D.t.n. Mamedov J.F., Akhmedova S.M., Maghommedli H.M.

Sumgajit State University, Azerbaijan

Simulation and investigation of dynamical technical

system working represented by final automat

by means of Petri network

One of the stages of flexible manufacture systems (FMS) creation at theirs system technical design level is definition of its creation productivity on the base of doing simulation and computer experiments of technical systems, speciality new automation units (industrial and intellectual robots, different types mechatron equipments - special manipulator, automatic conveyer). That problem is actuality as elements of FMS work at 3D area with one working zone contrary connected and at real objects application of dynamic systems are accompanied with some difficulty.

The last time for investigation with using simulation and computer experiment of technical systems as mathematical apparat speciality Petri network [1] is very popular. With using Petri network investigation of simulation of technical system allows to do analyz of characteristics of this network. As FMS has complex structure its representation with Petri network like iteration process is doing difficult, practical not real. Practical [2] is shown for solution of this problem it is needed to share FMS on some subsystems and its working present like an initial written. The expressions are investigated as them transformation to Petri network. For algorithm of transformation development different methods are used [3].

In the paper using for solution of the date problem transformation of an initial information represented like final automat to Petri network is considered. The control object consents a multitude of dynamical technic systems represented of “n” number of final automat and its complex expression is written as following:

(1)

where A_i - multitude of dynamical technic systems represented of final automat; G_i - multitude of inside alphabet of final automat; C_i - multitude of outside alphabet of final automat; V_i - multitude of status corresponded to object’s stability; j_i:V_ixG_iÞ V_i - multitude of transition functions; y_i:V_ixG_iÞC_i - multitude of outside functions.

At given of the problem for transformation of the represented control algorithm as final automat into Petri network a formal writing and its elements are consiedered.

Petri network at formal is defined as following [2]:

N={P, T, O, İ, M_o}, (2)

where, P={p₁, p₂, …, p_n}, n>0 – multitude of not empty final conditions; T={t₁, t₂, …, t_m}, m>0 – multitude of not emty final transitions; İ: TxPÞ{0,1} – inside intident function; O:PxTÞ{0,1} – outside intident function; M₀:PÞ{0,1,2,...} – initial symboling.

As see from formal representation of Petri network if P – multitude of final conditions and T - multitude of final transitions are defined, then inside and outside intident functionse able define in a view:

; (3)

, (4)

where, F(P) and F(t) are the functions of transformation from final automat into Petri net expressions are written as following:

; (5)

F(P) and F(t) are the special functions of transformation for determination of multitude of conditions and transition which are defined as below:

, (6)

, (7)

At using the functions of transformation elements of the multitude of conditions of transformations is defined as folowing:

(8)

At using the matrix of transition

, (9)

Decart multiplication is colculated by means of the algorithm:

(10)

For realisation of the date algorithm the software was worked out on TurboPascal programm system and its function was executed computer experiment for investigation by Petri net of representation like final automat.

References:

1. Piterson J. Petri network and system of simulation. – М.: Word, 1984, p. 264.

2. M.A.Akhmedov, H.M. Mammadli. Determination of the demands for architecture of computing design units of FMS. Sumgajit State University “Scientific news”, №1. 2010.

3. N.G. Zachrov, V.N. Rogov. Syntez of numerical automats. The lesson book UlSTU. 2003, 140 p.