Series excitation DC motor event trigger fault detection method

Abstract

The invention relates to a series excitation DC motor event trigger fault detection method, and solves the problem of event trigger fault detection under triple asynchronous characteristics in a series excitation DC motor circuit system. The method comprises the following specific steps: firstly, establishing a mathematical model for reflecting the state change of a series excitation direct current motor circuit system based on T-S fuzzy and Semi-Markov theories by using the random fluctuation of rotational inertia and the torque / reverse electromotive force constant change under different fuzzy rules; designing a T-S fuzzy antecedent variable asynchronous condition and an asynchronous event generator, and designing an asynchronous fault detection filter; the real-time monitoring of the system state and the timely detection of the fault are further realized; a Lyapunov function is further constructed, and the stability of the closed-loop series excitation direct-current motor circuit system is analyzed in combination with a probability density function; the obtained system random stability condition and the filter existence condition are converted into a group of linear matrix inequalities, and a feasible mathematical description and calculation method is provided for the practical application of the system.

Description

Technical Field

[0001] The invention relates to a series-excited DC motor circuit system technology, in particular to an event-triggered fault detection method for a series-excited DC motor based on triple asynchronous characteristics. Background Art

[0002] With the development of automation control technology, DC motors, as one of the important types of motors, are widely used in industrial equipment, robot control, automotive electric systems and other fields; in order to ensure the efficient and reliable operation of these systems, fault detection and diagnosis technology has become the focus of research.

[0003] Traditional series-excited DC motor circuit fault detection methods are mostly based on conventional signal processing techniques, such as vibration analysis, temperature monitoring, and current and voltage sensing. Although these methods can provide certain fault warnings, the change in rotational inertia in the series-excited DC motor circuit system is often accompanied by randomness and multimodality. At the same time, the torque / back electromotive force constant in the system also exhibits nonlinear characteristics, making system modeling very difficult and the state difficult to control.

[0004] At present, most of the stability analysis research on series-excited DC motor circuit systems is based on Markov theory. By constructing the Lyapunov function, the stability conditions of series-excited DC motor circuits based on linear matrix inequalities and the existence conditions of fault detection filters are derived; but in Markov theory, the residence time of the mode has a memoryless exponential distribution, and the transfer rate is independent of time, which leads to a certain conservatism in the system stability conditions and controller design schemes obtained based on Markov theory.

[0005] At the same time, the various components of the series-excited DC motor circuit or different motors usually need to realize data transmission and remote control through the network, and are accompanied by external disturbances, time delays, data packet loss and other phenomena. This puts higher requirements on the mastery of modal information between the system, event generator and fault detection filter, the utilization of limited network resources and the realization of system stability control.

[0006] In view of this, those skilled in the art are in urgent need of proposing a more accurate modeling method and a less conservative stability criterion to ensure effective control of the operating state of the DC motor circuit system. Summary of the invention

[0007] The present invention aims to overcome at least one of the shortcomings and deficiencies of the above-mentioned prior art, and provides an event-triggered fault detection method for a series-excited DC motor based on triple asynchronous characteristics. The method takes into account the random fluctuation of the moment of inertia in the series-excited DC motor circuit system, the nonlinear characteristics of the torque / back electromotive force constant, the system interference, and the bandwidth limitation and time lag phenomenon in the signal transmission process, and establishes a series-excited DC motor circuit model using TS fuzzy and Semi-Markov theory, thereby effectively solving the event-triggered fault detection problem under the triple asynchronous characteristics in the series-excited DC motor circuit system.

[0008] The object of the present invention is achieved based on the following technical solution: a method for detecting a series-excited DC motor event-triggered fault is provided, comprising the following steps:

[0009] S1, establish a series-excited DC motor circuit system model;

[0010] S2, design asynchronous antecedent variables, asynchronous event triggering conditions, asynchronous fault detection filters, evaluation functions and thresholds;

[0011] S3, random stability condition of given series-excited DC motor circuit system;

[0012] S4, solving the fault detection filter gain and designing the fault detection filter;

[0013] S5, fault detection filter performance test.

