CN107395402B - MVB network process data communication modeling method based on maximum algebra - Google Patents

MVB network process data communication modeling method based on maximum algebra Download PDF

Info

Publication number
CN107395402B
CN107395402B CN201710540290.2A CN201710540290A CN107395402B CN 107395402 B CN107395402 B CN 107395402B CN 201710540290 A CN201710540290 A CN 201710540290A CN 107395402 B CN107395402 B CN 107395402B
Authority
CN
China
Prior art keywords
process data
time
mvb
matrix
bus segment
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201710540290.2A
Other languages
Chinese (zh)
Other versions
CN107395402A (en
Inventor
胡黄水
赵思远
柳虹亮
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Changchun University of Technology
Original Assignee
Changchun University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Changchun University of Technology filed Critical Changchun University of Technology
Priority to CN201710540290.2A priority Critical patent/CN107395402B/en
Publication of CN107395402A publication Critical patent/CN107395402A/en
Application granted granted Critical
Publication of CN107395402B publication Critical patent/CN107395402B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L12/00—Data switching networks
    • H04L12/28—Data switching networks characterised by path configuration, e.g. LAN [Local Area Networks] or WAN [Wide Area Networks]
    • H04L12/40—Bus networks
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L12/00—Data switching networks
    • H04L12/28—Data switching networks characterised by path configuration, e.g. LAN [Local Area Networks] or WAN [Wide Area Networks]
    • H04L12/40—Bus networks
    • H04L2012/40267—Bus for use in transportation systems
    • H04L2012/40293—Bus for use in transportation systems the transportation system being a train

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Multi Processors (AREA)

Abstract

The invention relates to an MVB network process data communication modeling method based on a maximum algebra, which adopts the maximum algebra method to establish an MVB network process data communication model meeting IEC standard, and calculates and learns that the process data communication process can not be blocked when the time interval of reading a main frame by BA is not less than the maximum value in a process data time matrix by introducing period input control. Simulation test results show that under the condition of meeting the conditions, the MVB process data communication process is free from blocking, so that the reliability of the MVB process data communication is ensured.

