A set membership fault detection method for dc servo motor system based on time-delay unknown input observer

Abstract

The application discloses a set member fault detection method for a DC servo motor system based on a time delay unknown input observer, and belongs to the technical field of model-based control system fault detection. ∞ The set member fault detection method of the application adopts an unknown input observer, introduces L ∞ Performance index and H ∞ Performance index to make the residual error system robust to unknown interference and improve the sensitivity to actuator faults. The residual error threshold determination method based on the central symmetric polytope set member estimation with low conservativeness makes the fault detection method of the application high in detection precision and sensitivity, and less likely to cause missed reports and false reports. Compared with the fault detection method based on LBO, the fault detection threshold of the application is lower in conservativeness, and the fault detection performance is better. The method of the application can be applied to fault detection of a control system.

Description

Technical Field

[0001] This invention belongs to the field of model-based control system fault detection technology, specifically relating to a method for detecting cluster faults in a DC servo motor system based on a time-delay unknown input observer. Background Technology

[0002] DC servo motors are widely used in intelligent equipment and power equipment due to their linear mechanical characteristics, smooth adjustment characteristics, high overload capacity, and fast response speed. However, faults are inevitable in real-world systems, and if they are not detected and resolved in a timely manner, they can lead to serious casualties and property losses. Meanwhile, with the increasing demand for system reliability and safety, the problem of fault detection in real-world systems urgently needs to be solved. Model-based fault detection technology uses system models and measurement data to construct a residual generator, evaluating the residual signal against a preset threshold. If the residual signal is within the threshold range, the system is operating normally; if the residual signal exceeds the threshold range, a fault has occurred. It is worth noting that model-based fault detection methods rely on an accurate system model, which is difficult to obtain in real-world systems affected by unknown process interference and measurement errors. On the other hand, the difficulty of this type of method lies in determining the fault detection threshold. An unreasonable threshold may lead to missed detections, delayed alarms, and false alarms in the absence of faults. Existing experience-based and norm-based threshold setting methods determine relatively conservative thresholds, which have significant limitations when applied to real-world systems. The set membership estimation technique based on centrosymmetric multiple cells (MCCs) is suitable for fault detection threshold determination because it does not model the dynamics of the processing system and only assumes that process disturbances and measurement errors are unknown but bounded. It does not require knowledge of the specific probability distribution of unknown inputs, thus obtaining a low-conservatism residual signal centrosymmetric multiple cell threshold. The threshold determination technique based on set membership estimation depends on the selection of the fault detection observer; a suitable observer will further reduce the conservatism of the fault detection threshold design.

[0003] For example, the literature (Naima Sehli, et al. Fault Detection and Isolation for Linear discrete-time Delayed Systems based on L ∞ The method for detecting faults in centrally symmetric multicellular sets proposed in *Observer and Zonotopic Analysis* (IFAC-PapersOnline, Vol.55, No. 25 (2022) 169-174) employs a Luneburger observer (LBO) and introduces L... ∞Performance indicators mitigate the impact of unknown disturbances. However, the residual systems relied upon by existing fault detection techniques still exhibit poor robustness to unknown disturbances, low sensitivity to faults, and high conservatism in dynamic thresholds. Therefore, proposing a fault detection method for DC servo motor systems is a pressing issue that needs to be addressed. Summary of the Invention

[0004] The purpose of this invention is to address the problems of poor robustness, low sensitivity to faults, and high conservatism of dynamic thresholds in existing fault detection technologies for DC servo motor systems. Therefore, this invention proposes a method for detecting cluster faults in DC servo motor systems based on an observer with unknown time delay.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is: a method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer, the method specifically including the following steps:

[0006] Step 1: Establish a state-space model of the discrete time-delay DC servo motor system that considers process disturbances, measurement noise, and actuator failures;

[0007] Step 2: Determine the observer for detecting input faults with unknown time delay based on the state-space model of the discrete time-delay DC servo motor system;

[0008] Step 3: Obtain the DC servo motor residual system based on the unknown time delay input fault detection observer. The DC servo motor residual system is divided into a first residual subsystem and a second residual subsystem.

