CN108153262B - Chemical production control system - Google Patents
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Abstract
The invention belongs to the technical field of chemical production systems, and discloses a chemical production control system which is provided with: the monitoring system comprises a control module, a monitoring module and an acquisition/control module; the control module is connected with the monitoring module through a programmable controller; the control module comprises a data server, a historical data station, an engineer station, an operator station, a patrol inspector station and a dispatcher station; the data server, the engineer station, the operator station, the patrol inspector station and the dispatcher station are connected with a pair of mutually redundant Ethernet; the monitoring module comprises an on-site monitoring module, a remote monitoring module and a centralized monitoring module; the acquisition/control module is connected with the production/control object module. The invention has the advantages of high control precision, reliability, flexibility and openness, and can ensure the normal operation of the system to the maximum extent and reduce the risk of system paralysis by the centralized dispersion through the electric automation control such as field monitoring, remote monitoring, centralized monitoring and the like.
Description
Technical Field
The invention belongs to the field of chemical production systems, and particularly relates to a chemical production control system.
Background
At present, along with the production scale of chemical enterprises and the gradual expansion of realizable functions, the scale and the complexity of a production device configured by the chemical production are greatly improved, under the environment, the production control is carried out only by manpower, the production requirements of the chemical enterprises cannot be met, the information technology is sent out and the application thereof in multiple fields enables the chemical production automation to be more and more popularized, and the product production control of the chemical enterprises is gradually sent out to the direction of automation, intellectualization, scale and complication. The distributed control system which is launched by various comprehensive technologies such as various network technologies, communication technologies, control technologies, display technologies and the like is widely applied to chemical production control. The control system can automatically manage and control various devices in chemical production, can effectively improve the production efficiency of enterprises, reduce the management cost, save the energy consumption, can also provide inexhaustible power for continuous station issuance of the enterprises, and is a core means for the control of the modern chemical production. At present, the existing control system needs a larger memory and has a slower response speed.
With the rapid development of science and technology and the continuous improvement of industrial requirements, the complexity of various software and hardware designs is increasing, and the requirements on reliability and safety are also increasing. The reliability, safety and correctness of the system have received a great deal of attention from the scientific and industrial community. Formal verification and testing is the primary method to solve this problem. Formal verification methods began in the study of Floyd, Hoare, and Manna, etc., in terms of program specification and validation at the end of the 60's 20 th century. Formal verification methods fall into two broad categories: theorem-based certification and model-based. Model checking (Modelchecking) proposed in the beginning of the 20 th century and the 80 th era belongs to a formal verification method based on models, has relatively simple thought and high automation degree, and can be widely used for verification of hardware circuit systems and network protocol systems. The model detection is to model the system into a finite state transition system, describe the verified specification by temporal logic, perform an exhaustive search on the finite state transition system, determine whether the specification is satisfied, and if not, give a counter example to indicate why the specification is not satisfied. Model detection faces the problem of state explosion, i.e. the number of system states increases exponentially with the increase of the state scale. Researchers in this field use various methods to reduce the state space of the search, and abstract model detection based on counter example guidance is a common technique. The procedure of the counter-example-Guided Abstraction reference (CEGAR) technique is as follows: given a model and properties, an abstract model is first generated by an abstract method. The abstract model may contain more behavior than the original model, but the abstract model is simpler in structure and description than the original model, and therefore the state space explosion problem can be alleviated. A model detector is then invoked to detect whether the formula is valid in the abstract model. If valid, the program terminates; otherwise, a counterexample path is given, and then a reconstruction (reconstruction) process is carried out, namely in the original model, if a path corresponding to the counterexample path is found successfully, the procedure is ended; otherwise, the counterexample path is a false counterexample path, the next iteration process starts, the abstract model is regenerated again, and verification is carried out. This process is repeated until either a valid or invalid return is made or the state space explosion causes the program to stop. Dynamic symbol execution is a test instrument that combines symbol execution with concrete execution. Symbolic execution refers to representing values of program variables with symbolic values without executing a program, and then simulating program execution to perform correlation analysis. First, a Control Flow Graph (CFG) is constructed for a code to be analyzed, which is an abstract data structure inside a compiler that represents a program process by a directed Graph. And (3) starting simulation execution from an entry node on the CFG, judging which branch is feasible by using a constraint solver when a branch node is encountered, realizing traversal analysis of all paths in the process according to a pre-designed path scheduling strategy, and finally outputting an analysis result of each executable path. Dynamic symbolic execution takes a specific numerical value as an input, simultaneously starts a code simulation executor, and collects all symbolic constraints from predicates of branch statements of a current path. Then, a new feasible path constraint is constructed according to a branch in the strategy reversal constraint, a feasible new specific input is solved by using a constraint solver, and then the symbolic execution engine carries out a new round of analysis on the new input value. By using this method of iteratively generating new inputs with inputs, theoretically all possible paths can be calculated and analyzed once. The main bottleneck of the dynamic symbolic execution technique is the path explosion problem, i.e. as the number of branches in the program increases, the paths increase exponentially. Interpolation is an effective method for relieving the path explosion problem, mainly is a concept of pruning search, and marks interpolation for line nodes by using an infeasible path, wherein the interpolation means that conditional constraint marked as an error line cannot be reached. For a branch node, if every branch of the node is explored, the interpolation marked at the node is full interpolation, otherwise, half interpolation is performed. In the dynamic symbolic execution, if the path constraint from the starting node to the current node meets the full interpolation value of the current node, the path can be merged, namely, the path is not explored, so that the path explosion problem is effectively relieved. For a large-scale system, the number of thinning times of the abstract model during verification is too large, and the bottleneck of model detection is the problem of state explosion, so that the method for effectively and quickening the verification of the abstract model is not easy to provide.
In summary, the problems of the prior art are as follows: the required memory is large, the corresponding speed is slow, the centralization degree is high, the whole system is easy to be paralyzed after a certain part has a problem, and the requirement of a producer cannot be met.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a chemical production control system.
The invention is realized in such a way that a chemical production control system is provided with:
the system comprises a control module, a programmable controller, a monitoring module, an acquisition/control module and a production/control object module, wherein the control module is connected with the monitoring module through the programmable controller.
The control module comprises a data server, a historical data station, an engineer station, an operator station, an inspector station and a dispatcher station, wherein the data server, the engineer station, the operator station, the inspector station and the dispatcher station are connected with a pair of mutually redundant Ethernet.
The monitoring module comprises an on-site monitoring module, a remote monitoring module and a centralized monitoring module, and the acquisition/control module is connected with the production/control object module.
The control method of the programmable controller comprises the following steps:
1) generating a control flow graph CFG according to a program to be verified, adding 3 attributes of R interpolation, S interpolation and E interpolation to nodes in the CFG, wherein the R interpolation is a constraint condition that the nodes can reach, and judging the accessibility of one state; s interpolation and E interpolation are used for stipulating paths, and verification of a program is accelerated; adding an attribute W to an edge of the CFG; the W value of one edge represents the number of branches which are not traversed in the subgraph which takes the node pointed by the edge as a root node;
2) generating an abstract reachable graph ARG according to the generated CFG, if a new state s is generated along a path, if R interpolation corresponding to s is satisfied, indicating that the state s is reachable, and continuously traversing the path along the state s; otherwise, if the state s is not reachable, the path is terminated and other paths are traversed; for an accessible state s, if the E interpolation corresponding to the state s is implied by the path formula corresponding to the path, the fact that a path reaching the target state exists along the state is indicated, and the procedure is unsafe; if S interpolation corresponding to the state S is contained, all paths taking the state as a starting point are safe, and a program does not need to be searched along the state S; if the state S is reachable and neither the E interpolation nor the S interpolation is implied, continuing to traverse the path along the state S;
3) in the process of generating the ARG, a counter-example path is found, and when the target state is reached, whether the counter-example path is false needs to be further judged; if the program is not a false counterexample, the program is unsafe; otherwise, according to the false counter example, refining the model, respectively calculating and updating the R interpolation, the S interpolation and the E interpolation of the corresponding states, and executing the regeneration of the ARG until a true counter example path is found or no counter example path exists.
4) Adding attributes to nodes in the CFG by adopting a construction method of a fourth-order quartic B spline interpolation curve for R interpolation, S interpolation and E interpolation; the method specifically comprises the following steps:
an extended partition of a given interval [ a, b ]:
t-6≤t-4≤t-2≤a＝t0＜t1＜…＜t2i＜t2i+1＜…＜t2m-1＜t2m＝b≤t2(m+1)≤t2(m+2)≤t2(m+3)；
and de Boor control vertex sequence:
d-1,d0,d1,d2,…,dm,dm+1；
over the interval [ a, b ] with:
{t-6,t-4,t-2,t0,t2,…,t2i,…,t2(m-1),t2m,t2(m+1),t2(m+2),t2(m+3)}；
the fourth-order quartic B-spline curve for a spline node is noted as:
wherein the B-spline basis function omegaj(t) spline nodes on the support are:
t2(j-2),t2(j-1),t2j,t2(j+1),t2(j+2)，j＝-1,0,1,…,m+1；
on the basis of r (t), a fourth-order quartic B spline interpolation curve r is constructedI(t) so that it passes through the pattern value point sequence { dkAnd (4) that an interpolation condition is met:
rI(t2k)＝dk,k＝0,1,2,…,m；
connecting two ends r (t) of the curve segment r (t)2i) And r (t)2i+2) The straight line segment of (a) is noted as:
connecting two adjacent de Boor points diAnd di+1The straight line segment of (a) is noted as:
deployment function
The expression of (a) is:
wherein ei0Is a free parameter that is a function of,
further, the method for constructing the fourth-order quartic B-spline interpolation curve adopted by the R interpolation, the S interpolation and the E interpolation further comprises the following steps:
selecting a blending function, making a straight line connecting two end points between the spline cells and a straight line connecting two adjacent de Boor control vertexes and corresponding to the straight line, and making a difference between a point on a spline curve between the spline cells and a point on the straight line connecting the two end points between the spline cells to obtain an increment vector;
translating the incremental vector to a straight line connecting two adjacent de Boor control vertexes after expansion to obtain an interpolation curve of interpolation between various sample cells in the de Boor control vertexes;
and generating a corresponding interpolation curve by using an increment expansion translation method for the fourth-order quartic B spline curve, wherein the fitting function of the interpolation curve contains a free parameter and is a fourth-order quartic B spline polynomial.
Further, the method for constructing the interpolation curve comprises the following steps:
given set value point column d0,d1,d2,…,dmSupplementary auxiliary point d-2,d-1… and dm+1,dm+2…, the spline junction sequence is:
…≤t-1≤a＝t0＜t1＜t2＜…＜tm-1＜tm＝b≤tm+1≤…；
will { d }jTaking the curve as a de Boor control vertex sequence to obtain an n-order B spline curve, and recording the curve as:
wherein N isj,n(t) is an n-th order B-spline basis function whose support is set to an interval
Is a real number
Getting the whole;
constructional curve dI(t), the interpolation condition is satisfied:
dI(tk)＝dk,k＝0,1,2,…,m；
spline subinterval [ t ] at each intervali,ti+1](i-0, 1,2, …, m-1) connecting two end points d (t) of the B-spline curve segment d (t)i) And d (t)i+1) Is denoted by li(t), the equation is:
li(t)＝(1-Φi(t))d(ti)+Φi(t)d(ti+1),ti≤t≤ti+1；
and connecting two adjacent de Boor points diAnd di+1Is marked as Li(t), the equation is:
li(t)＝(1-Φi(t))d(ti)+Φi(t)d(ti+1),ti≤t≤ti+1；
Li(t)＝(1-Φi(t))di+Φi(t)di+1,ti≤t≤ti+1；
drawing a curved line segment d (t) and a straight line segment li(t) in the interval [ ti,ti+1]The difference vector of (a):
i(t)＝d(t)-li(t),ti≤t≤ti+1；
expanding and contracting the difference vector to obtain αi(t), α > 0, and translating it so that its origin falls on the straight line segment
At the corresponding point, namely:
dI(t)＝Li(t)+αi(t),ti≤t≤ti+1,i＝0,1,2,…,m-1；
or written as:
dI(t)＝[(1-Φi(t))di+Φi(t)di+1]+α[d(t)-(1-Φi(t))d(ti)-Φi(t)d(ti+1)]；
ti≤t≤ti+1,i＝0,1,2,…,m-1；
function phii(t) satisfies the following condition:
Φi(t) in the interval [ ti,ti+1]Has a continuous derivative up to order n-2;
obtaining:
Φi(t) in the interval [ ti,ti+1]Is a monotonically increasing function to avoid straight line segments li(t) and Li(t) the appearance of heavy nodes.
Further, according to the program to be verified, generating a control flow graph CFG, and initializing the attributes of nodes and edges, comprising the following steps:
(1) finding a target node in the CFG, and traversing the CFG from the target node in a reverse direction, wherein the traversed node and the traversed edge are reserved, and the nodes and the edges which are not traversed are deleted;
(2) obtaining the CFG after cutting, initializing values of attributes, initializing three interpolation values of each node, traversing the CFG for the first time, and generating the ARG, wherein the initial value of the R interpolation of each node is { true }; for S-interpolation, a doublet of (F, I) is defineds) Wherein, the value range of F is { full, half }, IsThe value of (a) is a conjunct composed of predicates; for a node l, if l has no successor node or S interpolation of all successor nodes of l is full, which is denoted as f, indicating that all successor nodes of l are traversed, then S interpolation of l is also full, otherwise, S interpolation of l is half, which is denoted as h, and the specific form is as follows:
l is an endpoint, and the initial value of S interpolation is (full, true), which indicates that the path must be safe if the endpoint is reached; l is a target node, the initial value of S interpolation is (full, false), which indicates that if the target node is reached, the path is a certain counterexample path; for other nodes, the initial value of S interpolation is (half, true), and the specific form is as follows:
l is a target node, and the initial value of the E interpolation is true, which indicates that the path is a true counter example; l is a terminal node, and the initial value of the E interpolation is false, which indicates that the path cannot reach a target node; for other nodes, the initial value of the E interpolation is false, and the target node cannot be reached initially; for each migrated W attribute, the initial value is ^ T, which indicates that traversal has not started, wherein the value range of W is { N +,. T }, and N + is a positive integer set.
Further, in the step 2), the traversal order of the branch edges is determined by using the W attribute, and meanwhile, the verification efficiency is accelerated by using the S interpolation and the E interpolation, and the specific steps include:
(1) obtaining an accessible state s', and generating a subsequent state according to the transfer relation of the CFG; if a plurality of possible successors exist, determining a traversal order according to the W value of the edge; the priority of the W value of an edge is: (>0)>⊥>0; if the W values of the edges are the same, randomly selecting; for a subsequent state s, according to the R interpolation, if the state s is not reachable, the current path is terminated, and other paths are traversed; if the current state s can be reached, firstly judging whether the E interpolation of s is false; if false, s [0] is indicated]The subsequent node is not traversed and jumps to the step (2); if not false, firstly, the SSA principle is adopted, each variable is assigned at most once, and the initial state s is obtained0Formula of path to s, denoted as Pf(s0…, s); judging P with solverf(s0…, s) whether or not E interpolation of s is implied; if yes, the program has a true counter example, the program is unsafe, and the verification is finished; otherwise, jumping to (2);
(2) s interpolation of S is judged to beWhether the interpolation is full; if not, jumping to (3); if full interpolation is used, the initial state s is obtained0Formula of path to s, denoted as Pf(s0…, s), then judging P with a solverf(s0…, S) whether or not S interpolation of S is implied; if yes, all paths with the state s as a starting point are safe, exploration is not needed, the current path is terminated, and other paths are traversed;
(3) judging whether the s is in a target state, if so, finding a counterexample path, and executing the step 3); if not, further judging whether s is covered by other states; if s is covered, traversing other paths without exploring the current path; if s is not covered, continuing to explore the current path;
(4) if the reachable state which is not traversed exists, jumping to (1); otherwise, the verification is finished and the program is safe.
Furthermore, the acquisition/control module is used for directly acquiring data and controlling functions of production objects, control objects and the like, transmitting the acquired data information of the production/control object module to the monitoring module in a centralized manner for analysis, and downloading and receiving control instructions and operation commands transmitted by the monitoring module to perform industrial control on specific objects.
Furthermore, the control module can provide software and hardware support for the whole system to assist in completing functions of production management, trial production operation and the like, monitors each link in the whole production process, summarizes, analyzes and files production control data, and enhances the automation office level of chemical enterprises.
Further, the on-site monitoring of the party is that the staff supervises the operation condition of the equipment through own experience before controlling the system.
Furthermore, the centralized monitoring has the advantages that the centralized management and the maintenance of the control system are convenient, the design scheme of the centralized management electric automation control system is relatively simple and easy to understand, and the protection requirement of the protection station is not high.
Furthermore, the remote monitoring can reduce the installation cost and save the investment of equipment such as materials, cables and the like.
The motor drives the crawler belt to rotate and controls the forward switch and the reverse switch, so that a practicer can press legs at will, can freely master the leg pressing force, improves the exercise enthusiasm and promotes the health of the body.
The invention has the advantages and positive effects that: the invention makes full use of the information provided by the false counterexample path in the model detection, and improves the detection efficiency by calculating S interpolation and E interpolation, so that the model detection algorithm can be better applied to large-scale programs; s interpolation can judge whether all possible path sequences subsequent to one state are safe or not, so that unnecessary exploration is avoided, and the state number of the ARG is greatly reduced; the E interpolation can be used for quickly judging whether a true counter example path exists in the program or not, so that the verification of the program is accelerated, and the efficiency is improved.
The invention cuts useless nodes and edges in the CFG, further reduces the ergodic state space, and adds the W attribute on the edges of the CFG, so that the efficiency of program verification is further improved. The path search space during verification of the abstract model is reduced, so that the problem of state explosion is relieved, and the verification efficiency is accelerated. Meanwhile, two kinds of optimization operation are provided, so that the verification process is more efficient; the method is mainly applied to formalized verification of correctness of software and hardware systems designed in the fields of industry, scientific research and the like, and formalized verification of safety and reliability of various communication protocols.
The interpolation curve construction method based on the B spline provided by the invention constructs a double four-order quartic B spline interpolation curved surface which is interpolated on a control vertex grid on a rectangular domain by using incremental stretching translation and tensor product methods, and the construction method of the interpolation curve/curved surface is concise, obvious in geometric significance, compatible with a BURBS method and meaningful for geometric modeling. The invention provides a new geometric modeling method, which solves the problem of interpolation control vertex and has important significance for chemical production control engineering.
Drawings
FIG. 1 is a schematic structural diagram of a chemical production control system according to an embodiment of the present invention;
in the figure: 1. a control module; 2. a programmable controller; 3. a monitoring module; 4. an acquisition control module; 5. a production/control object module; 6. a field monitoring module; 7. a remote monitoring module; 8. and a centralized monitoring module.
Detailed Description
In order to further understand the contents, features and effects of the present invention, the following embodiments are illustrated and described in detail with reference to the accompanying drawings.
The structure of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1, a chemical production control system provided in an embodiment of the present invention includes: the system comprises a control module 1, a programmable controller 2, a monitoring module 3, an acquisition/control module 4 and a production/control object module 5, wherein the control module 1 is connected with the monitoring module 3 through the programmable controller 2.
The control module 1 comprises a data server, a historical data station, an engineer station, an operator station, an inspector station and a dispatcher station, wherein the data server, the engineer station, the operator station, the inspector station and the dispatcher station are connected with a pair of mutually redundant Ethernet.
The monitoring module 3 comprises an on-site monitoring module 6, a remote monitoring module 7 and a centralized monitoring module 8, and the acquisition/control module 4 is connected with the production/control object module 5.
The acquisition/control module 4 is used for directly acquiring data and controlling functions of production objects, control objects and the like, transmitting the acquired data information of the production/control object modules to the monitoring module in a centralized manner for analysis, and downloading and receiving control instructions and operation commands transmitted by the monitoring module to perform industrial control on specific objects.
The control module 1 can provide software and hardware support for the whole system to assist in completing functions of production management, trial production operation and the like, monitors each link in the whole production process, summarizes, analyzes and files production control data, and enhances the automatic office level of a chemical enterprise.
The on-site monitoring module 6 is used for monitoring the running condition of the equipment by staff through own experience before controlling the system.
The centralized monitoring module 8 has the advantages that the centralized management and maintenance of the control system are facilitated, the design scheme of the centralized management electric automation control system is relatively simple and easy to understand, and the protection requirement of the protection station is not high.
The remote monitoring module 7 can reduce the installation cost and save the investment of equipment such as materials, cables and the like.
The invention has the advantages of high control precision, reliability, flexibility and openness, and can ensure the normal operation of the system to the maximum extent and reduce the risk of system paralysis by the centralized dispersion through the electric automation control such as field monitoring, remote monitoring, centralized monitoring and the like.
The control method of the programmable controller comprises the following steps:
1) generating a control flow graph CFG according to a program to be verified, adding 3 attributes of R interpolation, S interpolation and E interpolation to nodes in the CFG, wherein the R interpolation is a constraint condition that the nodes can reach, and judging the accessibility of one state; s interpolation and E interpolation are used for stipulating paths, and verification of a program is accelerated; adding an attribute W to an edge of the CFG; the W value of one edge represents the number of branches which are not traversed in the subgraph which takes the node pointed by the edge as a root node;
2) generating an abstract reachable graph ARG according to the generated CFG, if a new state s is generated along a path, if R interpolation corresponding to s is satisfied, indicating that the state s is reachable, and continuously traversing the path along the state s; otherwise, if the state s is not reachable, the path is terminated and other paths are traversed; for an accessible state s, if the E interpolation corresponding to the state s is implied by the path formula corresponding to the path, the fact that a path reaching the target state exists along the state is indicated, and the procedure is unsafe; if S interpolation corresponding to the state S is contained, all paths taking the state as a starting point are safe, and a program does not need to be searched along the state S; if the state S is reachable and neither the E interpolation nor the S interpolation is implied, continuing to traverse the path along the state S;
3) in the process of generating the ARG, a counter-example path is found, and when the target state is reached, whether the counter-example path is false needs to be further judged; if the program is not a false counterexample, the program is unsafe; otherwise, according to the false counter example, refining the model, respectively calculating and updating the R interpolation, the S interpolation and the E interpolation of the corresponding states, and executing the regeneration of the ARG until a true counter example path is found or no counter example path exists.
4) Adding attributes to nodes in the CFG by adopting a construction method of a fourth-order quartic B spline interpolation curve for R interpolation, S interpolation and E interpolation; the method specifically comprises the following steps:
an extended partition of a given interval [ a, b ]:
t-6≤t-4≤t-2≤a＝t0＜t1＜…＜t2i＜t2i+1＜…＜t2m-1＜t2m＝b≤t2(m+1)≤t2(m+2)≤t2(m+3)；
and de Boor control vertex sequence:
d-1,d0,d1,d2,…,dm,dm+1；
over the interval [ a, b ] with:
{t-6,t-4,t-2,t0,t2,…,t2i,…,t2(m-1),t2m,t2(m+1),t2(m+2),t2(m+3)}；
the fourth-order quartic B-spline curve for a spline node is noted as:
wherein the B-spline basis function omegaj(t) spline nodes on the support are:
t2(j-2),t2(j-1),t2j,t2(j+1),t2(j+2)，j＝-1,0,1,…,m+1；
on the basis of r (t), a fourth-order quartic B spline interpolation curve r is constructedI(t) passing it through the model valuesDot array { dkAnd (4) that an interpolation condition is met:
rI(t2k)＝dk,k＝0,1,2,…,m；
connecting two ends r (t) of the curve segment r (t)2i) And r (t)2i+2) The straight line segment of (a) is noted as:
connecting two adjacent de Boor points diAnd di+1The straight line segment of (a) is noted as:
deployment function
The expression of (a) is:
wherein ei0Is a free parameter that is a function of,
further, the method for constructing the fourth-order quartic B-spline interpolation curve adopted by the R interpolation, the S interpolation and the E interpolation further comprises the following steps:
selecting a blending function, making a straight line connecting two end points between the spline cells and a straight line connecting two adjacent de Boor control vertexes and corresponding to the straight line, and making a difference between a point on a spline curve between the spline cells and a point on the straight line connecting the two end points between the spline cells to obtain an increment vector;
translating the incremental vector to a straight line connecting two adjacent de Boor control vertexes after expansion to obtain an interpolation curve of interpolation between various sample cells in the de Boor control vertexes;
and generating a corresponding interpolation curve by using an increment expansion translation method for the fourth-order quartic B spline curve, wherein the fitting function of the interpolation curve contains a free parameter and is a fourth-order quartic B spline polynomial.
Further, the method for constructing the interpolation curve comprises the following steps:
given set value point column d0,d1,d2,…,dmSupplementary auxiliary point d-2,d-1… and dm+1,dm+2…, the spline junction sequence is:
…≤t-1≤a＝t0＜t1＜t2＜…＜tm-1＜tm＝b≤tm+1≤…；
will { d }jTaking the curve as a de Boor control vertex sequence to obtain an n-order B spline curve, and recording the curve as:
wherein N isj,n(t) is an n-th order B-spline basis function whose support is set to an interval
Is a real number
Getting the whole;
constructional curve dI(t), the interpolation condition is satisfied:
dI(tk)＝dk,k＝0,1,2,…,m；
spline subinterval [ t ] at each intervali,ti+1](i-0, 1,2, …, m-1) connecting two end points d (t) of the B-spline curve segment d (t)i) And d (t)i+1) Is denoted by li(t), the equation is:
li(t)＝(1-Φi(t))d(ti)+Φi(t)d(ti+1),ti≤t≤ti+1；
and connecting two adjacent de Boor points diAnd di+1Is marked as Li(t), the equation is:
li(t)＝(1-Φi(t))d(ti)+Φi(t)d(ti+1),ti≤t≤ti+1；
Li(t)＝(1-Φi(t))di+Φi(t)di+1,ti≤t≤ti+1；
drawing a curved line segment d (t) and a straight line segment li(t) in the interval [ ti,ti+1]The difference vector of (a):
i(t)＝d(t)-li(t),ti≤t≤ti+1；
expanding and contracting the difference vector to obtain αi(t), α > 0, and translating it so that its origin falls on the straight line segment
At the corresponding point, namely:
dI(t)＝Li(t)+αi(t),ti≤t≤ti+1,i＝0,1,2,…,m-1；
or written as:
dI(t)＝[(1-Φi(t))di+Φi(t)di+1]+α[d(t)-(1-Φi(t))d(ti)-Φi(t)d(ti+1)]；
ti≤t≤ti+1,i＝0,1,2,…,m-1；
function phii(t) satisfies the following condition:
Φi(t) in the interval [ ti,ti+1]Has a continuous derivative up to order n-2;
obtaining:
Φi(t) in the interval [ ti,ti+1]Is a monotonically increasing function to avoid straight line segments li(t) and Li(t) the appearance of heavy nodes.
Further, the generating the CFG of the program to be verified and initializing the attributes of the nodes and edges includes the following steps:
(1) finding a target node in the CFG, and traversing the CFG from the target node in a reverse direction, wherein the traversed node and the traversed edge are reserved, and the nodes and the edges which are not traversed are deleted;
(2) obtaining the CFG after cutting, initializing values of attributes, initializing three interpolation values of each node, traversing the CFG for the first time, and generating the ARG, wherein the initial value of the R interpolation of each node is { true }; for S-interpolation, a binary group (F, I) is defineds) Wherein, the value range of F is { full, half }, IsThe value of (a) is a conjunct composed of predicates; for a node l, if l has no successor node or S interpolation of all successor nodes of l is full, which is denoted as f, indicating that all successor nodes of l are traversed, then S interpolation of l is also full, otherwise, S interpolation of l is half, which is denoted as h, and the specific form is as follows:
l is an endpoint, and the initial value of S interpolation is (full, true), which indicates that the path must be safe if the endpoint is reached; l is a target node, the initial value of S interpolation is (full, false), which indicates that if the target node is reached, the path is a certain counterexample path; for other nodes, the initial value of S interpolation is (half, true), and the specific form is as follows:
l is a target node, and the initial value of the E interpolation is true, which indicates that the path is a true counter example; l is a terminal node, and the initial value of the E interpolation is false, which indicates that the path cannot reach a target node; for other nodes, the initial value of the E interpolation is false, and the target node cannot be reached initially; for each migrated W attribute, the initial value is ^ T, which indicates that traversal has not started, wherein the value range of W is { N +,. T }, and N + is a positive integer set.
Further, in the step 2), the traversal order of the branch edges is determined by using the W attribute, and meanwhile, the verification efficiency is accelerated by using the S interpolation and the E interpolation, and the specific steps include:
(1) obtaining an accessible state s', and generating a subsequent state according to the transfer relation of the CFG; if a plurality of possible successors exist, determining a traversal order according to the W value of the edge; the priority of the W value of an edge is: (>0)>⊥>0; if the W values of the edges are the same, randomly selecting; for a subsequent state s, according to the R interpolation, if the state s is not reachable, the current path is terminated, and other paths are traversed; if the current state s can be reached, firstly judging whether the E interpolation of s is false; if false, s [0] is indicated]The subsequent node is not traversed and jumps to the step (2); if not false, firstly, the SSA principle is adopted, each variable is assigned at most once, and the initial state s is obtained0Formula of path to s, denoted as Pf(s0…, s); judging P with solverf(s0…, s) whether or not E interpolation of s is implied; if yes, the program has a true counter example, the program is unsafe, and the verification is finished; otherwise, jumping to (2);
(2) judging whether the S interpolation of the S is full interpolation or not; if not, jumping to (3); if full interpolation is used, the initial state s is obtained0Formula of path to s, denoted as Pf(s0…, s), then judging P with a solverf(s0…, S) whether or not S interpolation of S is implied; if yes, all paths with the state s as a starting point are safe, exploration is not needed, the current path is terminated, and other paths are traversed;
(3) judging whether the s is in a target state, if so, finding a counterexample path, and executing the step 3); if not, further judging whether s is covered by other states; if s is covered, traversing other paths without exploring the current path; if s is not covered, continuing to explore the current path;
(4) if the reachable state which is not traversed exists, jumping to (1); otherwise, the verification is finished and the program is safe.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications, equivalent changes and modifications made to the above embodiment according to the technical spirit of the present invention are within the scope of the technical solution of the present invention.
Claims (5)
1. The utility model provides a chemical production control system which characterized in that, chemical production control system is provided with: the system comprises a control module, a programmable controller, a monitoring module, an acquisition/control module and a production/control object module; the control module is connected with the monitoring module through a programmable controller;
the control module comprises a data server, a historical data station, an engineer station, an operator station, a patrol inspector station and a dispatcher station; the data server, the engineer station, the operator station, the patrol inspector station and the dispatcher station are connected with a pair of mutually redundant Ethernet;
the monitoring module comprises an on-site monitoring module, a remote monitoring module and a centralized monitoring module, and the acquisition/control module is connected with the production/control object module;
the control method of the programmable controller comprises the following steps:
1) generating a control flow graph CFG according to a program to be verified, adding 3 attributes of R interpolation, S interpolation and E interpolation to nodes in the CFG, wherein the R interpolation is a constraint condition that the nodes can reach, and judging the accessibility of one state; s interpolation and E interpolation are used for stipulating paths, and verification of a program is accelerated; adding an attribute W to an edge of the CFG; the W value of one edge represents the number of branches which are not traversed in the subgraph which takes the node pointed by the edge as a root node;
2) generating an abstract reachable graph ARG according to the generated CFG, if a new state s is generated along a path, if R interpolation corresponding to s is satisfied, indicating that the state s is reachable, and continuously traversing the path along the state s; otherwise, if the state s is not reachable, the path is terminated and other paths are traversed; for an accessible state s, if the E interpolation corresponding to the state s is implied by the path formula corresponding to the path, the fact that a path reaching the target state exists along the state is indicated, and the procedure is unsafe; if S interpolation corresponding to the state S is contained, all paths taking the state as a starting point are safe, and a program does not need to be searched along the state S; if the state S is reachable and neither the E interpolation nor the S interpolation is implied, continuing to traverse the path along the state S;
3) in the process of generating the ARG, a counter-example path is found, and when the target state is reached, whether the counter-example path is false needs to be further judged; if the program is not a false counterexample, the program is unsafe; otherwise, according to the false counter example, refining the model, respectively calculating and updating the R interpolation, the S interpolation and the E interpolation of the corresponding states, and executing the regeneration of the ARG until a true counter example path is found or no counter example path exists;
4) adding attributes to nodes in the CFG by adopting a construction method of a fourth-order quartic B spline interpolation curve for R interpolation, S interpolation and E interpolation; the method specifically comprises the following steps:
an extended partition of a given interval [ a, b ]:
t-6≤t-4≤t-2≤a＝t0＜t1＜…＜t2i＜t2i+1＜…＜t2m-1＜t2m＝b≤t2(m+1)≤t2(m+2)≤t2(m+3)；
and de Boor control vertex sequence:
d-1,d0,d1,d2,…,dm,dm+1；
over the interval [ a, b ] with:
{t-6,t-4,t-2,t0,t2,…,t2i,…,t2(m-1),t2m,t2(m+1),t2(m+2),t2(m+3)}；
the fourth-order quartic B-spline curve for a spline node is noted as:
the spline nodes on the support of the B-spline basis function omega j (t) are as follows:
t2(j-2),t2(j-1),t2j,t2(j+1),t2(j+2)，j＝-1,0,1,…,m+1；
on the basis of r (t), a fourth-order quartic B spline interpolation curve r is constructedI(t) so that it passes through the pattern value point sequence { dkAnd (4) that an interpolation condition is met:
rI(t2k)＝dk,k＝0,1,2,…,m；
connecting two ends r (t) of the curve segment r (t)2i) And r (t)2i+2) The straight line segment of (a) is noted as:
connecting two adjacent de Boor points diAnd di+1The straight line segment of (a) is noted as:
deployment function
The expression of (a) is:
wherein ei0Is a free parameter that is a function of,
the method for constructing the fourth-order quartic B spline interpolation curve adopted by the R interpolation, the S interpolation and the E interpolation further comprises the following steps:
selecting a blending function, making a straight line connecting two end points between the spline cells and a straight line connecting two adjacent Boor control vertexes and corresponding to the straight line, and making a difference between a point on a spline curve between the spline cells and a point on the straight line connecting the two end points between the spline cells to obtain an increment vector;
translating the incremental vector to a straight line connecting two adjacent de Boor control vertexes after expansion to obtain an interpolation curve of interpolation between various sample cells in the de Boor control vertexes;
and generating a corresponding interpolation curve by using an increment expansion translation method for the fourth-order quartic B spline curve, wherein the fitting function of the interpolation curve contains a free parameter and is a fourth-order quartic B spline polynomial.
2. The chemical production control system of claim 1, wherein the method of constructing an interpolation curve comprises:
given set value point column d0,d1,d2,…,dmSupplementary auxiliary point d-2,d-1… and dm+1,dm+2…, the spline junction sequence is:
…≤t-1≤a＝t0＜t1＜t2＜…＜tm-1＜tm＝b≤tm+1≤…；
will { d }jTaking the curve as a de Boor control vertex sequence to obtain an n-order B spline curve, and recording the curve as:
wherein N isj,n(t)Is an n-th order B-spline basis function with its support set to the interval
Is a real number
Getting the whole;
constructional curve dI(t), the interpolation condition is satisfied:
dI(tk)＝dk,k＝0,1,2,…,m；
spline subinterval [ t ] at each intervali,ti+1](i-0, 1,2, …, m-1) connecting two end points d (t) of the B-spline curve segment d (t)i) And d (t)i+1) Is denoted by li(t), the equation is:
li(t)＝(1-Φi(t))d(ti)+Φi(t)d(ti+1),ti≤t≤ti+1；
and connecting two adjacent de Boor points diAnd di+1Is marked as Li(t), the equation is:
Li(t)＝(1-Φi(t))di+Φi(t)di+1,ti≤t≤ti+1；
drawing a curved line segment d (t) and a straight line segment li(t) in the interval [ ti,ti+1]The difference vector of (a):
i(t)＝d(t)-li(t),ti≤t≤ti+1；
expanding and contracting the difference vector to obtain αi(t), α > 0, and translating it so that its origin falls on the straight line segment
At the corresponding point, namely:
dI(t)＝Li(t)+αi(t),ti≤t≤ti+1,i＝0,1,2,…,m-1；
or written as:
dI(t)＝[(1-Φi(t))di+Φi(t)di+1]+α[d(t)-(1-Φi(t))d(ti)-Φi(t)d(ti+1)]
ti≤t≤ti+1,i＝0,1,2,…,m-1；
function phii(t) satisfies the following condition:
Φi(t) in the interval [ ti,ti+1]Has a continuous derivative up to order n-2;
Φi(ti)＝0，Φi(ti+1)＝1，
j＝1,2,…,n-2；
obtaining:
dI(tk)＝dk，
k＝0，1，2，…，m，j＝1，2，…，n-2；
Φi(t) in the interval [ ti,ti+1]Is a monotonically increasing function to avoid straight line segments li(t) and Li(t) the appearance of heavy nodes.
3. The chemical production control system according to claim 1,
generating a control flow graph CFG according to a program to be verified, and initializing the attributes of nodes and edges, comprising the following steps:
(1) finding a target node in the CFG, and traversing the CFG from the target node in a reverse direction, wherein the traversed node and the traversed edge are reserved, and the nodes and the edges which are not traversed are deleted;
(2) obtaining the CFG after cutting, initializing values of attributes, initializing three interpolation values of each node, traversing the CFG for the first time, and generating the ARG, wherein the initial value of the R interpolation of each node is { true }; for S interpolation, a binary group (F, Is) Is defined, wherein the value range of F Is { full, half }, and the value of Is a conjunctive expression composed of predicates; for a node l, if l has no successor node or S interpolation of all successor nodes of l is full, which is denoted as f, indicating that all successor nodes of l are traversed, then S interpolation of l is also full, otherwise, S interpolation of l is half, which is denoted as h, and the specific form is as follows:
l is an endpoint, and the initial value of S interpolation is (full, true), which indicates that the path must be safe if the endpoint is reached; l is a target node, the initial value of S interpolation is (full, false), which indicates that if the target node is reached, the path is a certain counterexample path; for other nodes, the initial value of S interpolation is (half, true), and the specific form is as follows:
l is a target node, and the initial value of the E interpolation is true, which indicates that the path is a true counter example; l is a terminal node, and the initial value of the E interpolation is false, which indicates that the path cannot reach a target node; for other nodes, the initial value of the E interpolation is false, and the target node cannot be reached initially; for each migrated W attribute, the initial value is ^ T, which indicates that traversal has not started, wherein the value range of W is { N +,. T }, and N + is a positive integer set.
4. The chemical production control system according to claim 3,
in the step 2), the traversal order of the branch edges is determined by using the W attribute, and meanwhile, the verification efficiency is accelerated by using the S interpolation and the E interpolation, and the specific steps include:
(1) obtaining an accessible state s', and generating a subsequent state according to the transfer relation of the CFG; if a plurality of possible successors exist, determining a traversal order according to the W value of the edge; the priority of the W value of an edge is: (> 0) >) 0; if the W values of the edges are the same, randomly selecting; for a subsequent state s, according to the R interpolation, if the state s is not reachable, the current path is terminated, and other paths are traversed; if the current state s can be reached, firstly judging whether the E interpolation of s is false; if false, it shows that the successor node of s [0] has not been traversed, and jumps to (2); if not false, firstly, an SSA principle is adopted, each variable is assigned at most once, and a path formula for reaching s from an initial state s0 is obtained and is marked as Pf (s0, …, s); judging whether Pf (s0, …, s) contains E interpolation of s by using a solver; if yes, the program has a true counter example, the program is unsafe, and the verification is finished; otherwise, jumping to (2);
(2) judging whether the S interpolation of the S is full interpolation or not; if not, jumping to (3); if the interpolation is full interpolation, obtaining a path formula from an initial state S0 to S, marking the path formula as Pf (S0, …, S), and judging whether the Pf (S0, …, S) contains S interpolation of S by using a solver; if yes, all paths with the state s as a starting point are safe, exploration is not needed, the current path is terminated, and other paths are traversed;
(3) judging whether the s is in a target state, if so, finding a counterexample path, and executing the step 3); if not, further judging whether s is covered by other states; if s is covered, traversing other paths without exploring the current path; if s is not covered, continuing to explore the current path;
(4) if the reachable state which is not traversed exists, jumping to (1); otherwise, the verification is finished and the program is safe.
5. The chemical production control system of claim 1, wherein the collection/control module is configured to directly perform data collection and function control on the production object and the control object, collect and transmit data information of the production/control object module to the monitoring module for analysis, and download and receive control commands and operation commands transmitted by the monitoring module to perform industrial control on specific objects.
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| CN104932474A (en) * | 2015-06-16 | 2015-09-23 | 滁州市西控电子有限公司 | Chemical production control system |
| CN106504297A (en) * | 2016-09-14 | 2017-03-15 | 陕西理工学院 | The flexible wrench tectonics method of the increment of interpolation curve or curved surface based on B-spline |
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