Description

MVB network process data communication modeling method based on maximum algebra
Technical Field
The invention relates to an MVB network process data communication modeling method, in particular to an MVB network process data communication modeling method based on maximum algebra. The method establishes a process data communication data model by analyzing the dynamic behavior of the MVB network process data. And periodic input control is introduced, the relation between the MVB network process data sending interval and the transmission time matrix and the MVB network system non-blocking is analyzed, and the reliability of MVB network process data communication is effectively improved.
Background
The MVB bus is mainly used in a train communication network, MVB Process variables reflect train states, speeds, accelerations, motor currents, operator commands, and the like, and the values of the Process variables are Process Data (Process Data), and the transmission time of the Process Data must be short and definite, so the Process Data is periodically transmitted and is unconfirmed broadcast information. Because the transmission delay of the process data has uncertainty, and the non-blocking communication of the data is the basis for ensuring the normal and reliable operation of the train, the research on the reliability of the process data communication is particularly important.
At present, more intensive research is carried out on improving the reliability of data communication in the process of the MVB network. Some methods start from the basic communication principle of MVB process data, and construct an MVB real-time scheduling table so as to improve the reliability of MVB network process data communication; some methods adopt a queuing theory to analyze the relation between the delay of process data and the MVB polling period and the communication rate; and a modeling analysis method based on a Petri network model is adopted to give message throughput, data transmission capability and bandwidth utilization rate of MVB process data.
Most of the existing methods for improving the reliability of process data transmission are realized by designing a scheduling algorithm so as to optimize a periodic scanning table. And the communication of the network is mostly modeled by Petri, Omnet + +, NS-2, Matlab and the like, the modeling is complex, and whether the network is blocked or not is difficult to determine.
Disclosure of Invention
The invention aims to solve the technical problems that the existing process data communication modeling is complex and whether the network is blocked or not is difficult to determine, a bus type open loop MVB network process data communication mathematical model is established by adopting a maximum algebra, and the controllability, the periodic steady-state characteristic and the non-blocking condition of the system under the condition of determining time parameters are analyzed by introducing periodic input control, so that the reliability of the MVB network process data communication is effectively improved.
The invention relates to a MVB network process data communication modeling method based on maximum algebra. The communication process analysis analyzes the primary basic communication process of the MVB network, and process data occupying an MVB slave device node and an MVB bus segment can be regarded as an event, so that the process data, the MVB slave device node and the MVB bus segment form a discrete event dynamic system. The communication process modeling obtains a system state equation and a system output equation which are formed by matrixes by defining system variables, introducing a maximum algebraic theory and researching the relation between the process variables and MVB bus segments or slave device node moments, introduces periodic input control and calculates to obtain that the process data communication process cannot be blocked when the time interval of reading the main frame by the BA is not less than the maximum value in a process data time matrix.
The system variables are defined input variables, state variables and output variables in the system in order to express the communication process of certain process data in the MVB network. Let u (k) be the time at which the bus manager reads out the kth main frame, xi(k) The moment when the kth process data is transmitted from the source device earliest (where i represents the ith slave node or MVB bus segment), and y (k) is the moment when the kth process data ends occupying the MVB bus. Expressed in vector form as follows: state vector X (k) ═ X1(k),x2(k),...,xn(k) ')'; output vector Y (k) is Y (k); the input vector U (k) is U (k). Time taken for kth process data to be broadcast once: t isk total＝y(k)-x1(k)。
The relationship between the process variables and the time of the MVB bus segment or the slave device node is two conditions of researching the time that the kth process data occupies the ith MVB bus segment and the slave device node at the earliest time when the buffer capacity bit is 1: if the process data broadcasted before does not occupy the ith MVB bus segment or the slave equipment node, the process data can occupy the ith MVB bus segment or the slave equipment node as long as the process data is operated in the (i-1) th MVB bus segment or the slave equipment node, and thus, the process data has the function of occupying the ith MVB bus segment or the slave equipment node
Figure GDA0001400071070000021
If the last process data still occupies the ith MVB bus segment and the slave node, and the process data is already operated in the (i-1) th MVB bus segment or the slave node, the process data needs to wait until the last process data does not occupy the ith MVB bus segment or the slave node, so that the process data has the advantages of being capable of saving the data and the data in the I-1 th MVB bus segment or the slave node