[0009] Step 4: Solve for the gain of the time delay unknown input fault detection observer based on the constraints of the DC servo motor residual system;

[0010] Step 5: Based on the set membership estimation method for centrosymmetric multicells and the observer gain, obtain the interval envelope of the centrosymmetric multicell residual threshold under fault-free conditions.

[0011] Step 6: Determine whether the DC servo motor system is faulty based on the interval envelope of the centrally symmetric multicell residual threshold under fault-free conditions and the fault residual signal.

[0012] The beneficial effects of this invention are:

[0013] The member fault detection method provided by this invention employs an Unknown Input Observer (UIO), by introducing L ∞The H-performance index enhances the robustness of the residual system to unknown disturbances while improving its sensitivity to actuator faults. Employing a residual threshold determination method based on centrosymmetric multicell set membership estimation, which exhibits low conservatism, the fault detection method proposed in this invention achieves high detection accuracy and sensitivity, reducing the likelihood of false negatives and false negatives. Compared to LBO-based fault detection methods, the fault detection threshold obtained in this invention exhibits lower conservatism and better fault detection performance. Attached Figure Description

[0014] Figure 1 This is a flowchart of a method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer, according to the present invention.

[0015] Figure 2(a) shows the state comparison between the fault detection observer and the Lumberjack observer of the present invention. Tracking performance comparison chart;

[0016] Figure 2(b) shows the state comparison between the fault detection observer and the Lumberjack observer of the present invention. Tracking performance comparison chart;

[0017] Figure 2(c) shows the state comparison between the fault detection observer and the Lumberjack observer of the present invention. Tracking performance comparison chart;

[0018] Figure 3(a) shows the fault detection observer and the Lumberjack observer of the present invention. Fault detection result diagram;

[0019] Figure 3(b) shows the fault detection observer and the Lumberjack observer of the present invention. The fault detection result diagram. Detailed Implementation

[0020] Specific implementation method one: Combining Figure 1 This embodiment describes a method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer. The method specifically includes the following steps:

[0021] Step 1: Establish a state-space model of the discrete time-delay DC servo motor system that considers process disturbances, measurement noise, and actuator failures;

[0022] Step 2: Determine the observer for detecting input faults with unknown time delay based on the state-space model of the discrete time-delay DC servo motor system;

[0023] Step 3: Obtain the DC servo motor residual system based on the unknown time delay input fault detection observer. The DC servo motor residual system is divided into a first residual subsystem and a second residual subsystem.

[0024] Step 4: Solve for the gain of the time delay unknown input fault detection observer based on the constraints of the DC servo motor residual system;

[0025] Step 5: Based on the set membership estimation method for centrosymmetric multicells and the observer gain, obtain the interval envelope of the centrosymmetric multicell residual threshold under fault-free conditions.

[0026] Step 6: Determine whether the DC servo motor system is faulty based on the interval envelope of the centrally symmetric multicell residual threshold under fault-free conditions and the fault residual signal.

[0027] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the specific process of step one is as follows:

[0028] 1. Based on the dynamic analysis of the DC servo motor, list the electrical and mechanical dynamic equations of the DC servo motor:

[0029] When the motor circuit is in a dynamic process, the armature circuit potential balance equation is:

[0030] (1)

[0031] in, It is the armature circuit inductance, measured in watts (H). This is the armature circuit current, measured in amperes (A). It is the armature circuit resistance, measured in Ω; This is the back electromotive force across the armature when the motor rotates, expressed in volts (V). It is the armature voltage, measured in volts (V).

[0032] The back electromotive force at the armature terminals is proportional to the motor speed:

[0033] (2)

[0034] in, It is the motor's electromotive force constant; The unit is rad / s.

[0035] The output torque of the motor is positively correlated with the armature current.

[0036] (3)

[0037] in, It is the electromagnetic torque generated when the motor rotates, and its unit is N·m; It is the torque constant.

