JPH0383138A - Modeling method for discrete event driving system - Google Patents

Abstract

PURPOSE:To specify a firing sequence of required transitions with a small calculation volume by combining positions of tokens, each of which is arranged in an individual partial network, to express the state of an object system and expressing transitions with firing conditions described in logical expressions of token positions. CONSTITUTION:The model of an object system 13 consists of plural partial networks 11, and one token 5 always exists in each partial network 11, and the state of the object system 13 is expressed by combination of positions of tokens 5. Each transition 2 in the partial network 11 is expressed with one input place, an output place, and a firing condition 12 described in the logical expression of the arrangement condition of the token 5 in another partial network 11. Thus, the model is generated which specifies the firing sequence of transitions required for arrival at a set of final marking from initial marking with a small calculation volume without obtaining a complete routing tree.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a modeling method for creating a model whose state can be easily analyzed for controlling a discrete event-driven system or diagnosing an abnormality.

[Conventional technology]

Figure 7 is an example of "Introduction to Petri Net", J.E.
11 Beater So 7 (J-L, Pstarson
), Atsunobu Ichikawa/Shigenobu Kobayashi translation, Kyoritsu Shuppan (translated), published in April 1980, p. 36 is a Petri net modeled on the machinist j11t, which is an example of a discrete event-driven system. .

In the figure, 1 is a type vy that describes the state of the system;
, 2 is a transition error that describes the operation of the system, 3 is an arc that relates the transition 2 and the place 1 that is its input (hereinafter referred to as input place), and 4 is the transition 2 and its output light. The arc related to place 1 (hereinafter referred to as output place), 5 is a token placed on place 1, and the state of the Petri net is determined by the arrangement of tokens on all places 1 (hereinafter referred to as marking). In other words, the state of the modeled system is described. 6 is a discrete event-driven system described by a Petri net.

Next, the operation will be explained. The execution of Petri Net 6 is
The number and distribution of tokens 5 in the Petri net 6 are controlled as follows. Execution of Petri Net 6 is transition 2
This refers to the ignition of the system (when the system performs a prescribed operation). Transition 2 is ready to fire if token 5 of arc 3 is present in all of its input places. When this transition 2 fires, tokens 5 as many as arcs 3 are removed from its input place, and tokens 5 as many as arcs 4 are added to its output place.
is injected. When the tiger/comb seal 2 fires, the marking U of the Petri net 6 changes to a new marking u1. In this way, the Petri net 6 models the behavior of a discrete event-driven system.

Petri Net 6 can be used for control and diagnosis of discrete event-driven systems. For example, when used for control, the current state of the system is set as an initial marking, and the state to be reached is set as a final marking. Set as a set of The firing sequence of the transition 2 that realizes such a transition becomes the operating procedure for the system.

By the way, as stated on page 187 of the above-mentioned document, the problem of finding such a firing sequence is so difficult to solve that there is no clear conclusion as to whether it is possible to solve it. Therefore, the only way to solve this problem is to find all the marking trees that can be reached from the initial marking, that is, the reachable tree.

[Problem to be solved by the invention]

Since the Petri net according to the conventional modeling method is constructed as described above, it is difficult to determine whether it is possible to transition from the initial marking to the set of final markings in which all place and transition learnings are combined and meet. In order to perform an analysis such as finding the firing sequence of the transition sequence that realizes it when It is necessary to find a marking tree, that is, a reachable tree, and in large-scale systems, finding a reachable tree requires a huge amount of calculations.

This invention was made to solve the above-mentioned problems, and it is possible to reach a set of final markings from an initial marking with less calculation than conventional modeling methods without requiring a complete reachability tree. The purpose of this study is to obtain a modeling method for a discrete event-driven system that can create a model that can specify the firing sequence of transitions necessary for the purpose of the system.

[Means to solve the problem]

The method for modeling a discrete event-driven system according to the present invention consists of constructing a model of a target system from a plurality of partial networks, making sure that one token always exists in each partial network, and changing the combination of the positions of the tokens. In addition to expressing the state of the target system, each transistor in the partial network is described by a logical expression for each input place, output place, and token placement conditions in other partial networks. This is expressed by firing conditions.

