A method for detecting abnormality in networked motion control systems

Abstract

The present invention discloses a method for detecting abnormalities in a networked motion control system. First, the adverse effects of potential safety hazards on the system are regarded as a combined unknown disturbance signal. Then, a terminal sliding mode observer with nonlinear switching terms and an equivalent input disturbance estimator are designed. At the same time, the structure of the estimator is improved to decouple the design process of the estimator and the observer. The unknown disturbance signal is estimated in real time, and the estimation error is converged in a finite time. Then, by calculating the similarity measurement index of the disturbance estimation error under different working conditions and combining the threshold judgment method, the detection and identification of potential safety hazards in the networked motion control system are finally realized. The technical solution of the present invention effectively improves the online abnormality detection performance of the networked motion control system.

Description

Technical Field

[0001] The present application belongs to the technical field of networked control system security protection, and specifically relates to a method for detecting anomalies in a networked motion control system. Background Art

[0002] With the rapid development of computer network technology and the growing demand for intelligent transformation of control systems, networked control systems have been widely used in manufacturing, construction, aerospace, smart home and other fields. Among them, networked motion control systems, as a typical application of networked control systems in manufacturing, have greatly improved the shortcomings of traditional motion control systems, such as complex wiring, strong system coupling and poor expansion performance. However, introducing computer network technology into motion control systems is actually a double-edged sword. While computer network technology brings network dividends such as resource sharing and efficient communication to motion control systems, it also breaks the closed nature of early motion control systems, making networked motion control systems not only face traditional functional security threats such as equipment failure and failure, but also face information security threats such as man-in-the-middle attacks, worm viruses and Trojans, which in turn affect the overall control performance of the motion control system. In severe cases, it may even cause system instability, limiting the further application and promotion of networked motion control systems. Therefore, it is urgent to study security protection measures suitable for networked motion control systems to ensure their safe and stable operation and further promote the development and implementation of networked control systems.

[0003] As an active security protection measure, anomaly detection technology can effectively identify patterns in monitoring data that do not conform to the expected normal behavior definition due to network intrusion or system failure. In recent years, it has received more and more attention and attention. At present, most of the anomaly detection methods for networked control systems are based on the computer field, mainly including data-driven methods such as statistical learning, machine learning and deep learning. Although such methods have the advantages of low dependence on equipment mathematical models and high detection accuracy, in engineering practice, they are often not directly applicable to networked control systems with high real-time requirements and complex processes due to the high learning complexity of the methods, poor model interpretability and difficulty in transplantation. In addition, a large number of existing anomaly detection methods lack consideration of the dynamic characteristics of the networked control system itself, and often require a large number of abnormal samples to train the model to obtain high-precision detection results, which is difficult to meet the anomaly detection needs of industrial scenarios such as zero samples or few samples.

[0004] In fact, for a networked motion control system, if the mathematical model of its dynamic system can be accurately obtained, the disturbance estimator can be designed through the model-based disturbance estimation method, and then the nonlinear dynamics caused by external disturbances such as network intrusion or system failure can be accurately estimated, and finally the purpose of active safety protection can be achieved. Compared with the data-driven method, the model-based disturbance estimation method does not require a large number of negative samples and supports online detection, which is more suitable for networked motion control systems with high real-time requirements. In the past few decades, a large number of disturbance estimation techniques have emerged, mainly including unknown input observers, disturbance observers, extended state observers, and equivalent input disturbance methods. Among them, the equivalent input disturbance method can handle matching disturbances and non-matching disturbances at the same time, and does not require the inverse model of the object. It is an effective and novel disturbance estimation method. However, most of the existing equivalent input disturbance methods are designed from a linear perspective, which limits their estimation performance in handling nonlinear disturbances. At the same time, the estimation error of the system is linearly convergent, which makes it unable to further meet the needs of online anomaly detection. In addition, the design of the observer and the estimator is usually coupled, which increases its design difficulty in engineering applications. Therefore, how to further improve the equivalent input disturbance estimation method, decouple the design process of its observer and estimator, enable it to have nonlinear disturbance estimation capabilities, and improve the convergence performance of its estimation error, is of great practical significance for improving the anomaly detection accuracy and efficiency of networked motion control systems with potential functional safety hazards and information security hazards. Summary of the invention