Figure GDA0001400071070000022
Since the bus manager reads the main frame periodically at a fixed time, there is a time difference τ between the end of the last process data broadcast and the time when the next main frame is read out, so that there is a time difference τ between the end of the last process data broadcast and the time when the next main frame is read out
Figure GDA0001400071070000023
Two expression forms of the operation time of the kth process variable at the ith MVB bus segment or the slave equipment node at the earliest start are obtained from the two conditions, and the state equation and the output equation of the system are obtained by discussing the value of i
The introduction period input control is that in the actual sending process of the process data, the polling time is determined, and meanwhile, the process data is ensured to finish one-time communication at certain intervals, so that the introduction period input controls an MVB network system, and two definitions are given as follows:
definition 1: setting mu as a non-epsilon number on a maximum algebra R, and making U (k) equal to mu U (k-1), then referring to U as a period input, wherein mu is a polling time interval;
definition 2: if λ ≠ - ∞ existsPositive integer n0So that
Figure GDA0001400071070000024
Then A is called a D-order lambda periodic array, where the multiplication in D is the normal addition, lambdadIs the normal d λ;
introducing periodic input control for U (k), then for any positive integer n, one can derive:
Figure GDA0001400071070000031
from the above formula, the state quantity of the system is determined by the matrixes a × F and μ E; for the convenience of analysis, a new time matrix T 'is introduced on the basis of the original process data message transmission time matrix T, and the new time matrix T' is formed by adding the message transmission time in T to the time difference tau from the end of the previous process data broadcast to the time when the next main frame is read. Wherein the matrix A x F is a periodic matrix, the characteristic value is the maximum value in T', the period order is 1,
Figure GDA0001400071070000032
also a periodic array, the order of the period is 1, and if ω is its eigenvalue, then when μ ≦ max (T '), ω ═ max (T'); when μ > max (T'), ω ═ μ; then the following conclusions can be drawn:
let λ be the characteristic value of the matrix A x F, i.e. max (T'), then n must be present when μ ≦ λ1For any n > n1X (n +1) ═ λ X (n); when μ > λ, n must be present2For any n > n2With X (n +1) ═ μ X (n), and n2Not greater than matrix
Figure GDA0001400071070000033
Dimension (d) of (a). After the periodic input control is introduced, the state quantity of the data transmission network in the whole process must enter a periodic steady state with the period of 1, and meanwhile, the input quantity of the system
Figure GDA0001400071070000034
It also enters a period steady state with period 1, which is referred toThe number depends on the maximum value of the time matrix T'.
When the time interval for the bus manager BA to read the main frame is not less than the maximum value in the process data time matrix, if the whole communication process is not blocked, for each process data, the time that the slave node or the MVB bus segment is occupied at the earliest is the time that the slave node or the MVB bus segment ends running in the previous MVB bus segment, the following expression is required to be satisfied:
Figure GDA0001400071070000035
if the time difference τ existing from the end of the previous process data broadcast to the moment when the next main frame is read out is taken into account, then:
Figure GDA0001400071070000036
can be expressed as a state equation
Figure GDA0001400071070000037
Can also be recorded as
Figure GDA0001400071070000038
In combination with the above analysis, when
Figure GDA0001400071070000039
And if U (k) is more than or equal to T '(i) + U (k-1), namely the time interval for reading the main frame by the device manager is not less than the maximum value in T', the process data communication network is free from blocking.
Drawings
FIG. 1 MVB network Process data communication of the present invention
FIG. 2 Process data working time comparison of the present invention
FIG. 3 time difference of the invention
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The maximum algebraic method principle of MVB process data communication is MThe VB network adopts a master-slave working mode, a Bus Administrator (BA) of a MVB network master device periodically reads a master frame (F _ code ═ 0-4) from a communication memory and broadcasts the master frame onto an MVB Bus, an address-related slave device (source) responds to the master frame and reads a slave frame from the communication memory of the source device for transmission, and an addressed sink device receives the slave frame, which is a basic communication process, as shown in fig. 1. The maximum algebra is a special algebra structure and is arranged in
Figure GDA0001400071070000041
Above, a set of binary operations is defined:
Figure GDA0001400071070000042
wherein
Figure GDA0001400071070000043
+ is addition in the general sense, and multiplication are usually omitted. Order to
Figure GDA0001400071070000044
Then, D is called a maximum algebra, and ε and 0 are the addition zero element and multiplication unit element of D respectively[6]。
The matrix operation of the maximum algebra is defined as:
Figure GDA0001400071070000045
wherein
Figure GDA0001400071070000046
Wherein
Figure GDA0001400071070000047
Can be recorded as sigma. Correspondingly, the square matrix A has a power of k of Ak＝AAk-1。
