CN113359650A - Method for controlling automatic manufacturing system with uncontrollable event - Google Patents

Method for controlling automatic manufacturing system with uncontrollable event Download PDF

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CN113359650A
CN113359650A CN202110753595.8A CN202110753595A CN113359650A CN 113359650 A CN113359650 A CN 113359650A CN 202110753595 A CN202110753595 A CN 202110753595A CN 113359650 A CN113359650 A CN 113359650A
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CN113359650B (en
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冉宁
雷帅帅
郝晋渊
郝真鸣
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Heibei University
Hebei University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM]
    • G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/32—Operator till task planning
    • G05B2219/32339—Object oriented modeling, design, analysis, implementation, simulation language
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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Abstract

The invention provides a control method of an automatic manufacturing system with an uncontrollable event. The method comprises the following steps: firstly, constructing a corresponding Petri net model according to the production relation of an automatic manufacturing system; secondly, providing constraint conditions (w, k) which should be met by the Petri net model in the step I according to an actual production relation; thirdly, converting the forbidden state problem in the step II into an integer linear programming problem according to the model in the step I; solving the integer linear programming problem in the step (c) to obtain allowable linear constraint; fifthly, directly designing the controller in the original model by using a library invariant method according to the result obtained in the step IV. The invention can effectively solve the problem of forbidden states of automatic manufacturing systems containing uncontrollable events, realize the control of various automatic manufacturing systems and reduce the cost and difficulty of system control.

