Feedback control system fault detection method based on interference decoupling observer

Abstract

The invention provides a feedback control system fault detection method based on an interference decoupling observer. The method comprises the following steps: constructing a linear discrete feedback control system containing unknown disturbance; under the condition that the feedback control quantity is known, an interference decoupling observer DDO is constructed, parameter configuration is carried out, and an estimation error and a closed-loop residual error under the condition that the feedback control is static and unchanged are calculated; a feedback control law is substituted, an interference decoupling observer DDO is reconstructed, the structure of the interference decoupling observer DDO is adjusted, parameter reconfiguration is carried out, and an estimation error and a closed-loop residual error under dynamic change of feedback control are calculated; and comparing the estimation error and the closed-loop residual error under the static and dynamic conditions, and checking the performance of the DDO after structure adjustment and parameter reconfiguration. According to the method, the DDO-based fault detection problem of a closed-loop system under feedback control is emphatically considered, and the observer is enabled to be still applicable under the condition of dynamic change of feedback control by changing the structure of the observer and redesigning parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of state estimation and fault detection in the field of safety control, and in particular to a feedback control system fault detection method based on a disturbance decoupling observer. Background Art

[0002] Among the current fault detection methods, observer-based methods have been widely studied. Among them, the classic Luenberger observer has been widely used in fully observable linear systems due to its excellent stability and simple form. Subsequently, some improved Luenberger observers were used to deal with nonlinear systems. In recent years, the robust observer method that sets certain key parameter structures in the observer has been applied to the fault detection and separation problems of systems with random disturbances. When there is an unknown disturbance in the system under study, the disturbance decoupling observer (DDO) method can achieve complete decoupling between the residual signal and the unknown disturbance. At present, the DDO method has been used in a variety of control systems, such as uncertain systems, distributed systems, singular systems, etc.

[0003] At present, all observer-based fault detection methods require the assumption that the feedback control quantity is accurately known at each step. However, in practical applications, if the pre-set control law is substituted as a known quantity, the closed-loop dynamic characteristics of the system are directly studied. In this case, how the feedback control law affects the performance of the fault detection method; if the performance is reduced, how to improve the traditional observer method so that it is still usable under the action of the feedback control law are unresolved issues. Summary of the invention

[0004] In view of the problems existing in the above-mentioned prior art, the present invention proposes a feedback control system fault detection method based on a disturbance decoupling observer; it focuses on the fault detection problem based on DDO of a class of closed-loop systems under feedback control, and aims to change the observer structure and redesign the parameters so that the observer is still applicable when the feedback control changes dynamically.

[0005] In order to achieve the above technical objectives, the present invention provides the following technical solutions:

[0006] A method for fault detection of a feedback control system based on a disturbance decoupling observer specifically comprises the following steps:

[0007] S1. Construct a linear discrete feedback control system containing unknown disturbances, which is expressed as:

[0008]

[0009] in, is the system status, is the feedback control quantity, To measure the output, Unknown disturbance, For failure, and are system noise and measurement noise respectively; A, B, C and E are known matrices with appropriate dimensions, k, k+1 represent time, Represents n-dimensional real number space;

[0010] S2, in the feedback control quantity u k When the disturbance is known, the disturbance decoupling observer DDO is constructed, the parameters are configured, and the estimation error and closed-loop residual under the static invariance of feedback control are calculated;

[0011] S3. Considering the feedback controller, that is, substituting the feedback control law, constructing the disturbance decoupling observer DDO, adjusting the structure of the DDO and reconfiguring the parameters, and calculating the estimation error and closed-loop residual under the dynamic change of the feedback control;

[0012] S4. Compare the estimation errors and closed-loop residuals in static and dynamic situations to verify the performance of the disturbance decoupling observer DDO after structural adjustment and parameter reconfiguration.

[0013] Furthermore, step S2 specifically includes:

[0014] S21. Construct a disturbance decoupling observer DDO; its expression is:

[0015]

[0016] in, is the observer state, is the system state estimation;

[0017] S22, configure the parameters F, T, K, H of DDO;

[0018] S23. Define the estimated error and obtain the estimated error e according to the configured parameters k The dynamic equation and closed-loop residual r k The dynamic equations of

[0019] S24, determining necessary and sufficient conditions for the constructed disturbance decoupling observer DDO to be applicable to the feedback control system constructed in step S1.

[0020] More specifically, in step S22, each parameter is specifically configured as follows:

[0021] K = K1 + K2;

[0022] E = HCE;

[0023] T = I-HC;

[0024] F = A-HCA-K1C;

[0025] K2=FH;

[0026] Where F is a stable matrix and I is an identity matrix with appropriate dimensions.