The communication process analysis shows that the MVB process data communication process is a process in which process data continuously has a relationship with an MVB slave device node and an MVB bus segment, and process data occupying the MVB slave device node and the MVB bus segment is regarded as an event, so that the process data, the MVB slave device node and the MVB bus segment form a discrete event dynamic system, and therefore, the MVB process data communication can be researched by using a maximum algebraic method which occupies an important position in the discrete event dynamic system.
Because the transmission time of the process data on the MVB bus and the processing time of the process data on the slave node have great regularity, a matrix formed by the transmission time of the process data message is set as T, and the T is recorded as (T ═ T)1,t2,...,tn) And in order to ensure that the MVB network system works normally, it is specified that one MVB bus segment and node are occupied by at most one process data, and because the MVB network system is a bus type network, the MVB bus segment and node can be occupied by only one process data at the same time. For the MVB bus, the slave node or the MVB bus segment is occupied by at most one process data, so the MVB network communication system can be regarded as a rigid production line system with a buffer capacity of 1.
The communication process modeling is to facilitate the communication process of expressing certain process data in the MVB network, and input variables, state variables and output variables in a system need to be defined. Let u (k) be the time at which the bus manager reads out the kth main frame, xi(k) The moment when the kth process data is transmitted from the source device earliest (where i represents the ith slave node or MVB bus segment), and y (k) is the moment when the kth process data ends occupying the MVB bus. Expressed in vector form as follows: state vector X (k) ═ X1(k),x2(k),...,xn(k) ')'; output vector Y (k) is Y (k); the input vector U (k) is U (k). Then the time it takes for the kth process data to be broadcast once is: t isk total＝y(k)-x1(k)。
Since the buffer capacity is 1, for the kth process data, the time when the ith MVB bus segment and the slave node are occupied at the earliest needs to be considered in two cases: if the process data broadcasted before does not occupy the ith MVB bus segment or the slave equipment node, the process data can occupy the ith MVB bus segment or the slave equipment node as long as the process data is operated in the (i-1) th MVB bus segment or the slave equipment nodeA node of the device, thus having
Figure GDA0001400071070000051
If the last process data still occupies the ith MVB bus segment and the slave node, and the process data is already operated in the (i-1) th MVB bus segment or the slave node, the process data needs to wait until the last process data does not occupy the ith MVB bus segment or the slave node, so that the process data has the advantages of being capable of saving the data and the data in the I-1 th MVB bus segment or the slave node
Figure GDA0001400071070000052
Since the bus manager reads the main frame periodically at a fixed time, there is a time difference τ between the end of the last process data broadcast and the time when the next main frame is read out, so that there is a time difference τ between the end of the last process data broadcast and the time when the next main frame is read out
Figure GDA0001400071070000053
Then, as can be seen from the above two cases, the operation time at the i-th MVB bus segment or slave node for the k-th process variable starting earliest can be expressed in the following two forms:
Figure GDA0001400071070000054
Figure GDA0001400071070000061
when i is 1, i.e. the kth process data occupies the first slave node earliest, it must be satisfied that the previous process variable is not occupying the first slave node, there are:
Figure GDA0001400071070000062
when i is n, i.e. the kth process variable occupies the last interval the earliest, it should be satisfied:
Figure GDA0001400071070000063
from this, the state equation and the output equation of the system are as follows:
Figure GDA0001400071070000064
the matrix A represents the relationship between the time when the kth process data occupies the current MVB bus segment or the slave node earliest and the time when the kth process data occupies the previous MVB bus segment or the slave node earliest, the matrix B represents the relationship between the time when the kth process data occupies each MVB bus segment or the slave node earliest and the time when the kth process data is ready to occupy the MVB, the matrix F represents the relationship between the time when the kth process data occupies the current MVB bus segment or the slave node earliest and the working state of the previous process data, and the matrix C represents the relationship between the time when the kth process variable completes the polling and the time when each slave node or the MVB bus segment is occupied earliest, and the matrix A represents the following relationship:
Figure GDA0001400071070000065
define A for matrix A*Operating, then the system state equation (7) can be expressed as the following expression:
Figure GDA0001400071070000066
matrix A*F represents the relationship between the state of the kth process data and the state of the (k-1) th process data, matrix A*B represents the relationship between the state of the kth process data and the time at which the process data begins to occupy the MVB bus. Equation (7) can be simplified by calculating equation (9). Matrix A*F,A*B is as follows.
Figure GDA0001400071070000071
Figure GDA0001400071070000072
From the above expression, all states of the system depend on the value of each message transmission time of the message transmission time matrix T.