[Effect]

The method of modeling a discrete event-driven system according to the present invention constructs a model of the target system from a plurality of subnetworks, and further uses a combination of digits ffi[) of only one token placed in each subnetwork. In addition to expressing the state of the target system, each transition
Since each token is expressed by a firing condition described by a logical formula for each input place, output place, and the position of the token in other networks, the movement of the token can be performed in each partial network. limited,
The relationship with other subnetworks is limited to the logical expression of the condition regarding the position of the token.

For each partial network, from the place where the token is currently placed and the set of places where the place must ultimately exist (hereinafter referred to as the final place set), there is a possibility that the token will be placed in the current case or in the future. A set of places (hereinafter referred to as a possible place set) and a set of transitions that may be included in a firing sequence (hereinafter referred to as a possible transition set) are easily obtained.

Furthermore, if a network appears where the intersection set of the possible place set and the final place set is an empty set, or if ignitable transisirane ceases to exist, it can be determined that the final marking cannot be reached from that marking.

[Embodiments of the invention]

An embodiment of the present invention will be described below with reference to the drawings.

Figure 1 shows a discrete event-driven system composed of multiple partial networks modeled according to the present invention. The explanation will be omitted.

In the figure, 11 is a partial network, there is always one token 5, and each transition 2
is configured to be coupled to one input place, one output place, and one firing condition 12. 12 is another partial network 1 that describes the firing conditions of transisilane 2.
Logical formula of condition for placement of token 5 on 1, 13
is the entire model (target system) of a discrete event-driven system.

Next, the operation will be explained. The condition of this model 13 is
It is described by the position of the token 5 on each partial network 11. Execution of this model 13 means ignition of transisilane 2 (the system performs a predetermined operation). Transisiran 2 has 5 tokens in the input place.
exists and the conditional formula 12 regarding the position of the token 5 on the other partial network 11 is satisfied. When Transisilan 2 fires, token 5 is removed from its input place and token 5 is placed in its output place. When the transisilane 2 ignites, the marking U of the partial network 11 changes to a new marking ul. In this way, the behavior of a discrete event-driven system is modeled.

This model 13 can be used to control or make decisions about discrete event-driven systems. For example, when used for control, the current state of the system is set as an initial marking, and the state to be reached is set as a final marking. Set as a set of The firing sequence of the trigger 2 that realizes such a transition becomes the operating procedure for the system.

Next, a procedure for analyzing a model created according to the present invention when controlling a target system will be described, but first, terms and symbols that will be commonly used hereinafter will be defined. Model 13 is expressed as M-(M[i], i
= x , , , n) (M[i] is each partial network 11, n is the number of partial networks 11),
Let each partial network 11 be M[i[P[i]
, T [i] , D [i co , I [1] , 0
[1] tC[i] ). here,
p[t] = (p[i-j co-j = 1, -pni) is a set of places 1, and pni is the number thereof.

T[1]=(t[i-j]-j=1.,..., tni) is a set of transisilane 2, and tni is the number thereof. D [t] - (d[i, j * j = 1 * - ed
ni) is a set of logical expressions 12 of conditions regarding the position of the token 5 in the other partial network 11, and dni is the number thereof. I[1koniT[1k→p[i] is a mapping that associates the string 2 with the input place. 0[1koniT[1k→p[:t] is a mapping that associates transisilane 2 with an output place. C [
lconi T[t]→D[ico is a mapping expressing the correspondence between the logical expression 12 of the condition regarding the position of the token 5 of the transisirane 2 and the other partial network 11. The expression format of d[i,j] mentioned above is simply written as p[1゜'' to represent the presence of token 5 in p[i,j, and the representation of (one partial network 11
The expression that combines p[i, J written inside with or or is the unit expression, and the unit expression is and '! When logical expressions connected by or are called an and expression or an or expression, respectively, the arrangement of tokens 5 on the other partial network 11 p[l', j''
It is expressed as a unit expression, an and expression, or an or expression.