[0014] In the present invention, in step S1, the expression for establishing the series-excited DC motor circuit system model is:

[0015] Where R represents the resistance R a and the field winding resistance R f The sum of L is the armature inductance L a and the field winding inductance L f The sum of J represents the moment of inertia, D represents the viscous friction coefficient, and K represents the torque / back electromotive force constant. Represents the actual angular velocity ω(t) and the desired angular velocity ω ref (t), Represents the actual current η(t) and the expected current η ref (t), It refers to the difference between the actual input voltage V(t) and the expected voltage V ref (t) The deviation between

[0016] In the present invention, when there is an external disturbance w(t) and a fault signal f(t), the state space model of the series-excited DC motor circuit system is established as:

[0017]

[0018] In the formula, the moment of inertia J vt There are three modes, and the jump between modes satisfies the Semi-Markov random process; x2(t) is the nonlinear uncertainty term in the series-excited DC motor circuit, and its value range is x2(t)∈[N1,N2], and it is defined as The antecedent variable is x2(t), the TS fuzzy condition is selected, and the membership function is established as follows:

[0019]

[0020] When x2(t) equals N1, or When x2(t) equals N2, or

[0021] The nonlinear random system model of the above series-excited DC motor is transformed into the TS fuzzy and Semi-Markov series-excited DC motor system model, specifically:

[0022]

[0023] in

[0024]

[0025] In the formula represents the degree of membership, Represents fuzzy weight.

[0026] In the present invention, step S2 is specifically:

[0027] S2.1 Based on TS fuzzy and Semi-Markov random processes, a series-excited DC motor circuit system is constructed and the asynchronous event triggering conditions are designed:

[0028]

[0029] In the formula, Indicates the current sampling data. Indicates the latest trigger data, δ ρ ∈[0,1) are parameters related to the event generator mode, Λ1(ζ1(t)) and Λ2(ζ1(t)) are the event trigger weight matrices that need to be determined, and ζ1(t) represents the modal information actually received by the event trigger condition.

[0030] S2.2 Design asynchronous event-triggered fault detection filter,

[0031] Filter Rule 1: When is N1, then

[0032]

[0033] Filter Rule 2: When is N2, then

[0034]

[0035] In the formula, represents the time when data is transmitted to the fault detection filter, x f (t) is the filter state, r f (t) is the residual signal, and j = 1, 2 is the determined filter gain, ζ2(t) represents the modal information actually received by the filter;

[0036] S2.3 uses the following conditions to simplify the description of the conversion of asynchronous membership functions in series-excited DC motor circuit systems:

[0037]

[0038] Can get

[0039] In the formula and for are the minimum and maximum values ​​in the operation process, and satisfy

[0040] Further, the following results are obtained

[0041]

[0042] S2.4 In order to improve the fault detection performance of the series-excited DC motor circuit system, a weighted function f(s) is introduced into the fault detection system;

[0043] Design ω (s)=F(s)f(s), where f ω (s) and f(s) are respectively f ω (t) and the Laplace transform of f(t). F(s) is given in advance and is used to assign a frequency weight in the spectrum of the fault signal to facilitate the implementation of the fault detection scheme. The following formula can be obtained:

[0044]

[0045] The above formula is f ω (s) is a state space realization, and x ω (t) is The state vector of x ω (0) = 0;

[0046] S2.5 Select the following evaluation function

[0047]

[0048] In the formula, t0 and are the moment of initial evaluation time and evaluation time respectively;

[0049] Then, select the following threshold form of the evaluation function:

[0050]

[0051] Based on the above two equations, if J rf (t)>J th , indicating that a fault has been detected, otherwise it means that no fault has occurred;

[0052] S2.6 combines the series-excited DC motor circuit system model with asynchronous antecedent variables, event trigger conditions and filters to obtain a closed-loop series-excited DC motor circuit system model:

[0053]

[0054] in

[0055]

[0056] Construct a Lyapunov function that depends on the system mode change and the dwell time within the mode; give the stability criterion of the series-excited DC motor circuit system, and then realize the stability analysis of the series-excited DC motor circuit system;

[0057] Series-excited DC motor circuit system model, all conversion rates depend on the dwell time h. When the system mode changes, h is updated to 0. For all modes m=1,2,3, ρ=1,2, If there exists a set of positive definite matrices P with appropriate dimensions 1m ,P,P m ,F, Λ 1ρ , Λ 2ρ , a normal number δ ρ ,ù1,ù2,χ1,χ2 make the following matrix inequality hold:

[0058]

[0059] in

[0060]

[0061]

[0062] Where I represents the identity matrix, * represents the symmetric term in the matrix, sym{A}=A T +A, then the series-excited DC motor circuit system is called stochastically stable and satisfies H ∞ performance.