[0027] More specifically, step S23 is as follows:

[0028] Define the estimation error e k for: Its dynamic equation is:

[0029] e k+1 =Fe k -Hv k+1 -K1v k +(I-HC)w k +(I-HC)f k ;

[0030] Calculate the closed-loop residual r k , its dynamic equation is:

[0031]

[0032] The estimated error e k and the closed-loop residual r k Both with unknown disturbance d k Decoupling.

[0033] More specifically, the necessary and sufficient conditions in step S24 are:

[0034] 1) rank(CE) = rank(E);

[0035] 2) (C, A-HCA) can be detected.

[0036] Furthermore, the expression of the feedback control law in step S3 is:

[0037]

[0038] Among them, l,Q p and Q i It is a pre-set parameter to ensure the stability of the feedback control system.

[0039] Furthermore, step S3 specifically includes:

[0040] S31, substituting the feedback control law into the feedback control system constructed in step S1;

[0041] The system expression after substitution is:

[0042]

[0043] S32, augmenting the system state and measurement noise, and obtaining the augmented form of the system expression;

[0044] Augmented system status and measurement noise Respectively expressed as:

[0045]

[0046] Substituting the augmented system state and the measurement noise into the feedback control system expression in step S31, we obtain:

[0047]

[0048] in,

[0049] S33. Based on the feedback control system expression obtained in step S32, the following disturbance decoupling observer DDO is constructed:

[0050]

[0051] in, is the augmented observer state, To augment the system state estimation;

[0052] S34, in order to offset the influence of the integral link in the feedback control and ensure that the parameters can be effectively configured, the DDO obtained in step S33 is structurally adjusted;

[0053] S35, reconfiguring parameters of the DDO after the structure adjustment in step S34;

[0054] S36. Calculate the dynamic equation of the estimated error and the dynamic equation of the closed-loop residual under dynamic changes of the feedback control based on the reconfigured parameters.

[0055] More specifically, step S34 is as follows:

[0056] Augmented Measurement Output That is,

[0057] in,

[0058] Then adjust the structure of DDO to:

[0059] More specifically, the parameter reconfiguration in step S35 specifically includes:

[0060] To ensure that the closed-loop residual is still decoupled from the unknown disturbance, configure the parameters satisfy:

[0061] Right now

[0062] To ensure that there is no dynamic equation with y in the estimated error k Directly related items, configuration parameters satisfy:

[0063]

[0064] In order to make the closed-loop residual under dynamic feedback control consistent with the closed-loop residual obtained under static conditions, the configuration parameters satisfy:

[0065]

[0066] Stable Matrix Then configure as

[0067] More specifically, step S36 specifically includes:

[0068] The estimation error under dynamic changes of feedback control is defined as Then when the initial estimation error satisfy When combined with the DDO parameters and The structure can be obtained Recursion shows that

[0069] The estimated error The dynamic equation is:

[0070]

[0071] Closed-loop residual r k The dynamic equation is:

[0072] Based on the above technical solution, the present invention has the following beneficial effects:

[0073] The present invention focuses on solving the fault detection problem of a closed-loop system under feedback control. When there is an unknown disturbance in the system, a feedback control system fault detection method based on the disturbance decoupling observer DDO is proposed, which solves the problem that the observer method is no longer applicable under closed-loop conditions when the feedback control law is introduced. By appropriately changing the observer structure and redesigning the parameters, the closed-loop residuals and estimation errors under dynamic transformation are completely consistent with those in the static unchanged situation. The method proposed by the present invention is a breakthrough in the prior art, while taking into account a wide range of applicability. It has made a significant contribution to promoting the development of the field of dynamic system fault detection and provides a beneficial patent effect for the relevant technical field. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 The overall flow chart of the method proposed by the present invention;

[0075] Figure 2 is the residual error of the traditional DDO method when there is no fault;

[0076] Figure 3 The method proposed in the present invention uses 100 Monte-Carlo experiments to obtain fault detection results. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention 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 invention and are not used to limit the present invention.

[0078] Although the steps in the present invention are arranged with numbers, they are not used to limit the order of the steps. Unless the order of the steps is clearly stated or the execution of a certain step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" used in this article involves and covers any and all possible combinations of one or more of the associated listed items.