Also, the initial marking is set to 5=(s[i*l-1e-*
, n) (exists in each partial network 11),
The final marking set is F=(f[i], i=1.,
, n) (exists in each partial network 11), then s[i is one place 1 belonging to P[i, and f[t] is a set of places 1 belonging to P[i. It is.

transitions that may be included in the firing sequence from a certain marking u''(u[iLl''L---*H) (a set of token placements in each subnetwork 11) to a final marking set F. 2 set as PT(u)=(PT[
i](u), i=1 , , , , n), and the set of places 1 where token 5 may be placed is defined as PP(
u)=(PP[tco(u)+i=1 ,,,,,n
).

When the firing condition is satisfied at U, &p, the set of transitions 2 included in PT(u) ftpr(u)ε. U to t
[1, mark the result of firing jl as q(u.

Let t[i, j). q(u, t[i, jl) and U differ in the position of token 5 on partial network M(1).

Next, in order to represent a set of continuous markings in a graph, the markings are made to correspond to nodes, the fired transitions are made to correspond to arcs, and the marking of node X is defined as u (X). This node X can be classified as a leading node, a successful node, a failed node, a duplicate node, or an internal node. Classified as a duplicate node, an internal node, or an internal node. Let the gathering of tip nodes be Y (set Y
The components of are all the tip nodes of each partial network, and the same applies to each set of 7-does below).

A successful node is a node whose marking is included in the final set of markings. Let A be the set of successful nodes. A failed node is a node whose markings cannot reach the final set of markings. Let B be the set of failed nodes. A duplicate node is a node for which a node with the same marking already exists. Duplicate nodes are removed as soon as they are identified, and the end node of the arc entering the duplicate node is replaced with an already existing node with the same marking. The internal node is the node that generated the node by firing the transition 2 from its marking. Let E be the set of internal nodes. Let r be the node corresponding to the initial marking, then u(r)=s
It is. Then, the firing sequence of transistor 2 to be sought is K.
shall be.

No. 25i3 is a flowchart showing a procedure for determining the firing sequence of transin 1 and 2 that can reach the JIk final marking from the initial marking to the final marking, and will be explained below using this flowchart. First, each node Y, A, B, E
PT(s) and PP( for the initial marking 8) according to the procedure shown in FIG.
s)=FT(!I) is determined (step ST2). Using an appropriate search method from the tip node Y, find the node X at a distance of 1 m.
is selected, this node X is removed from the tip node Y (step 5T3), and whether or not the node X is a duplicate node is checked based on whether the same marking already exists (step 5T4).

If it is a duplicate node, the arc that enters node You can check whether it is a node. If it is a successful node (U(x) 6 F ), node X is added to successful node A (step 5T
7) If it is not a successful node (U(x)4F), follow the procedure shown in FIG.
(x)) and FT(u(x)) (step 5T8
), it is checked whether node X is a failed node (step ST9). In this step ST9, PP [
1] (u(x)) and f[1] are empty sets, or if FT [1](u(x) ) is an empty set, then from u (x) to F It is impossible to reach 11. Node X is concluded to be a failed node.

If node X is a failed node, this node A node 2 is generated in correspondence with the marking, and an arc to this node 2 is made to correspond to the fired transition desire 2. In this case, the marking of node 2 is q (u (x)).

t [1, JU), node 2 is added to tip node Y (step 5TII), and node X is added to E (step 5T12). And transif 9f 20
If there is some kind of dominance relationship (priority order) in the firing sequence, use it to move some nodes in the tip node Y to the failed node B Step 5T13
), it is checked whether the tip node Y is an empty set (step 5T14). If the tip node Y is not an empty set, return to step ST3 again, and if it is an empty set, reversely rearrange the transitions 2 on the path from each node belonging to the successful node A to the root node, and Add the desired transition sequence 2 to the set K of firing sequences in step 5T15.
), outputs K (step 5T16), and specifies the firing sequence in each partial network 11.

Figure 3 shows PT (s), PP (s), FT (s) from the initial marking line and the final marking set F.
Here is a 70-chart showing the steps to initialize the
From only the connection relationship between place 1 and transition place 2 of each partial network 11, PP (m), PT (s)
(Step 5T17). For example, from the partial network 11 as shown in FIG.
), 8[1 co=p[1・1 co and f
When [1]=(p[1-4]), it is easy to calculate PT(a
)−(t[1・1]・t[x・2], t[1,3]
, t[1,4]), PP[1](s)=(p[1,
xco, p[1,2], p[1,3] = p
[1-4) is required.