[0005] In order to improve the shortcomings of existing equivalent input disturbance estimation methods in dealing with observer and estimator design, nonlinear disturbance estimation and online anomaly detection, the present application proposes an anomaly detection method for a networked motion control system. First, the adverse effects of potential safety hazards on the system are regarded as a combined unknown disturbance signal. Secondly, a terminal sliding mode observer and an equivalent input disturbance estimator with nonlinear switching terms are designed. At the same time, the structure of the estimator is improved to decouple it from the design process of the observer, and the unknown disturbance signal is estimated in real time. The estimation error is converged in a finite time. Then, by calculating the similarity measurement index of the disturbance estimation error under different working conditions and combining the threshold judgment method, the detection and identification of potential safety hazards in the networked motion control system are finally realized.

[0006] In order to achieve the above purpose, the technical solution of this application is as follows:

[0007] A method for detecting abnormality in a networked motion control system, comprising:

[0008] Collect the feedback control input signal time series and measurement output signal time series of the networked motion control system under historical normal working conditions, and obtain the estimated value of the system state under historical normal working conditions through the terminal sliding mode observer;

[0009] The equivalent input disturbance estimation value of the system is calculated by the equivalent input disturbance estimator, and the equivalent input disturbance estimation time series under the historical normal working condition of the networked motion control system is obtained, and the arithmetic average is calculated point by point as the normal working condition reference series;

[0010] Collect the feedback control input signal time series and the measurement output signal time series of the networked motion control system under the current working condition, and obtain the estimated value of the system state under the current working condition through the terminal sliding mode observer;

[0011] The equivalent input disturbance estimation value of the system is calculated by an equivalent input disturbance estimator to obtain the equivalent input disturbance estimation time series of the current working condition of the networked motion control system;

[0012] The similarity score between the reference sequence of normal working condition and the equivalent input disturbance estimation time series of current working condition is calculated, and then combined with the threshold judgment to identify whether the current working condition is in an abnormal state.

[0013] Furthermore, the terminal sliding mode observer is expressed as the following formula:

[0014]

[0015] Among them, the system state is represented by x(t), and the estimated value of the system state is represented by for The derivative of f (t) is the feedback control input, A, B, C are the system gain matrices, L is the terminal sliding mode observer gain, is the estimated value of the measured output y(t), It is a designed nonlinear switching term.

[0016] Furthermore, the equivalent input interference estimation value of the system is calculated by an equivalent input interference estimator, and the calculation formula used is expressed as follows:

[0017]

[0018] in, is the inverse Laplace transform, is the equivalent input disturbance estimation value under the decoupling strategy. The decoupling strategy selects M(s)=K h (s+1) / s, s is a complex variable, v(s), X(s) and They are and The Laplace transform of, the generalized inverse matrix B + =(B T B) -1 B T .

[0019] Furthermore, the calculating of the similarity score between the normal operating condition reference sequence and the current operating condition equivalent input disturbance estimation time series includes:

[0020] For the normal working condition reference sequence D history Equivalent input disturbance estimation time series D new Perform Fourier transform to get the set and Where Lf , is the length of the set;

[0021] The set is calculated by the following formula and The similarity between the normal working condition reference sequence and the equivalent input disturbance estimation time series of the current working condition is taken as the similarity score R s :

[0022]

[0023] in, and The collections are and collection The mean of .

[0024] The present application proposes a method for detecting anomalies in a networked motion control system, which has the following advantages: 1. By regarding the adverse effects of potential safety hazards on the system as a combined unknown disturbance signal, the anomaly detection problem of the networked motion control system is converted into an unknown disturbance estimation problem, which provides a new idea for using disturbance estimation methods in the field of automation to identify abnormal conditions of industrial control systems. 2. Compared with the traditional equivalent input disturbance method, the proposed equivalent input disturbance method based on the terminal sliding mode observer can not only handle nonlinear disturbances, but also the estimation error converges in a finite time, which effectively improves the online anomaly detection performance of the networked motion control system. 3. The decoupling strategy simplifies the design process of the observer and the estimator, making the proposed method more suitable for engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Improved block diagram of the finite time observer for this application;

