Set membership fault detection method of direct current servo motor system based on time delay unknown input observer

Abstract

The invention discloses a set membership fault detection method of a direct current servo motor system based on a time delay unknown input observer, and belongs to the technical field of model-based control system fault detection. According to the method, the problems of poor robustness, low fault sensitivity and high dynamic threshold conservative property of a residual error system on which an existing direct-current servo motor system fault detection technology depends are solved. According to the set membership fault detection method, an unknown input observer is adopted, and the sensitivity to actuator faults is improved while a residual error system is robust to unknown interference by introducing L infinity and H-performance indexes. A residual threshold determination method with low conservative property based on centrosymmetric multi-cell set membership estimation is adopted, so that the fault detection method disclosed by the invention is high in detection precision and high in sensitivity, and the phenomena of missing report and false report are not easy to occur. Compared with an LBO-based fault detection method, the fault detection threshold conservative property is lower, and the fault detection performance is better. The method can be applied to fault detection of the control system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of model-based control system fault detection, and particularly relates to a set-membership fault detection method for a DC servo motor system based on a time-delay unknown input observer. BACKGROUND

[0002] DC servo motors are widely used in intelligent equipment and power equipment fields due to their linear mechanical characteristics, smooth regulation characteristics, high overload capacity and fast response speed. However, the occurrence of faults in actual systems is inevitable, and if the faults cannot be detected and solved in time, it will lead to serious personnel casualties and property losses. At the same time, with the increasing demand for system reliability and safety, the problem of fault detection in actual systems needs to be solved. The fault detection technology based on analytical model uses the system model and measurement data to construct a residual generator, and the residual signal is compared with the preset threshold value for residual evaluation. If the residual signal is within the threshold value range, the system is normal; if the residual signal exceeds the threshold value range, it means that a fault has occurred. It is worth noting that the model-based fault detection method depends on the accurate model of the system, which is difficult to obtain in actual systems affected by unknown process disturbances and measurement errors. On the other hand, the difficulty of this method lies in the determination of the fault detection threshold value. Unreasonable threshold value may lead to false negatives, delayed alarms under faults and false positives under no faults. The threshold values determined by the existing experience-based and norm-based threshold setting methods are relatively conservative, and have great limitations when applied to actual systems. The set-membership estimation technology based on central symmetric zonotope does not need to know the specific probability distribution of unknown inputs, and only needs to assume that the process disturbance and measurement error are unknown but bounded, so it is suitable for fault detection threshold value determination. The threshold value determination technology based on set-membership estimation depends on the selection of fault detection observers, and a suitable observer will further reduce the conservatism of fault detection threshold value design.

[0003] For example, the central symmetric zonotope set-membership fault detection method proposed in the document (Naima Sehli, et al. Fault Detection and Isolation for Linear discrete-time Delayed Systems based on L ∞ Observer and Zonotopic Analysis. IFAC-PapersOnline, Vol.55, No. 25 (2022) 169-174) adopts the L ∞The performance index weakens the influence of unknown interference. However, the residual system relied on by the existing fault detection technology is still poor in robustness to unknown interference, still low in sensitivity to faults, and still high in conservativeness of dynamic threshold, so it is an urgent problem to be solved to propose a fault detection method for a DC servo motor system. SUMMARY

[0004] The purpose of the present application is to solve the problems of poor robustness, low sensitivity to faults and high conservativeness of dynamic threshold of the residual system relied on by the existing fault detection technology for a DC servo motor system, and a set-membership fault detection method for a DC servo motor system based on a time-delay unknown input observer is proposed.

[0005] The technical scheme adopted by the present application to solve the above technical problems is: a set-membership fault detection method for a DC servo motor system based on a time-delay unknown input observer, which specifically comprises the following steps:

[0006] Step one, establishing a state space model of a discrete time-delay DC servo motor system considering process disturbance, measurement noise and actuator fault;

[0007] Step two, determining a time-delay unknown input fault detection observer according to the state space model of the discrete time-delay DC servo motor system;

[0008] Step three, obtaining a DC servo motor residual system according to the time-delay unknown input fault detection observer, wherein the DC servo motor residual system is divided into a residual first subsystem and a residual second subsystem;

[0009] Step four, solving the gain of the time-delay unknown input fault detection observer according to the constraint of the DC servo motor residual system;

[0010] Step five, obtaining the interval envelope of the central symmetric polytope residual threshold under no fault according to the set-membership estimation method based on a central symmetric polytope and the observer gain;

[0011] Step six, determining whether the DC servo motor system is faulty according to the interval envelope of the central symmetric polytope residual threshold under no fault and the fault residual signal.