Here, by removing transition 2, which cannot fire when considering D[1], PP(Otori), PT(a)
must be corrected (step 5T18).

To this end, PP(s) is used to simplify d IJ *J by removing terms that always hold or terms that do not hold. The simplified d[i,j] is transformed into g[Ii,j(
s), and G [11(g) = (g [t,
j co(s)+j=i+-0-rdnt), G(g)=
(G[il(s) el=1e-men). Here, T[il and G[il(a) are associated with C[1] as follows. [i,j]
Let the set of (il) be PC[il(s) and PG(s)
=(PG[il(s), i=1., , , n).

The procedure for simplifying d[i,j] is to set the equation that always holds true as 1 and the equation that always holds as O that never holds true. Unit expressions in d[1°j that are not included in PP[11](a) (place 1 where token 5 may be placed in another partial network 11) are removed. As a result, if an element of the unit expression becomes 0, that unit expression always fails, so it is replaced with 0.

P[11 such that it contains all the elements of PP[il](s)
The unit formula for ko always holds true, so replace it with ko. an
If there is a 0 in the d expression, replace the and expression with O. The 1 in the and expression is removed. If there is a 1 in the or expression, replace the or expression with 1. O in the or expression is removed. Among them, such a reduction is d[1,j] corresponding to any t[1,j] belonging to PT[il(g)
This is done only for (8), and other d[1°j] are simplified to g[i,j]=0.

d [i tj koya g [1ej ko(s) is a subnetwork M(1> to another subnetwork M(il)
g[it], which expresses dependence on g[it.

If we record the set of PP[il(s) as H[il(8), then H[il(s) is the set of p[il(s) that belongs to PP[il(s)]. 11・jl](
s), H(s)−(H[il(a), 1=
11. ---n). This H[il(a) is PP
It means a set of g [i, j (8) that may be reduced when [il(s) changes].

When k, g[1,j](s) is simplified, H[il(8) is also modified accordingly.

As a result of the agreement, g [t
, j](s)= .

If something appears, the transition t[i,j] that uses it will be unable to fire, so taking this into consideration, set PT[1](s), PP[il(,) , P.G.
[il(s) is modified. For example, in Figure 5, d
When [1°1 = 0, PT[l(s) = (t[
x, 2], t[1°4]), PP[1ko(g)=(p
[x, 1, p [1,3], p [1,4]).

When pP[il(s) decreases in this way, H[
Since there is a possibility that g[il, il(!I) which is included in il(s) can be simplified, we will try to simplify it. and,
If g[tx, jx](s)=0 appears, PT[il(8), pP[1l(a)] is corrected.

In step 5T18, the above processing is performed as PT[1]
(1), P P [l] (s) stops changing 1
Repeat with .

Furthermore, g [i・j co(s
), and correct PT(=!I) and PP(s) by removing the transition 2 that makes it impossible (step 5T19).

This must hold g [i, j](s
) is calculated as follows. Considering only the transition t[i,j] included in PT[il(s),
t[i required to move token 5 from u[il to f[i.

Let the set of firing sequences of [j] be NT [1](s). N
g [1, j included in all the series where t [i, j] is replaced with g [i, j (B) in T[ll(s)]
](s) must necessarily hold true. That more g
Let the set of [i = j](a) be NG[il(i),
NG(s)=(NG[il(s)-i=1.,,,n)
shall be.

