CN114325164A - Multi-fault diagnosis method for single-phase three-level rectifier - Google Patents

Abstract

The invention provides a multi-fault diagnosis method for a single-phase three-level rectifier, and belongs to the field of power fault diagnosis. The method comprises the following steps: establishing a hybrid logic dynamic model, establishing a state space expression comprising an actuator fault and two voltage sensing fault systems, carrying out state augmentation transformation to construct a new system, carrying out primary coordinate transformation, carrying out matrix transformation, carrying out secondary coordinate transformation, calculating the state quantity of a reduced-order system, designing a self-adaptive reduced-order sliding-mode observer, and giving a self-adaptive diagnosis threshold value to carry out multi-fault diagnosis. The reduced-order sliding mode observer provided by the invention does not need a system to provide a very accurate dynamic model, only needs to reasonably design a sliding mode surface by utilizing a tracking error of a track, and can adaptively switch an approach rate, thereby accelerating the approach speed, reducing buffeting of sliding mode motion, improving the diagnosis accuracy, and simultaneously diagnosing 3 different faults.

Description

Multi-fault diagnosis method for single-phase three-level rectifier

Technical Field

The invention relates to the field of power fault diagnosis, in particular to a multi-fault diagnosis method for a single-phase three-level rectifier.

Background

In an electric traction drive system, a single-phase three-level rectifier plays an increasingly important role, wherein the single-phase three-level rectifier is one of core components of a traction drive system of a high-speed train. Aiming at a single-phase three-level rectifier, on one hand, the output end of the rectifier is provided with two voltage sensors, and the aging and damage of the voltage sensors can be caused by the long-time running of a high-speed train and the interference of the external environment, so that the measurement feedback data of the sensors is abnormal, and serious casualties and property loss are caused; on the other hand, the single-phase three-level rectifier can also simultaneously generate actuator faults, the actuator faults generated in the actual transportation process can cause the abnormal function of a traction transmission system of a high-speed train, serious traffic accidents are caused, and the difficulty of fault diagnosis can be greatly increased.

The diagnosis methods for the voltage sensor fault and the actuator fault of the single-phase three-level rectifier mainly comprise the following two diagnosis methods:

1. the method is based on a data driving method, and realizes corresponding fault diagnosis by acquiring fault data information and analyzing and processing the data information; corresponding papers and patents such as a data-driven adaptive to actuator and sensor fault detection, isolation and estimation in discrete-time linear systems, a data-driven transmission sensor fault diagnosis method (application publication No. CN202011201104.0), etc. although this method does not need to establish an accurate mathematical model, it needs a large amount of data bases, and on this basis, it also needs to perform complex data processing, and the algorithm is complex, the workload is large and the difficulty is high.

2. The method is based on an analytic model, compares the information quantity obtained from the mathematical model of the actual system to be diagnosed with the actual measurement by knowing and establishing the mathematical model of the actual system, and carries out fault diagnosis by analyzing the residual error; meanwhile, if multi-fault diagnosis is performed, fault decoupling is performed, a corresponding mathematical model or observer is established to obtain an estimated quantity, and a residual error analysis is performed after the estimated quantity is compared with an actual measured quantity, wherein the corresponding papers are as follows:

simultaneous robust activator and sensor fault evaluation for non-linear Lipschitz systems, which aims at the multi-fault diagnosis of faults of an actuator and a sensor, complex fault decoupling needs to be carried out on the faults of the actuator and the sensor to form two subsystems, and then observers are respectively designed for the two subsystems to carry out fault diagnosis;

Sensor-Fault-Estimation-Based Tolerant Control for Single-Phase Two-Level PWM Rectifier in Electric conduction System, which aims at multi-Fault diagnosis of faults of an actuator and a Sensor, although the Fault System is subjected to step reduction processing, the diagnosis object is a Single-Phase Two-Level Rectifier instead of a mainstream Single-Phase three-Level Rectifier;

when a Sliding Mode Observer is established to diagnose the Fault of a Sensor, the adopted Approach law also generates buffeting when the Approach rate is slow in the observation process, so that the observed value is inaccurate;

the paper only expands the Fault amount of one voltage sensor, namely, only carries out Fault diagnosis of one voltage sensor when carrying out multi-Fault diagnosis of faults of an actuator and a sensor.

In summary, the single-phase three-level rectifier plays an extremely important role in the electric traction drive system, and the existing diagnosis methods for the sensor fault and the actuator fault of the single-phase three-level rectifier have disadvantages, so that the technical problems to be solved in the whole research field are solved by solving the disadvantages of the prior art.

Disclosure of Invention

The invention aims to provide a multi-fault diagnosis method for a single-phase three-level rectifier, aiming at the problems in the background art. Specifically, the problem that an accurate system model is difficult to establish is solved by designing a reduced-order sliding-mode observer and using proper sliding-mode control, but the method can generate jitter characteristics in the control process, further designs a self-adaptive approach rate, reduces the jitter characteristics in the control process through the self-adaptive switching approach rate, and further improves the accuracy of system fault diagnosis; meanwhile, a reduced-order sliding mode observer is used, the harsh precondition established by the observer is overcome, and the fault diagnosis of two voltage sensors and one actuator is carried out simultaneously; finally, during fault diagnosis, the bounded voltage disturbance quantity and the bounded external disturbance which are possibly generated during measurement of the voltage sensor are also considered, so that the accuracy of the diagnosis method is improved, and the diagnosis precision is improved.

In order to achieve the aim, the invention provides a multi-fault diagnosis method for a single-phase three-level rectifier, and a circuit topology related to the method comprises a network side voltage source U_sNetwork side equivalent inductor L_sAnd net side equivalent resistance R_sRectifier bridge, two identical support capacitors C_d1，C_d2A DC side load and two identical voltage sensors; support capacitor C_d1And a support capacitor C_d2Connected in parallel between a DC positive bus P and a DC negative bus Q1 of a DC side load after being connected in series, and supporting a capacitor C_d1And a support capacitor C_d1The contact point of (2) is marked as a direct current bus midpoint O; two identical voltage sensors are respectively marked as a voltage sensor 1 and a voltage sensor 2, and the voltage sensor 1 is connected with a supporting capacitor C_d1At both ends of which the voltage sensor 2 is connected to the supporting capacitor C_d2Both ends of (a);

the rectifier bridge is divided into two-phase bridge arms, and the two-phase bridge arms are connected with the direct-current side load in parallel; marking two-phase bridge arms as bridge arms k, wherein k is a bridge sequence, and k is a, b; in two-phase bridge arm, each phase of bridge arm includes 4 switching tubes with reverse-connected diodes, two clamping diodes, i.e. the rectifier bridge contains 8 switching tubes with reverse-connected diodes and 4 clampsThe 8 switching tubes form an actuator of the single-phase three-level rectifier; marking 8 switch tubes as switch tubes V_kγγ denotes the number of the switching tube, γ is 1, 2, 3, 4, and 4 clamping diodes are denoted as clamping diodes D_ckρρ is the serial number of the clamping diode, and ρ is 1, 2; in each of the two-phase arms, a switching tube V_k1Switch tube V_k2Switch tube V_k3Switch tube V_k4Are sequentially connected in series, wherein, the switch tube V_k2And a switching tube V_k3Is marked as the input point tau of the rectifier bridge_kK is a, b; in each of the two-phase arms, a clamping diode D_ck1The cathode of the switch tube is connected with the switch tube V_k1And a switching tube V_k2Between, the clamping diode D_ck1Anode of (2) is connected to a clamping diode D_ck2Cathode of (2), clamping diode D_ck2Anode of the switch tube is connected with the switch tube V_k3And a switching tube V_k4And clamping diode D_ck1And a clamping diode D_ck2The connecting point of the direct current bus is connected with the midpoint O of the direct current bus;

the network side equivalent inductance L_sOne end of is connected with an input point tau of the rectifier bridge_aThe other end is connected with the equivalent resistance R of the network side in sequence_sGrid side voltage source U_sThe other end of the series network side voltage source is connected with an input point tau of the rectifier bridge_b；

The multi-fault diagnosis method comprises the steps of fault diagnosis of an actuator of a single-phase three-level rectifier and weak fault diagnosis of a multi-voltage sensor, and specifically comprises the following steps:

step 1, establishing a hybrid logic dynamic model of a single-phase three-level rectifier, and calculating a phase voltage U of an input end of a rectifier bridge_abIs estimated value of

Sampling the current of the network side and recording the current of the network side as the current i of the network side_sSampling support capacitor C_d1And a support capacitor C_d2And is denoted as DC voltage u₁，u₂Sampling the DC side voltage U_dc(ii) a Establishing a single phaseHybrid logic dynamic model of three-level rectifier and calculating input phase voltage U of rectifier bridge_abIs estimated value of