Description

Method for controlling automatic manufacturing system with uncontrollable event
Technical Field
The invention relates to the technical field of automatic manufacturing systems, in particular to a Petri network-based control method of an automatic manufacturing system containing uncontrollable events.
Background
With the rapid development and widespread use of information technology, many manufacturing systems are gradually turning into more flexible automated manufacturing systems. While an uncontrollable event is a problem that must be considered and addressed when designing an automated manufacturing system. For an actual system, due to the limited technical level of the existing control, the cost of event control is too high, and the failure of devices and lines, the existence of an uncontrollable event is inevitable. A properly functioning system may uncontrollably enter a state where people are not expected to reach due to the occurrence of an uncontrollable event, which is often referred to as a disabled state. In order to ensure the safe and stable operation of the system and simultaneously ensure the economic benefit, the research on the uncontrollable events of the automatic manufacturing system is also more widely regarded. Such as: a piece of machining equipment may fail uncontrollably when machining a piece, where the machining process has to be terminated, but for economic reasons it is often desirable that the machine not affected by the failed equipment can continue to operate. However, in actual production, one process is affected by a faulty device and tends to block the other processes. How does the control system cause the production process to operate according to established requirements when a device fails? In the prior art, a Petri network is often adopted to model an automatic manufacturing system, and such uncontrollable events are abstracted into uncontrollable transitions in the Petri network. Given that any automated manufacturing system containing uncontrollable events is controlled so that the system operates consistently and smoothly and orderly according to established requirements, the prior art does not provide an effective method.
At present, researchers in researching the prohibition state control strategy of the automatic manufacturing system with uncontrollable events have the following defects: the constraint method for the uncontrollable event is only effective for some special systems, so the application range of the methods is limited; most control strategies are computationally expensive and are not suitable for use in complex automated manufacturing systems.
Disclosure of Invention
The invention aims to provide a control method of an automatic manufacturing system with an uncontrollable event, which can solve the problem of forbidden states of the automatic manufacturing system with the uncontrollable event, realize the control of various automatic manufacturing systems and reduce the cost and difficulty of system control.
The invention is realized by the following steps:
a method of controlling an automated manufacturing system having an uncontrollable event, comprising the steps of:
the method comprises the following steps: and constructing a corresponding Petri net model according to the production relation of the automatic manufacturing system.
Step two: and giving out constraint conditions (w, k) which should be met by the Petri net model in the step one according to the actual production relation.
Step three: and converting the forbidden state problem in the step two into an integer linear programming problem according to the model in the step one.
Step four: and solving the integer linear programming problem in the step three to obtain allowable linear constraint.
Step five: and D, directly designing the controller in the original model by using a library invariant method according to the result obtained in the step four.
Further, the first step abstracts the automatic manufacturing system into a Petri net model as follows:
links representing resources or processes in the automatic manufacturing system are represented by libraries P (represented by circles in the drawing), and the set of libraries P is denoted as P. Events at the beginning or end of a certain process are represented by transitions t (represented by unfilled rectangles in the figure), and uncontrollable events correspond to uncontrollable transitions in the Petri net model (represented by filled black rectangles in the figure). T for uncontrollable transition setuTo indicate. p and t, connected by a directed arc ("→") according to actual production relationships; the resource in actual production is token, which is denoted by "·" in the figure. The Petri net model constructed by the steps is marked as (N, m)0)，m0Is the initial state of the system.
Further, the steps write out constraint conditions and represent the constraint conditions by (w, k) according to the relation between the resources in actual production, wherein w is a weighted value of the library, and k is a given non-negative integer.
Further, the third step comprises the following specific steps:
step 1: determining Petri nets (N, m)0) And linear constraints (w, k).
Step 2: if any uncontrollable transition exists, the weight value lambda (t) of the transition is less than or equal to 0 (lambda (t) is calculated as follows), the value of w is given to w*And obtaining an output conversionConstraint (w) of*K); otherwise, step 3 is executed.
Figure BDA0003146308210000021
t·A post set of transitions t is represented,·t represents the preamble set of transition t.
Let x be the node of Petri net, and the prefix set of x·x is defined as·x ∈ { y ∈ P | (y, x) ∈ F }, a postset x of x·Is defined as x·＝{y∈P∪T|(x,y)∈F}。
And step 3: obtaining an integer linear programming problem:
step 3.1: and taking the minimum value of the sum of the weights of all the libraries in the Petri network model as an objective function.
Step 3.2: constructing constraint 1: recording the weight value of the library in the transformed Petri network model as w*(p), the weight of the library before conversion is w (p); for all libraries about w*(p)≥w(p)；
And (3) constructing constraint 2: for any uncontrollable transition, lambda (t) is less than or equal to 0.
Further, the fourth step specifically comprises: step three is executed, the constraint condition (w) after conversion is calculated under the constraint condition of the objective function*K). The invention recommends using LINGO for the calculation.
Further, the step five controller (i.e. control store p)c) The design method comprises the following steps:
step 1: input is based on the linear constraint (w) resulting from the transformation*,k)。
Step 2: for any transition t, if the weight lambda of the transition after conversion*(t) > 0, adding a control library p in the original Petri networkcDrawing a control place pcArc pointing to transition t and assigned as lambda*(t)|。
And step 3: for any transition t, if the weight lambda of the transition after conversion*(t) < 0, draw a place p pointing to the control library from the transition tcAnd is assigned as | λ*(t)|。
And 4, step 4: adding a control base place p to the original Petri networkcAnd forming a new Petri net according to the arcs added in the steps 2 and 3 to be marked as (N)*,m0 *) The initial mark is