[0079] The present invention considers the substitution of feedback control law, that is, the dynamic change of feedback control, and achieves the same fault detection performance as when the feedback control quantity is known, that is, the control feedback is static and unchanged, by adjusting the observer structure and reconfiguring the parameters. Figure 1 As shown, a feedback control system fault detection method based on a disturbance decoupling observer proposed in the present invention specifically includes the following steps:

[0080] S1. Construct a linear discrete feedback control system containing unknown disturbances, which is expressed as:

[0081]

[0082] in, is the system status, is the feedback control quantity, To measure the output, Unknown disturbance, For failure, and are system noise and measurement noise respectively; A, B, C and E are known matrices with appropriate dimensions, k, k+1 represent time, Represents n-dimensional real number space;

[0083] S2, in the feedback control quantity u k When the disturbance is known, the disturbance decoupling observer DDO is constructed, the parameters are configured, and the estimation error and closed-loop residual under the static invariance of feedback control are calculated;

[0084] As a preferred implementation, step S2 specifically includes:

[0085] S21. Construct a disturbance decoupling observer DDO; its expression is:

[0086]

[0087] in, is the observer state, is the system state estimation;

[0088] S22. Configure the DDO parameters F, T, K, and H. Specifically:

[0089] K = K1 + K2;

[0090] E = HCE;

[0091] T = I-HC;

[0092] F = A-HCA-K1C;

[0093] K2=FH;

[0094] Where F is a stable matrix and I is an identity matrix with appropriate dimensions.

[0095] S23. Define the estimated error and obtain the estimated error e according to the configured parameters k The dynamic equation and closed-loop residual r k The dynamic equations of

[0096] Specifically, this embodiment defines the estimation error e k for: Its dynamic equation is:

[0097] e k+1 =Fe k -Hv k+1-K1v k +(I-HC)w k +(I-HC)f k ;

[0098] Calculate the closed-loop residual r k , its dynamic equation is:

[0099]

[0100] The estimated error e k and the closed-loop residual r k Both with unknown disturbance d k Decoupling.

[0101] S24, determining necessary and sufficient conditions for the constructed disturbance decoupling observer DDO to be applicable to the feedback control system constructed in step S1.

[0102] The necessary and sufficient conditions are specifically:

[0103] 1) rank(CE) = rank(E);

[0104] 2) (C, A-HCA) can be detected.

[0105] S3. Considering the feedback controller, that is, substituting the feedback control law, constructing the disturbance decoupling observer DDO, adjusting the structure of the DDO and reconfiguring the parameters, and calculating the estimation error and closed-loop residual under the dynamic change of the feedback control;

[0106] In this embodiment, the following control law is applied to the system:

[0107]

[0108] As a preferred implementation, under the influence of the above control law: step S3 specifically includes:

[0109] S31, substituting the feedback control law into the feedback control system constructed in step S1;

[0110] The system expression after substitution is:

[0111]

[0112] S32, augmenting the system state and measurement noise, and obtaining the augmented form of the system expression;

[0113] Augmented system status and measurement noise Respectively expressed as:

[0114]

[0115] Substituting the augmented system state and the measurement noise into the feedback control system expression in step S31, we obtain:

[0116]

[0117] in,

[0118] S33. Based on the feedback control system expression obtained in step S32, the following disturbance decoupling observer DDO is constructed:

[0119]

[0120] in, is the augmented observer state, To augment the system state estimation;

[0121] S34, in order to offset the influence of the integral link in the feedback control and ensure that the parameters can be effectively configured, the DDO obtained in step S33 is structurally adjusted;

[0122] S35, reconfiguring parameters of the DDO after the structure adjustment in step S34;

[0123] S36. Calculate the dynamic equation of the estimated error and the dynamic equation of the closed-loop residual under dynamic changes of the feedback control based on the reconfigured parameters.

[0124] For steps S34-S36, in this embodiment, firstly, for the DDO obtained in step S33, in order to ensure that the closed-loop residual is still decoupled from the unknown disturbance, the configuration parameters satisfy:

[0125]

[0126] Considering The structure, that is, the configuration

[0127] At this time, the stability matrix becomes:

[0128]

[0129] In order to make the closed-loop residual under dynamic feedback control consistent with the closed-loop residual obtained under static conditions, it is assumed that only proportional control u is considered. k =Q p y k ,

[0130] Then configure

[0131] At this time, the stable matrix Can be further transformed into:

[0132]

[0133] In addition, to ensure that there is no error in the dynamic equation of the estimated error k Directly related items will and It should be calculated according to the following formula:

[0134]

[0135] The estimation error under dynamic changes of feedback control is defined as Then when the initial estimation error satisfy When combined with the DDO parameters and The structure can be obtained Recursion shows that