The input end phase voltage U of the rectifier bridge_abFor input point tau of rectifier bridge_aAnd the input point tau of the rectifier bridge_bA voltage in between;

the expression of the hybrid logic dynamic model of the single-phase three-level rectifier is as follows:

wherein,

is an estimate of the voltage of the a-phase,

is an estimate of the b-phase voltage, T_hIs a DC voltage u₁Mixed logic dynamic function of, T_lIs a DC voltage u₂The hybrid logical dynamic function of (1);

the input end phase voltage U of the rectifier bridge_abIs estimated value of

The expression of (a) is:

step 2, establishing a multi-fault-containing single-phase three-level rectifier system state space expression, and recording the expression as a multi-fault system 1, wherein the expression is as follows:

wherein x (t) is the state variable of the multi-fault system 1 and is marked as the primary state variable x (t),

x (t) is n₁Dimension state variable, as

t is a variable of time and is,

the first derivative of the first state variable x (t),

wherein

Is a net side current i_sThe derivative of (a) of (b),

are respectively DC voltage u₁，u₂A derivative of (a); u (t) is the input of the multi-fault system 1 and is recorded as primary system input u (t), u (t)_sU (t) is n₂Dimension state variable, as

f_a(t) actuator failure for multiple failure System 1, denoted as actuator failure f_a(t)，f_a(t) is n₃Dimension state variable, as

Eta (t) is the harmonic disturbance quantity of the multi-fault system 1 and is recorded as harmonic disturbance eta (t), and eta (t) is n₄Dimension state variable, as

y (t) is the output of the multi-fault system 1 and is recorded as the system output y (t), and y (t) is n₅Dimension state variable, as

f_s(t) Voltage sensor Fault for multiple Fault System 1, denoted System Voltage sensor Fault f_s(t)，f_s(t) is n₆Dimension state variable, as

Wherein

For a fault in voltage sensor 1, it is noted as a fault f in voltage sensor 1_u1(t)，f_u1(t) is n₇Dimension state variable, as

f_u2(t) is a voltage sensor 2 failure, denoted as voltage sensor 2 failure f_u2(t)，f_u2(t) is n₈Dimension state variable, as

A₁The state matrix for the multi-fault system 1 is marked as a primary state matrix A₁，

Wherein L is equivalent inductance L at network side_sR is the equivalent resistance R of the network side_sResistance value of C₁，C₂Are respectively a support capacitor C_d1And a support capacitor C_d2The capacitance value of (a); b is₁The input matrix for the multiple fault system 1 is marked as a primary input matrix B₁，

G₁For actuator failure f_a(t) the coefficient matrix is recorded as a primary actuator fault coefficient matrix,

N₁the coefficient matrix of harmonic disturbance eta (t) is recorded as a primary disturbance coefficient matrix N₁，

C_y1The output matrix of the multi-fault system 1 is recorded as a primary output matrix

F₁For system voltage sensor fault f_s(t) coefficient matrix, which is recorded as primary voltage sensor fault coefficient matrix F₁，

System voltage sensor fault f_s(t) actuator failure f_a(t) and harmonic disturbances η (t) are both continuous and bounded functions satisfying a time variable t, denoted as | | f_s(t)||≤r_s，||f_a(t)||≤r_a，||η(t)||≤r_ηWherein | | | f_s(t) | | is f_sNorm of (t, | f_a(t) | | is f_aThe norm of (t), where | | | η (t) | | is the norm of η (t), r_sFor system voltage sensor fault f_sUpper limit of (t), r_aFor actuator failure f_aUpper limit of (t), r_ηIs a supremum of harmonic disturbance η (t), and r_s、r_aAnd r_ηAre all normal numbers and are recorded as r_s＞0，r_a＞0，r_η＞0；

Step 3, introducing system state variable augmentation transformation to the multi-fault system 1, and defining the following augmentation matrixes and vectors, wherein the expression is as follows:

a new system of the multi-fault system 1 after system state variable augmentation transformation can be obtained, and the new system is marked as a multi-fault system 2, and the state space expression of the new system is as follows:

wherein z is₁(t) is the state variable of the multiple fault system 2, noted as the secondary state variable z₁(t)，z₁(t) is n₁+n₃+n₆Dimensional space vector, is

Is a quadratic state variable z₁(ii) the derivative of (t),

wherein

Is a fault f of the voltage sensor 1_u1(ii) the derivative of (t),

for failure of the voltage sensor 2

A derivative of (a); f. of₁(t) is a fault variable of the multi-fault system 2, and is recorded as a system fault quantity f₁(t)；

E₁As the second state variable derivative

Is recorded as a first derivative coefficient matrix E₁In a

In the expression of (a) in (b),

represents n₁The dimension-unit matrix is a matrix of the dimension units,

represents n₃A dimension unit matrix;

A₂the state matrix for the multi-fault system 2 is denoted as a quadratic state matrix A₂；

B₂The input matrix of the multi-fault system 2 is marked as a secondary input matrix B₂；

F₂Is the amount of system failure f₁(t) coefficient matrix, denoted as quadratic failure coefficient matrix F₂In a

In the expression of (a) in (b),

represents n₇The dimension-unit matrix is a matrix of the dimension units,

represents n₈A dimension unit matrix;

N₂the coefficient matrix of harmonic disturbance eta (t) in the multi-fault system 2 is recorded as a secondary disturbance coefficient matrix N₂；

Output matrix for multiple fault system 2

Is recorded as a quadratic output matrix

Step 4, carrying out one-time coordinate transformation on the multi-fault system 2

Step 4.1, outputting the secondary output matrix

Transposing, recording the transposed output matrix as

Handle

The matrix is decomposed into the product of an orthogonal matrix and an upper triangular matrix, and the product is recorded as

U is an orthogonal matrix and Q is an upper triangular matrix; let P be U^T，J＝Q^T，U^TIs the transpose of the orthogonal matrix U, Q^TIs the transpose matrix of the upper triangular matrix Q, then the obtained

Wherein P satisfies P^T＝P^-1，P^TIs the transpose of the matrix P, P^-1Is the inverse matrix of the matrix P, and takes P as a primary coordinate transformation matrix;

step 4.2, introduce coordinate transformation z₂(t)＝Pz₁(t), the multi-fault system 2 can be converted into a new system through coordinate transformation, the new system is recorded as a multi-fault system 3, and the state space expression of the new system is as follows:

wherein z is₂(t) is the state variable of the multiple fault system 3, noted as the third state variable z₂(t)；

Is a cubic state variable z₂(t) derivative of;

E₂is a third state variable derivative

Is denoted as the second derivative coefficient matrix E₂，E₂＝E₁P^T；A₃The state matrix of the multi-fault system 3 is marked as a cubic state matrix A₃，A₃＝A₂P^T；B₃The input matrix of the multi-fault system 3 is recorded as a cubic input matrix B₃；F₃For faults f of the multiple fault system 3₁(t) coefficient matrix, denoted as cubic failure coefficient matrix F₃；N₃The coefficient matrix of harmonic disturbance eta (t) for the multi-fault system 3 is recorded as a third-order disturbance coefficient matrix N₃(ii) a J is the output matrix of the multiple fault system 3, denoted as the cubic output matrix J, and is denoted as a block matrix, i.e., J ═ J (J)₁0), wherein J₁Left blocking submatrix of J, J₁Belong to n₅Dimensional space, is denoted as

And J₁Is a non-singular matrix;

step 5, matrix transformation is carried out on the multi-fault system 3

Step 5.1, the second derivative coefficient matrix E₂Conversion into a block matrix, i.e. E₂＝(E₂₁E₂₂) In which E₂₁Is a coefficient matrix E of the second derivative₂Left blocking submatrix of (E)₂₁Is (n)₁+n₃+n₆)×n₅Dimensional space, is denoted as

E₂₂Is a coefficient matrix E of the second derivative₂Right blocking submatrix, E₂₂Is (n)₁+n₃+n₆)×(n₁+n₃+n₆-n₅) Dimensional space, is denoted as

Then designing a transformation matrix xi, recording as the matrix transformation matrix xi,

wherein xi₁₁Being the upper part of the submatrix xi of the transform matrix xi₁₁Is n₅×(n₁+n₃+n₆) Dimensional space, is denoted as

Ξ₂₁A lower blocking submatrix of the transform matrix xi, xi₂₁Belong to (n)₁+n₃+n₆-n₅)×(n₁+n₃+n₆) Dimensional space, is denoted as

And xi₁₁Satisfies E₂₂ ^TΞ₁₁ ^T0, solution E₂₂ ^TΞ₁₁ ^T0, then xi may be obtained₁₁Wherein the matrix E₂₂ ^TIs a coefficient matrix E of the second derivative₂Right blocking submatrix E₂₂Transpose of (2), matrix xi₁₁ ^TAn upper blocking submatrix xi being a transform matrix xi₁₁Transposing; xi₂₁＝E₂₂ ^T(E₂₂E₂₂ ^T)^-1Matrix (E)₂₂E₂₂ ^T)^-1Is a matrix E₂₂E₂₂ ^TThe inverse of (1);

step 5.2, the left and right state space expressions of the multi-fault system 3 are multiplied by the transformation matrix xi to obtain a new transformed system, the new system is marked as a multi-fault system 4, and the state space expressions are as follows:

wherein z is₃(t) is the state variable of the multiple fault system 4, noted as the quartile state variable z₃(t)；