Figure BDA0003146308210000031
And 5: the initial identification of the control store is
Figure BDA0003146308210000032
The invention provides a controller synthesis method based on integer linear programming, aiming at the problem of forbidden states of a Petri network with uncontrollable transition. Compared with the prior art, the invention has the beneficial effects that:
1. the control method of the invention has no special requirements on the type of the manufacturing system, thereby effectively solving the problem of the forbidden state of the manufacturing system containing the uncontrollable event.
2. The control method provided by the invention does not need accessibility analysis, thereby avoiding the problem of 'state explosion'.
3. The method for solving the integer linear programming problem is quite mature by utilizing the idea of integer linear programming, so that the method has higher calculation efficiency.
4. The closed loop system model can be calculated by standard synthesis techniques.
Drawings
FIG. 1 is a schematic view of a part manufacturing process.
FIG. 2 is a Petri net model of a part production process.
FIG. 3 shows a control library pc1And pc2Closed loop Petri Net (N)*,m0 *) The structure is schematic.
Detailed Description
For the purpose of further explaining the objects, technical solutions and advantages of the present invention, the following is further described with reference to examples. The specific embodiments described below are merely illustrative of the present invention and do not limit the present invention.
A part processing system is shown in fig. 1, and the processing system includes a feeding unit, a part processing unit, and a part storage unit, wherein the part storage unit includes a completed processing waiting part stack area, a completed processing part stack area, and an uncompleted processing part stack area due to equipment failure. The technological process is that the material of the material supply unit is sent to the part processing unit by the transmission belt 1; after the parts are processed, the parts are conveyed to the next workstation (a processed part stacking area) by the conveyor belt 2 to wait for transfer; then the part is conveyed to a part stacking area after being processed by a conveyor belt 3; if the part processing unit has a fault, the unfinished parts are sent to the unfinished parts stacking area by the conveyor belt 4 and then sent to the feeding unit by the conveyor belt 5.
The method comprises the following steps: construction of the Petri Net model (N, m) according to the above description0)，m0Is the initial state of the system, N is a Petri net, the common Petri net is a triple N ═ P, T, F, P and T are respectively a library P set and a transition T set,
Figure BDA0003146308210000041
is a stream relationship, connecting the library locations and transitions, representing a set of directed arcs between the library locations and transitions.
As shown in FIG. 2, where m0(2,0,0,0,0,0, 0), transition t2And t4Is an uncontrolled transition. The physical significance of the libraries and transitions in FIG. 2 are shown in Table 1.
TABLE 1
Figure BDA0003146308210000042
Step two: according to its characteristics, the parts waiting to be transferred to the stack area are in the same position of the apparatus, so that the store p3And p5At most one of them, i.e. the system should satisfy the linear constraint (w)1,k1) Wherein w is1＝(0,0,1,0,1,0,0,0)，k11 (i.e. m (p))3)+m(p5) Less than or equal to 1). In addition, due to the presence of equipmentStop working when failure occurs, so that the library p2And p6At most one of them, i.e. the system should satisfy the linear constraint (w)2,k2) Wherein w is2＝(0,1,0,0,0,1,0,0)，k21 (i.e. m (p))2)+m(p6) Less than or equal to 1). m (p) represents the number of tokens in pool p, w is the pool weight, and k is a given non-negative integer.
Step three: for linear constraint (w)1,k1) And (5) constraint conversion.
Step 1: input Petri Net (N, m)0) And linear constraint (w)1,k1)。
Step 2: due to t2And t4Is an uncontrollable transition, and λ (t)2)＝1，λ(t4) If 1 is greater than 0, step 3 is performed.
λ (t) is the weight of the transition t, given a Petri net N and a linear constraint (w, k), λ (t) is as follows:
Figure BDA0003146308210000044
t·a post set of transitions t is represented,·t represents the preamble set of transition t.
Let x be the node of Petri net, and the prefix set of x·x is defined as·x ∈ { y ∈ P | (y, x) ∈ F }, a postset x of x·Is defined as x·＝{y∈P∪T|(x,y)∈F}。
And step 3: obtaining an integer linear programming problem:
step 3.1: writing out an objective function:
Figure BDA0003146308210000043
w*(pi) Representing the weight of the constraint transformed library;
step 3.2: obtaining a constraint condition:
constraint 1
Figure BDA0003146308210000051
Constraint 2
Figure BDA0003146308210000052
Step four: the integer linear programming problem described above is calculated. Obtaining allowable linear constraints
Figure BDA0003146308210000053
Wherein
Figure BDA0003146308210000054
k11. After conversion
Figure BDA0003146308210000055
The weights of other transitions are all zero.
Step five: design controller library pc1。
Step 1: inputting the allowable linear constraint obtained according to the step four
Figure BDA0003146308210000056
Step 2: for transition t1，
Figure BDA0003146308210000057
Draw a controlled library pc1Pointing to transition t1And assigned a value of 1.
And step 3: for transition t3、t5，
Figure BDA0003146308210000058
Then draw two transitions t3、t5Point to control store pc1And assigned 1, respectively.
And 4, step 4: for any library P belonging to P, the initial identification of the library P after constraint conversion
Figure BDA0003146308210000059
Equal to the initial identifier m of the pre-constraint transformation library0(p) that is
Figure BDA00031463082100000510
And 5: the initial identification of the control store is
Figure BDA00031463082100000511
Similarly, the linearity is constrained (w) according to step three and step four2,k2) Conversion to allowable Linear constraint
Figure BDA00031463082100000512
Wherein
Figure BDA00031463082100000513
k21. Designing a control place p according to the step fivec2The structure of the control library is shown in FIG. 3.
Example results analysis. All reachable identifiers of the model shown in FIG. 2 are shown in Table 2. from Table 2, it can be seen that the forbidden states of the model shown in FIG. 2 are before constraint transformation is performed
Figure BDA0003146308210000061
Figure BDA0003146308210000062
Representing a set of forbidden states before constraint transition. Obtaining a closed loop Petri network after implementing the constraint conversion method provided by the invention
Figure BDA0003146308210000063
The reachable identifiers are shown in Table 3, and can be seen from Table 3
Figure BDA0003146308210000064
TABLE 2
Figure BDA0003146308210000065
TABLE 3
Figure BDA0003146308210000071
From the above analysis, it can be seen that the controller pc1And pc2Under the action of (2), a closed loop Petri net
Figure BDA0003146308210000072
The controller according to the invention can make all the states of the system meet the constraint after conversion, and can realize the control target.