[0012] The present application has the following beneficial effects:

[0013] The set-membership fault detection method provided by the present application adopts an unknown input observer (UIO), introduces L ∞The H_-performance index makes the residual system robust to unknown disturbances while increasing sensitivity to actuator failures. By employing a low-conservatism residual threshold determination method based on centrosymmetric polytope set membership estimation, the proposed fault detection method achieves high accuracy and sensitivity, making it less susceptible to missed and false positives. Compared to LBO-based fault detection methods, the fault detection thresholds obtained in this invention are less conservative and offer better fault detection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of a method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to the present invention;

[0015] FIG2(a) shows the state of the fault detection observer and the Lumberg observer of the present invention. Tracking performance comparison chart;

[0016] FIG2( b ) shows the state of the fault detection observer and the Lumberg observer of the present invention. Tracking performance comparison chart;

[0017] FIG2(c) shows the state of the fault detection observer and the Lumberg observer of the present invention. Tracking performance comparison chart;

[0018] FIG3(a) is a diagram of the fault detection observer and the Lumberg observer of the present invention. Fault detection result diagram;

[0019] FIG3(b) shows the fault detection observer of the present invention and the Lumberg observer. Fault detection result diagram. DETAILED DESCRIPTION

[0020] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer, the method specifically comprising the following steps:

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

[0022] Step 2: determining a time-delay unknown input fault detection observer based on a state space model of the discrete time-delay DC servo motor system;

[0023] Step 3: obtaining a DC servo motor residual system according to a time-delay unknown input fault detection observer, wherein the DC servo motor residual system is split into a first residual subsystem and a second residual subsystem;

[0024] Step four, solve the gain of time delay unknown input fault detection observer according to the constraint of the residual system of the DC servo motor;

[0025] Step five, obtain the interval envelope of the central symmetric polytope residual threshold under no fault according to the set membership estimation method based on the central symmetric polytope and the observer gain;

[0026] Step six, determine whether the DC servo motor system is faulty according to the interval envelope of the central symmetric polytope residual threshold under no fault and the fault residual signal.

[0027] Specific implementation method two: the difference between this implementation method and the specific implementation method one is that the specific process of step one is:

[0028] 1. According to the dynamic analysis of the DC servo motor, the electrical and mechanical power equations of the DC servo motor are listed:

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

[0030] (1)

[0031] wherein, L is the inductance of the armature loop, with the unit of H; I is the armature loop current, with the unit of A; R is the armature loop resistance, with the unit of Ω; E is the back electromotive force at both ends of the armature when the motor rotates, with the unit of V; U is the armature voltage, with the unit of V.

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

[0033] (2)

[0034] wherein, K is the motor potential constant; , with the unit of rad / s.

[0035] The output torque of the motor is proportional to the armature current

[0036] (3)

[0037] wherein, T is the electromagnetic torque generated when the motor rotates, with the unit of N·m; Kt is the torque constant.

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

[0039] (4)

[0040] (5)

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

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

[0043] (6)

[0044] 3. According to the speed subsystem and current subsystem, the state space model of the DC servo motor is obtained:

[0045] (7)

[0046] in, , is the system state vector at time t; is the angular position of the motor rotation; , is the measurement output at time t; 、 and denote the known system matrices with appropriate dimensions, , , .

[0047] 4. According to the DC servo motor state space model, obtain the discretized DC servo motor state space model:

[0048] (8)

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

[0050] The state space model of the discrete time-delay DC servo motor system subject to time delay, process disturbance, measurement noise and actuator fault can be determined based on the discretized state space model:

[0051] (9)

[0052] in, for The system state vector at time t, for The system state vector at time t, for The system state vector at time t, is a constant delay, and is the system matrix, yes The armature voltage at time represents the actuator fault vector, represents the process disturbance vector, represents the measurement noise vector, 、 、 and represents a constant matrix of suitable dimension, 、 and They are The process disturbance term, measurement error disturbance term and actuator fault term at time , is a function of the initial system state, the system matrix , for The measurement output at the moment, Represents the system state vector Dimensionality;

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

[0054] Other steps and parameters are the same as those in the first embodiment.