The periodic input control is known from the IEC protocol, the time for the master to complete one polling is called the fundamental period, and the time interval between two consecutive transmissions of the same process data from the same source is called the signature period. The polling time is determined during the actual transmission of the process data, while ensuring that the process data completes a communication at regular intervals. The MVB network system is controlled by introducing periodic input for the purpose, and two definitions are given below.
Definition 1: let U be a non-epsilon number on the maximum algebraic R, let U (k) be μ U (k-1), then we call U a periodic input, where μ is the polling interval.
Definition 2: if λ ≠ - ∞ and there is a positive integer n0So that
Figure GDA0001400071070000073
Then a is called a d-order λ periodic array. Where the multiplication in D is ordinary addition, λdIs the normal d λ.
Introducing periodic input control for U (k) in the previous chapter (9) of equations, then for any positive integer n, one can derive:
Figure GDA0001400071070000074
from the above formula, the state quantity of the system is determined by the matrices a × F and μ E. For the convenience of analysis, a new time matrix T 'is introduced on the basis of the original process data message transmission time matrix T, and the new time matrix T' is formed by adding the message transmission time in T to the time difference tau from the end of the previous process data broadcast to the time when the next main frame is read. Wherein the matrix A x F is a periodic matrix, the characteristic value is the maximum value in T', the period order is 1,
Figure GDA0001400071070000081
also a periodic array, the order of the period is 1, and if ω is its eigenvalue, then when μ ≦ max (T '), ω ═ max (T'); when μ > max (T'), ω ═ μ. Then the following conclusions can be drawn:
let λ be the characteristic value of the matrix A x F, i.e. max (T'), then n must be present at that time1For any n > n1X (n +1) ═ λ X (n); when μ > λ, n must be present2For any n > n2With X (n +1) ═ μ X (n), and n2Not greater than matrix
Figure GDA0001400071070000082
Dimension (d) of (a). After the periodic input control is introduced, the data transmission network state quantity in the whole process must enter a stable state with the period mu being equal to or less than lambda and the period being 1, and simultaneously the input quantity of the system
Figure GDA0001400071070000083
A period steady state of period 1 is also entered, the parameters of which depend on the maximum value of the time matrix.
The performance analysis of network blocking is to ensure that the data communication process of the MVB process can be perfectly operated, and the best condition is to require the data communication process to be performed without blocking. From the above model, if the whole communication process is not blocked, the time of occupying the slave node or MVB bus segment at the earliest is the time of ending the operation in the previous MVB bus segment for each process data. Then the following expression needs to be satisfied:
Figure GDA0001400071070000084
if the time difference τ existing from the end of the previous process data broadcast to the moment when the next main frame is read out is taken into account, then:
Figure GDA0001400071070000085
can be expressed as a state equation
Figure GDA0001400071070000086
Can also be recorded as
Figure GDA0001400071070000087
In combination with the above analysis, it can be seen that the process data communication network needs to be satisfied if it is non-blocking
Figure GDA0001400071070000088
U (k) ≧ T '(i) + U (k-1), i.e., the time interval for the device manager to read the primary frame is not less than the maximum value in T'.
The present invention is further described in detail below with reference to fig. 2 and 3, wherein IEC standard specifies that the transmission delay of process data from two nodes of MVB is at most 42.7 μ s, and the difference between the maximum delay and the minimum delay between two consecutive messages cannot exceed 4.0BT (1.0BT ≈ 666.7ns), i.e. t ≈ t £ t $)1,t2,...,tnThe difference between two pairs cannot exceed 4.0BT, and the sum of the inter-frame intervals between one main frame and another main frame needs to be greater than 9.0BT, it can be found that the time difference τ between the end of the previous process data broadcast and the time when the next main frame is read is 5.0BT at most. In practice, however, the transmission delay may fluctuate, which may reduce the time interval between frames and thereby cause frame-to-frame overlap and blocking. The blocking performance of the process data communication model is analyzed, so that the characteristic periods of the (k-1) th and k-th process data can be both basic periods of 1ms, 10 polling times are selected, the starting time and the ending time of the (k-1) th process data and the starting time of the (k-1) th process data are compared, and whether the process data are blocked or not is observed. As can be seen from the simulation result fig. 2, the time when the kth process data starts to operate is always greater than the time when the previous process data ends, and it can be seen more intuitively from fig. 3 that the difference value is always kept as a positive number, that is, no blockage occurs in the communication process.
The invention adopts a maximum algebra method to establish an MVB network process data communication model which accords with the IEC standard, and calculates and learns that the process data communication process can not be blocked when the time interval of reading the main frame by the bus manager BA is not less than the maximum value in the process data time matrix by introducing period input control. Simulation test results show that under the condition of meeting the conditions, the MVB process data communication process is free from blocking, so that the reliability of the MVB process data communication is ensured.