[0026] Figure 2 This is a flow chart of the abnormality detection method of the networked motion control system of this application;

[0027] Figure 3 is a comparison diagram between the combined unknown disturbance signal and the estimated equivalent input disturbance;

[0028] Figure 4 Spectra and similarity scores estimated for equivalent input disturbances under different operating conditions. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0030] Reference Figure 1 This application designs an improved finite-time observer structure for abnormality detection in networked motion control systems. The improved finite-time observer structure mainly includes a controlled object, a terminal sliding mode observer with a nonlinear switching term, and an improved equivalent input disturbance estimator. Based on the design of the improved finite-time observer, the similarity factor and the threshold judgment method are combined to achieve the purpose of abnormality detection in networked motion control systems.

[0031] In one embodiment, Figure 2 As shown, a method for detecting abnormality in a networked motion control system is provided, comprising:

[0032] Step S1, collecting the feedback control input signal time series and the measurement output signal time series of the networked motion control system under the historical normal working conditions, and obtaining the estimated value of the system state under the historical normal working conditions through the terminal sliding mode observer.

[0033] This embodiment collects and records L s The processing cycle under normal working conditions is T s The networked motion control system feedback control input signal time series is denoted as And the measured output signal time series, denoted as

[0034] Then, the system state x is obtained through the designed terminal sliding mode observer. h,l Estimated value of (t) The terminal sliding mode observer is expressed as follows:

[0035]

[0036] The system state is represented by x h,l (t), the estimated value of the system state is expressed as for The derivative of h,l(t) is the feedback control input, A, B, C are the system gain matrices, L is the terminal sliding mode observer gain, is the measured output y h,l The estimated value of (t), is a designed nonlinear switching term, Its components can be further expressed as:

[0037]

[0038] Among them, α and β i is a positive integer, 1≤i≤n, sgn is the sign function, p and q are odd numbers, and p>q, The system state x h,l (t) and state estimation The first component of .

[0039] Step S2, calculate the equivalent input disturbance estimation value of the system through the equivalent input disturbance estimator, obtain the equivalent input disturbance estimation time series under the historical normal working condition of the networked motion control system, and calculate the arithmetic average point by point as the normal working condition reference sequence.

[0040] The equivalent input interference estimator designed in this embodiment calculates the equivalent input interference estimation value of the system. The equivalent input interference estimator is expressed by the formula:

[0041]

[0042] in, is the inverse Laplace transform, d h,l (t) is the equivalent input disturbance estimation value under the decoupling strategy. The decoupling strategy selects M(s) = K h (s+1) / s, s is a complex variable. In addition, v h,l (s),X h,l (s) and They are and The Laplace transform of, the generalized inverse matrix B + =(B T B) -1 B T .

[0043] Therefore, collect L s The processing cycle under normal working conditions is T s The system equivalent input disturbance estimation time series is denoted as

[0044] In this embodiment, for the system equivalent input interference estimation time series Find the arithmetic mean point by point, that is:

[0045]

[0046] Thus, the normal operating condition reference sequence is obtained The influence of randomness and chance is eliminated and it will serve as the reference sequence for the current working condition identification task.

[0047] Step S3: collecting the feedback control input signal time series and the measurement output signal time series of the networked motion control system under the current working condition, and obtaining the estimated value of the system state under the current working condition through the terminal sliding mode observer.

[0048] Step S4: Calculate the equivalent input disturbance estimation value of the system through the equivalent input disturbance estimator to obtain the equivalent input disturbance estimation time series of the current working condition of the networked motion control system.

[0049] Similarly, according to the method of step S1-2, the feedback control input signal time series and the measurement output signal time series of the networked motion control system under the current working condition are collected, and the estimated value of the system state is obtained through the terminal sliding mode observer. Then, the equivalent input disturbance estimation value of the system is calculated by the equivalent input disturbance estimator to obtain the system equivalent input disturbance estimation time series under the current working condition of the networked motion control system.

[0050] Denoted as D new ={d new (t),t∈(0,T s ]},and:

[0051]

[0052] Among them, v new (s),,X new (s) and Under the current working conditions x new (t) and The Laplace transform of, the generalized inverse matrix B + =(B T B) - 1 B T .