Is a quartic state variable z₃(t) derivative of;

E₃is the fourth derivative of the state variable

Is recorded as a coefficient matrix of the third derivative E₃，

Wherein E₃₁Is a coefficient matrix E of the third derivative₃Upper left blocking sub-matrix of (E)₃₂Is a coefficient matrix E of the third derivative₃The lower left block sub-matrix of (a),

is n₁+n₃+n₆-n₅A dimension unit matrix; a. the₄The state matrix of the multi-fault system 4 is marked as a fourth state matrix A₄，

Wherein A is₄₁₁Is a four-times state matrix A₄Upper left blocking sub-matrix of, A₄₁₂Is a four-times state matrix A₄Upper right blocking sub-matrix of, A₄₂₁Is a four-times state matrix A₄Left lower blocking submatrix of, A₄₂₂Is a four-times state matrix A₄The lower right blocking submatrix; b is₄An input matrix for the multiple fault system 4, denoted as a quadruple input matrix B₄，

Wherein B is₄₁Is a four-input matrix B₄Upper block matrix of, B₄₂Is a four-input matrix B₄A lower block matrix of (a); f₄For faults f of the multiple fault system 4₁(t) ofCoefficient matrix, denoted as quad-failure coefficient matrix F₄，

Wherein F₄₁Is a four-fault coefficient matrix F₄₁Upper block matrix of F₄₂Is a four-fault coefficient matrix F₄A lower block matrix of (a); n is a radical of₄The coefficient matrix for the harmonic disturbance η (t) of the sensor fault system 4 is noted as the fourth-order disturbance coefficient matrix N₄，

Wherein N is₄₁Is a four-times disturbance coefficient matrix N₄₁Upper block submatrix of, N₄₂Is a four-times disturbance coefficient matrix N₄A lower block submatrix of (a);

step 6, carrying out secondary coordinate transformation on the multi-fault system 4

Step 6.1, a coordinate transformation matrix T is designed and recorded as a quadratic coordinate transformation matrix T, and T is expressed as a block matrix, namely

Wherein therein

Is n₅The dimension-unit matrix is a matrix of the dimension units,

is n₁+n₃+n₆-n₅Dimension unit matrix, L is a free matrix, denoted as free matrix L, which belongs to (n)₁+n₃+n₆-n₅)×n₅Dimensional space, is denoted as

Step 6.2 introduction of coordinate transformation z₄(t)＝Tz₃(t) a transformed new system is obtained, and the new system is marked as a multi-fault system 5, and the state space expression of the new system is as follows:

wherein z is₄(t) is the state variable of the multiple fault system 5, noted as the quintic state variable z₄(t) for the fifth state variable z₄(t) blocking, i.e.

z₄₁(t) is a five-state variable z₄(t) upper block subvector z₄₁(t)，z₄₁(t) is n₅Dimension vector, z₄₂(t) is a five-state variable z₄(t) lower block subvector z₄₂(t)，z₄₂(t) is n₁+n₃+n₆-n₅A dimension vector;

is a five-fold state variable z₄Derivative of (t), i.e.

Is z₄(t) upper block vector z₄₁(ii) the derivative of (t),

is z of the upper block vector₄₂(t) derivative of; then z is transformed from the above coordinate₄(t)＝Tz₃(t) it can be seen that,

E₄fifth order state variable derivative

A coefficient matrix of (a), and

A₅the state matrix for the multi-fault system 5 is denoted as the five-time state matrix A₅，

Wherein A is₅₁₁Is a quintic state matrix A₅Upper left blocking sub-matrix of, A₅₁₂Is a quintic state matrix A₅Upper right blocking sub-matrix of, A₅₂₁Is a quintic state matrix A₅Left lower blocking submatrix of, A₅₂₂Is a quintic state matrix A₅The lower right blocking submatrix; t is^-1An inverse matrix of the quadratic coordinate transformation matrix T; b is₅The input matrix for the multiple fault system 5 is marked as five-times input matrix B₅，

Wherein B is₅₁For five inputs of matrix B₅Upper blocking submatrix of, B₅₂For five inputs of matrix B₅A lower block submatrix of (a); f₅The coefficient matrix of the fault F (t) of the multi-fault system 5 is marked as a five-fault coefficient matrix F₅，

Wherein F₅₁Is a quintic fault coefficient matrix F₅Upper blocking submatrix of F₅₂Is a quintic fault coefficient matrix F₅A lower block submatrix of (a); n is a radical of₅The coefficient matrix of harmonic disturbance eta (t) of the multi-fault system 5 is recorded as a quintic disturbance coefficient matrix N₅，

Wherein N is₅₁For a quintic disturbance coefficient matrix N₅Upper block submatrix of, N₅₂For a quintic disturbance coefficient matrix N₅Lower blocking submatrix, J^*Is the output matrix of the multiple fault system 5 and knows the following relationship:

step 7, designing a self-adaptive reduced-order sliding mode observer

Step 7.1, calculating the state quantity theta of the order-reduced system according to the multi-fault system 5, and recording the state quantity theta as the state quantity theta of the order-reduced system, wherein the calculation formula is as follows:

Θ＝(LE₃₁+E₃₂-L)z₄₁(t)+z₄₂(t)

and solving a state space expression of the reduced-order system according to the reduced-order system state quantity theta, wherein the state space expression is as follows:

wherein,

is the derivative of the state quantity theta of the reduced-order system, and delta is the state expression z of the reduced-order system₄₁The coefficient matrix of (t) is marked as a reduced system coefficient matrix delta, and the expression is as follows:

Δ＝-(LA₅₁₂+A₅₂₂)(LE₅₁+E₅₂-L)+L(A₅₁₁-A₅₁₂L)+A₅₁₁-A₅₂₂L

step 7.2, designing a self-adaptive reduced order sliding mode observer aiming at a state space expression of a reduced order system, wherein the expression is as follows:

wherein,

is the estimated value of the state quantity theta of the reduced order system and is recorded as the estimated value of the state quantity theta of the reduced order system

Is an estimate of the state quantity of the reduced order system

Is a sliding mode gain matrix, where Γ is (LF) ═ f₅₁+F₅₂) V is the approach law,

wherein,

in order to be able to vary the parameter 1,

tanh () is a hyperbolic tangent function,

is variable parameter 2, and

sigma is variable parameter 3, sigma belongs to (0, 1), theta is variable parameter 4, theta is more than 1, rho is variable parameter 5, beta is more than 0, psi is positive definite symmetrical matrix, chi is diagonal matrix,

e is a constant number, e > 1_Θ(t) is the error of the estimation,

let S be e_Θ(t), wherein S is a sliding mode surface of the designed adaptive reduced-order sliding mode observer;

step 7.3, obtaining a free matrix L by solving a Lyapunov equation, wherein the expression of the Lyapunov equation is as follows:

(LA₄₁₂+A₄₂₂)^TP+P(LA₄₁₂+A₄₂₂)＝-I

wherein (LA)₄₁₂+A₄₂₂)^TIs LA₄₁₂+A₄₂₂P is a positive definite symmetric matrix, and I is a unit matrix;

step 8, fault diagnosis of the actuator and the sensor is carried out

Step 8.1, sampling the value of the system output y (t) of the multi-fault system 1 in step 1, and substituting the sampled value into z in step 6.2₄₁(t)＝z₃₁(t)＝J₁ ^-1y (t), thenTo obtain five state variables z₄(t) upper block subvector z₄₁(t) value, again according to the known five state variable z₄(t) upper block vector z₄₁The value of (t), Θ in step 7.1 ═ (LE)₃₁+E₃₂-L)z₄₁(t)+z₄₂(t), step 7.2

And the error e is estimated in step 7.2_Θ(t) is 0, and z can be obtained₄₂(t), the expression of which is:

then the five state variables z are obtained₄(t) upper block subvector z₄₁(t) value and five state variables z₄(t) lower block subvector z₄₂(t) value substituted into step 6.2

The state variable z can be calculated five times₄(t) value;

step 8.2, starting from the multiple fault system 2, according to a coordinate transformation z₂(t)＝Pz₁(t) and quadratic coordinate transformation z₄(t)＝Tz₃(t) and the matrix transformation does not change the cubic state variable z in the sensor failure system 3 in step 5₂(t) obtaining z₃(t)＝z₂(t) thereby obtaining z₄(t)＝TPz₁(t) calculating a secondary state variable z by inverse operation of the matrix₁(t)＝P^TT^-1z₄(t), and the five state variables z calculated in step 8.1 are further added₄(t) substitution of formula z₁(t)＝P^TT^-1z₄(t) obtaining a secondary state variable z₁(t)；

Step 8.3, mixing

Is recorded as a primary state variable estimation value,

is recorded as the estimated value of the actuator fault

Is recorded as the fault estimation value of the voltage sensor 1

Is recorded as the fault estimation value of the voltage sensor 2

Calculating a primary state variable estimate

Actuator fault estimation

Voltage sensor fault 1 estimation

And voltage sensor 2 fault estimation

The specific calculation formula is as follows:

step 8.4, diagnosing faults of the actuator, the voltage sensor 1 and the voltage sensor 2, and giving a self-adaptive diagnosis threshold value T_th；

Defining fault location quantity Z₁，

And positioned as follows:

if Z is₁When the fault is equal to 0, the multi-fault system 1 has no actuator fault;

if Z is₁1, the multi-fault system 1 has an actuator fault;

defining fault location quantity Z₂，

And positioned as follows:

if Z is₂When the voltage sensor 1 fails, the multi-fault system 1 is not failed;

if Z is₂1, the multi-fault system 1 has a fault in the voltage sensor 1;

defining fault location quantity Z₃，

And positioned as follows:

if Z is₃When the failure rate is 0, the multi-failure system 1 has no failure of the voltage sensor 2;

if Z is₃The multiple fault system 1 has a voltage sensor 2 fault 1.

Preferably, the DC voltage u in step 1₁Hybrid logic dynamic function T of_hAnd a DC voltage u₂Hybrid logic dynamic function T of_lThe calculation process of (2) is as follows:

recording the switching function of the k-phase bridge arm as S_kAnd k is a, b, then:

recording the pulse control signal of the switching tube as v_kγK is a, b, γ is 1, 2, 3, 4, then k-phase bridge arm switching function S_k＝v_k1v_k2-v_k3v_k4。

Preferably, the diagnostic adaptive threshold T of step 8.4_thThe expressions are respectively as follows:

T_th＝E₁+Γ₁(ζ₁+ζ₂)

wherein E is₁Is a constant 1, Γ₁Is a constant number 2, and Γ₁∈(1，2)，ζ₁For a bounded external disturbance, ζ₂Is a bounded voltage perturbation.

Compared with the prior art, the invention has the beneficial effects that:

1. the fault state and the fault value of the system can be accurately estimated by designing the reduced-order sliding-mode observer, and the defect of poor robustness for weak fault diagnosis in the existing analytical model-based method is overcome;

2. by designing a self-adaptive sliding mode approach rate and a self-adaptive switching approach rate, buffeting influence in observation of the reduced-order sliding mode observer is reduced, the approach rate is accelerated, and the accuracy of system fault diagnosis is further improved;

3. through the increase of system state variables, the fault diagnosis of two voltage sensors and one actuator is carried out simultaneously, and the types of fault diagnosis are increased;

4. by designing the self-adaptive diagnosis threshold, bounded voltage disturbance possibly existing in the fault value of the voltage sensor is considered, and the accuracy of fault diagnosis is improved.

Drawings

FIG. 1 is a topology of a single phase three level rectifier in an example of the invention;

FIG. 2 is a schematic diagram of a single phase three level rectifier fault diagnostic method of the present invention;

FIG. 3 is a flow chart of a single phase three level rectifier fault diagnosis method of the present invention;

FIG. 4 shows an actuator failure f in the present embodiment_a(t) actuator estimation value

And an adaptive threshold T_thA simulation graph of (1);

FIG. 5 shows the failure of the voltage sensor 1 in this example

Voltage sensor 1 fault estimation

And an adaptive threshold T_thA simulated waveform diagram of (1);

FIG. 6 shows the failure f of the voltage sensor 2 in this example_u2(t) Voltage sensor 2 Fault estimation

And an adaptive threshold T_thThe simulated waveform of (2).

Detailed Description

Fig. 1 is a topology diagram of a single-phase three-level rectifier in an embodiment of the invention. It can be seen from the figure that the circuit topology according to the invention comprises a network-side voltage source U_sNetwork side equivalent inductance s and network side equivalent resistance R_sRectifier bridge, two identical support capacitors C_d1，C_d2A DC side load and two identical voltage sensors; support capacitor C_d1And a support capacitor C_d2Connected in parallel between a DC positive bus P and a DC negative bus Q1 of a DC side load after being connected in series, and supporting a capacitor C_d1And a support capacitor C_d2The contact point of (2) is marked as a direct current bus midpoint O; two identical voltage sensors are respectively marked as a voltage sensor 1 and a voltage sensor 2, and the voltage sensor 1 is connected with a supporting capacitor C_d1At both ends of which the voltage sensor 2 is connected to the supporting capacitor C_d2At both ends of the same. In FIG. 1, S_V1Is a voltage sensor 1, S_V2As a voltage sensor 2, two sensorsFor the measurement of voltage values.

The rectifier bridge is divided into two-phase bridge arms, and the two-phase bridge arms are connected with the direct-current side load in parallel; marking two-phase bridge arms as bridge arms k, wherein k is a bridge sequence, and k is a, b; in the two-phase bridge arms, each phase of bridge arm comprises 4 switching tubes with reverse connection diodes and two clamping diodes, namely a rectifier bridge comprises 8 switching tubes with reverse connection diodes and 4 clamping diodes, and the 8 switching tubes form an actuator of a single-phase three-level rectifier; marking 8 switch tubes as switch tubes V_kγγ denotes the number of the switching tube, γ is 1, 2, 3, 4, and 4 clamping diodes are denoted as clamping diodes D_ckρρ is the serial number of the clamping diode, and ρ is 1, 2; in each of the two-phase arms, a switching tube V_k1Switch tube V_k1Switch tube V_k3Switch tube V_k4Are sequentially connected in series, wherein, the switch tube V_k2And a switching tube V_k3Is marked as the input point tau of the rectifier bridge_kK is a, b; in each of the two-phase arms, a clamping diode D_ck1The cathode of the switch tube is connected with the switch tube V_k1And a switching tube V_k2Between, the clamping diode D_ck1Anode of (2) is connected to a clamping diode D_ck2Cathode of (2), clamping diode D_ck2Anode of the switch tube is connected with the switch tube V_k3And a switching tube V_k4And clamping diode D_ck1And a clamping diode D_ck2The connecting point of the direct current bus is connected with the midpoint O of the direct current bus.

The network side equivalent inductance L_sOne end of is connected with an input point tau of the rectifier bridge_aThe other end is connected with the equivalent resistance R of the network side in sequence_sGrid side voltage source U_sThe other end of the series network side voltage source is connected with an input point tau of the rectifier bridge_b。

Fig. 2 is a schematic diagram of a multi-fault diagnosis method for a single-phase three-level rectifier according to the present invention, fig. 3 is a flowchart of the multi-fault diagnosis method for the single-phase three-level rectifier according to the present invention, and as can be seen from fig. 2 to fig. 3, the multi-fault diagnosis method includes an actuator fault diagnosis for the single-phase three-level rectifier and a multi-voltage sensor weak fault diagnosis, and specifically includes the following steps:

step 1, buildingHybrid logic dynamic model of vertical single-phase three-level rectifier and calculating input phase voltage U of rectifier bridge_abIs estimated value of

Sampling the current of the network side and recording the current of the network side as the current i of the network side_sSampling support capacitor C_d1And a support capacitor C_d2And is denoted as DC voltage u₁，u₂Sampling the DC side voltage U_dc(ii) a Establishing a mixed logic dynamic model of the single-phase three-level rectifier, and calculating the phase voltage U of the input end of the rectifier bridge_abIs estimated value of

The input end phase voltage U of the rectifier bridge_abFor input point tau of rectifier bridge_aAnd the input point tau of the rectifier bridge_bThe voltage in between.

The expression of the hybrid logic dynamic model of the single-phase three-level rectifier is as follows:

wherein,

is an estimate of the voltage of the a-phase,

is an estimate of the b-phase voltage, T_hIs a DC voltage u₁Mixed logic dynamic function of, T_lIs a DC voltage u₂Mixed logical dynamic functions of (1).

The input end phase voltage U of the rectifier bridge_abIs estimated value of

The expression of (a) is:

in this embodiment, the DC voltage u₁Hybrid logic dynamic function T of_hAnd a DC voltage u₂Hybrid logic dynamic function T of_lThe calculation process of (2) is as follows:

recording the switching function of the k-phase bridge arm as S_kAnd k is a, b, then:

recording the pulse control signal of the switching tube as v_kγK is a, b, γ is 1, 2, 3, 4, then k-phase bridge arm switching function S_k＝v_k1v_k2-v_k3v_k4。

Step 2, establishing a multi-fault-containing single-phase three-level rectifier system state space expression, and recording the expression as a multi-fault system 1, wherein the expression is as follows:

wherein x (t) is the state variable of the multi-fault system 1 and is marked as the primary state variable x (t),

x (t) is n₁Dimension state variable, as

t is a variable of time and is,

the first derivative of the first state variable x (t),

wherein

Is a net side current i_sThe derivative of (a) of (b),

are respectively DC voltage u₁，u₂A derivative of (a); u (t) is the input of the multi-fault system 1 and is recorded as primary system input u (t), u (t)_sU (t) is n₂Dimension state variable, as

f_a(t) actuator failure for multiple failure System 1, denoted as actuator failure f_a(t)，f_a(t) is n₃Dimension state variable, as

Eta (t) is the harmonic disturbance quantity of the multi-fault system 1 and is recorded as harmonic disturbance eta (t), and eta (t) is n₄Dimension state variable, as

y (t) is the output of the multi-fault system 1 and is recorded as the system output y (t), and y (t) is n₅Dimension state variable, as

f_s(t) Voltage sensor Fault for multiple Fault System 1, denoted System Voltage sensor Fault f_s(t)，f_s(t) is n₆Dimension state variable, as

Wherein

For a fault in voltage sensor 1, it is noted as a fault f in voltage sensor 1_u1(t)，f_u1(t) is n₇Dimension state variable, as

f_u2(t) is a voltage sensor 2 failure, denoted as voltage sensor 2 failure f_u2(t)，f_u2(t) is n₈Dimension state variable, as

A₁The state matrix for the multi-fault system 1 is marked as a primary state matrix A₁，

Wherein L is equivalent inductance L at network side_sR is the equivalent resistance R of the network side_sResistance value of C₁，C₂Are respectively a support capacitor C_d1And a support capacitor C_d2The capacitance value of (a); b is₁The input matrix for the multiple fault system 1 is marked as a primary input matrix B₁，

G₁For actuator failure f_a(t) the coefficient matrix is recorded as a primary actuator fault coefficient matrix,

N₁the coefficient matrix of harmonic disturbance eta (t) is recorded as a primary disturbance coefficient matrix N₁，

C_y1The output matrix of the multi-fault system 1 is recorded as a primary output matrix

F₁For system voltage sensor fault f_s(t) coefficient matrix, which is recorded as primary voltage sensor fault coefficient matrix F₁，

System voltage sensor fault f_s(t) actuator failure f_a(t) and harmonic disturbances η (t) are both continuous and bounded functions satisfying a time variable t, denoted as | | f_s(t)||≤r_s，||f_a(t)||≤r_a，||η(t)||≤r_ηWherein | | | f_s(t) | | is f_sNorm of (t, | f_a(t) | | is f_aThe norm of (t), where | | | η (t) | | is the norm of η (t), r_sFor system voltage sensor fault f_sUpper limit of (t), r_aFor actuator failure f_aUpper limit of (t), r_ηIs a supremum of harmonic disturbance η (t), and r_s、r_aAnd r_ηAre all normal numbers and are recorded as r_s＞0，r_a＞0，r_η＞0。

In this embodiment, R is 0.34 Ω, and L is 2.2 × 10^-3H，C₁＝16×10^-3F，C₂＝16×10^-3F，

n₁＝3，n₂＝1，n₃＝1，n₄＝1，n₅＝5，n₆＝2，n₇＝1，n₈＝1，

f_u1(t)＝0，t＜10s，

t≥10s，

f_u2(t)＝0，t＜10s，

t≥10s。

System voltage sensor fault f_s(t) actuator failure f_a(t) and harmonic disturbance η (t) are both continuous and bounded functions that satisfy the time t, denoted | | f_s(t)||≤r_s，||f_a(t)||≤r_a，||η(t)||≤r_ηWherein | | | f_s(t) | | is f_sNorm of (t, | f_a(t) | | is f_aThe norm of (t), where | | | η (t) | | is the norm of η (t), r_sFor system voltage sensor fault f_sUpper limit of (t), r_aFor actuator failure f_aUpper limit of (t), r_ηIs a supremum of harmonic disturbance η (t), and r_s、r_aAnd r_ηAre all normal numbers and are recorded as r_s＞0，r_a＞0，r_η＞0。

Step 3, introducing system state variable augmentation transformation to the multi-fault system 1, and defining the following augmentation matrixes and vectors, wherein the expression is as follows:

a new system of the multi-fault system 1 after system state variable augmentation transformation can be obtained, and the new system is marked as a multi-fault system 2, and the state space expression of the new system is as follows:

wherein z is₁(t) is the state variable of the multiple fault system 2, noted as the secondary state variable z₁(t)，z₁(t) is n₁+n₃+n₆Dimensional space vector, is

Is a quadratic state variable z₁(ii) the derivative of (t),

wherein

Is a fault f of the voltage sensor 1_u1(ii) the derivative of (t),

for failure of the voltage sensor 2

A derivative of (a); f. of₁(t) is a fault variable of the multi-fault system 2, and is recorded as a system fault quantity f₁(t)；

E₁As the second state variable derivative

Is recorded as a first derivative coefficient matrix E₁In a

In the expression of (a) in (b),

represents n₁The dimension-unit matrix is a matrix of the dimension units,

represents n₃A dimension unit matrix;

A₂the state matrix for the multi-fault system 2 is denoted as a quadratic state matrix A₂；

B₂The input matrix of the multi-fault system 2 is marked as a secondary input matrix B₂；

F₂Is the amount of system failure f₁(t) coefficient matrix, denoted as quadratic failure coefficient matrix F₂In a

In the expression of (a) in (b),

represents n₇The dimension-unit matrix is a matrix of the dimension units,

represents n₈A dimension unit matrix;

N₂the coefficient matrix of harmonic disturbance eta (t) in the multi-fault system 2 is recorded as a secondary disturbance coefficient matrix N₂；

Output matrix for multiple fault system 2

Is recorded as a quadratic output matrix

The parameters in this example are as follows:

step 4, carrying out one-time coordinate transformation on the multi-fault system 2

Step 4.1, outputting the secondary output matrix

Transposing, recording the transposed output matrix as

Handle

The matrix is decomposed into the product of an orthogonal matrix and an upper triangular matrix, and the product is recorded as

U is an orthogonal matrix and Q is an upper triangular matrix; let P be U^T，J＝Q^T，U^TIs the transpose of the orthogonal matrix U, Q^TIs the transpose matrix of the upper triangular matrix Q, then the obtained

Wherein P satisfies P^T＝P^-1，P^TIs the transpose of the matrix P, P^-1Is the inverse of matrix P, and is denoted as primary coordinate transformation matrix.

Step 4.2, introduce coordinate transformation z₂(t)＝Pz₁(t), the multi-fault system 2 can be converted into a new system through coordinate transformation, the new system is recorded as a multi-fault system 3, and the state space expression of the new system is as follows:

wherein z is₂(t) is the state variable of the multi-fault system 3, and is recorded as the third state variableQuantity z₂(t)；

Is a cubic state variable z₂(t) derivative of;

E₂is a third state variable derivative

Is denoted as the second derivative coefficient matrix E₂，E₂＝E₁P^T；A₃The state matrix of the multi-fault system 3 is marked as a cubic state matrix A₃，A₃＝A₂P^T；B₃The input matrix of the multi-fault system 3 is recorded as a cubic input matrix B₃；F₃For faults f of the multiple fault system 3₁(t) coefficient matrix, denoted as cubic failure coefficient matrix F₃；N₃The coefficient matrix of harmonic disturbance eta (t) for the multi-fault system 3 is recorded as a third-order disturbance coefficient matrix N₃(ii) a J is the output matrix of the multiple fault system 3, denoted as the cubic output matrix J, and is denoted as a block matrix, i.e., J ═ J (J)₁0), wherein J₁Left blocking submatrix of J, J₁Belong to n₅Dimensional space, is denoted as

And J₁Is a non-singular matrix.

In the present embodiment, it is preferred that,

step 5, matrix transformation is carried out on the multi-fault system 3

Step 5.1, the second derivative coefficient matrix E₂Conversion into a block matrix, i.e. E₂＝(E₂₁E₂₂) In which E₂₁Is a coefficient matrix E of the second derivative₂Left blocking submatrix of (E)₂₁Is (n)₁+n₃+n₆)×n₅Dimensional space, is denoted as

E₂₂Is a coefficient matrix E of the second derivative₂Right blocking submatrix, E₂₂Is (n)₁+n₃+n₆)×(n₁+n₃+n₆-n₅) Dimensional space, is denoted as

Then designing a transformation matrix xi, recording as the matrix transformation matrix xi,

wherein xi₁₁Being the upper part of the submatrix xi of the transform matrix xi₁₁Is n₅×(n₁+n₃+n₆) Dimensional space, is denoted as

Ξ₂₁A lower blocking submatrix of the transform matrix xi, xi₂₁Belong to (n)₁+n₃+n₆-n₅)×(n₁+n₃+n₆) Dimensional space, is denoted as

And xi₁₁Satisfies E₂₂ ^TΞ₁₁ ^T0, solution E₂₂ ^TΞ₁₁ ^T0, then xi may be obtained₁₁Wherein the matrix E₂₂ ^TIs a coefficient matrix E of the second derivative₂Right blocking submatrix E₂₂Transpose of (2), matrix xi₁₁ ^TAn upper blocking submatrix xi being a transform matrix xi₁₁Transposing; xi₂₁＝E₂₂ ^T(E₂₂E₂₂ ^T)^-1Matrix (E)₂₂E₂₂ ^T)^-1Is a matrix E₂₂E₂₂ ^TThe inverse of (c).