Claims (1)

1. A MVB network process data communication modeling method based on maximum algebra is characterized in that: the method comprises the steps of analyzing and modeling the communication process; the communication process analysis analyzes the primary basic communication process of the MVB network, and process data occupying an MVB slave device node and an MVB bus segment are regarded as an event, so that the process data, the MVB slave device node and the MVB bus segment form a discrete event dynamic system; in the communication process modeling, a system state equation and a system output equation which are formed by matrixes are obtained by defining system variables, introducing a maximum algebraic theory and researching the relation between the process variables and MVB bus segments or slave device node moments, and periodic input control is introduced to calculate and obtain that when the time interval of reading a main frame by a bus manager is not less than the maximum value in a process data time matrix, the process data communication process cannot be blocked; the communication process modeling defines system variables, input variables, state variables and output variables in the system, and sets u (k) as the time when the bus manager reads out the kth main frame, xi(k) The moment when the kth process data is transmitted from the source device earliest, wherein i represents the ith slave device node or the MVB bus segment, and y (k) is the moment when the kth process data occupies the MVB bus, which is expressed in a vector form as follows: state vector X (k) ═ X1(k),x2(k),...,xn(k) ')'; output vector Y (k) is Y (k); an input vector U (k) is U (k); then the time it takes for the kth process data to be broadcast once is: t isk total＝y(k)-x1(k) (ii) a The maximum algebraic theory is introduced, the relation between the process variables and the MVB bus segment or the slave device node time is researched, and the buffering capacity is 1, so for the kth process data, the time of occupying the ith MVB bus segment and the slave device node at the earliest time needs to be considered in two situations: if the ith MVB bus segment or slave is not occupied by the previously broadcast process dataIf the spare node is in the i-1 th MVB bus segment or the slave node, the spare node can occupy the i th MVB bus segment or the slave node as long as the operation of the process data is finished in the i-1 th MVB bus segment or the slave node, so that
Figure FDA0002424319000000011
Wherein, the process data message transmission time ti-1A message transmission time matrix T is formed, and is marked as T ═ T1,t2,...,tn) (ii) a If the last process data still occupies the ith MVB bus segment and the slave node, and the process data is already operated in the (i-1) th MVB bus segment or the slave node, the process data needs to wait until the last process data does not occupy the ith MVB bus segment or the slave node, so that the process data has the advantages of being capable of saving the data and the data in the I-1 th MVB bus segment or the slave node
Figure FDA0002424319000000012
Since the bus manager reads the main frame periodically at a fixed time, there is a time difference τ between the end of the last process data broadcast and the time when the next main frame is read out, so that there is a time difference τ between the end of the last process data broadcast and the time when the next main frame is read out
Figure FDA0002424319000000013
Then, as can be seen from the above two cases, the operation time at the i-th MVB bus segment or slave node for the k-th process variable starting earliest can be expressed in the following two forms:
Figure FDA0002424319000000014
Figure FDA0002424319000000015
when i is 1, i.e. the kth process data occupies the first slave node earliest, it must be satisfied that the previous process variable is not occupying the first slave node, there are:
Figure FDA0002424319000000016
when i is n, that is, the kth process data occupies the last slave node at the earliest time, it should satisfy:
Figure FDA0002424319000000021
from this, the state equation and the output equation of the system are as follows:
Figure FDA0002424319000000022
the matrix A represents the relationship between the time when the kth process data occupies the current MVB bus segment or the slave node earliest and the time when the kth process data occupies the previous MVB bus segment or the slave node earliest, the matrix B represents the relationship between the time when the kth process data occupies each MVB bus segment or the slave node earliest and the time when the kth process data is ready to occupy the MVB, the matrix F represents the relationship between the time when the kth process data occupies the current MVB bus segment or the slave node earliest and the working state of the previous process data, and the matrix C represents the relationship between the time when the kth process variable completes the polling and the time when each slave node or the MVB bus segment is occupied earliest, and the matrix A represents the following relationship:
Figure FDA0002424319000000023
wherein epsilon is an addition zero element of a maximum algebra D;
define A for matrix A*Operating, then the system state equation (5) can be expressed as the following expression:
Figure FDA0002424319000000024
matrix A*F represents the relationship between the state of the kth process data and the state of the (k-1) th process data, matrix A*B represents the kthThe relationship between the state of the process data and the time when the process data starts to occupy the MVB bus; equation (5) can be simplified by calculating equation (7), matrix A*F,A*B are each as follows
Figure FDA0002424319000000031
Figure FDA0002424319000000032
As can be seen from the above expression, all states of the system depend on the value of each message transmission time of the message transmission time matrix T;
the introduction period input control is that in the actual sending process of the process data, the polling time is determined, and meanwhile, the process data is ensured to finish one-time communication at certain intervals, so that the introduction period input controls an MVB network system, and two definitions are given as follows:
definition 1: let mu be maximum algebra
Figure FDA0002424319000000033
If U (k) ═ μ U (k-1), then U is said to be a periodic input, where μ is the polling time interval;
is arranged at
Figure FDA0002424319000000034
Above, a set of binary operations is defined:
Figure FDA0002424319000000035
wherein
Figure FDA0002424319000000036
+ is addition in the general sense, multiplication and usually omitted; order to
Figure FDA0002424319000000037
Then, D is called a maximum algebra, ε and0 is the addition zero element and multiplication unit element of D respectively;
definition 2: if λ ≠ - ∞ and there is a positive integer n0So that
Figure FDA0002424319000000039
Then A is called a D-order lambda periodic array, where the multiplication in D is the normal addition, lambdadIs the normal d λ;
introducing periodic input control for U (k) in equation (7), then for any positive integer n, one can derive:
Figure FDA0002424319000000038
from the above formula, the state quantity of the system is determined by the matrixes a × F and μ E; for convenient analysis, a new time matrix T 'is introduced on the basis of the original process data message transmission time matrix T, and the new time matrix T' is formed by adding the message transmission time in T to the time difference tau from the end of the previous process data broadcast to the time when the next main frame is read out; wherein the matrix A x F is a periodic matrix, the characteristic value is the maximum value in T', the period order is 1,
Figure FDA0002424319000000041
also a periodic array, the order of the period is 1, and if ω is its eigenvalue, then when μ ≦ max (T '), ω ═ max (T'); when μ > max (T'), ω ═ μ; then the following conclusions can be drawn:
let λ be the characteristic value of the matrix A x F, i.e. max (T'), then n must be present when μ ≦ λ1For any n > n1X (n +1) ═ λ X (n); when μ > λ, n must be present2For any n > n2With X (n +1) ═ μ X (n), and n2Not greater than matrix
Figure FDA0002424319000000042
The dimension of (a); after the periodic input control is introduced, the state quantity of the data transmission network in the whole process must enter a periodic steady state with the period of 1, and meanwhile, the input quantity of the system
Figure FDA0002424319000000043
A periodic steady state with a period of 1 is also entered, the parameters of which depend on the maximum value of the time matrix T';
when the time interval for reading the main frame by the bus manager is not less than the maximum value in the process data time matrix, if the whole communication process is not blocked, for each process data, the time for occupying the slave node or the MVB bus segment at the earliest time is the time for finishing the operation in the previous MVB bus segment, the following expression is required to be satisfied:
Figure FDA0002424319000000044
if the time difference τ existing from the end of the previous process data broadcast to the moment when the next main frame is read out is taken into account, then:
Figure FDA0002424319000000045
can be expressed as a state equation
Figure FDA0002424319000000046
Can also be recorded as
Figure FDA0002424319000000047
In combination with the above analysis, when
Figure FDA0002424319000000048
And if U (k) is more than or equal to T '(i) + U (k-1), namely the time interval for reading the main frame by the device manager is not less than the maximum value in T', the process data communication network is free from blocking.
CN201710540290.2A 2017-07-04 2017-07-04 MVB network process data communication modeling method based on maximum algebra Active CN107395402B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710540290.2A CN107395402B (en) 2017-07-04 2017-07-04 MVB network process data communication modeling method based on maximum algebra