[0053] It should be noted that the working principle of the terminal sliding mode observer is the same under historical normal working conditions or under current working conditions, and is uniformly expressed as the following formula:

[0054]

[0055] Among them, the system state is represented by x(t), and the estimated value of the system state is represented by for The derivative of f (t) is the feedback control input, A, B, C are the system gain matrices, L is the terminal sliding mode observer gain, is the estimated value of the measured output y(t), It is a designed nonlinear switching term.

[0056] Similarly, the equivalent input disturbance estimation value of the system is calculated by the equivalent input disturbance estimator, which is uniformly expressed as the following formula:

[0057]

[0058] in, is the inverse Laplace transform, is the equivalent input disturbance estimation value under the decoupling strategy. The decoupling strategy selects M(s)=K h (s+1) / s, s is a complex variable, v(s), X(s) and They are x(t) and The Laplace transform of, the generalized inverse matrix B + =(B T B) -1 B T .

[0059] Step S5: Calculate the similarity score between the normal operating condition reference sequence and the current operating condition equivalent input disturbance estimation time series, and then combine the threshold to determine whether the current operating condition is in an abnormal state.

[0060] This embodiment introduces a similarity measurement factor to calculate the similarity score between the current working condition and the equivalent input disturbance estimation time series under the historical normal working condition, and then combines the threshold judgment to identify whether the current working condition is in an abnormal state.

[0061] Specifically, by respectively analyzing the time series D history ,D new Perform Fourier transform to get the set and Where L f , is the length of the set.

[0062] Then, we introduce the similarity measurement factor and calculate and Similarity:

[0063]

[0064] in, and The collections are and collection Finally, under the condition that the threshold is κ∈(0,1), when the calculated similarity score Rs≤κ, the current system is judged to be in an abnormal condition, otherwise, the current system is judged to be in a normal condition.

[0065] This application conducts simulation experiments on a two-degree-of-freedom networked engraving machine motion control system to verify the effectiveness of this application:

[0066] Through system identification, the state space model of the networked engraving machine motion control system can be obtained as follows:

[0067]

[0068] Among them, the matrix A o2 =diag{51.58,47.77},B o1 =[4.41 4.10] T , the identity matrix is ​​I n×n , the current system state, control input and measurement output are x o (t),u o (t) and y o (t). System (7) satisfies the observable and controllable conditions, and has no zero point on the imaginary axis. Considering that system (7) has both functional safety hazards and information security hazards, they are expressed as:

[0069] f o (t)=0.2sin(5πt),t∈[5s,20s] (8)

[0070] h o (t)=cos(5πt)+sin(2πt),t∈[10s,15s] (9)

[0071] And the matrix E=H=[I 2×2 0] T That is, the impact of potential safety hazards on the system output can be regarded as external interference applied outside the control input channel, and can be estimated in real time using the equivalent input interference method.

[0072] The parameters of the terminal sliding mode observer are configured as q = 1, p = 7, p 11 =p 12 =0.3380, p 21 =p 22 =0.0198, l 11 = l 12 =3.0137, l 21 = l 22 =17.0379, α = 0.5742, β1 = β2 = 5.3661. In addition, the configuration similarity score threshold is κ = 0.9.

[0073] Reference Figure 3 , the figure compares the potential safety hazards of the networked engraving machine motion control system with the estimated equivalent input interference. In the figure, the dotted line represents the estimated value of the equivalent input interference, and the solid line represents the given unknown interference signal. Between 5s-10s and 15s-20s, the system only has functional safety hazards, and between 10s-15s, the system has both functional safety hazards and information security hazards. It can be seen that for the adverse effects of only functional safety hazards on the system between 5s-10s and 15s-20s, the improved finite-time observer designed in this application can achieve accurate estimation, that is, the equivalent input interference estimate obtained is highly consistent with the unknown interference signal; for the system between 10s-15s, there are both functional safety hazards and information security hazards. The improved finite-time observer designed in this application has a higher sensitivity, that is, the output signal amplitude is larger.