Step 5.2, the left and right state space expressions of the multi-fault system 3 are multiplied by the transformation matrix xi to obtain a new transformed system, the new system is marked as a multi-fault system 4, and the state space expressions are as follows:

wherein z is₃(t) is the state variable of the multiple fault system 4, noted as the quartile state variable z₃(t)；

Is a quartic state variable z₃(t) derivative of;

E₃is the fourth derivative of the state variable

Is recorded as a coefficient matrix of the third derivative E₃，

Wherein E₃₁Is a coefficient matrix E of the third derivative₃To the left ofUpper blocking submatrix, E₃₂Is a coefficient matrix E of the third derivative₃The lower left block sub-matrix of (a),

is n₁+n₃+n₆-n₅A dimension unit matrix; a. the₄The state matrix of the multi-fault system 4 is marked as a fourth state matrix A₄，

Wherein A is₄₁₁Is a four-times state matrix A₄Upper left blocking sub-matrix of, A₄₁₁Is a four-times state matrix A₄Upper right blocking sub-matrix of, A₄₂₁Is a four-times state matrix A₄Left lower blocking submatrix of, A₄₂₂Is a four-times state matrix A₄The lower right blocking submatrix; b is₄An input matrix for the multiple fault system 4, denoted as a quadruple input matrix B₄，

Wherein B is₄₁Is a four-input matrix B₄Upper block matrix of, B₄₂Is a four-input matrix B₄A lower block matrix of (a); f₄For faults f of the multiple fault system 4₁(t) coefficient matrix, denoted as Quaternary failure coefficient matrix F₄，

Wherein F₄₁Is a four-fault coefficient matrix F₄₁Upper block matrix of F₄₂Is a four-fault coefficient matrix F₄A lower block matrix of (a); n is a radical of₄The coefficient matrix for the harmonic disturbance η (t) of the sensor fault system 4 is noted as the fourth-order disturbance coefficient matrix N₄，

Wherein N is₄₁Is a four-times disturbance coefficient matrix N₄₁Upper block submatrix of, N₄₂Is a four-times disturbance coefficient matrix N₄The lower block submatrix of (1).

In the present embodiment, it is preferred that,

step 6, carrying out secondary coordinate transformation on the multi-fault system 4

Step 6.1, a coordinate transformation matrix T is designed and recorded as a quadratic coordinate transformation matrix T, and T is expressed as a block matrix, namely

Wherein therein

Is n₅The dimension-unit matrix is a matrix of the dimension units,

is n₁+n₃+n₆-n₅Dimension unit matrix, L is a free matrix, denoted as free matrix L, which belongs to (n)₁+n₃+n₆-n₅)×n₅Dimensional space, is denoted as

Step 6.2 introduction of coordinate transformation z₄(t)＝Tz₃(t) a transformed new system is obtained, and the new system is marked as a multi-fault system 5, and the state space expression of the new system is as follows:

wherein z is₄(t) is the state variable of the multiple fault system 5, noted as the quintic state variable z₄(t) for the fifth state variable z₄(t) blocking, i.e.

z₄₁(t) is a five-state variable z₄(t) upper block subvector z₄₁(t)，z₄₁(t) is n₅Dimension vector, z₄₂(t) is a five-state variable z₄(t) lower block subvector z₄₂(t)，z₄₂(t) is n₁+n₃+n₆-n₅A dimension vector;

is a five-fold state variable z₄Derivative of (t), i.e.

Is z₄(t) upper block vector z₄₁(ii) the derivative of (t),

is z of the upper block vector₄₂(t) derivative of; then z is transformed from the above coordinate₄(t)＝Tz₃(t) it can be seen that,

E₄fifth order state variable derivative

A coefficient matrix of (a), and

A₅the state matrix for the multi-fault system 5 is denoted as the five-time state matrix A₅，

Wherein A is₅₁₁Is a quintic state matrix A₅Upper left blocking sub-matrix of, A₅₁₂Is a quintic state matrix A₅Upper right blocking sub-matrix of, A₅₂₁Is a quintic state matrix A₅Left lower blocking submatrix of, A₅₂₂Is a quintic state matrix A₅The lower right blocking submatrix; t is^-1An inverse matrix of the quadratic coordinate transformation matrix T; b is₅The input matrix for the multiple fault system 5 is marked as five-times input matrix B₅，

Wherein B is₅₁For five inputs of matrix B₅Upper blocking submatrix of, B₅₂For five inputs of matrix B₅A lower block submatrix of (a); f₅The coefficient matrix of the fault F (t) of the multi-fault system 5 is marked as a five-fault coefficient matrix F₅，

Wherein F₅₁Is a quintic fault coefficient matrix F₅Upper blocking submatrix of F₅₂Is a quintic fault coefficient matrix F₅A lower block submatrix of (a); n is a radical of₅The coefficient matrix of harmonic disturbance eta (t) of the multi-fault system 5 is recorded as a quintic disturbance coefficient matrix N₅，

Wherein N is₅₁For a quintic disturbance coefficient matrix N₅Upper block submatrix of, N₅₂For a quintic disturbance coefficient matrix N₅Lower blocking submatrix, J^*Is the output matrix of the multiple fault system 5, and the following relationship can be known:

in the present embodiment, it is preferred that,

step 7, designing a self-adaptive reduced-order sliding mode observer

Step 7.1, calculating the state quantity theta of the order-reduced system according to the multi-fault system 5, and recording the state quantity theta as the state quantity theta of the order-reduced system, wherein the calculation formula is as follows:

Θ＝(LE₃₁+E₃₂-L)z₄₁(t)+z₄₂(t)

and solving a state space expression of the reduced-order system according to the reduced-order system state quantity theta, wherein the state space expression is as follows:

wherein,

is the derivative of the state quantity theta of the reduced-order system, and delta is the state expression z of the reduced-order system₄₁The coefficient matrix of (t) is marked as a reduced system coefficient matrix delta, and the expression is as follows:

Δ＝-(LA₅₁₂+A₅₂₂)(LE₅₁+E₅₂-L)+L(A₅₁₁-A₅₁₂L)+A₅₁₁-A₅₂₂L

step 7.2, designing a self-adaptive reduced order sliding mode observer aiming at a state space expression of a reduced order system, wherein the expression is as follows:

wherein,

is the estimated value of the state quantity theta of the reduced order system and is recorded as the estimated value of the state quantity theta of the reduced order system

Is an estimate of the state quantity of the reduced order system

Is a sliding mode gain matrix, where Γ is (LF) ═ f₅₁+F₅₂) V is the approach law,

wherein,

in order to be able to vary the parameter 1,

tanh () is a hyperbolic tangent function,

is variable parameter 2, and

sigma is variable parameter 3, sigma belongs to (0, 1), theta is variable parameter 4, theta is more than 1, rho is variable parameter 5, beta is more than 0, psi is positive definite symmetrical matrix, chi is diagonal matrix,

e is a constant number, e > 1_Θ(t) is the error of the estimation,

let S be e_Θ(t), wherein S is a sliding mode surface of the designed adaptive reduced-order sliding mode observer;

step 7.3, obtaining a free matrix L by solving a Lyapunov equation, wherein the expression of the Lyapunov equation is as follows:

(LA₄₁₂+A₄₂₂)^TP+P(LA₄₁₂+A₄₂₂)＝-I

wherein (LA)₄₁₂+A₄₂₂)^TIs LA₄₁₂+A₄₂₂P is a positive definite symmetric matrix, and I is an identity matrix.

In the present embodiment, it is preferred that,

σ＝0.1，ρ＝2，θ＝20，

step 8, fault diagnosis of the actuator and the sensor is carried out

Step 8.1, sampling the value of the system output y (t) of the multi-fault system 1 in step 1, and substituting the sampled value into z in step 6.2₄₁(t)＝z₃₁(t)＝J₁ ^-1y (t), the state variable z can be obtained five times₄(t) upper block subvector z₄₁(t) value, again according to the known five state variable z₄(t) upper block vector z₄₁The value of (t), Θ in step 7.1 ═ (LE)₃₁+E₃₂-L)z₄₁(t)+z₄₂(t), step 7.2

And the error e is estimated in step 7.2_Θ(t) is 0, and z can be obtained₄₂(t), the expression of which is:

then the five state variables z are obtained₄(t) upper block subvector z₄₁(t) value and five state variables z₄(t) lower block subvector z₄₂(t) value substituted into step 6.2

The state variable z can be calculated five times₄(t) value;

step 8.2, starting from the multiple fault system 2, according to a coordinate transformation z₂(t)＝Pz₁(t) and quadratic coordinate transformation z₄(t)＝Tz₃(t) and the matrix transformation does not change the cubic state variable z in the sensor failure system 3 in step 5₂(t) obtaining z₃(t)＝z₂(t) thereby obtaining z₄(t)＝TPz₁(t) calculating a secondary state variable z by inverse operation of the matrix₁(t)＝P^TT^-1z₄(t), and the five state variables z calculated in step 8.1 are further added₄(t) substitution of formula z₁(t)＝P^TT^-1z₄(t) obtaining a secondary state variable z₁(t)；

Step 8.3, mixing

Is recorded as a primary state variable estimation value,

is recorded as the estimated value of the actuator fault

Is recorded as the fault estimation value of the voltage sensor 1

Is recorded as the fault estimation value of the voltage sensor 2

Calculating a primary state variable estimate

Actuator fault estimation

Voltage sensor fault 1 estimation

And voltage sensor 2 fault estimation

The specific calculation formula is as follows:

step 8.4, diagnosing faults of the actuator, the voltage sensor 1 and the voltage sensor 2, and giving a self-adaptive diagnosis threshold value T_th。