[0038] The relationship between output torque and load is as follows:

[0039] (4)

[0040] (5)

[0041] in, It is the total moment of inertia of the rotating parts referred to the motor shaft, with units of N·m·s. 2 ; This is the load torque, measured in N·m. It is the coefficient of viscous friction.

[0042] Based on the electrical and mechanical dynamic equations of the DC servo motor, the speed subsystem and current subsystem are obtained:

[0043] (6)

[0044] 3. Based on the speed subsystem and current subsystem, obtain the state-space model of the DC servo motor:

[0045] (7)

[0046] in, , Let t be the system state vector at time t; It is the angular position of the motor's rotation; , The measurement output at time t; , and Each represents a known system matrix with appropriate dimensions. , , .

[0047] 4. Based on the state-space model of the DC servo motor, obtain the discretized state-space model of the DC servo motor:

[0048] (8)

[0049] Among them, the system matrix ; ; This is the simulation sampling time.

[0050] The state-space model of a discrete-time-delay DC servo motor system subjected to time delay, process disturbances, measurement noise, and actuator failure can be determined based on the discretized state-space model.

[0051] (9)

[0052] in, for The system state vector at any given time. for The system state vector at any given time. for The system state vector at any given time. It is a constant delay. and For the system matrix, yes Armature voltage at time t, Represents the actuator fault vector. Represents the process interference vector. Represents the measurement noise vector. , , and This represents a constant matrix with appropriate dimensions. , and They are The time-based process interference items, measurement error interference items, and actuator fault items are as follows: It is a function of the initial system state, and the system matrix is... , for The measurement output at time, Represents the system state vector dimensionality;

[0053] Formula (9) satisfies the rank condition: ,in The dimension of the system state vector x(k) is represented by . Represents the identity matrix. This represents the rank of the matrix.

[0054] The other steps and parameters are the same as in Specific Implementation Method 1.

[0055] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the unknown delay input fault detection observer is:

[0056] (10)

[0057] Among them, matrix , , , , and For observer gain, Indicates an input observer with unknown time delay. The state vector at time t, Indicates an input observer with unknown time delay. The state vector at time t, Indicates an input observer with unknown time delay. The state vector at time t, for The measurement output at time, yes The estimated vector of the system state at time t, the initial state , Represents a given initial function;

[0058] The observer gain satisfies:

[0059] (11)

[0060] in, This represents the observer parameter matrix to be designed. Represents the system state vector The dimension of.

[0061] Other steps and parameters are the same as in specific implementation method one or two.

[0062] Based on the rank condition satisfied by formula (9), the matrix equation can be obtained. There is a solution, and its general solution is: ; , This indicates the dimension of the system's measurement output. Indicates dimension as The identity matrix; , This represents the pseudo-inverse of a matrix.

[0063] Determining an observer for unknown input fault detection based on the state-space model of a DC servo motor fault system can make the residual system robust to unknown disturbances and sensitive to actuator faults.

[0064] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the step of obtaining the DC servo motor residual system based on the time-delay unknown input fault detection observer is specifically as follows:

[0065] (12)

[0066] in, Represents the residual system of DC servo motor Error vector at time step, Represents the residual system of DC servo motor Error vector at time step, Represents the residual system of DC servo motor Error vector at time step, express The measurement noise vector at time step, express The measurement noise vector at time step, express The measurement noise vector at time step, express The residual vector at time step, matrix , .

[0067] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0068] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the first residual subsystem and the second residual subsystem are respectively:

[0069] (13)

[0070] (14)

[0071] in, , , Represents the first residual subsystem Error vector at time step, Represents the second residual subsystem Error vector at time step, Represents the first residual subsystem Error vector at time step, Represents the second residual subsystem Error vector at time +1 Represents the first residual subsystem The residual vector at time step, Represents the second residual subsystem The residual vector at time step.