[0055] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the delay unknown input fault detection observer is:

[0056] (10)

[0057] Among them, the matrix 、 、 、 、 and is the observer gain, represents the time-delay unknown input observer The state vector at time t, represents the time-delay unknown input observer The state vector at time t, represents the time-delay unknown input observer the state vector at time k, is the measurement output at time k, is the estimation vector of system state at time k, the initial state , denotes a given initial function;

[0058] the observer gain satisfies:

[0059] (11)

[0060] wherein, denotes the observer parameter matrix to be designed, denotes the dimension of the system state vector .

[0061] The other steps and parameters are the same as those in the first or second embodiment.

[0062] According to the rank condition satisfied by formula (9), the matrix equation has a solution, and the general solution is: ; , denotes the dimension of the system measurement output, denotes a unit matrix with the dimension of ; , denotes the pseudo-inverse of the matrix.

[0063] According to the state space model of the DC servo motor fault system, the time delay unknown input fault detection observer is determined, which can make the residual system robust to unknown disturbance and sensitive to actuator fault.

[0064] The fourth embodiment is different from one of the first to third embodiments in that the DC servo motor residual system is obtained according to the time delay unknown input fault detection observer, specifically:

[0065] (12)

[0066] wherein, denotes the error vector of the DC servo motor residual system at time k, denotes the error vector of the DC servo motor residual system at time k, denotes the error vector of the DC servo motor residual system at time k, denotes the measurement noise vector at time k, express The measurement noise vector at time , express The measurement noise vector at time , express The residual vector at time t, matrix , .

[0067] The other steps and parameters are the same as those in the first to third embodiments.

[0068] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the residual first subsystem and the residual second subsystem are respectively:

[0069] (13)

[0070] (14)

[0071] in, , , represents the first residual subsystem The error vector at time t, represents the second residual subsystem The error vector at time , represents the first residual subsystem The error vector at time t, represents the second residual subsystem The error vector at time +1, represents the first residual subsystem The residual vector at time , represents the second residual subsystem The residual vector at time .

[0072] The other steps and parameters are the same as those in the first to fourth embodiments.

[0073] Splitting the residual system into the following two subsystems can better analyze the robustness of the desired residual system to unknown disturbances and its sensitivity to actuator failures.

[0074] Specific embodiment 6: This embodiment differs from the specific embodiments 1 to 5 in that The process disturbance term, measurement error disturbance term and initial state under no fault condition at the moment The range of is defined by the centrosymmetric polyhedron, specifically:

[0075] (15)

[0076] in, , and is a given constant, is a diagonal matrix, , and is the generating matrix of the central symmetric polytope (determines the shape and volume of the central symmetric polytope), is the central symmetric polytope.

[0077] The other steps and parameters are the same as one of the first to fifth embodiments.

[0078] A central symmetric polytope of order s is an affine transformation of the hypercube : where, is the Minkowski sum; is the center of , is the generating matrix of . For the convenience of representation, the central symmetric polytope is defined as .

[0079] The seventh embodiment is different from one of the first to sixth embodiments in that the specific process of the fourth step is as follows:

[0080] Step four I, in order to make the residual system robust to unknown disturbances while being sensitive to actuator faults, the constraint of the DC servo motor residual system is defined as:

[0081] (16)

[0082] (17)

[0083] wherein the scalar , , (i.e. H_-performance index), , , represents the initial error vector of the first residual subsystem, , represents the 2-norm, represents the -norm;

[0084] Step four II, the constraint condition of the DC servo motor residual system is converted into the following linear matrix inequality:

[0085] (18)

[0086] (19)

[0087] (20)

[0088] wherein, , , and are positive definite matrices (which can be solved based on equations (18) to (20)); , and can be solved based on equations (18) to (20)); denotes the dimension of the process disturbance vector; denotes the dimension of the measurement noise vector; denotes the dimension of the actuator fault vector; is an invertible matrix (which can be solved based on equations (18) to (20)); is an arbitrary matrix; scalar ; ; ; ; ; ; ; ; system matrix , is the motor potential constant, is the viscous friction coefficient, is the torque constant, is the armature circuit inductance, is the armature circuit resistance, is the total moment of inertia of the rotating parts reduced to the motor shaft;

[0089] Step four three, solve linear matrix inequalities (18), (19) and (20) to obtain the time delay unknown input fault detection observer gain matrix , , , , and .