[0074] Further references Figure 4 The figure shows the spectrum and similarity score of the equivalent input interference estimation of the networked engraving machine motion control system under four different operating conditions. Among them, the reference curve represents the normal operating condition, case (a) indicates that the system only has functional safety hazards, case (c) indicates that the system only has information security hazards, and case (d) indicates that the system has two potential safety hazards at the same time. Figure 4 It can be obtained that the potential safety hazards of the system are inversely proportional to the similarity score, and the similarity score will drop sharply as the degree of the potential safety hazards of the system increases, thereby verifying the effectiveness of the present invention in identifying abnormal working conditions of the networked engraving machine motion control system. In addition, it should be noted that the present application is not only applicable to networked engraving machine motion control systems, but also to a class of networked motion control systems whose system state space model is in the form of formula (10).

[0075] The design of the improved finite time observer in this application is further described in detail below through the evolution of the mathematical model. The design process includes the following steps:

[0076] Step 1) Establish a state space model of the networked motion control system.

[0077] like Figure 1 As shown in the figure, considering the potential functional safety hazards and information security hazards of the n-DOF networked motion control system, the state space equation of the system can be expressed as:

[0078]

[0079] in, represents the system state, x1(t), They are the position vector and velocity vector of the motion control system respectively, u(t) is the control input, and y(t) is the measurement output. represents the derivative of x(t), s -1 I -1 represents the inverse Laplace transform and I represents the identity matrix.

[0080] The adverse effects of potential functional safety hazards and information security hazards on the system are equivalent to the external interference caused by a combined unknown signal, that is, g(t) = Ef(t) + Hh(t). The state matrix of the system is The input matrix is ​​B = [0 B1] T , the output matrix is ​​C = [I n×n 0] T , the identity matrix is ​​I n×n , and the external gain matrix E = [E1 E2] T and H=[H1 H2] T In addition, the system described by equation (10) needs to meet the following assumptions: First, the system composed of the matrix (A, B, C) is observable and controllable, and has no zero point on the imaginary axis. Second, the equivalent external interference needs to meet the Lipschitz continuity condition.

[0081] Step 2) further construct a mathematical model with equivalent input disturbance for the networked motion control system.

[0082] Since the adverse effects of potential safety hazards on the system can be regarded as additive external disturbances g(t) that cause system performance degradation, according to the concept and definition of the equivalent input disturbance method, there is an equivalent input disturbance in the control input channel of the system, which makes its impact on the system output equivalent to the comprehensive effect of the additive external disturbance g(t). Therefore, system (10) can be further described as:

[0083]

[0084] Among them, d e (t) represents the equivalent input disturbance of the control input channel.

[0085] Step 3) Design a terminal sliding mode observer with nonlinear switching terms.

[0086] For system (11), the nonlinear switching term is defined as Its components can be further expressed as:

[0087]

[0088] Among them, α and β iis a positive integer, 1≤i≤n, sgn is the sign function, p and q are odd numbers, and p>q, are the system state x(t) and state estimate Secondly, for system (11), the nonlinear switching term shown in equation (12) is introduced: And construct the terminal sliding mode observer as:

[0089]

[0090] in, represents the estimated value of the system state x(t), is the estimated value of the measured output y(t), u f (t) is the feedback control input, L is the observer gain, and the state estimation error of the observer is:

[0091]

[0092] Among them, the estimated error e1=[e 11 ,e 12 ,…e 1n ] T ,e2=[e 2i , e 22 ,…,e 2n ] T .

[0093] Step 4) Based on the design of the terminal sliding mode observer, an improved equivalent input disturbance estimator is constructed to realize the decoupling design of the observer and the estimator, and at the same time, the real-time estimated value of the equivalent input disturbance is calculated.

[0094] According to formula (11) and formula (14), we can get:

[0095]

[0096] in, And the estimated value of equivalent input interference for:

[0097]

[0098] Where, Δd e (t) is the estimation error of the equivalent input disturbance.