[0072] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0073] Decomposing the residual system into the following two subsystems allows for a better analysis of the desired residual system's robustness to unknown disturbances and its sensitivity to actuator failures.

[0074] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the... Process disturbances at any given time, measurement error disturbances, and initial state under fault-free conditions The scope is defined by the centrosymmetric multicellular structure, specifically as follows:

[0075] (15)

[0076] in, , and Given a constant, It is a diagonal matrix. , and The generation matrix for a centrosymmetric polycell (which determines the shape and volume of the centrosymmetric polycell). It is a centrosymmetric multicellular organism.

[0077] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0078] A centrosymmetric multicell of order s It is a hypercube Affine transformation: ,in, For Minkowski and; yes The center yes The generating matrix. For simplicity, the centrally symmetric multicell is defined as... .

[0079] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that the specific process of step four is as follows:

[0080] Step 41: To make the residual system robust to unknown disturbances while being sensitive to actuator failures, the constraints of the DC servo motor residual system are defined as follows:

[0081] (16)

[0082] (17)

[0083] Among them, scalar , , (i.e., H-performance metrics) , , This represents the initial error vector of the first residual subsystem. , Describing the 2-norm, express Norm;

[0084] Step 42: Transform the constraints of the DC servo motor residual system into the following linear matrix inequalities:

[0085] (18)

[0086] (19)

[0087] (20)

[0088] in, , , and It is a positive definite matrix ( , and It can be solved based on formulas (18) to (20). The dimension of the process disturbance vector; This represents the dimension of the measurement noise vector; The dimension of the actuator fault vector; It is an invertible matrix (which can be solved based on formulas (18) to (20)); It is an arbitrary matrix; scalar ; ; ; ; ; ; ; System matrix , It is the motor potential constant. It is the coefficient of viscous friction. It is the torque constant. It is the armature circuit inductance. It is the armature circuit resistance. It is the total moment of inertia of the rotating parts referred to the motor shaft;

[0089] Step 4.3 Solve the linear matrix inequalities (18), (19) and (20) to obtain the gain matrix of the time-delay unknown input fault detection observer. , , , , and .

[0090] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0091] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the specific process of step five is as follows:

[0092] Calculate the residual threshold ;

[0093] in, , It is the identity matrix. It is a centrosymmetric multicell dimensionality reduction operator. express The dimensionality reduction result of the generation matrix of the time-major centrosymmetric multicell. express The dimensionality reduction result of the generation matrix of the time-matter centrosymmetric multicell; and The dimensionality reduction result of the time-major symmetric multicell generation matrix is:

[0094] (twenty one)

[0095] The interval envelope of the residual threshold under fault-free conditions is ;

[0096] in, Indicates to The first Sum of row elements, i.e. , express Inner Line 1 Column elements, This indicates taking the absolute value. yes The number of columns, , yes The order of.

[0097] The steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0098] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the specific process of step six is ​​as follows:

[0099] The fault residual signal is calculated according to formula (12). According to get ;

[0100] If satisfied (It should be noted that for the residual vector) The condition is satisfied only when all components are within the interval envelope. If the following conditions are met, then the DC servo motor system is fault-free. If this occurs, the DC servo motor system will malfunction.

[0101] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0102] Example

[0103] This embodiment proposes a fault detection method for DC servo motor clusters based on an observer with unknown time delay, which specifically includes the following steps:

[0104] Step 1: Determine the discretized spatial model of the time-delay DC servo motor system suffering from process disturbances, measurement noise, and actuator failures:

[0105] When the motor circuit is in a dynamic process, the armature circuit potential balance equation is:

[0106] (1)

[0107] in It is the armature circuit inductance, measured in watts (H). This is the armature circuit current, measured in amperes (A). It is the armature circuit resistance, measured in Ω; This is the back electromotive force across the armature when the motor rotates, expressed in volts (V). It is the armature voltage, measured in volts (V).

[0108] The back electromotive force at the armature terminals is proportional to the motor speed:

[0109] (2)

[0110] in It is the motor's electromotive force constant; It is the angular velocity of the motor, and the unit is rad / s.