[0090] The other steps and parameters are the same as one of the first to sixth embodiments.

[0091] Embodiment eight: different from one of the first to seventh embodiments, the specific process of the step five is:

[0092] Calculate the residual threshold ;

[0093] wherein, , is the unit matrix, is the dimension reduction result of the generation matrix of the central-symmetric polytope at the moment, represents the dimension reduction result of the generation matrix of the central-symmetric polytope at the moment, represents the dimension reduction result of the generation matrix of the central-symmetric polytope at the moment; and the dimension reduction result of the generation matrix of the central-symmetric polytope at the moment is:

[0094] (21)

[0095] The interval envelope of the residual threshold under no fault is ;

[0096] wherein, represents the summation of the elements in the i-th row of , , , represents the element in the i-th row and the j-th column of , represents taking the absolute value, is the column number of , , is the order of . The steps and parameters are the same as one of the first to seventh embodiments.

[0097] The ninth embodiment is different from one of the first to eighth embodiments in that the specific process of the step six is as follows:

[0098] The ninth embodiment is different from one of the first to eighth embodiments in that the specific process of the step six is as follows:

[0099] The fault residual signal is calculated according to the formula (12), that is, , ;

[0100] If (specifically, for all components of the residual vector , all components are in the interval envelope, and ), the DC servo motor system is fault-free, and if , the DC servo motor system is faulty.

[0101] The other steps and parameters are the same as one of the first to eighth embodiments.

[0102] Embodiment

[0103] The embodiment provides a DC servo motor set member fault detection method based on a time delay unknown input observer, and specifically includes the following steps:​

[0104] Step 1: Determine the discrete-time model of the DC servo motor system with time delay, process disturbance, measurement noise and actuator faults:

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

[0106] (1)

[0107] Where is the inductance of the armature loop, with the unit of H; is the armature loop current, with the unit of A; is the armature loop resistance, with the unit of Ω; is the back EMF of the armature, with the unit of V; is the armature voltage, with the unit of V.

[0108] The back EMF of the armature is proportional to the motor speed:

[0109] (2)

[0110] Where is the motor potential constant; is the motor angular velocity, with the unit of rad / s.

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

[0112] (3)

[0113] Where is the electromagnetic torque generated when the motor rotates, with the unit of N·m; is the torque constant.

[0114] The relationship between the output torque and the load is:

[0115] (4)

[0116] (5)

[0117] Where, is the total moment of inertia of the rotating part converted to the motor shaft, with the unit of N·m·s 2 ; is the load torque, with the unit of N·m; is the viscous friction coefficient.

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

[0119] (6)

[0120] The state-space model of the DC servo motor is:

[0121] (7)

[0122] where is defined as the system state vector at time t; is the angular position of the motor rotation; is defined as the measurement output at time t; , , and

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

[0124] (8)

[0125] Step 2: Take the simulation sampling time , the system matrix can be obtained by Euler's method;

[0126] .

[0127] The DC servo motor system (8) suffers from time delay, process disturbance, measurement noise, and actuator faults, which can be described as follows:

[0128] (9)

[0129] where ; ; ; ; introduce fault ; control input , ; is a constant time delay; is a function of the initial system state, .

[0130] Equation (9) satisfies the rank condition: rank( = , where represents the dimension of the system state vector x(k), indicates the identity matrix.

[0131] Step 3: Determine the time delay unknown input fault detection observer based on the DC servo motor fault system model:

[0132] (10)

[0133] where is the observation state vector, whose initial state is , denotes a given initial function, .

[0134] matrix , , , , and are the time-delay unknown input fault detection observer gains, and satisfy the following conditions:

[0135] (11)

[0136] According to the rank condition satisfied by formula (9), the matrix equation has a solution, and its general solution is: ; , .

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

[0138] (12)

[0139] where the matrix ; ; the residual system (12) includes a residual first subsystem and a residual second subsystem:

[0140] (13)

[0141] (14)

[0142] where ; .