[0063] In the present invention, in step S2.1, when ζ1(t)=ρ, ρ=1,2, v t Asynchronous with ζ1(t) and satisfying the conditional probability P r {ζ1(t)=ρ|v t =m}=θ mρ , 0≤θ mρ ≤1,

[0064] The holding interval time of the zero-order holder is in Consider data delay in network transmission in η1 and η2 represent the lower and upper bounds of the time-varying delay η(t), respectively;

[0065] The event triggering conditions are transformed into the following forms:

[0066]

[0067] In the present invention, in step S2.2, when v t Asynchronous with ζ2(t) and satisfying the conditional probability

[0068] In the present invention, in step S2.3, when and for and

[0069] get in as well as

[0070] In the present invention, in step S4,

[0071] For all modes m=1,2,3,ρ=1,2, If there exists a set of positive definite matrices P with appropriate dimensions 1m ,P, F, Λ 1ρ , Λ2ρ , normal number δ ρ ,ù1,ù2,χ1,χ2 make the following matrix inequality hold:

[0072]

[0073] in

[0074]

[0075] The series-excited DC motor circuit system is said to be stochastically stable and satisfies H ∞ performance, then determine the fault detection filter gain as:

[0076] In the present invention, in step S5, a linear matrix inequality toolbox in Matlab is used to determine whether the system parameter matrix under all given modes satisfies the fault detection filter design conditions given in step S4. If so, it can be determined that based on the designed asynchronous antecedent variables, asynchronous event triggering conditions and asynchronous fault detection filters, the series-excited DC motor circuit system is stochastically stable.

[0077] The present invention utilizes the linear matrix inequality toolbox in Matlab to determine whether the system parameter matrix under all given modes satisfies the fault detection filter design conditions given in step S4. If so, it is determined that the series-excited DC motor circuit system is stochastically stable based on the designed fault detection filter.

[0078] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0079] 1. By introducing TS fuzzy and Semi-Markov process, the random change of the moment of inertia and the nonlinear characteristics of the torque / back electromotive force constant of the series-excited DC motor circuit system can be described more accurately and reasonably;

[0080] 2. By conducting stability analysis and fault detection filter design on the established series-excited DC motor circuit system model based on TS and fuzzy Semi-Markov theory, the triple asynchronous event-triggered fault detection problem of the series-excited DC motor circuit system can be solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a flow chart of the steps of the present invention;

[0082] Figure 2 It is a schematic diagram of the circuit system of a series-excited DC motor;

[0083] Figure 3 It is the modal change diagram of the series-excited DC motor circuit system, event triggering conditions, and fault detection filter;

[0084] Figure 4 It is the release time and release interval diagram of the event triggering condition;

[0085] Figure 5 is the state response diagram of the fault detection filter;

[0086] Figure 6 Evaluation function and threshold diagram for system failure. DETAILED DESCRIPTION

[0087] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0088] The present invention utilizes the linear matrix inequality toolbox in Matlab to determine whether the system parameter matrix under all given modes satisfies the fault detection filter design conditions given in step S4. If so, it is determined that the series-excited DC motor circuit system is stochastically stable based on the designed fault detection filter.

[0089] A method for detecting a series-excited DC motor event-triggered fault is provided, comprising the following steps:

[0090] S1, establish a series-excited DC motor circuit system model;

[0091] S2, design asynchronous antecedent variables, asynchronous event triggering conditions, asynchronous fault detection filters, evaluation functions and thresholds;

[0092] S3, random stability condition of given series-excited DC motor circuit system;

[0093] S4, solving the fault detection filter gain and designing the fault detection filter;

[0094] S5, fault detection filter performance test.

[0095] In step S1 of the present invention, the expression for establishing the series-excited DC motor circuit system model is:

[0096] Where R represents the resistance R a and the field winding resistance R f The sum of L is the armature inductance L a and the field winding inductance Lf The sum of J represents the moment of inertia, D represents the viscous friction coefficient, and K represents the torque / back electromotive force constant. Represents the actual angular velocity ω(t) and the desired angular velocity ω ref (t), Represents the actual current η(t) and the expected current η ref (t), It refers to the difference between the actual input voltage V(t) and the expected voltage V ref (t) The deviation between

[0097] When there is an external disturbance w(t) and a fault signal f(t), the state space model of the series-excited DC motor circuit system is established as follows:

[0098]

[0099] In the formula, the moment of inertia J vt There are three modes, and the jump between modes satisfies the Semi-Markov random process; x2(t) is the nonlinear uncertainty term in the series-excited DC motor circuit, and its value range is x2(t)∈[N1,N2], and it is defined as The antecedent variable is x2(t), the TS fuzzy condition is selected, and the membership function is established as follows:

[0100]

[0101] When x2(t) equals N1, or When x2(t) equals N2, or

[0102] The nonlinear random system model of the above series-excited DC motor is transformed into the TS fuzzy and Semi-Markov series-excited DC motor system model, specifically:

[0103]

[0104] in

[0105]

[0106] In the formula represents the degree of membership, Represents fuzzy weight.