[0111] The output torque of the motor is directly proportional to the armature current:

[0112] (3)

[0113] in It is the electromagnetic torque generated when the motor rotates, and its unit is N·m; It is the torque constant.

[0114] Relationship between output torque and load:

[0115] (4)

[0116] (5)

[0117] in, It is the total moment of inertia of the rotating parts referred to the motor shaft, with units of N·m·s. 2 ; This is the load torque, measured in N·m. It is the coefficient of viscous friction.

[0118] The speed subsystem and the current subsystem are as follows:

[0119] (6)

[0120] The state-space model of a DC servo motor is as follows:

[0121] (7)

[0122] in Defined as the system state vector at time t; It is the angular position of the motor's rotation; Defined as the measurement output at time t; , , These represent known system matrices with appropriate dimensions.

[0123] The discretized state-space model of the DC servo motor is as follows:

[0124] (8)

[0125] Step 2: Obtain the simulation sampling time The system matrix can be obtained using Euler's one-step method. ;

[0126] .

[0127] The DC servo motor system (8) suffers from time delay, process interference, measurement noise and actuator failure, which can be described in the following form:

[0128] (9)

[0129] in, ; ; ; ; Introducing faults Control input , ; It is a constant delay; It is a function of the initial system state. .

[0130] Formula (9) satisfies the rank condition: rank( = ,in The dimension of the system state vector x(k) is represented by . Represents the identity matrix.

[0131] Step 3: Based on the DC servo motor fault system model, determine the observer for detecting input faults with unknown time delay as follows:

[0132] (10)

[0133] in It is the observation state vector, and its initial state is , Represents a given initial function. .

[0134] matrix , , , , and Let the gain of the fault detection observer be the input with unknown time delay, and satisfy the following condition:

[0135] (11)

[0136] Based on the rank condition satisfied by formula (9), the matrix equation can be obtained. There is a solution, and its general solution is: ; , .

[0137] The residual system of the DC servo motor is as follows:

[0138] (12)

[0139] Among them, matrix ; The residual system (12) includes a first residual subsystem and a second residual subsystem:

[0140] (13)

[0141] (14)

[0142] in, ; .

[0143] Process interference of DC servo motor residual system Noise measurement Initial state under fault-free conditions The extent is defined by the following centrally symmetric multicellular structures:

[0144] (15)

[0145] The definition of a centrosymmetric multicellular body is as follows:

[0146] A centrosymmetric multicell of order s It is a hypercube Affine transformation: .in For Minkowski and; yes The center; Generating matrix This determines the shape and volume of a centrosymmetric multicellular organism. For simplicity, we define... .

[0147] The residual system of a DC servo motor based on a fault detection observer with unknown time delay satisfies the following constraints:

[0148] (16)

[0149] (17)

[0150] scalar , , , ; ; .

[0151] Step 4: The constraints are transformed into linear matrix inequalities as follows:

[0152] (18)

[0153] (19)

[0154] (20)

[0155] in , , and It is a positive definite matrix; It is an invertible matrix; It is an arbitrary matrix; scalar ; ; ; ; ; ; ; ; .

[0156] Solving the linear matrix inequalities (18), (19) and (20) yields the gain matrix of the observer for the time-delay unknown input fault detection.

[0157] Step 5: Obtain scalar quantity ; ; ; It can be obtained The observer gain is: ; ; ;

[0158] ; ; .

[0159] Step 6: The residual threshold under fault-free conditions based on the set membership estimation method is: :

[0160] in, , It is the identity matrix. It is a centrosymmetric multicell dimensionality reduction operator used to reduce the dimension of the generated matrix to a predetermined positive integer. express The dimensionality reduction result of the generation matrix of the time-major centrosymmetric multicell. express The dimensionality reduction result of the generation matrix of the time-matter centrosymmetric multicell; and The dimensionality reduction result of the time-major symmetric multicell generation matrix is:

[0161] (twenty one)

[0162] The interval envelope of the residual threshold under fault-free conditions is ;

[0163] in, Indicates to The first Sum of row elements, i.e. , express Inner Line number Column elements, This indicates taking the absolute value. yes The number of columns, , yes The order of.