[0143] The process disturbance , the measurement noise and the initial state of the residual system of the DC servo motor under the fault-free condition are bounded by the following central symmetric polytope:

[0144] (15)

[0145] The central symmetric polytope is defined as follows:

[0146] A central symmetric polytope of order s is an affine transformation of the hypercube : . Where is the center of the Minkowski sum; is the center of the Minkowski sum; is the generating matrix of the Minkowski sum determines the shape and volume of the centrally symmetric polytope. For simplicity, define .

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

[0148] (16)

[0149] (17)

[0150] where the scalar , , , ; ; .

[0151] Step 4: The constraint conditions are converted into linear matrix inequalities as follows:

[0152] (18)

[0153] (19)

[0154] (20)

[0155] where , , and are positive definite matrices; is a reversible matrix; is an arbitrary matrix; the scalar ; ; ; ; ; ; ; ; .

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

[0157] Step 5: Take the scalar ; ; ; ; the ; The observer gain is: ; ; ;

[0158] ; ; .

[0159] Step 6: The residual threshold under no-fault conditions based on the set membership estimation method is :

[0160] in, , is the identity matrix, It is a centrosymmetric polytope dimensionality reduction operator, which is used to reduce the dimension of the generated matrix to a set positive integer. express The dimensionality reduction result of the generator matrix of the moment-centrosymmetric polytope, express The dimensionality reduction result of the generator matrix of the moment-centrosymmetric polytope; and The dimensionality reduction result of the moment-centrosymmetric polytope generation matrix is:

[0161] (twenty one)

[0162] The interval envelope of the residual threshold under no fault is ;

[0163] in, Express The first The sum of row elements, that is , express Neidi Rank Elements of the column, Indicates taking the absolute value, yes The number of columns, , yes The order of .

[0164] Step 7: According to get , determine the fault detection logic relationship as follows:

[0165] If satisfied , then the DC servo motor system has no fault, if it satisfies , then the DC servo motor system fails;

[0166] in, Is the fault detection result signal, when When the residual signal is always within the interval envelope, it indicates that no fault occurs. When the residual signal is always beyond the interval envelope, it indicates that a fault has occurred.

[0167] Figures 2(a) to 2(c) The time-delay unknown input fault detection observer (UIO) designed in the present application and the Luenberger observer (LBO) adopted in the literature (Naima Sehli, et al. Fault Detection and Isolation for Linear discrete-time Delayed Systems based on Observer and Zonotopic Analysis. IFAC-PapersOnline, Vol. 55, No. 25 (2022) 169-174) are used to track the state of the fault system of the DC servo motor, wherein, is the first component in the system state vector, is the second component in the system state vector, is the third component in the system state vector, it can be seen that the UIO designed in the present application has higher tracking accuracy. In addition, Figures 3(a) and 3(b) show the threshold values and fault residual signals based on the UIO and the LBO. When no fault occurs, the amplitude of the residual signal fluctuates little, indicating that the method proposed in the present application is robust to unknown disturbances. When a fault is introduced at 14s, it can be seen that the fault residual signal can be detected by the threshold value based on the UIO at about 17s and the fluctuations in the subsequent time can also be detected, while the threshold value based on the LBO cannot detect the fault until 26s. It is embodied that the threshold value based on the UIO proposed in the present application is less conservative, sensitive to faults, and has better fault detection performance.

[0168] The above calculation examples of the present application are only to illustrate the calculation model and calculation process of the present application, and are not a limitation on the embodiments of the present application. For ordinary skilled persons in the art, other different forms of changes or variations can be made on the basis of the above description, and it is impossible to exhaust all the embodiments here, and any obvious changes or variations derived from the technical solutions of the present application still fall within the protection scope of the present application.

Claims

1. A method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer, characterized in that: The method specifically comprises the following steps: Step 1: Establish a state space model of the discrete time-delay DC servo motor system considering process disturbance, measurement noise and actuator fault; Step 2: determining a time-delay unknown input fault detection observer based on a state space model of the discrete time-delay DC servo motor system; Step 3: obtaining a DC servo motor residual system according to a time-delay unknown input fault detection observer, wherein the DC servo motor residual system is split into a first residual subsystem and a second residual subsystem; Step 4: Solve the gain of the time-delay unknown input fault detection observer according to the constraints of the DC servo motor residual system; Step 5: According to the set membership estimation method based on the centrosymmetric polyhedron and the observer gain, the interval envelope of the centrosymmetric polyhedron residual threshold under no fault condition is obtained; Step 6: Determine whether the DC servo motor system is faulty based on the interval envelope of the centrosymmetric polyhedral residual threshold under no-fault conditions and the fault residual signal.