[0136] Furthermore, the following dynamic equation can be obtained:

[0137]

[0138] Due to the delay estimation error e k-1 ,L,e k-l Even if all eigenvalues ​​of F are stable, the estimation error may not be stable, and the delay error is introduced by the integral link in the feedback control. Considering the closed-loop measurement matrix The sparse nature of The characteristic values ​​of cannot be effectively configured. In order to solve the above problems, the method proposed in the present invention adjusts the structure of the DDO under the feedback control law, specifically:

[0139] Augmented Measurement Output That is,

[0140] in,

[0141] Then adjust the structure of DDO to:

[0142] At this time, reconfigure the parameters as follows:

[0143]

[0144] At this time, the estimated error under the action of the feedback control law is obtained and the closed-loop residual r k The dynamic equations are:

[0145]

[0146] Through the above structural adjustment and parameter reconfiguration of DDO, the following conclusions can be drawn:

[0147] Conclusion 1:

[0148] System Applying feedback control law

[0149] Consider the form The disturbance decoupling observer DDO,

[0150] Set the initial estimate error. If the initial estimate error is When the observer parameters are configured as described above, the estimated error value and closed-loop residual value that are completely consistent with those when the feedback control quantity remains unchanged can be obtained.

[0151] In this embodiment, the conclusion will be verified in step S4.

[0152] S4. Compare the estimation errors and closed-loop residuals in static and dynamic situations to verify the performance of the disturbance decoupling observer DDO after structural adjustment and parameter reconfiguration.

[0153] As a preferred implementation, step S4 is specifically as follows:

[0154] Proof of Conclusion 1

[0155] for consider We can get:

[0156]

[0157] Substitute the system equation and stability matrix into We can get:

[0158]

[0159] For the augmented measurement output because Available According to The dynamic equation of the estimation error can be further transformed into:

[0160]

[0161] Then simplify the stability matrix:

[0162]

[0163] That is

[0164] According to the given DDO parameters, when the initial estimation error hour, Can be divided into Recombination

[0165] The dynamic equation of the final estimation error under the feedback control law, that is, the dynamic change of feedback control, can be obtained:

[0166] e k+1 =Fe k -Hv k+1 -K1v k +(I-HC)w k +(I-HC)f k ;

[0167] And the dynamic equation of the closed-loop residual:

[0168]

[0169] This is completely consistent with the case where the feedback control quantity remains static and unchanged, and Conclusion 1 is proven.

[0170] In addition, in order for researchers in the field to better understand the implementation of the present invention and verify the reliability of the method proposed by the present invention, the present invention uses Matlab software for simulation.

[0171] The specific information of the simulation software is as follows:

[0172] Software name: MATLAB;

[0173] Version information: 9.8.0.1380330 (R2020a) Update 2;

[0174] License Number: 919961

[0175] Operating system: Microsoft Windows 10 Home Chinese Edition Version 10.0 (Build 19042);

[0176] Java version: Java 1.8.0_202-b08 with Oracle Corporation Java HotSpot(TM)64-Bit Server VM mixedmode;

[0177] Special toolboxes: Statistics and Machine Learning Toolbox-11.7(R2020a), Aircraft Control Toolbox-1.0

[0178] The present invention is simulated and verified using a three-tank system, and the model parameters are as follows:

[0179]

[0180] The closed-loop feedback control law parameters are:

[0181] The unknown input and noise are Gaussian distributions that are independent of each other, and their variances are: 1×10 -10 I,1×10 - 12 I,1×10 -12 I, the observer parameters are designed as:

[0182]

[0183] Consider a system failure of the following form:

[0184]

[0185] Finally, we get Figure 2 , Figure 3 Results shown. Figure 2 The residual of the traditional DDO method when there is no fault is given. It can be seen that even when there is no fault in the system, the residual signal tends to diverge, and such a signal obviously cannot be used for fault diagnosis. Figure 3 The fault detection threshold obtained by the method proposed in the present invention using 100 Monte-Carlo experiments is given. As can be seen from the figure, the method of the present invention can effectively detect possible faults in the system.

[0186] In summary, the present invention solves the problem that the disturbance decoupling observer DDO is no longer applicable under the action of the feedback control law. By adjusting the structure and reconfiguring the parameters of the DDO, it is ensured that the observer can still perform fault detection on the closed-loop system in a dynamic state, while also maintaining good detection performance.

[0187] It should be noted that it is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be regarded as exemplary and non-restrictive from any point of view, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any reference numerals in the claims should not be regarded as limiting the claims involved.

[0188] 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 fault detection method for a feedback control system based on a disturbance decoupling observer, characterized in that: The specific steps include: S1. Construct a linear discrete feedback control system containing unknown disturbances, which is expressed as: in, is the system status, is the feedback control quantity, To measure the output, Unknown disturbance, For failure, and are system noise and measurement noise respectively; A, B, C and E are known matrices with appropriate dimensions, k, k+1 represent time, Represents n-dimensional real number space; S2, in the feedback control quantity u k When the disturbance is known, the disturbance decoupling observer DDO is constructed, the parameters are configured, and the estimation error and closed-loop residual under the static invariance of feedback control are calculated; S3. Considering the feedback controller, that is, substituting the feedback control law, constructing the disturbance decoupling observer DDO, adjusting the structure of the DDO and reconfiguring the parameters, and calculating the estimation error and closed-loop residual under the dynamic change of the feedback control; S4. Compare the estimation errors and closed-loop residuals in static and dynamic situations to verify the performance of the disturbance decoupling observer DDO after structural adjustment and parameter reconfiguration.

2. The fault detection method according to claim 1, characterized in that: Step S2 specifically includes: S21. Construct a disturbance decoupling observer DDO; its expression is: in, is the observer state, is the system state estimation; S22, configure the parameters F, T, K, H of DDO; S23. Define the estimated error and obtain the estimated error e according to the configured parameters k The dynamic equation and closed-loop residual r k The dynamic equations of S24, determining necessary and sufficient conditions for the constructed disturbance decoupling observer DDO to be applicable to the feedback control system constructed in step S1.

3. The fault detection method according to claim 2, characterized in that: The specific configuration of each parameter in step S22 is: K = K1 + K2; E = HCE; T = I-HC; F = A-HCA-K1C; K2=FH; Where F is a stable matrix and I is an identity matrix with appropriate dimensions.

4. The fault detection method according to claim 3, characterized in that: Step S23 is specifically as follows: Define the estimation error e k for: Its dynamic equation is: e k+1 =Fe k -Hv k+1 -K1v k +(I-HC)w k +(I-HC)f k ; Calculate the closed-loop residual r k , its dynamic equation is: The estimated error e k and the closed-loop residual r k Both with unknown disturbance d k Decoupling.

5. The fault detection method according to claim 3, characterized in that: The necessary and sufficient conditions in step S24 are specifically: 1) rank(CE) = rank(E); 2) (C, A-HCA) can be detected.

6. The fault detection method according to claim 1, characterized in that: The expression of the feedback control law in step S3 is: Among them, l,Q p and Q i It is a pre-set parameter to ensure the stability of the feedback control system.

7. The fault detection method according to claim 6, characterized in that: Step S3 specifically includes: S31, substituting the feedback control law into the feedback control system constructed in step S1; The system expression after substitution is: S32, augmenting the system state and measurement noise, and obtaining the augmented form of the system expression; Augmented system status and measurement noise Respectively expressed as: Substituting the augmented system state and the measurement noise into the feedback control system expression in step S31, we obtain: in, S33. Based on the feedback control system expression obtained in step S32, the following disturbance decoupling observer DDO is constructed: in, is the augmented observer state, To augment the system state estimation; S34, in order to offset the influence of the integral link in the feedback control and ensure that the parameters can be effectively configured, the DDO obtained in step S33 is structurally adjusted; S35, reconfiguring parameters of the DDO after the structure adjustment in step S34; S36. Calculate the dynamic equation of the estimated error and the dynamic equation of the closed-loop residual under dynamic changes of the feedback control based on the reconfigured parameters.

8. The fault detection method according to claim 7, characterized in that: Step S34 is specifically as follows: Augmented Measurement Output That is, in, Then adjust the structure of DDO to:

9. The fault detection method according to claim 8, characterized in that: The parameter reconfiguration in step S35 specifically includes: To ensure that the closed-loop residual is still decoupled from the unknown disturbance, configure the parameters satisfy: To ensure that there is no dynamic equation with y in the estimated error k Directly related items, configuration parameters satisfy: In order to make the closed-loop residual under dynamic feedback control consistent with the closed-loop residual obtained under static conditions, the configuration parameters satisfy: Stable Matrix Then configure as 10. The fault detection method according to claim 8, characterized in that: Step S36 specifically includes: The estimation error under dynamic changes of feedback control is defined as Then when the initial estimation error e0 satisfies When combined with the DDO parameters and The structure can be obtained Recursion shows that The estimated error The dynamic equation is: Closed-loop residual r k The dynamic equation is:

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