Claims (4)

1. A method for controlling an automated manufacturing system having uncontrollable events, comprising the steps of:
a. constructing a corresponding Petri net model according to the production relation of the automatic manufacturing system, and recording the Petri net model as (N, m)0)，m0Is an initial state;
b. b, listing constraint conditions (w, k) which should be met by the Petri net model in the step a according to an actual production relation, wherein w is a weight value of the library, and k is a non-negative integer;
c. converting the constraint conditions (w, k) in the step b to obtain converted constraint conditions (w)*K); the method comprises the following specific steps:
c-1, if the weight lambda (t) of any uncontrollable transition is less than or equal to 0, then assigning the value of w to w*Otherwise, executing step c-2;
Figure FDA0003146308200000014
p is the depot, t·A post set of transitions t is represented,·t represents a preamble set of transition t;
t·＝{y∈P∪T|(t,y)∈F}，·t＝{y∈P∪T|(y,t)∈F}；
p is the set of libraries P, T is the set of transitions T,
Figure FDA0003146308200000011
is a stream relationship;
c-2, taking the minimum value of the sum of the weights of all the libraries in the Petri network model as a target function;
c-3, constructing constraint conditions: the weight value of the post-conversion library is more than or equal to the weight value of the pre-conversion library, namely: w is a*(p) w (p) or more; for any uncontrollable transition, the weight lambda (t) of the transition is less than or equal to 0;
c-4, calculating the constraint condition (w) after conversion according to the step c-3*,k)；
d. Construction of a control store pc：
d-1, constraint (w) after conversion*K) to find the weight λ of each transition t after conversion*(t)；
d-2, adding a control base place p in the original Petri networkc；
d-3, for any transition t, if the weight lambda of the transition after conversion*(t) > 0, draw a place p by the control librarycArc pointing to transition t and assigned as lambda*(t) |; for any transition t, if the weight lambda of the transition after conversion*(t) < 0, draw a place p pointing to the control library from the transition tcAnd is assigned as | λ*(t)|；
d-4, added control store pcAnd arcs, which together with the original Petri net form a new Petri net, denoted as (N)*,m0 *) And is and
Figure FDA0003146308200000012
control depot pcInitial identification in (1)
Figure FDA0003146308200000013
2. The method of claim 1, wherein for each additional constraint (w, k), a corresponding additional control store p is addedc。
3. The method of claim 1, wherein in step b, the constraint (w, k) comprises: waiting for transferring the parts to a part stack area which is finished to be machined and waiting for transferring the parts to a part stack area which is not finished to be machined, wherein at most one truken is arranged in a corresponding library; the machine is working and the machine is being repaired, and at most one of the libraries corresponding to the two machines is determined.
4. The method of claim 1, wherein step c-4 uses LINGO to calculate the converted constraints (w)*,k)。
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