2. The method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 1, characterized in that: The specific process of step one is: (9) in, for The system state vector at time t, for The system state vector at time t, for The system state vector at time t, is a constant delay, and is the system matrix, yes The armature voltage at time represents the actuator fault vector, represents the process disturbance vector, represents the measurement noise vector, 、 、 and represents a constant matrix, 、 and They are The process disturbance term, measurement error disturbance term and actuator fault term at time , is a function of the initial system state, the system matrix , for Measurement output at the moment; Formula (9) satisfies the rank condition: ,in represents the dimension of the system state vector x(k), represents the identity matrix, Represents the rank of the matrix.

3. The method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 2, characterized in that: The time-delay unknown input fault detection observer is: (10) Among them, the matrix 、 、 、 、 and is the observer gain, represents the time-delay unknown input observer The state vector at time t, represents the time-delay unknown input observer The state vector at time t, represents the time-delay unknown input observer The state vector at time t, for The measurement output at the moment, 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 collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 3, characterized in that: The DC servo motor residual system is obtained according to the time-delay unknown input fault detection observer, specifically: (12) in, Represents the DC servo motor residual system The error vector at time , Represents the DC servo motor residual system The error vector at time , Represents the DC servo motor residual system The error vector at time , express The measurement noise vector at time , express The measurement noise vector at time , express The measurement noise vector at time , express The residual vector at time t, matrix , .

5. The method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 4, characterized in that: The residual first subsystem and the residual second subsystem are respectively: (13) (14) in, , , represents the first residual subsystem The error vector at time , represents the second residual subsystem The error vector at time , represents the first residual subsystem The error vector at time , represents the second residual subsystem The error vector at time +1, represents the first residual subsystem The residual vector at time , represents the second residual subsystem The residual vector at time .

6. The method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 5, characterized in that: described The process disturbance term, measurement error disturbance term and initial state under no fault condition at time The range of is defined by the centrosymmetric polyhedron, specifically: (15) in, 、 and is a constant, is a diagonal matrix, 、 and is the generating matrix of the centrosymmetric polyhedron, It is a centrosymmetric polyhedron.

7. The method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 6, characterized in that: The specific process of step 4 is as follows: Step 4.

1. The constraints of the DC servo motor residual system are: (16) (17) Among them, the scalar , , , , , represents the initial error vector of the first residual subsystem, , represents the 2-norm, express norm; Step 42: Convert the constraints of the DC servo motor residual system into the following linear matrix inequality: (18) (19) (20) in, 、 、 and is a positive definite matrix; Represents the dimension of the process disturbance vector; represents the dimension of the measurement noise vector; represents the dimension of the actuator fault vector; is a reversible matrix; is an arbitrary matrix; scalar ; ; ; ; ; ; ; ; System matrix , is the motor potential constant, is the coefficient of viscous friction, is the torque constant, is the armature circuit inductance, is the armature circuit resistance, It is the total moment of inertia of the rotating parts converted to the motor shaft; 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 .

8. The method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 7, characterized in that: The specific process of step five is: Calculate the residual threshold ; in, , is the identity matrix, is the centrosymmetric polytope dimensionality reduction operator, express The dimensionality reduction result of the generator matrix of the moment-centrosymmetric polytope, express The dimensionality reduction result of the generator matrix of the moment-centrosymmetric polytope; and The dimensionality reduction result of the moment-centrosymmetric polytope generation matrix is: (21) The interval envelope of the residual threshold under no fault is ; in, Express The first The sum of row elements, that is , express Neidi Rank Elements of the column, Indicates taking the absolute value, yes The number of columns, , yes The order of .

9. The method for collective fault detection of a DC servo motor system based on a time-delay unknown input observer according to claim 8, characterized in that: The specific process of step six is ​​as follows: According to formula (12), the fault residual signal is calculated ; If satisfied , then the DC servo motor system has no fault, if it satisfies , the DC servo motor system fails.

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