[0164] Step 7: According to get The fault detection logic is determined as follows:

[0165] If satisfied If the DC servo motor system is fault-free, then the following conditions must be met. If so, the DC servo motor system will malfunction;

[0166] in, It is a fault detection result signal, when When the residual signal remains within the interval envelope, it indicates that no fault has occurred. When the residual signal consistently exceeds the interval envelope and is detected, it indicates that a fault has occurred.

[0167] Figures 2(a) to 2(c) This invention presents the Unknown Input Fault Detection Observer (UIO) designed for time delay and is related to the literature (Naima Sehli, et al. Fault Detection and Isolation for Linear Discrete-Time Delayed Systems based on...). The Luneburger Observer (LBO) used in *Observer and Zonotopic Analysis. IFAC-PapersOnline, Vol. 55, No. 25(2022)169-174* demonstrates its ability to track the state of a DC servo motor fault system. The first component in the system state vector. It is the second component in the system state vector. As the third component in the system state vector, it can be seen that the UIO tracking accuracy designed in this invention is higher. Furthermore, Figures 3(a) and 3(b) show the threshold and fault residual signals based on UIO and LBO. When no fault occurs, the residual signal amplitude fluctuation is small, indicating that the proposed method is robust to unknown interference. When a fault is introduced at 14s, it can be seen that the fault residual signal can be detected by the UIO-based threshold at around 17s, and fluctuations at subsequent times can also be detected, while the LBO-based threshold can only detect the fault at 26s. This demonstrates that the UIO-based threshold design proposed in this invention is less conservative, more sensitive to faults, and has better fault detection performance.

[0168] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for detecting cluster faults in a DC servo motor system based on an observer with unknown time delay, characterized in that, The method specifically includes the following steps: Step 1: Establish a state-space model of the discrete time-delay DC servo motor system that considers process disturbances, measurement noise, and actuator failures; Step 2: Determine the observer for detecting input faults with unknown time delay based on the state-space model of the discrete time-delay DC servo motor system; Step 3: Obtain the DC servo motor residual system based on the unknown time delay input fault detection observer. The DC servo motor residual system is divided into a first residual subsystem and a second residual subsystem. Step 4: Solve for the gain of the time delay unknown input fault detection observer based on the constraints of the DC servo motor residual system; The constraints of the DC servo motor residual system are: (16) (17) Among them, scalar , , , , , This represents the initial error vector of the first residual subsystem. , Describes the 2-norm. express Norm; Represents the first residual subsystem The residual vector at time step, It is a positive definite matrix. Represents the process interference vector. express The measurement noise vector at time step, express The measurement noise vector at time step, express The measurement noise vector at time step, Represents the second residual subsystem The residual vector at time step, Represents the actuator fault vector; Step 5: Based on the set membership estimation method for centrosymmetric multicells and the observer gain, obtain the interval envelope of the centrosymmetric multicell residual threshold under fault-free conditions. Step 6: Determine whether the DC servo motor system is faulty based on the interval envelope of the centrally symmetric multicell residual threshold under fault-free conditions and the fault residual signal.

2. The method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer as described in claim 1, characterized in that, The specific process of step one is as follows: (9) in, for The system state vector at any given time. for The system state vector at any given time. for The system state vector at any given time. It is a constant delay. and For the system matrix, yes Armature voltage at time t, Represents the actuator fault vector. Represents the process interference vector. Represents the measurement noise vector. , , and Represents a constant matrix. , and They are The time-based process interference items, measurement error interference items, and actuator fault items are as follows: It is a function of the initial system state, and the system matrix is... , for The measurement output of time; Formula (9) satisfies the rank condition: ,in The dimension of the system state vector x(k) is represented by . Represents the identity matrix. This represents the rank of the matrix.