[0107] Step S2 of the present invention is specifically:

[0108] S2.1 Based on TS fuzzy and Semi-Markov random processes, a series-excited DC motor circuit system is constructed and the asynchronous event triggering conditions are designed:

[0109]

[0110] In the formula, Indicates the current sampling data. Indicates the latest trigger data, δ ρ ∈[0,1) are parameters related to the event generator mode, Λ1(ζ1(t)) and Λ2(ζ1(t)) are the event trigger weight matrices that need to be determined, and ζ1(t) represents the modal information actually received by the event trigger condition.

[0111] S2.2 Design asynchronous event-triggered fault detection filter,

[0112] Filter Rule 1: When is N1, then

[0113]

[0114] Filter Rule 2: When is N2, then

[0115]

[0116] In the formula, represents the time when data is transmitted to the fault detection filter, x f (t) is the filter state, r f (t) is the residual signal, and j = 1, 2 is the determined filter gain, ζ2(t) represents the modal information actually received by the filter;

[0117] S2.3 uses the following conditions to simplify the description of the conversion of asynchronous membership functions in series-excited DC motor circuit systems:

[0118]

[0119] Can get

[0120] In the formula and for are the minimum and maximum values ​​in the operation process, and satisfy

[0121] Further, the following results are obtained

[0122]

[0123] S2.4 In order to improve the fault detection performance of the series-excited DC motor circuit system, a weighted function f(s) is introduced into the fault detection system;

[0124] Design ω (s)=F(s)f(s), where f ω (s) and f(s) are respectively f ω The Laplace transform of f(t) and f(t).

[0125] Where F(s) is given in advance and is used to assign a frequency weight in the spectrum of the fault signal to facilitate the implementation of the fault detection scheme. The following formula is obtained:

[0126]

[0127] The above formula is f ω (s) is a state space realization, and x ω (t) is The state vector of x ω (0) = 0;

[0128] S2.5 Select the following evaluation function

[0129]

[0130] In the formula, t0 and are the moment of initial evaluation time and evaluation time respectively;

[0131] Then, select the following threshold form of the evaluation function:

[0132]

[0133] Based on the above two equations, if J rf (t)>J th , indicating that a fault has been detected, otherwise it means that no fault has occurred;

[0134] S2.6 combines the series-excited DC motor circuit system model with asynchronous antecedent variables, event trigger conditions and filters to obtain a closed-loop series-excited DC motor circuit system model:

[0135]

[0136] in

[0137]

[0138] Construct a Lyapunov function that depends on the system mode change and the dwell time within the mode; give the stability criterion of the series-excited DC motor circuit system, and then realize the stability analysis of the series-excited DC motor circuit system;

[0139] Series-excited DC motor circuit system model, all conversion rates depend on the dwell time h. When the system mode changes, h is updated to 0. For all modes m=1,2,3, ρ=1,2, If there exists a set of positive definite matrices P with appropriate dimensions 1m ,P,P m ,F, Λ 1ρ , Λ 2ρ , a normal number δ ρ ,ù1,ù2,χ1,χ2 make the following matrix inequality hold:

[0140]

[0141] in,

[0142]

[0143] Where I represents the identity matrix, * represents the symmetric term in the matrix, sym{A}=A T +A, then the series-excited DC motor circuit system is called stochastically stable and satisfies H ∞ performance.

[0144] In step S2.1 of the present invention, when ζ1(t)=ρ, ρ=1,2, v t Asynchronous with ζ1(t) and satisfying the conditional probability P r {ζ1(t)=ρ|v t =m}=θ mρ , 0≤θ mρ ≤1,

[0145] The holding interval time of the zero-order holder is in Consider data delay in network transmission in η1 and η2 represent the lower and upper bounds of the time-varying delay η(t), respectively;

[0146] The event triggering conditions are transformed into the following forms:

[0147]

[0148] In step S2.2 of the present invention, when v t Asynchronous with ζ2(t) and satisfying the conditional probability