In this embodiment, the adaptive threshold T is diagnosed_thThe expressions are respectively as follows:

T_th＝E₁+Γ₁(ζ₁+ζ₂)

wherein E is₁Is a constant 1, Γ₁Is a constant number 2, and Γ₁∈(1，2)，ζ₁For a bounded external disturbance, ζ₂Is a bounded voltage perturbation. Specifically, in the present embodiment, E₁＝0.01，Γ₁＝1.01，ζ₁＝0.02sin(10t)，

Defining fault location quantity Z₁，

And positioned as follows:

if Z is₁When the fault is equal to 0, the multi-fault system 1 has no actuator fault;

if Z is₁1, the multi-fault system 1 has an actuator fault;

defining fault location quantity Z₂，

And positioned as follows:

if Z is₂When the voltage sensor 1 fails, the multi-fault system 1 is not failed;

if Z is₂1, the multi-fault system 1 has a fault in the voltage sensor 1;

defining fault location quantity Z₃，

And positioned as follows:

if Z is₃When the failure rate is 0, the multi-failure system 1 has no failure of the voltage sensor 2;

if Z is₃The multiple fault system 1 has a voltage sensor 2 fault 1.

And the multi-fault diagnosis of the single-phase three-level rectifier is finished.

In order to prove the technical effect of the invention, the invention is simulated.

FIG. 4 shows an actuator failure f in this example_a(t) actuator failure estimation value

And an adaptive threshold T_thThe simulated waveform of (2). As can be seen from this graph, no actuator failure occurred before 8s, and the estimated value of actuator failure after 8s

The actuator fault f can be well estimated_a(t) and an actuatorFault estimation

Has exceeded the adaptive diagnostic threshold T_thI.e. an actuator failure has occurred.

FIG. 5 shows the failure of the voltage sensor 1 in this example

Voltage sensor 1 fault estimation

Subject to adaptive threshold T_thThe simulated waveform of (2). As can be seen from this graph, no failure occurred in the voltage sensor 1 before 8s, and the estimated value of the failure in the voltage sensor 1 after 8s

The failure f of the voltage sensor 1 can be well estimated_u1(t) and voltage sensor 1 failure estimation value

Has exceeded the adaptive diagnostic threshold T_thNamely, the voltage sensor 1 malfunction occurs.

FIG. 6 shows the failure f of the voltage sensor 2 in this example_u2(t) Voltage sensor 2 Fault estimation

And an adaptive threshold T_thThe simulated waveform of (2). As can be seen from this graph, no failure occurred in the voltage sensor 2 before 8s, and after 8s, a failure occurred in the voltage sensor 2, and an estimated value of the failure in the voltage sensor 2

The voltage sensor fault 2f can be well estimated_u2(t) and voltage sensor 2 failure estimation

Exceed the self-adaptationDiagnostic threshold T_thI.e. a voltage sensor 2 failure has occurred.

Claims (3)

1. A multi-fault diagnosis method for a single-phase three-level rectifier relates to a circuit topology structure comprising a network side voltage source U_sNetwork side equivalent inductor L_sAnd net side equivalent resistance R_sRectifier bridge, two identical support capacitors C_d1，C_d1A DC side load and two identical voltage sensors; support capacitor C_d1And a support capacitor C_d2A DC positive bus P and a DC negative bus Q connected in parallel with a DC side load after being connected in series₁Between, support the capacitor C_d1And a support capacitor C_d2The contact point of (2) is marked as a direct current bus midpoint O; two identical voltage sensors are respectively marked as a voltage sensor 1 and a voltage sensor 2, and the voltage sensor 1 is connected with a supporting capacitor C_d1At both ends of which the voltage sensor 2 is connected to the supporting capacitor C_d2Both ends of (a);

the rectifier bridge is divided into two-phase bridge arms, and the two-phase bridge arms are connected with the direct-current side load in parallel; marking two-phase bridge arms as bridge arms k, wherein k is a bridge sequence, and k is a, b; in the two-phase bridge arms, each phase of bridge arm comprises 4 switching tubes with reverse connection diodes and two clamping diodes, namely a rectifier bridge comprises 8 switching tubes with reverse connection diodes and 4 clamping diodes, and the 8 switching tubes form an actuator of a single-phase three-level rectifier; marking 8 switch tubes as switch tubes V_kγγ denotes the number of the switching tube, γ is 1, 2, 3, 4, and 4 clamping diodes are denoted as clamping diodes D_ckρρ is the serial number of the clamping diode, and ρ is 1, 2; in each of the two-phase arms, a switching tube V_k1Switch tube V_k2Switch tube V_k3Switch tube V_k4Are sequentially connected in series, wherein, the switch tube V_k2And a switching tube V_k3Is marked as the input point tau of the rectifier bridge_kK is a, b; in each of the two-phase arms, a clamping diode D_ck1The cathode of the switch tube is connected with the switch tube V_k1And a switching tube V_k2Between, the clamping diode D_ck1Anode of (2) is connected to a clamping diode D_ck2Cathode of (2), clampingPolar tube D_ck2Anode of the switch tube is connected with the switch tube V_k3And a switching tube V_k4And clamping diode D_ck1And a clamping diode D_ck2The connecting point of the direct current bus is connected with the midpoint O of the direct current bus;

the network side equivalent inductance L_sOne end of is connected with an input point tau of the rectifier bridge_aThe other end is connected with the equivalent resistance R of the network side in sequence_sGrid side voltage source U_sThe other end of the series network side voltage source is connected with an input point tau of the rectifier bridge_b；

The multi-fault diagnosis method is characterized by comprising the following steps of performing fault diagnosis on an actuator of a single-phase three-level rectifier and performing weak fault diagnosis on a multi-voltage sensor:

step 1, establishing a hybrid logic dynamic model of a single-phase three-level rectifier, and calculating a phase voltage U of an input end of a rectifier bridge_abIs estimated value of

Sampling the current of the network side and recording the current of the network side as the current i of the network side_sSampling support capacitor C_d1And a support capacitor C_d2And is denoted as DC voltage u₁，u₂Sampling the DC side voltage U_dc(ii) a Establishing a mixed logic dynamic model of the single-phase three-level rectifier, and calculating the phase voltage U of the input end of the rectifier bridge_abIs estimated value of

The input end phase voltage U of the rectifier bridge_abFor input point tau of rectifier bridge_aAnd the input point tau of the rectifier bridge_bA voltage in between;

the expression of the hybrid logic dynamic model of the single-phase three-level rectifier is as follows:

wherein,

is an estimate of the voltage of the a-phase,

is an estimate of the b-phase voltage, T_hIs a DC voltage u₁Mixed logic dynamic function of, T_lIs a DC voltage u₂The hybrid logical dynamic function of (1);

the input end phase voltage U of the rectifier bridge_abIs estimated value of

The expression of (a) is:

step 2, establishing a multi-fault-containing single-phase three-level rectifier system state space expression, and recording the expression as a multi-fault system 1, wherein the expression is as follows:

wherein x (t) is the state variable of the multi-fault system 1 and is marked as the primary state variable x (t),

x (t) is n₁Dimension state variable, as

t is a variable of time and t is,

the first derivative of the first state variable x (t),

wherein

Is a net side current i_sThe derivative of (a) of (b),

are respectively DC voltage u₁，u₂A derivative of (a); u (t) is the input of the multi-fault system 1 and is recorded as primary system input u (t), u (t)_sU (t) is n₂Dimension state variable, as

f_a(t) actuator failure for multiple failure System 1, denoted as actuator failure f_a(t)，f_a(t) is n₃Dimension state variable, as

Eta (t) is the harmonic disturbance quantity of the multi-fault system 1 and is recorded as harmonic disturbance eta (t), and eta (t) is n₄Dimension state variable, as

y (t) is the output of the multi-fault system 1 and is recorded as the system output y (t), and y (t) is n₅Dimension state variable, as

f_s(t) Voltage sensor Fault for multiple Fault System 1, denoted System Voltage sensor Fault f_s(t)，f_s(t) is n₆Dimension state variable, as

Wherein

For a fault in voltage sensor 1, it is noted as a fault f in voltage sensor 1_u1(t)，f_u1(t) is n₇Dimension state variable, as

f_u2(t) is a voltage sensor 2 failure, denoted as voltage sensor 2 failure f_u2(t)，f_u2(t) is n₈Dimension state variable, as

A₁The state matrix for the multi-fault system 1 is marked as a primary state matrix A₁，

Wherein L is equivalent inductance L at network side_sR is the equivalent resistance R of the network side_sResistance value of C₁，C₂Are respectively a support capacitor C_d1And a support capacitor C_d2The capacitance value of (a); b is₁The input matrix for the multiple fault system 1 is marked as a primary input matrix B₁，

G₁For actuator failure f_a(t) the coefficient matrix is recorded as a primary actuator fault coefficient matrix,