Process g[:i,j](s) belonging to NG(s) to obtain a unit formula of P[:i 1] and g[i-j]
Find a logical formula that includes (s). We will call such a logical expression a necessary unit expression. Here, and
If we express or with ``f:A, for example, (
p [1-11p[1°2]) (p [1=3]Ap
[2-1] ), the required unit expression is p[1,1]
p[l·2]V and p[i·3] are obtained. Also,(
From p[1-x]p[x,2]) Ap[2,1,
As the required unit formula, p [1=1]■p[1・2] and p[
2.1] is required. Since the necessary unit formula Fi must be satisfied at a certain point, we can use this fact to PT(
s), PP(+s) is corrected. For example, in FIG. 6, P T [1] (a) = (t [1,1], t [1
,2],t[1,3,t[1,4]),P P
[1](s)=(p[1,1]-p[1-2], p[1
, 3]-p [1-4]). Here, it is assumed that p[1=2] is given as the necessary unit expression. p[1・3]
is not continuous from p[1, 2], nor is it continuous from p[1, 2]. Therefore, in order for the necessary unit expression p[1°2] to hold, p[1,3 No tokens may be placed on . Therefore, PT [1](s) = (t[1-1
ko, t [:1,3] ), PP [1] (Hatake) = (
p[ll-11, p[1,2], p[1,4J)
is corrected. Among them, when the number of elements of PP(a) is reduced in this way, transitions that cannot be ignited due to this effect are removed.

Also, all g[i,j](
+s) to find the required unit formula and use it to calculate PT(s
), PP(s) will be modified. In addition, even when g[i・j](s) belonging to NG(a) is simplified, the necessary unit formula is found and the sinusoidal processing is performed until PT(s+) and PP(s) do not change. Repeat.

Finally, a PT(a) that satisfies the firing conditions at that time is selected, and an FT(s) is created (step 5T20).

Figure 4 shows the transition from the node before the firing of transition 2 to the PT (
u(x)) , PP(u(x)) , FT(u(x))
This is a flowchart showing the procedure for determining PT(ul), PP(ul), P
Step 5T21) to create G(ul), G(ul), H(ul), NG(ul), and then transition t.
P for marking ul after firing of [i,j]
T [j co(ul), PP[i co(ul), PG[f co(
ul), NT[j(ul), NG[i(ul)] (step 5T22). Here, PP[il(ul
) has decreased (step 5T23), and if it has not decreased, step 5T26 is executed.

If it is decreasing, H[
Attempt to simplify g[il, il(ul) belonging to il(ul), and modify PT(ul), PP(ul). However, the simplified g[i, j(ul) at this time shall be recorded (step 5T24). g [i ej ko(ul
) and included in NG(ul), calculate the necessary unit formula again and use it to calculate PT(ul), PP(ul)
) in step 5T25), select the one that satisfies the firing conditions from PT(ul), and select FT(ul).
) and step 5T26), PT(uω), PP(u(x)), FT(u(x)) at the marking of node
f: Find.

Although the control of the discrete event-driven system has been described here, the same effects as in the above embodiments can be achieved in diagnosis as well.

〔Effect of the invention〕

As described above, according to the present invention, a plurality of partial networks constituting a model of a target system are expressed by a combination of the positions of only one token placed in each partial network, and the state of the target system is expressed. each,
Since each transaction is expressed by a firing condition described by a logical formula for each input place, output place, and the position of the token in other partial networks, we can obtain a complete recursive tree. This method has the advantage that the firing sequence of transitions required to reach the final marking set from the initial marking for each 5-part network can be specified with a smaller amount of calculation than conventional modeling methods.

[Brief explanation of drawings]

FIG. 1 is a diagram showing a discrete event-driven system modeled according to an embodiment of the present invention; FIGS. 2, 3, and 4 are flowcharts illustrating state analysis according to the present invention; FIG. is a diagram explaining the initialization process of FIG. 3 according to the present invention, FIG. 6 is a diagram explaining the modification process of FIG. 4 according to the present invention, and FIG. 7 is a diagram explaining the Petri net of a discrete event-driven system. FIG. In the figure, 1 is a place, 2 is a transition, 5 is a token, 11 is a partial net soak, 12 is a firing condition,
13 is a target system. In the figures, the same reference numerals indicate the same or corresponding parts.

Claims (1)

[Claims] A model of a discrete event-driven system is composed of a plurality of partial networks, each of which always has only one token, and each transition in the plurality of partial networks is defined as one input place, one output place, and one other. A method of modeling a discrete event-driven system expressed by firing conditions of the transition described by logical expressions of token placement conditions in a partial network.