A Fault Diagnosis Method for Ultra-precision Motion Stage Based on Robust Optimization

Abstract

A method for diagnosing ultra-precision motion table faults based on robust optimization relates to the technical field of ultra-precision equipment manufacturing. Expected position signals, position interference signals and position fault signals are input into a control system to obtain position signals, control signals and control objects; the position signals, control signals and control objects are output to a fault diagnosis system, wherein the control objects are subjected to left coprime factorization to obtain decomposition matrices M(s) and N(s), which are respectively multiplied by the position signals and control signals and then subtracted to obtain residual errors; the residual errors are input into a robust fault diagnosis filter to obtain the fault detection signal of the ultra-precision motion table, which is compared with a set threshold to determine whether a fault occurs. Under the premise of ensuring sensitivity to fault signals, it has a better suppression effect on errors and external interference caused by system uncertainty, significantly improving the robustness and accuracy of fault diagnosis.

Description

Technical Field

[0001] The invention relates to the technical field of ultra-precision equipment manufacturing, and in particular to an ultra-precision motion table fault diagnosis method based on robust optimization. Background Art

[0002] In recent years, with the progress of my country's ultra-precision high-end equipment manufacturing industry, the complexity and automation level of mechatronic systems have gradually increased, and there is a greater demand for improving system safety and reliability. At present, one of the most important issues when designing mechatronic systems is the reliability of the system, which is closely related to high production uptime. Therefore, minimizing downtime is crucial for mechatronic systems.

[0003] The best way to improve system reliability is to improve the quality and robustness of components such as actuators. However, failures are inevitable due to mechanical and electrical wear of system components. At this stage, the industry is turning to the use of predictive maintenance to enable mechatronic systems to avoid overly expensive maintenance while ensuring safety and reliability. Therefore, process monitoring and fault diagnosis are becoming important aspects of modern automatic control systems, especially ultra-precision control systems. Aiming at the ultra-precision motion table, which is essential for the manufacturing of ultra-precision high-end equipment, in order to solve the problem of motor failure during the operation of the ultra-precision motion table, which may lead to deterioration of the platform servo performance and decreased positioning accuracy, a fault diagnosis method based on robust optimization is proposed, which is of great significance to improving system reliability. Summary of the invention

[0004] In order to address the shortcomings of the background technology, the present invention provides an ultra-precision motion table fault diagnosis method based on robust optimization, which has a better suppression effect on errors and external interference caused by system uncertainty while ensuring sensitivity to fault signals, and significantly improves the robustness and accuracy of fault diagnosis.

[0005] To achieve the above object, the present invention adopts the following technical solution: a method for diagnosing ultra-precision motion table faults based on robust optimization, comprising the following steps:

[0006] Step 1: The interference signal d passes through the interference transfer function G d (s) generates position interference signal y d , the fault signal f passes through the fault transfer function G f (s) Generate position fault signal y f , where s is the Laplace operator, the expected position signal r, the position interference signal y d and position fault signal y f Input control system Obtain position signal y, control signal u and control object P;

[0007] Step 2: Output the position signal y, control signal u and control object P to the fault diagnosis system Ψ, wherein the control object P is subjected to left coprime factorization to obtain decomposition matrices M(s) and N(s), and the decomposition matrices M(s) and N(s) are multiplied with the position signal y and control signal u to obtain the decomposition signal y m and n , decompose signal y m and n Subtract and obtain the residual error e;

[0008] Step 3: Input the residual error e into the robust fault diagnosis filter R to obtain the fault detection signal ε of the ultra-precision motion stage, and compare the fault detection signal ε with the set threshold to determine whether a fault occurs.

[0009] Furthermore, in step 2, the residual error e is expressed as:

[0010]

[0011] Among them, since the actual expression of the control object P is recorded as P(s,Δ), Δ represents parameter uncertainty, the left coprime factorization matrices M(s) and N(s) of the control object P should satisfy the following form:

[0012] P(s,0)=M -1 (s)·N(s)

[0013] Where P(s,0) represents the theoretical expression of the control object without considering parameter uncertainty, G e1 (s,Δ) represents the transfer function matrix from the desired position signal and the interference signal to the residual error, G e2 (s,Δ) represents the transfer function matrix from fault signal to residual error.

[0014] Furthermore, in step 3, the robust fault diagnosis filter R is designed as follows:

[0015] Replace G in step 2 e1 The Laplace operator s of (s, Δ) is replaced by jω to obtain the frequency response of the transfer function matrix from the desired position signal and the interference signal to the residual error, where j is the imaginary unit and ω is the angular frequency. Find the following formula that is valid for any parameter uncertainty within the range of parameter uncertainty Δ.

[0016]

[0017] In the formula, Represents G e1 The conjugate transposed matrix of (jω,Δ), express The conjugate transposed matrix of ;

[0018] make Where γ is the adjustment coefficient, pass The common factorization of is obtained, which satisfies:

[0019]

[0020] In the formula, I is the unit matrix, G e1o (s) is the outer factorization matrix of the common factorization, G e1i (s) is the inner factorization matrix of the common factorization;

[0021] Finally, the fault detection signal ε of the ultra-precision motion stage is expressed as:

[0022]

[0023] By monitoring the fault detection signal ε and determining whether it exceeds a set threshold, if so, it is diagnosed as a fault of the ultra-precision motion stage.

[0024] Compared with the prior art, the beneficial effects of the present invention are: the present invention introduces the idea of ​​robust optimization to the fault diagnosis filter, and designs a robust fault diagnosis filter according to the characteristics of the system and the fault. Compared with the traditional fault diagnosis method, while ensuring sensitivity to the fault signal, it has a better suppression effect on the errors and external interference caused by system uncertainty, and can significantly improve the robustness and accuracy of ultra-precision motion table fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a system topology diagram of the fault diagnosis method of the present invention;

[0026] Figure 2 is a system topology diagram in an embodiment;

[0027] Figure 3 is a fault signal in the embodiment;

[0028] Figure 4 is the interference signal in the embodiment;

[0029] Figure 5 is the expected position signal in the embodiment;

[0030] Figure 6 is a fault detection signal output by the robust fault diagnosis filter in the embodiment;

[0031] Figure 7 The transfer function RG before and after improvement in the embodiment is e1 (s) The maximum singular value versus frequency. DETAILED DESCRIPTION

[0032] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0033] like Figure 1 As shown, a method for fault diagnosis of an ultra-precision motion stage based on robust optimization comprises the following steps:

[0034] Step 1: The interference signal d passes through the interference transfer function G d (s) generates position interference signal y d , the fault signal f passes through the fault transfer function G f (s) Generate position fault signal y f , where s is the Laplace operator, the expected position signal r, the position interference signal y d and position fault signal y f Input control system Obtain position signal y, control signal u and control object P;

[0035] Step 2: Output the position signal y, control signal u and control object P to the fault diagnosis system Ψ, wherein the control object P is subjected to left coprime factorization to obtain decomposition matrices M(s) and N(s), and the decomposition matrices M(s) and N(s) are multiplied with the position signal y and control signal u to obtain the decomposition signal y m and n , decompose signal y m and n The residual error e is obtained by subtraction.

[0036] Since the control object P has parameter uncertainty, its actual expression is recorded as P(s,Δ), where Δ represents parameter uncertainty. Therefore, the left coprime factorization matrices M(s) and N(s) of the control object P should satisfy the following form:

[0037] P(s,0)=M -1 (s)·N(s)

[0038] Where P(s,0) represents the theoretical expression of the control object without considering parameter uncertainty.

[0039] Then the residual error e is expressed as:

[0040] e=M(s)yN(s)u

[0041] After substituting M(s) and N(s), the residual error e can be converted into:

[0042]

[0043] In the formula, G e1 (s,Δ) represents the transfer function matrix from the desired position signal and the interference signal to the residual error, G e2 (s, Δ) represents the transfer function matrix from fault signal to residual error. Therefore, the residual error e contains information about fault signal, interference signal and parameter uncertainty;

[0044] Step 3: Input the residual error e into the robust fault diagnosis filter R to obtain the fault detection signal ε of the ultra-precision motion stage, and compare the fault detection signal ε with the set threshold to determine whether a fault occurs.

[0045] Among them, the robust fault diagnosis filter R is designed as follows:

[0046] Replace G in step 2 e1 The Laplace operator s of (s,Δ) is replaced by jω to obtain the frequency response of the transfer function matrix from the desired position signal and the interference signal to the residual error, where j is the imaginary unit and ω is the angular frequency. e1 (jω,Δ) upper bound, that is, by finding the following equation that holds true for any parameter uncertainty within the range of parameter uncertainty Δ

[0047]

[0048] In the formula, Represents G e1 The conjugate transposed matrix of (jω,Δ), express The conjugate transposed matrix of .

[0049] make Where γ is the adjustment coefficient, pass The common factorization of is obtained, which satisfies:

[0050]

[0051] In the formula, I is the unit matrix, G e1o (s) is the outer factorization matrix of the common factorization, G e1i (s) is the inner factorization matrix of the common factorization.

[0052] Therefore, the transfer function of the interference signal d and the expected position signal r to the fault detection signal ε can be calculated as The maximum singular value of is limited, so that the influence of the interference signal d and the error caused by parameter uncertainty Δ on the fault detection signal ε becomes smaller.

[0053] Finally, the fault detection signal ε of the ultra-precision motion stage is expressed as:

[0054]

[0055] A threshold is set according to actual needs. The fault detection signal ε is monitored and judged whether it exceeds the set threshold. If it exceeds, it is diagnosed as a fault of the ultra-precision motion stage.

[0056] Example

[0057] Combination Figure 2 As shown, suppose the single-input single-output system contains parameter uncertainty Δ∈[-1,1], and its model is:

[0058]

[0059] The feedback controller C under closed-loop conditions is selected as:

[0060]

[0061] The fault signal f and the interference signal d are as follows: Figure 3 and Figure 4 shown.

[0062] The residual error e is obtained as follows:

[0063] Get control object Without considering parameter uncertainty, the left coprime factorization is: M(s) = 1, Then the expression of the residual error e is:

[0064]

[0065] The residual error e contains information about the fault signal, interference signal and parameter uncertainty. After further simplification, the residual error e can be expressed as follows:

[0066]

[0067] The robust fault diagnosis filter R is designed as follows:

[0068] When Δ∈[-1,1], take G e1 The upper bound of (jω,Δ) is:

[0069]

[0070] Pick The common factorization result of is:

[0071]

[0072] G e1i (s)=1

[0073] but

[0074] When the adjustment coefficient γ=1, the robust fault diagnosis filter R is:

[0075]

[0076] The fault detection signal ε of the ultra-precision motion stage is expressed as:

[0077]

[0078] Therefore, the robust fault diagnosis filter R monitors the system operation status according to the control signal u and the position signal y, and determines whether a fault occurs in the monitored system by whether the change of the fault detection signal ε exceeds the set threshold.

[0079] The expected position signal r used is Figure 5 As shown, the system is fault diagnosed, and the fault detection signal ε output by the robust fault diagnosis filter R is combined with Figure 6 It can be observed that the fault detection signal ε output by the robust fault diagnosis filter R increases significantly after the 10th second, and the system is diagnosed as having a fault, thus meeting the requirements for fault diagnosis of the monitored system.

[0080] In order to verify the superiority of this method, Figure 7 As shown in FIG. 1 , the transfer function from the interference signal d and the expected position signal r to the fault detection signal ε before and after the improvement by the method of the present invention is shown. The maximum singular value of changes with frequency. Among them, the value of the fault diagnosis filter R in the unimproved transfer function is:

[0081]

[0082] It can be observed that after applying the method of the present invention, the maximum singular value of the transfer function from parameter uncertainty Δ and interference signal d to the robust fault diagnosis filter R output fault detection signal ε in the low frequency band is significantly reduced compared with the case where the method of the present invention is not applied. Therefore, the method of the present invention has a good suppression effect on system uncertainty and interference signals while ensuring sensitivity to fault signals. The accuracy and robustness of fault diagnosis of ultra-precision motion systems are improved.

[0083] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0084] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for fault diagnosis of ultra-precision motion platform based on robust optimization, characterized in that: The following steps are involved: Step 1: The interference signal d passes through the interference transfer function G d (s) generates position interference signal y d , the fault signal f passes through the fault transfer function G f (s) Generate position fault signal y f , where s is the Laplace operator, the expected position signal r, the position interference signal y d and position fault signal y f Input control system Obtain position signal y, control signal u and control object P; Step 2: Output the position signal y, control signal u and control object P to the fault diagnosis system Ψ, wherein the control object P is subjected to left coprime factorization to obtain decomposition matrices M(s) and N(s), and the decomposition matrices M(s) and N(s) are multiplied with the position signal y and control signal u to obtain the decomposition signal y m and n , decompose signal y m and n Subtract and obtain the residual error e; Step 3: Input the residual error e into the robust fault diagnosis filter R to obtain the fault detection signal ε of the ultra-precision motion stage, and compare the fault detection signal ε with the set threshold to determine whether a fault occurs.

2. The ultra-precision motion stage fault diagnosis method based on robust optimization according to claim 1, characterized in that: In step 2, the residual error e is expressed as: Among them, since the actual expression of the control object P is recorded as P(s,Δ), Δ represents parameter uncertainty, the left coprime factorization matrices M(s) and N(s) of the control object P should satisfy the following form: P(s,0)=M -1 (s)·N(s) Where P(s,0) represents the theoretical expression of the control object without considering parameter uncertainty, G e1 (s,Δ) represents the transfer function matrix from the desired position signal and the interference signal to the residual error, G e2 (s,Δ) represents the transfer function matrix from fault signal to residual error.

3. The ultra-precision motion stage fault diagnosis method based on robust optimization according to claim 2, characterized in that: In step 3, the robust fault diagnosis filter R is designed as follows: Replace G in step 2 e1 The Laplace operator s of (s, Δ) is replaced by jω to obtain the frequency response of the transfer function matrix from the desired position signal and the interference signal to the residual error, where j is the imaginary unit and ω is the angular frequency. Find the following formula that is valid for any parameter uncertainty within the range of parameter uncertainty Δ. In the formula, Represents G e1 The conjugate transposed matrix of (jω,Δ), express The conjugate transposed matrix of ; make Where γ is the adjustment coefficient, pass The common factorization of is obtained, which satisfies: In the formula, I is the unit matrix, G e1o (s) is the outer factorization matrix of the common factorization, G e1i (s) is the inner factorization matrix of the common factorization; Finally, the fault detection signal ε of the ultra-precision motion stage is expressed as: By monitoring the fault detection signal ε and determining whether it exceeds a set threshold, if so, it is diagnosed as a fault of the ultra-precision motion stage.

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