The use of fuzzy Coloured Petri Net in modeling and simulation of flexible manufacturing cell.

Blaga, Florin-Sandu ; Pop, Alin ; Stanasel, Iulian 等

1. INTRODUCTION

The functioning optimization of the flexible manufacturing system requires them modeling and simulation. One of the tools used in this is Coloured Petri Net (David & Alla 1992).

The controlling systems witch are serving the components of the flexible manufacturing systems are using more often automatic fuzzy regulators (Preitl & Precup 1997).

It may be combined Coloured Petri Net and Fuzzy sets so to result a new tool for modeling, simulation and control of flexible manufacturing system components. This possibility is materializing through Fuzzy Coloured Petri Net (Yeung et al., 1996).

2. THE MODEL OF THE CELL

We consider a cell (figure 1) with a robot 1 which is able to pick up an electronic component from a storage room 3 and this robot moves around a Printed Circuit Board (PCB) in order to assemble component in PCB. After mounting the component, robot returns to pick up a new electronic component from storage room. Therefore, the process will keep on operating until PCB is complete and able to abandon the system.

The application problem is how to use Fuzzy Coloured Petri Nets in modeling robotic assembly. In order to create the model, we will use specific Coloured Petri Nets concepts, (Jensen, 1995) (Blaga et al, 2008).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Model structure is presents in figure 2. We will begin from initial marking with T1 transition so r marking moves out from P1 position, c marking moves out from P2 position and f marking from P3 position. In the same time, in the P2 position is stored a complex color {r,c}. This complex color will appear in the model until robot moves out from the PCB area (after execution of T4 transition). During the insertion process of an electronic component into PCB, the robot must rotate in an angle such that the legs of the components are perpendicular to the PCB area.

The rotation of the robot is ordered and controlled by a system witch can be modeled with a Fuzzy Coloured Petri Net (figure 3).

The adjustment procedure follows these sequences (steps):

* Sequence 1. At first, we have to read the values of the displacements on tree angles of the component witch will be inserted into the PCB. The three measurements are used as inputs and these are associated with a finite set of colors d={x_d, y_d, z_d}.

* Sequence 2. Every color can be considered as a fuzzy variable and all these are fuzzified as the followings:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

* Sequence 3. These eight fuzzy variables are used as inputs to so called fuzzy production rules. The rules outputs sets the velocity needed to rotate electronic component until it will be in the right position for inserting into PCB. Fuzzy variables are fuzzified as the followings:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

For the velocity component v_y we have the same linguistic degree (v_yn, v_ys, v_ymd, v_yB).

This set of ten fuzzy production rules are modeled by transitions: T10, T11, ..., T19. The T10 transaction models the following rule:

IF x_s = x_m AND z_s = z_m THEN v_x = v_xn (5)

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The other 9 rules are defined in the same way as the first one.

The adjustment of the displacement can be implemented in Fuzzy Logic Toolbox from Matlab. In figure 4 presents the system based on fuzzy sets with tree inputs (the arm position in comparison with x,y,z axes) and two outputs: displacement on x axis (v_x) and displacement on y axis (v_y).

The inference engine is compound by ten roles. These are the same like the roles defined in Fuzzy Colored Petri Nets.

3. CONCLUSION

Future researches will pursue modeling with Coloured Petri Net of same system in witch will find more components (robots, machine and others). By using the features of Fuzzy Sets it will pursue the accuracy improvement of the model, so that this to be closer to the real system.

The combine use of Coloured Petri Nets and Fuzzy Sets in modeling flexible manufacturing systems succeeds in mixing advantages of both methods. The main advantage is that such a complex system can be relatively simple modeled.

4. REFERENCES

Blaga, F., Pop, A., Stanasel, I., Pele, A-V, (2008), Coloured Petri nets modeling using CPN Tools, ANNALS of the ORADEA UNIVERSITY, Fascicle of Management and Technological Engineering, Volume VII (XVII), pp. 12241228, ISSN 1583-0691

David, R. ,Alla, H. (1992), Grafcet on Petri Nets, Ed. Hermes, (in French), Paris, ISBN: 2866013255

Jensen, K. (1995) Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use (Volume 2), Springer Verlag, Berlin, ISBN: 3-540-58276-2

Preitl, S., Precup, E. (1997), Introduction to fuzzy control, Ed. Tehnica, (in Romanian), Bucharest, ISBN 973-31-1081-1

Yeung, D.S.; Liu, J.N.K.; Shiu, S.C.K.; Fung, G.S.K. (1996) Fuzzy coloured petri nets in modelling flexible manufacturing systems, ISAI/IFIS, pp. 100-107, ISBN: 968-29-9437-3