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710540290.2A CN107395402B (en) 2017-07-04 2017-07-04 MVB network process data communication modeling method based on maximum algebra

Publications (2)

Publication Number Publication Date
CN107395402A CN107395402A (en) 2017-11-24
CN107395402B true CN107395402B (en) 2020-05-19

Family

ID=60335056

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710540290.2A Active CN107395402B (en) 2017-07-04 2017-07-04 MVB network process data communication modeling method based on maximum algebra

Country Status (1)

Country Link
CN (1) CN107395402B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6480224B1 (en) * 1999-08-27 2002-11-12 International Truck Intellectual Property Company, L.L.C. Mobile multiplexed slow scan video system
CN103514074A (en) * 2013-09-06 2014-01-15 清华大学 MVB network card development method and platform
CN104579606A (en) * 2014-09-19 2015-04-29 长春工业大学 Redundant design method for multifunction vehicle bus (MVB) network system
CN105577478A (en) * 2016-01-05 2016-05-11 中车株洲电力机车有限公司 Train network control system based on TCN (Train Communication Network)

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6480224B1 (en) * 1999-08-27 2002-11-12 International Truck Intellectual Property Company, L.L.C. Mobile multiplexed slow scan video system
CN103514074A (en) * 2013-09-06 2014-01-15 清华大学 MVB network card development method and platform
CN104579606A (en) * 2014-09-19 2015-04-29 长春工业大学 Redundant design method for multifunction vehicle bus (MVB) network system
CN105577478A (en) * 2016-01-05 2016-05-11 中车株洲电力机车有限公司 Train network control system based on TCN (Train Communication Network)

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
《基于OMNeT++的MVB网络模型》;刘峰等;《长春工业大学学报》;20150831;第36卷(第4期);361-368 *

Also Published As

Publication number Publication date
CN107395402A (en) 2017-11-24

Similar Documents

Publication Publication Date Title
Ling Bit rate conditions to stabilize a continuous-time scalar linear system based on event triggering
Peng et al. Event-triggered communication and H∞ control co-design for networked control systems
Mamduhi et al. Error-dependent data scheduling in resource-aware multi-loop networked control systems
Yu et al. Stabilization of networked control systems with data packet dropout via switched system approach
Fu et al. Structure-aware stochastic control for transmission scheduling
Yue et al. A delay system method to design of event-triggered control of networked control systems
Tan et al. Distributed hybrid-triggered H∞ filter design for sensor networked systems with output saturations
Chen et al. A robust adaptive congestion control strategy for large scale networks with differentiated services traffic
Phan et al. Optimal scheduling over time-varying channels with traffic admission control: Structural results and online learning algorithms
Zhang et al. Wireless/wired integrated transmission for industrial cyber-physical systems: risk-sensitive co-design of 5G and TSN protocols
Van Huynh et al. Joint coding and scheduling optimization for distributed learning over wireless edge networks
Ildiz et al. Pull or wait: How to optimize query age of information
CN107395402B (en) MVB network process data communication modeling method based on maximum algebra
CN110611599A (en) Network control system and control method thereof
Yin et al. Event-triggered tracking control for discrete-time multi-agent systems
CN109672227B (en) Economic operation scheduling method for power system
Shen et al. Nonfragile H∞ output feedback control of linear systems with an event-triggered scheme against unreliable communication links
JP5372699B2 (en) In-vehicle network device
Bankhamer et al. Positive aging admits fast asynchronous plurality consensus
Tabbara et al. Networked control systems: Emulation-based design
Ruan et al. Dual-stage periodic event-triggered output-feedback control for linear systems
Zhou et al. Quantized gradient-descent algorithm for distributed resource allocation
Yu et al. Robust stabilization of nonlinear sampled-data systems
Ashjaei et al. The design and implementation of a simulator for switched ethernet networks
Naskali et al. Random network delay in model based predictive networked control systems.

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant