A control system fault injection method based on signed directed graph

Abstract

The application discloses a control system fault injection method based on a symbolic directed graph, and the steps of the method comprise the following steps: a simplified model of a single-loop control loop and signal composition and a fault scene under a constant bias fault mode are given; an SDG model graph is created according to the transfer functions of each device unit in a three-loop control loop of a telescope main shaft driving control system, and the correctness of the SDG model graph is verified; each state node is sorted according to node importance; and a fault injection position is determined according to repeated coverage of the state node by the node importance and a fault propagation path. The application provides a control system fault injection method based on a symbolic directed graph. The method combines the three-loop characteristics of the telescope main shaft driving control system, realizes that the same fault scene as that under other fault injection positions can be generated by only injecting a fault into a specific position of the system, and thus avoids invalid operations of repeatedly injecting fault signals, and improves the fault injection efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer simulation, and in particular to a fault injection method based on a signed directed graph and applicable to simulating faults of a main shaft driving control system of a telescope. BACKGROUND

[0002] The Antarctic can provide observation conditions with good seeing and little light pollution, but it is accompanied by a more extreme and harsh natural environment. In addition, the aperture of the Antarctic telescope is becoming larger and larger to pursue higher resolution, and the number of electronic components is also increasing. Both the external environment and the changes in the above themselves pose a great challenge to the stable operation of the main shaft driving control system of the telescope, greatly increasing the probability of failure during operation.

[0003] In order to reduce the occurrence of system failure, there are currently a large number of cutting-edge researches on fault-tolerant mechanism design, fault detection and diagnosis of the main shaft driving control system of the telescope at home and abroad. However, these new technical methods need a large amount of real and effective fault data to verify their effectiveness. However, the daily maintenance of the main shaft driving control system of the large telescope in the Antarctic is difficult, costly, and the actual failure probability is small, and it is difficult to obtain operation data under various fault scenarios in time. Therefore, a convenient and effective fault injection method is needed to generate fault scenario data, and then to verify the effectiveness of the fault-tolerant mechanism design, fault detection and diagnosis method of the main shaft driving control system of the telescope.

[0004] Existing fault injection methods include three platforms based on hardware, software simulation and hardware-in-the-loop, which first appeared in the field of electronics and electrical engineering, and have been applied in the fields of autonomous driving, aerospace, weapon guidance, etc. However, there are still few fault injection researches for the main shaft driving control system of the telescope. In addition, due to the existence of error compensation characteristics of the control system, when the fault signal injected into a certain module is transferred in time and space, it will no longer affect the output of the other module. SUMMARY

[0005] In view of the above problems existing in the prior art, the present application provides a control system fault injection method based on a signed directed graph.

[0006] To achieve the above purpose, the present application provides the following technical scheme:

[0007] A control system fault injection method based on a signed directed graph, comprising the following steps:

[0008] S1: Give a single-loop control loop model structure, and give a signal composition and a fault scenario under a constant bias fault mode;

[0009] S2: According to the characteristics of the three-loop control loop of the telescope main shaft driving control system, the single-loop control loop SDG model diagram is applied to the current loop, the speed loop and the position loop of the telescope main shaft driving control system respectively, so that the SDG model diagram of the whole system is created, and the correctness of the model diagram is verified through the simulation software;

[0010] S3: According to the node contraction and node coverage, the fault injection position is determined as the motor shaft torque output, the speed sensor output and the position sensor output, the fault signal is injected into the three positions, and the fault scene when other device units fail is realized.

[0011] Further, in S1, the model structure of the single-loop control loop includes four device units of the controller, the actuator, the controlled object and the sensor, when a certain device unit fails, it is defined as a fault object, the output signal thereof is decomposed into a normal output signal and a fault signal, and the two are combined in the form of algebraic superposition, and the fault signal contains the fault information of the constant bias fault mode.

[0012] Further, in S2, the transfer function and the PID algorithm of each device unit in the single-loop control loop are converted into a differential algebraic equation under the initial response, and the SDG model diagram of the single-loop control loop is obtained from the steady-state response equation.

[0013] Further, the single-loop control loop SDG model diagram constructed in S2 is applied to the current loop, the speed loop and the position loop of the telescope main shaft driving control system respectively; the output of the position loop controller is equivalent to the expected input of the speed loop, and the output of the speed loop controller is equivalent to the expected input of the current loop; the single-loop control loop SDG model diagram is modified in combination with the transfer function of each loop device unit in the three-loop control loop, and the SDG model diagram of the telescope main shaft driving control system is obtained after being connected at the beginning and the end.

[0014] Further, in S3, the state nodes are sorted according to the node contraction method from large to small in importance, and the fault injection operation is performed from the most important one, the state nodes covered by the fault propagation path generated when the fault signal is injected into the state node are observed, if all the state nodes covered by the fault propagation path have a state node that has not been covered by the fault propagation path generated by the previous fault injection operation, the injected fault signal is recorded, otherwise not; finally, a set of injected fault signals is obtained, and the fault injection positions are reversely deduced as the motor shaft torque output, the speed sensor output and the position sensor output.

[0015] Compared with the prior art, the beneficial effects of the present application are:

[0016] The application provides a control system fault injection method based on a signed directed graph. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a single loop control loop block diagram;

[0018] Figure 2 is a three-loop control loop block diagram of a telescope main shaft driving control system;

[0019] Figure 3 is an SDG model diagram of a single loop control loop under a steady state response;

[0020] Figure 4 is a change curve of each state node after a fault is injected in software simulation;

[0021] Figure 5 is an SDG model diagram of a telescope main shaft control system at a steady state;

[0022] Figure 6 is a two propagation paths when a T ei fault is injected;

[0023] Figure 7 is a control system fault injection method based on a signed directed graph. DETAILED DESCRIPTION

[0024] The application will be further described in detail below with reference to the drawings.

[0025] The application is supported by the National Natural Science Foundation Project "Research and Evaluation Method of Unintended State Evolution of Extremely Large Telescope Direct Driving System in Extreme Environment" (11973065), "Intelligent Research of Large Astronomical Optical Telescope Control System" (U1931207), Jiangsu Province Excellent Postdoctoral Program (2022ZB449), China Scholarship Council (CSC201904910254) and China Academy of Sciences Overseas Scholarship Fund (Xu Lingzhe).

[0026] The model graph of the signed directed graph can intuitively see the fault propagation path under the fault injection operation, and the fault propagation paths under different fault injection positions can be overlapped. In order to avoid the invalid operation of repeated injection and improve the fault injection efficiency, the fault injection position can be optimized by combining the node importance calculation. In order to better understand, the flow chart of the control system fault injection method based on the signed directed graph is shown in the figure. Figure 7

[0027] Step 1:

[0028] The single-loop control loop block diagram is shown in the figure, which can be simplified as four device units of controller, actuator, controlled object and sensor, which are potential fault objects when the system operation is disturbed. Constant deviation is used as the fault mode of the fault object. When a certain device unit fails, it is defined as a fault object, the output signal thereof can be decomposed into a normal output signal and a fault signal, and the two are combined in the form of algebraic superposition, and the fault signal contains the fault information of the constant deviation fault mode.

[0029] State variables u, q, x, x m are used as the output signals of the controller, the actuator, the controlled object and the sensor respectively; u0, q0, x0, x m0 represent the normal output signals of the controller, the actuator, the controlled object and the sensor; state variables u i , q i , x i , x mi represent fault signals, since the fault mode is constant deviation, these fault signals are constants. By means of computer simulation technology, the fault of the device unit can be simulated, that is, the output signal of the fault object is artificially injected to simulate the fault, and the fault injection position is selected between the normal output signal of the fault object and the input signal of the next device unit. At this time, the fault signal u i , q i , x i , x mi is also called an injection signal, and the specific injection signal can be seen in the figure. The relationship among the output signal of the fault object, the normal output signal and the injection signal is as follows:

[0030]

[0031] It is assumed that there are z observable state variables and L fault objects, and only one device unit fails each time. When the lth (l=1, 2, …, L) device unit fails, the observation value of the zth (z=1, 2, …, Z) observation point is The fault scene is defined as the observation value set S l of all observation points under the lth fault object.​

[0032]

[0033] When the controller fails, artificially inject u after u0 in the software simulation i The observed state variables {r, e, u, q, x, x m} constitute the fault scenario when the controller fails.

[0034] Step 2:

[0035] The telescope main shaft driving control system is equivalent to a three-loop control circuit, specifically a three-loop control circuit, which is a current loop, a speed loop and a position loop, as shown in Figure 2 In order to build the SDG model diagram of the system, it is necessary to first build the SDG model diagram of the single-loop control circuit to prepare for the construction of the SDG model diagram of the telescope main shaft driving control system. The controller adopts a classic PID control algorithm as follows:

[0036]

[0037]

[0038] Without loss of generality, the transfer functions of the actuator, the controlled object and the sensor are k a , k o and k s , which are first set as constant gain coefficients, equivalent to the role of an amplifier. According to the figure, equation (3) and equation (4), the differential algebraic equation (DAE) of the single-loop control circuit under initial response is given, as shown in the first column of Table 1. Then, the differential algebraic equation of the single-loop control circuit under steady-state response is derived from e = 0 at steady-state response, as shown in the third column of Table 1. In practice, considering that the initial response is a transient process and facilitating causal analysis, the sign directed graph under steady-state response is only considered in the present application.

[0039] Table 1 DAE at different response stages and state variables matched with SDG state nodes

[0040]

[0041] The composition of the sign directed graph and the algorithm for creating the SDG model diagram according to the differential algebraic equation are introduced below.

[0042] 1) Composition of the sign directed graph

[0043] 2) Definition 1: Model diagram γ

[0044] The model diagram γ is composed of a directed graph G and a function :

[0045]

[0046] In the above formula, G is a quadruple containing the following:

[0047] A. A set of state nodes N = {n1, n2, ..., nn} m};

[0048] B. Directed edge set E = {e1, e2, ..., e...} n}, where e i Representing two nodes n k →n l The edge between;

[0049] C. A pair of adjacency symbols N→E and E→N, representing the start and end points of the edge, respectively.

[0050] and

[0051] function Mapping all directed edges in E to "+" and "-" is called... That is, E→{+,-}, where each symbol represents the positive or negative influence between the starting node and the ending node.

[0052] Definition 2: Node sample ψ

[0053] The node samples ψ on the model graph γ are the symbol set of all state nodes in N. The symbol function of the state nodes in N is called ψ(n i There are only three possible outcomes for N: N → {+, 0, -}. A detailed explanation follows:

[0054]

[0055] In the above formula, Represents state node n i The observed values, and n i The ideal normal value, This is its threshold. The sign of the state node is denoted by "+", representing that the observed value is higher than the upper limit of the normal value; similarly, "-" and "0" represent that the value is lower than the lower limit of the normal value and within the normal threshold range. If ψ(n i If ) ≠ 0, then node n i This is a valid node.

[0056] Definition 3: Branch Compatibility Theorem

[0057] When a node sample ψ is given on the model graph γ, a branch e k is consistent if it satisfies equation (7), and the fault propagation path must satisfy the branch consistency theorem.

[0058]

[0059] 3) Algorithm to create SDG model graph from differential algebraic equations

[0060] A. Differential equations describing the dynamic system:

[0061] (d / dt)x i = f i (x1, x2,..., x j ,..., x M ∈ X; y1, y2,..., y l ,..., y N ∈ Y), (i = 1, 2,..., L) (8)

[0062] Create directed edges x j → x i , (j = 1, 2,..., M), y l → x i , (l = 1, 2,..., N) in the model graph γ, the symbol of each edge is the partial derivative of the equation:

[0063]

[0064] If y l has dynamic characteristics, add a separate node dy l / dt and construct a branch between it and x i . For high-order differential equations, they can be approximated as first-order differential equations with delay factors.

[0065] B. For each algebraic equation, we have:

[0066] 0 = f i (x1, x2,..., x j ,..., x M ∈ X; y1, y2,..., y l ,..., y N ∈ Y), (i = 1, 2,..., L) (10)

[0067] Since the causal relationship in the algebraic system is not clear, there may be more than one perfect matching model graph γ. In most cases, the state node is matched with which state variable is chosen according to the physical meaning. If the i-th equation is matched with x j , then construct the directed edge xk →x j (k≠j), y l →x j , (l=1,2,...,N), its symbol is and Where [·] denotes the sign-taking operation. In SDG, the sign of a state node follows a mathematical relationship: the sign of the node is equal to the sum of the products of the signs of each directed edge connected to it and the sign of the initial state node of that directed edge.

[0068]

[0069] Based on the algorithm for creating the SDG model diagram described above, first list the state variables that match the state nodes in Table 1, then calculate the signs of the directed edges, and finally obtain the SDG model diagram of the single-loop control loop under steady-state response, as shown below. Figure 3 As shown, solid arrows indicate directed edges with a "+" sign, dashed arrows indicate directed edges with a "-" sign, and gray nodes represent injected fault signals. In the software simulation, a step function is applied to the state nodes corresponding to the injected signals as a constant deviation fault mode, with an amplitude of 0.1, starting from 15 seconds. The obtained fault scenarios allow for the determination of node sample symbols. The fault propagation path based on this model graph satisfies the branch compatibility theorem, verifying the correctness of the model graph, as shown in Table 2 and... Figure 4 As shown.

[0070] Table 2. Node samples and fault propagation paths at different fault locations.

[0071]

[0072] Step 3:

[0073] With the foundation of establishing the SDG model diagram for a single-loop control system, it becomes relatively easy to establish the SDG model diagram for the telescope's main shaft drive control system. Based on the differential-algebraic equations of the SDG model diagram, an algorithm is created, combined with... Figure 2 The transfer functions of each element in the three-loop control system of the telescope spindle drive control system are shown below, resulting in the SDG model diagram of the telescope spindle drive control system, as follows. Figure 5 As shown. Similar to the verification steps of the single-loop control circuit model, the node samples of all state nodes when faults occur in different parts are observed in the software simulation. The fault propagation path based on this model diagram satisfies the branch compatibility theorem, therefore the model diagram is correct.

[0074] Step 4:

[0075] From the above analysis, in order to make all state nodes be covered by the fault propagation path, and avoid being repeatedly covered by different fault propagation paths, the fault injection position needs to be optimized to improve the fault injection efficiency. The node contraction method can be used to sort the importance of each state node in the SDG model graph from large to small, and the fault injection position is optimized according to the order.

[0076] The node contraction method is used to calculate the node importance, which is consistent with the physical meaning of device failure. The specific method is to take the change degree of the SDG model graph caused by deleting a state node as the basis for evaluating the importance of the state node, which is related to the cohesion degree α(γ) and the average path length l(γ) between state nodes. γ represents the SDG model graph, α(γ) represents the concentration degree of each state node in the model graph, and l(γ) represents the arithmetic mean of the shortest distance between all state nodes in the model graph.

[0077] According to the description of formula (5), the importance calculation method of the state node in the SDG model graph can be given:

[0078]

[0079]

[0080]

[0081] I(n i ) in formula (12) is used to evaluate the importance of state node n i , d ij in formula (14) is the shortest path between state nodes n i and n j , N is the state node set, and m is the total number of state nodes. The specific calculation steps of node importance are to delete node n i to generate a new contracted model graph γ′(n i ), and all nodes adjacent to node n i in the original γ(n i ) will converge into a new node n′ i in γ′(n i ).

[0082] Step 5:

[0083] The state nodes, already arranged in descending order of importance, are sequentially subjected to fault injection operations, starting with the most important. The state nodes covered by the fault propagation path generated when a fault signal is injected into a state node are observed. If any state node covered by this fault path has not been covered by the fault propagation path generated by the previous fault injection operation, the injected fault signal is recorded; otherwise, it is not recorded. Finally, a set of injected fault signals is obtained. The fault injection location can be deduced by reverse engineering using equation (1). This fault injection method avoids the ineffective operation of repeated injections, thereby optimizing the fault injection efficiency.

[0084] The fault propagation path is clearly visible in the SDG model diagram of the telescope's main shaft drive control system. Compared to a single-loop control system, the fault propagation path of this cascaded control system is more complex. Some state nodes are unaffected by the injection of a fault into them. For example, injecting a fault into the ω state node... i After a fault signal is received, the fault signal is directly shielded and will not affect other state nodes. Similarly, when injecting θ into the θ state node... i After a fault signal is received, other state nodes are unaffected. If state node θ is given... m Inject θ mi After a fault signal, only state node θ is affected; other state nodes remain unaffected. For example... Figure 6 As shown, in the direction of T e State Node Injection T ei Fault signals have two propagation paths: T ei →i q →u q →u r →u ccI and These two fault propagation paths will cover the fault signal i qi u qi u ri i qmi , ω mi The fault propagation path generated during injection will then be intersected with the fault propagation path generated when these fault signals are injected again. ei The fault propagation path generated by the fault signal is repeated.

[0085] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A control system fault injection method based on signed directed graph, characterized in that, The method comprises the following steps: S1: a single-loop control loop model structure is given, and signal composition and fault scenarios under a constant bias fault mode are given; S2: according to the characteristics of the three-loop control loop of the telescope main shaft driving control system, the single-loop control loop SDG model diagram is applied to the current loop, the speed loop and the position loop of the telescope main shaft driving control system respectively, so as to create the SDG model diagram of the whole system, and the correctness of the model diagram is verified through simulation software; S3: according to node contraction and node coverage, the fault injection positions are determined as motor shaft torque output, speed sensor output and position sensor output, and fault signals are injected into the three positions, so as to realize the fault scenarios when other device units fail.

2. The control system fault injection method based on signed directed graph according to claim 1, characterized in that, In S1, the model structure of the single-loop control loop comprises four device units, namely a controller, an actuator, a controlled object and a sensor, when a certain device unit fails, it is defined as a fault object, its output signal is decomposed into a normal output signal and a fault signal, and the two are combined in the form of algebraic superposition, and the fault signal contains fault information of the constant bias fault mode.

3. The control system fault injection method based on signed directed graph according to claim 1, characterized in that, In S2, the transfer functions and PID algorithms of the device units in the single-loop control loop are converted into differential algebraic equations under initial response, and the SDG model diagram of the single-loop control loop is obtained from the steady-state response equation.

4. The control system fault injection method based on signed directed graph according to claim 1, characterized in that, The single-loop control loop SDG model diagram constructed in S2 is applied to the current loop, the speed loop and the position loop of the telescope main shaft driving control system respectively; the output of the position loop controller is equivalent to the expected input of the speed loop, and the output of the speed loop controller is equivalent to the expected input of the current loop; the single-loop control loop SDG model diagram is modified in combination with the transfer functions of the device units in the three-loop control loop, and the SDG model diagram of the telescope main shaft driving control system is obtained after being connected at the beginning and the end.

5. The control system fault injection method based on signed directed graph according to claim 1, characterized in that, In S3, the state nodes are sorted according to the node contraction method from large to small in importance, and the fault injection operation is performed from the most important one, the fault propagation path generated when the fault signal is injected into the state node is observed, if all the state nodes covered by the fault propagation path have not been covered by the fault propagation path generated by the previous fault injection operation, the injected fault signal is recorded, otherwise it is not recorded; Finally, a set of injected fault signals is obtained, and the fault injection positions are reversely deduced as the motor shaft torque output, the speed sensor output and the position sensor output.

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