. The evolution of the considered systems is supposed to be continuous and non-stochastic. A separate implementation of the system elements is detailed. These elements are then connected together in order to obtain a global net that simulates the behavior of the real system. The obtained model is modular and can be adapted easily for any modification of the system. Permanent correction rules are developed to control the speed of the machines according to a desired profile and to take into consideration the buffers limited capacities. The convergence of the control design is proved. The proposed approach is applied on an exhaust valves assembly workshop.

REDUCED ORDER MODELLING OF TWO-TIME-SCALE DISCRETE NON-LINEAR SYSTEMS

Abstract Application of two-time scale discrete singular perturbation methods have been limited to the linear systems. The area of discrete-time non-linear systems has received little attention. This paper deals with the singular perturbation model of non-linear discrete-time dynamic systems. We present a specific modelling and a mode decoupling approach well adapted for such systems. A comparison principle is used for grouping slow and fast states of a class of non-linear discrete systems. Finally, an example is given to show the feasibility of the theoretical results.

Transient analysis of manufacturing systems using continuous Petri nets

The analysis of manufacturing system is a complex problem. A manufacturing system is often considered as a discrete event system and has always a discrete model. These models give an exact description of discrete systems and give analytical results about steady state. But it does not always allow the transient analysis. The continuous approach of Petri nets modelling gives an analytical expression and permits some analysis of these systems.

Control of Discrete-Event Systems Modelled by Continuous Petri Nets Case of Closed Manufacturing Lines

Abstract In this work, a methodology to study the control of a class of discrete-event systems, more precisely of closed manufacturing lines is proposed. Our contribution is based on the variable speeds and the controlled maximal speeds continuous Petri net model. The computation of the control is made using standard linear programming methods. Through illustrative examples, the simplicity as well as the efficiency of this method will be put in a prominent.

Analysis of manufacturing lines using a phase space algorithm: open line case

This paper presents a study concerning the minimization of the evolution time of a class of manufacturing systems. The study passed by several steps beginning by modeling the manufacturing system using continuous Petri Nets. The second step uses the developed model to construct the different phases of evolution using the phase algorithm that will be defined later in the paper. The constructed phase schema helps in solving the proposed problem and helps at the same time in defining a control sequence that could be applied to the system. The variable parameter is the source speed or in other words the rate by which the pieces to be manufactured are supplied to the system. In this paper the class of an open manufacturing line will be presented. At the same time changing the source speed could have an important affect on the manufacturing line. We will study the effect of changing the speed of the source on the throughput of the system. One of the important advantages in using the developed algorithm is its ability to conserve the continuity of the system and also to show the dynamic behavior of the studied system.

Analysis of hybrid Petri nets based on the hybrid state equation

In this paper we are interested in a mathematical description of the class of hybrid systems, which can be modelled by hybrid Petri nets (HPN). A state space model using the conventional algebra for the continuous subsystem and the minplus algebra for the discrete subsystem is given, This model is used in the analysis of a special class of HPN.

Proportional correction rule for the control design of manufacturing systems using neural networks

Presents a control design for a particular class of manufacturing systems modeled by artificial neural networks. A dynamic implementation of manufacturing systems deduced from a modular approach of modeling using neural networks is described. An adaptive control is applied on the network model of the system. The proposed control is inspired from the learning property of neural networks. The obtained results are illustrated on an industrial manufacturing system.

Digital control design of an optimal regulator of a class of nonlinear singularly perturbed systems

In this paper, the digital implementation of an optimal regulator for a class of nonlinear singularly perturbed systems is investigated. The two-time-scale nature of the system is explored by developing a multirate digital control using multirate measurements and computation. Boundedness responses and stability properties of the overall system driven by multirate digital control are studied.

ON THE CALCULATION OF THE TRANSFER FUNCTION OF TIMED EVENT PETRI NETS

In this paper, a method for the calculation of the transfer function of timed event graphs is developed. The transfer function has the form of a formal series in one or two formal variables. The knowledge of this formal series plays a crucial role in the max-plus system theory. It is very important in the investigation of the problem of controllability of a system, because it provides us with the input-output relation as an equation in the dioid of formal series. The direct approach to this calculation requires the computation of a star operation of a matrix with entries in this dioid,which seems to be difficult for matrices of large dimensions. For this reason, we propose another approach using only the max-plus modeling of a system, that is, the daters description. We have considered the multivariable case with several input and output transitions. We can obtain the transfer function as the output corresponding to a special control. This control follows from the daters description of the zero and iden...

On the calculation of transfer function of timed event Petri nets

In this paper, a method for the calculation of transfer function of timed event graphs is developed. The transfer function has form of a formal series in one or two formal variables. The knowledge of this formal series plays a crucial role in the max-plus system theory. Namely, it is very important in the investigation of the problem of controllability of a system, because it provides the input-output relation as an equation in the dioid of formal series. The direct approach to this calculation requires the computation of a star operation of a matrix with entries in this dioid which seems to be difficult for matrices of large dimensions. This is why the authors propose another approach using only the max-plus modelling of a system. The authors have considered the multivariable case with several input and output transitions. The authors can obtain the transfer function as the output corresponding to a special control. To illustrate this approach the authors give two examples. The purpose of the first one is to compare different approaches to this problem, whereas the second one may serve as an application. The authors use their approach to determine the transfer function of a manufacturing system.