[0149] In step S2.3 of the present invention, when and for and

[0150] get in as well as

[0151] In step S4 of the present invention,

[0152] For all modes m=1,2,3,ρ=1,2, If there exists a set of positive definite matrices P with appropriate dimensions 1m ,P, F, Λ 1ρ , Λ 2ρ , normal number δ ρ ,ù1,ù2,χ1,χ2 make the following matrix inequality hold:

[0153]

[0154] in

[0155]

[0156] The series-excited DC motor circuit system is said to be stochastically stable and satisfies H ∞ performance, then determine the fault detection filter gain as:

[0157] In step S5 of the present invention, the linear matrix inequality toolbox in Matlab is used to determine whether the system parameter matrix under all given modes satisfies the fault detection filter design conditions given in step S4. If so, it can be determined that based on the designed asynchronous antecedent variables, asynchronous event triggering conditions and asynchronous fault detection filters, the series-excited DC motor circuit system is stochastically stable.

[0158] The embodiments of the present invention are described below: Figure 2 As shown, the modeled related system matrix is ​​given as follows:

[0159]

[0160] Aω =-5, B ω =5, C ω =1, δ1=0.5, δ2=0.6, eta1=0.01, eta2=0.03, χ1=0.7, χ2=1.

[0161] Set the perturbation to:

[0162]

[0163] Where rand is a random number between 0 and 1.

[0164] The fault signals are:

[0165]

[0166] The control input is:

[0167] u(t)=2.6cost

[0168] The conditional probability matrices Γ1 and Γ2 are given as follows:

[0169]

[0170] Based on the above parameters, the method of the present invention is used to simulate and test the series-excited DC motor circuit system. Figure 3 The modal changes of the series-excited DC motor circuit system, fault detection filter, and event generator based on TS fuzzy and Semi-Markov theory are described. Figure 4 Describes the release time and release interval of the event trigger scheme, Figure 5 Depicts the state response of the fault detection filter of the series-excited DC motor circuit system with and without faults. Figure 6 The fault evaluation function and threshold value of the series-excited DC motor circuit system are depicted.

[0171] The threshold value of the present invention can be calculated as

[0172]

[0173] exist Figure 6 The results obtained in That is, the system fault can be detected 0.28s after the fault occurs. The present invention establishes a more general series-excited DC motor circuit fault detection model, and the designed triple asynchronous fault detection filter is effective and can detect the occurrence of faults in a shorter time.

Claims

1. A method for detecting event-triggered faults in a series-excited DC motor, characterized in that: The steps include: S1, establish a series-excited DC motor circuit system model; S2, design asynchronous antecedent variables, asynchronous event triggering conditions, asynchronous fault detection filters, evaluation functions and thresholds; S3, random stability condition of given series-excited DC motor circuit system; S4, solving the fault detection filter gain and designing the fault detection filter; S5, fault detection filter performance test.

2. The method for detecting a series-excited DC motor event-triggered fault according to claim 1, characterized in that: In step S1, the expression for establishing the series-excited DC motor circuit system model is: Where R represents the resistance R a and the field winding resistance R f The sum of L is the armature inductance L a and the field winding inductance L f The sum of J represents the moment of inertia, D represents the viscous friction coefficient, and K represents the torque / back electromotive force constant. Represents the actual angular velocity ω(t) and the desired angular velocity ω ref The deviation between (t), Represents the actual current η(t) and the expected current η ref The deviation between (t), It refers to the difference between the actual input voltage V(t) and the expected voltage V ref (t) The deviation between 3. The method for detecting a series-excited DC motor event-triggered fault according to claim 2, characterized in that: When there are external disturbances w(t) and fault signals f(t), the state space model of the series-excited DC motor circuit system is established as: In the formula, the moment of inertia There are three modes, and the jump between modes satisfies the Semi-Markov random process; x2(t) is the nonlinear uncertainty term in the series-excited DC motor circuit, and its value range is x2(t)∈[N1,N2], and it is defined as The antecedent variable is x2(t), the TS fuzzy condition is selected, and the membership function is established as follows: When x2(t) equals N1, or When x2(t) equals N2, or The nonlinear random system model of the above series-excited DC motor is transformed into the TS fuzzy and Semi-Markov series-excited DC motor system model, specifically: in In the formula represents the degree of membership, Represents fuzzy weight.