[0099] Secondly, according to equations (13) and (15), the equivalent input interference estimate is The least squares solution of is:

[0100]

[0101] Among them, the generalized inverse matrix B + =(B T B) -1 B T It is not difficult to find that The calculation of needs to use the control input itself, so that It cannot be directly calculated by formula (17). To solve the above problem, the existing equivalent input interference method usually introduces a low-pass filter:

[0102]

[0103]

[0104] Where F(s) is a function of the complex variable s and represents a first-order low-pass filter. and They are and The Laplace transform of is the estimated value after filtering, T is the time constant of the filter, s=jω represents the corresponding relationship between Laplace transform and Fourier transform, ω is the angular frequency, ω r is the maximum angular frequency selected by the disturbance estimator. However, the introduced first-order low-pass filter has a phase lag, which will reduce the stability margin of the system. At the same time, the design process of the equivalent input disturbance estimator and observer under this structure is coupled, which increases the design difficulty of engineering applications. In order to simplify the design process of the system, this application designs an improved decoupling strategy:

[0105]

[0106]

[0107] in, and They are x(t) and The Laplace transform of For the decoupling strategy, e The design of the function M(s) is the key to the entire decoupling strategy. hour, Therefore, by properly designing M(s), As close as possible to the specified frequency range

[0108] Furthermore, according to equations (11)-(14) and (20), the estimation error dynamics is obtained as:

[0109]

[0110] From this, the characteristic polynomial of the observer is obtained as λ(s)=sI-(A-LC), where I is the unit matrix and For input and The open-loop transfer function of the subsystem with the output can be expressed as:

[0111] G op (s)=M(s)B + LC[sI-(A-LC)] -1 B (23)

[0112] Among them, the function M(s) is selected as:

[0113]

[0114] Among them, K h is the function gain. According to equations (22) and (23), the stability of the observer mainly depends on the position of the poles of the characteristic polynomial on the complex plane, while the disturbance suppression ability of the estimator depends on the design of the function M(s). Since system (1) is observable, the poles of the observer can be configured to be located in the left half plane of the complex plane by the pole configuration method, so that the observer remains stable. At the same time, the pole configuration of the observer is independent of the stability of the open-loop transfer function in equation (23), and as long as the subsystem (23) is stable, the state estimation error e(t) of the observer and the equivalent input disturbance estimation error of the estimator is bounded. Therefore, the design of the function M(s) only needs to satisfy |M(jω)|>>1, Here, let K h >> 1. Finally, the decoupled design of the observer and the estimator can be achieved, thus simplifying the overall design process.

[0115] Step 5) Based on the design of the terminal sliding mode observer and the improved equivalent input disturbance estimator, a convergence analysis of the estimation error system is given.

[0116] According to formula (22), Let matrix A0 = A-LC, and through pole placement method, matrix A0,, can be made to satisfy the Hurwitz stability criterion. In addition, the error system needs to satisfy the following assumptions: satisfies the Lipschitz continuity condition, and the Lipschitz constant satisfies It should be noted that since the external gain matrices E and H are linear, the unknown combined signal g(t) satisfies the Lipschitz continuity condition. Secondly, the impact of the equivalent input interference on the system output is equivalent to the external interference caused by the combined unknown signal, then d e (t) and It also satisfies the Lipschitz continuity condition.

[0117] According to formula (13), the stability of the terminal sliding mode observer (13) with nonlinear switching terms mainly depends on the stability of its linear part and the stability of its nonlinear part. The former can be solved by designing the observer gain matrix Make the matrix A0 satisfy the Hurwitz stability criterion, for example, select L1 = diag{l 11 ,l 12 ,…,l 1n} and L2=diag{l 21 ,l 22 ,…,l 2n On this basis, the stability of the designed terminal sliding mode observer is only related to the stability of its nonlinear part.

[0118] First, define Where P = diag{P1,P2}>0, P1 = diag{p 11 ,p 12 ,…,p 1n}, P2 = diag{p 21 ,p 22 ,…,p 2n},Φ=diag{0 n×n ,εγ 2 I n}and γ>0, and the Lyapunov function is selected as:

[0119] V(t)=e Τ (t)Pe(t) (25)

[0120] Then its derivative with respect to time can be expressed as:

[0121]

[0122] Among them, P β is defined as:

[0123] P β =[0 1×n p 21 β1sgn(e 11 (t)) … p 2n β n sgn(e 1n (t))] (27)

[0124] Using Young's inequality We can get:

[0125]

[0126]

[0127] Substituting equations (28) and (29) into equation (26), we can obtain:

[0128]

[0129] because Then we have:

[0130]

[0131] If Q<0, then there exists a positive scalar μ=-λ(Q) max , using the Rayleigh inequality for the first term of equation (31):

[0132]

[0133] Among them, the radius From formula (32), we can get that if ||e(t)||>R holds, then That is, the value of ‖e(t)‖ will decrease if it is outside the ball with radius R. Thus, the conclusion that the estimated error e(t) converges in a finite time is proved.