3. The method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer as described in claim 2, characterized in that, The unknown delay input fault detection observer is: (10) Among them, matrix , , , , and For observer gain, Indicates an input observer with unknown time delay. The state vector at time t, Indicates an input observer with unknown time delay. The state vector at time t, Indicates an input observer with unknown time delay. The state vector at time t, for The measurement output at time, yes The estimated vector of the system state at time t, the initial state , Represents a given initial function; The observer gain satisfies: (11) in, Represents the observer parameter matrix, Represents the system state vector The dimension of.

4. The method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer as described in claim 3, characterized in that, The process of obtaining the DC servo motor residual system based on the unknown time delay input fault detection observer is as follows: (12) in, Represents the residual system of DC servo motor Error vector at time step, Represents the residual system of DC servo motor Error vector at time step, Represents the residual system of DC servo motor Error vector at time step, express The measurement noise vector at time step, express The measurement noise vector at time step, express The measurement noise vector at time step, express The residual vector at time step, the matrix , .

5. The method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer according to claim 4, characterized in that, The first residual subsystem and the second residual subsystem are respectively: (13) (14) in, , , Represents the first residual subsystem Error vector at time step, Represents the second residual subsystem Error vector at time step, Represents the first residual subsystem Error vector at time step, Represents the second residual subsystem Error vector at time +1 Represents the first residual subsystem The residual vector at time step, Represents the second residual subsystem The residual vector at time step.

6. The method for detecting cluster faults in a DC servo motor system based on a time-delay unknown input observer as described in claim 5, characterized in that, The Process disturbances at any given time, measurement error disturbances, and initial state under fault-free conditions The scope is defined by the centrosymmetric multicellular structure, specifically as follows: (15) in, , and It is a constant. It is a diagonal matrix. , and The generation matrix of a centrosymmetric multicell. It is a centrosymmetric multicellular organism.

7. The method for detecting cluster faults in a DC servo motor system based on a time-delay unknown input observer as described in claim 6, characterized in that, In step four, the gain of the time-delay unknown input fault detection observer is solved based on the constraints of the DC servo motor residual system. The specific process is as follows: The constraints of the DC servo motor residual system are transformed into the following linear matrix inequalities: (18) (19) (20) in, , , and It is a positive definite matrix; The dimension of the process disturbance vector; The dimension of the measurement noise vector; The dimension of the actuator fault vector; It is an invertible matrix; It is an arbitrary matrix; scalar ; ; ; ; ; ; ; System matrix , It is the motor potential constant. It is the coefficient of viscous friction. It is the torque constant. It is the armature circuit inductance. It is the armature circuit resistance. It is the total moment of inertia of the rotating parts referred to the motor shaft; Solving the linear matrix inequalities (18), (19), and (20), we obtain the gain matrix of the observer for the time-delay unknown input fault detection. , , , , and .

8. The method for detecting cluster faults in a DC servo motor system based on an unknown time-delay input observer according to claim 7, characterized in that, The specific process of step five is as follows: Calculate the residual threshold ; in, , It is the identity matrix. It is a centrosymmetric multicell dimensionality reduction operator. express The dimensionality reduction result of the generation matrix of the time-major centrosymmetric multicell. express The dimensionality reduction result of the generation matrix of the time-matter centrosymmetric multicell; and The dimensionality reduction result of the time-major symmetric multicell generation matrix is: (21) The interval envelope of the residual threshold under fault-free conditions is ; in, Indicates to The first Sum of row elements, i.e. , express Inner Line 1 Column elements, This indicates taking the absolute value. yes The number of columns, , yes The order of.

9. The method for detecting cluster faults in a DC servo motor system based on a time-delay unknown input observer as described in claim 8, characterized in that, The specific process of step six is ​​as follows: The fault residual signal is calculated according to formula (12). ; If satisfied If the DC servo motor system is fault-free, then the following conditions must be met. If this occurs, the DC servo motor system will malfunction.

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