4. The method for detecting a series-excited DC motor event-triggered fault according to claim 3, characterized in that: Step S2 is specifically as follows: S2.1 Based on TS fuzzy and Semi-Markov random processes, a series-excited DC motor circuit system is constructed and the asynchronous event triggering conditions are designed: In the formula, Indicates the current sampling data. Indicates the latest trigger data, δ ρ ∈[0,1) are parameters related to the event generator mode, Λ1(ζ1(t)) and Λ2(ζ1(t)) are the event trigger weight matrices that need to be determined, and ζ1(t) represents the modal information actually received by the event trigger condition. S2.2 Design asynchronous event-triggered fault detection filter, Filter Rule 1: When is N1, then Filter Rule 2: When is N2, then In the formula, represents the time when data is transmitted to the fault detection filter, x f (t) is the filter state, r f (t) is the residual signal, and j = 1, 2 is the determined filter gain, ζ2(t) represents the modal information actually received by the filter; S2.3 uses the following conditions to simplify the description of the conversion of asynchronous membership functions in series-excited DC motor circuit systems: Can get In the formula and for are the minimum and maximum values ​​in the operation process, and satisfy Further, the following results are obtained S2.4 In order to improve the fault detection performance of the series-excited DC motor circuit system, a weighted function f(s) is introduced into the fault detection system; Design ω (s)=F(s)f(s), where f ω (s) and f(s) are respectively f ω The Laplace transform of f(t) and f(t); F(s) is given in advance and is used to assign a frequency weight in the spectrum of the fault signal to facilitate the implementation of the fault detection scheme, and the following formula is obtained: The above formula is f ω (s) is a state space realization, and x ω (t) is The state vector of x ω (0) = 0; S2.5 Select the following evaluation function In the formula, t0 and are the moment of initial evaluation time and evaluation time respectively; Then, select the following threshold form of the evaluation function: Based on the above two equations, if J rf (t)>J th , indicating that a fault has been detected, otherwise it means that no fault has occurred; S2.6 combines the series-excited DC motor circuit system model with asynchronous antecedent variables, event trigger conditions and filters to obtain a closed-loop series-excited DC motor circuit system model: in Construct a Lyapunov function that depends on the system mode change and the dwell time within the mode; give the stability criterion of the series-excited DC motor circuit system, and then realize the stability analysis of the series-excited DC motor circuit system; Series-excited DC motor circuit system model, all conversion rates depend on the dwell time h. When the system mode changes, h is updated to 0. For all modes m=1,2,3, ρ=1,2, If there exists a set of positive definite matrices P with appropriate dimensions 1m ,P,P m ,F, Λ 1ρ , Λ 2ρ , a normal number δ ρ ,ù1,ù2,χ1,χ2 make the following matrix inequality hold: in, Where I represents the identity matrix, * represents the symmetric term in the matrix, sym{A}=A T +A, then the series-excited DC motor circuit system is called stochastically stable and satisfies H ∞ performance.

5. The method for detecting a series-excited DC motor event-triggered fault according to claim 4, characterized in that: In step S2.1, when ζ1(t)=ρ,ρ=1,2,v t Asynchronous with ζ1(t) and satisfying the conditional probability P r {ζ1(t)=ρ|v t =m}=θ mρ , 0≤θ mρ ≤1, The holding interval time of the zero-order holder is in Consider data delay in network transmission in η1 and η2 represent the lower and upper bounds of the time-varying delay η(t), respectively; The event triggering conditions are transformed into the following forms:

6. The method for detecting a series-excited DC motor event-triggered fault according to claim 4, characterized in that: In step S2.2, when v t Asynchronous with ζ2(t) and satisfying the conditional probability 7. The method for detecting a series-excited DC motor event-triggered fault according to claim 4, characterized in that: In step S2.3, when and for and get in as well as 8. The method for detecting a series-excited DC motor event-triggered fault according to claim 4, characterized in that: In step S4, For all modes m=1,2,3,ρ=1,2, If there exists a set of positive definite matrices P with appropriate dimensions 1m ,P, F, Λ 1ρ , Λ 2ρ , normal number δ ρ ,ù1,ù2,χ1,χ2 make the following matrix inequality hold: in The series-excited DC motor circuit system is said to be stochastically stable and satisfies H ∞ performance, then determine the fault detection filter gain as:

9. The method for detecting a series-excited DC motor event-triggered fault according to claim 4, characterized in that: In step S5, the linear matrix inequality toolbox in Matlab is used to determine whether the system parameter matrix under all given modes satisfies the fault detection filter design conditions given in step S4. If so, it can be determined that based on the designed asynchronous antecedent variables, asynchronous event triggering conditions and asynchronous fault detection filters, the series-excited DC motor circuit system is stochastically stable.

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