[0134] Furthermore, consider the candidate Lyapunov function Then V s,i The derivative of (t) with respect to time is:

[0135]

[0136] in, According to equations (26)-(32), within a finite time, ‖e(t)‖ satisfies R≥||e(t)||≥|e 2i (t)|. Therefore, if there exists a positive scalar η such that Then there is At the same time, the sliding motion will occur in a limited time. And the conclusion that the estimation error e1(t) converges in a finite time is proved.

[0137] In addition, consider another candidate Lyapunov function Assume that the sliding mode motion is On, then V st The derivative of (t) with respect to time is:

[0138]

[0139] in, If Q2<0, then:

[0140]

[0141] Among them, the matrix Ψ β =diag{β1,β2,…,β n}, According to formula (35), select Then we have:

[0142]

[0143] From this we can get Where V t,0 and t s,τ They are defined as V st The initial value of (t) and V st (t) The time required for convergence to zero. At the same time, the conclusion that the estimated error e2 converges to zero in a finite time is proved.

[0144] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A method for detecting abnormality in a networked motion control system, characterized in that: The networked motion control system abnormality detection method comprises: Collect the feedback control input signal time series and measurement output signal time series of the networked motion control system under historical normal working conditions, and obtain the estimated value of the system state under historical normal working conditions through the terminal sliding mode observer; The equivalent input disturbance estimation value of the system is calculated by the equivalent input disturbance estimator, and the equivalent input disturbance estimation time series under the historical normal working condition of the networked motion control system is obtained, and the arithmetic average is calculated point by point as the normal working condition reference series; Collect the feedback control input signal time series and the measurement output signal time series of the networked motion control system under the current working condition, and obtain the estimated value of the system state under the current working condition through the terminal sliding mode observer; The equivalent input disturbance estimation value of the system is calculated by an equivalent input disturbance estimator to obtain the equivalent input disturbance estimation time series of the current working condition of the networked motion control system; The similarity score between the reference sequence of normal working condition and the equivalent input disturbance estimation time series of current working condition is calculated, and then combined with the threshold judgment to identify whether the current working condition is in an abnormal state.

2. The abnormality detection method of a networked motion control system according to claim 1, characterized in that: The terminal sliding mode observer is expressed as follows: Among them, the system state is represented by x(t), and the estimated value of the system state is represented by for The derivative of f (t) is the feedback control input, A, B, C are the system gain matrices, L is the terminal sliding mode observer gain, is the estimated value of the measured output y(t), v(x(t), It is a designed nonlinear switching term.

3. The abnormality detection method of networked motion control system according to claim 2, characterized in that: The equivalent input interference estimation value of the system is calculated by the equivalent input interference estimator, and the calculation formula adopted is expressed as follows: in, is the inverse Laplace transform, is the equivalent input disturbance estimation value under the decoupling strategy. The decoupling strategy selects M(s)=K h (s+1) / s, s is a complex variable, v(s), X(s) and They are v(x(t), x(t) and The Laplace transform of, the generalized inverse matrix B + =(B T B) -1 B T .

4. The abnormality detection method of a networked motion control system according to claim 1, characterized in that: The calculating of the similarity score between the normal operating condition reference sequence and the current operating condition equivalent input disturbance estimation time series includes: For the normal working condition reference sequence D history Equivalent input disturbance estimation time series D new Perform Fourier transform to get the set and Where L f , is the length of the set; The set is calculated by the following formula and The similarity of is taken as the similarity score Rs between the normal working condition reference sequence and the equivalent input disturbance estimation time series of the current working condition: in, and The collections are and collection The mean of .

Images