N₁the coefficient matrix of harmonic disturbance eta (t) is recorded as a primary disturbance coefficient matrix N₁，

C_y1The output matrix of the multi-fault system 1 is recorded as a primary output matrix

F₁For system voltage sensor fault f_s(t) coefficient matrix, which is recorded as primary voltage sensor fault coefficient matrix F₁，

System voltage sensor fault f_s(t) actuator failure f_a(t) and harmonic disturbances η (t) are both continuous and bounded functions satisfying a time variable t, denoted as | | f_s(t)||≤r_s，||f_a(t)||≤r_a，||η(t)||≤r_ηWherein | | | f_s(t) | | is f_sNorm of (t, | f_a(t) | | is f_aThe norm of (t), where | | | η (t) | | is the norm of η (t), r_sFor system voltage sensor fault f_sUpper limit of (t), r_aFor actuator failure f_aUpper limit of (t), r_ηIs a supremum of harmonic disturbance η (t), and r_s、r_aAnd r_ηAre all normal numbers and are recorded as r_s＞0，r_a＞0，r_η＞0；

Step 3, introducing system state variable augmentation transformation to the multi-fault system 1, and defining the following augmentation matrixes and vectors, wherein the expression is as follows:

a new system of the multi-fault system 1 after system state variable augmentation transformation can be obtained, and the new system is marked as a multi-fault system 2, and the state space expression of the new system is as follows:

wherein z is₁(t) is the state variable of the multiple fault system 2, noted as the secondary state variable z₁(t)，z₁(t) is n₁+n₃+n₆Dimensional space vector, is

Is a quadratic state variable z₁(ii) the derivative of (t),

wherein

Is a fault f of the voltage sensor 1_u1(ii) the derivative of (t),

for failure of the voltage sensor 2

A derivative of (a); f. of₁(t) is a fault variable of the multi-fault system 2, and is recorded as a system fault quantity f₁(t)；

E₁As the second state variable derivative

Is recorded as a first derivative coefficient matrixE₁In a

In the expression of (a) in (b),

represents n₁The dimension-unit matrix is a matrix of the dimension units,

represents n₃A dimension unit matrix;

A₂the state matrix for the multi-fault system 2 is denoted as a quadratic state matrix A₂；

B₂The input matrix of the multi-fault system 2 is marked as a secondary input matrix B₂；

F₂Is the amount of system failure f₁(t) coefficient matrix, denoted as quadratic failure coefficient matrix F₂In a

In the expression of (a) in (b),

represents n₇The dimension-unit matrix is a matrix of the dimension units,

represents n₈A dimension unit matrix;

N₂the coefficient matrix of harmonic disturbance eta (t) in the multi-fault system 2 is recorded as a secondary disturbance coefficient matrix N₂；

Output matrix for multiple fault system 2

Is recorded as a quadratic output matrix

Step 4, carrying out one-time coordinate transformation on the multi-fault system 2

Step 4.1, outputting the secondary output matrix

Transposing, recording the transposed output matrix as

Handle

The matrix is decomposed into the product of an orthogonal matrix and an upper triangular matrix, and the product is recorded as

U is an orthogonal matrix and Q is an upper triangular matrix; let P be U^T，J＝Q^T，U^TIs the transpose of the orthogonal matrix U, Q^TIs the transpose matrix of the upper triangular matrix Q, then the obtained

Wherein P satisfies P^T＝P^-1，P^TIs the transpose of the matrix P, P^-1Is the inverse matrix of the matrix P, and takes P as a primary coordinate transformation matrix;

step 4.2, introduce coordinate transformation z₂(t)＝Pz₁(t), the multi-fault system 2 can be converted into a new system through coordinate transformation, the new system is recorded as a multi-fault system 3, and the state space expression of the new system is as follows:

wherein z is₂(t) is the state variable of the multiple fault system 3, noted as the third state variable z₂(t)；

Is a cubic state variable z₂(t) derivative of;

E₂is a third state variable derivative

Is denoted as the second derivative coefficient matrix E₂，E₂＝E₁P^T；A₃The state matrix of the multi-fault system 3 is marked as a cubic state matrix A₃，A₃＝A₂P^T；B₃The input matrix of the multi-fault system 3 is recorded as a cubic input matrix B₃；F₃For faults f of the multiple fault system 3₁(t) coefficient matrix, denoted as cubic failure coefficient matrix F₃；N₃The coefficient matrix of harmonic disturbance eta (t) for the multi-fault system 3 is recorded as a third-order disturbance coefficient matrix N₃(ii) a J is the output matrix of the multiple fault system 3, denoted as the cubic output matrix J, and is denoted as a block matrix, i.e., J ═ J (J)₁0), wherein J₁Left blocking submatrix of J, J₁Belong to n₅Dimensional space, is denoted as

And J₁Is a non-singular matrix;

step 5, matrix transformation is carried out on the multi-fault system 3

Step 5.1, the second derivative coefficient matrix E₂Conversion into a block matrix, i.e. E₂＝(E₂₁ E₂₂) In which E₂₁Is a coefficient matrix E of the second derivative₂Left blocking submatrix of (E)₂₁Is (n)₁+n₃+n₆)×n₅Dimensional space, is denoted as

E₂₂Is a coefficient matrix E of the second derivative₂Right blocking submatrix, E₂₂Is (n)₁+n₃+n₆)×(n₁+n₃+n₆-n₅) Dimensional space, is denoted as

Then designing a transformation matrix xi, recording as the matrix transformation matrix xi,

wherein xi₁₁Being the upper part of the submatrix xi of the transform matrix xi₁₁Is n₅×(n₁+n₃+n₆) Dimensional space, is denoted as

Ξ₂₁A lower blocking submatrix of the transform matrix xi, xi₂₁Belong to (n)₁+n₃+n₆-n₅)×(n₁+n₃+n₆) Dimensional space, is denoted as

And xi₁₁Satisfies E₂₂ ^TΞ₁₁ ^T0, solution E₂₂ ^TΞ₁₁ ^T0, then xi may be obtained₁₁Wherein the matrix E₂₂ ^TIs a coefficient matrix E of the second derivative₂Right blocking submatrix E₂₂Transpose of (2), matrix xi₁₁ ^TAn upper blocking submatrix xi being a transform matrix xi₁₁Transposing; xi₂₁＝E₂₂ ^T(E₂₂E₂₂ ^T)^-1Matrix (E)₂₂E₂₂ ^T)^-1Is a matrix E₂₂E₂₂ ^TThe inverse of (1);

step 5.2, the left and right state space expressions of the multi-fault system 3 are multiplied by the transformation matrix xi to obtain a new transformed system, the new system is marked as a multi-fault system 4, and the state space expressions are as follows:

wherein z is₃(t) is the state variable of the multiple fault system 4, noted as the quartile state variable z₃(t)；

Is a quartic state variable z₃(t) derivative of;

E₃is the fourth derivative of the state variable

Is recorded as a coefficient matrix of the third derivative E₃，

Wherein E₃₁Is a coefficient matrix E of the third derivative₃Upper left blocking sub-matrix of (E)₃₂Is a coefficient matrix E of the third derivative₃The lower left block sub-matrix of (a),

is n₁+n₃+n₆-n₅A dimension unit matrix; a. the₄The state matrix of the multi-fault system 4 is marked as a fourth state matrix A₄，

Wherein A is₄₁₁Is a four-times state matrix A₄Upper left blocking sub-matrix of, A₄₁₂Is a four-times state matrix A₄Upper right blocking sub-matrix of, A₄₂₁Is a four-times state matrix A₄Left lower blocking submatrix of, A₄₂₂Is a four-times state matrix A₄The lower right blocking submatrix; b is₄An input matrix for the multiple fault system 4, denoted as a quadruple input matrix B₄，

Wherein B is₄₁Is a four-input matrix B₄Upper block matrix of, B₄₂Is a four-input matrix B₄A lower block matrix of (a); f₄For faults f of the multiple fault system 4₁(t) coefficient matrix, denoted as Quaternary failure coefficient matrix F₄，

Wherein F₄₁Is a four-fault coefficient matrix F₄₁Upper block matrix of F₄₂Is a four-fault coefficient matrix F₄A lower block matrix of (a); n is a radical of₄The coefficient matrix for the harmonic disturbance η (t) of the sensor fault system 4 is noted as the fourth-order disturbance coefficient matrix N₄，

Wherein N is₄₁Is a four-times disturbance coefficient matrix N₄₁Upper block submatrix of, N₄₂Is a four-times disturbance coefficient matrix N₄A lower block submatrix of (a);

step 6, carrying out secondary coordinate transformation on the multi-fault system 4

Step 6.1, a coordinate transformation matrix T is designed and recorded as a quadratic coordinate transformation matrix T, and T is expressed as a block matrix, namely

Wherein therein

Is n₅The dimension-unit matrix is a matrix of the dimension units,

is n₁+n₃+n₆-n₅Dimension unit matrix, L is a free matrix, denoted as free matrix L, which belongs to (n)₁+n₃+n₆-n₅)×n₅Dimensional space, is denoted as

Step 6.2 introduction of coordinate transformation z₄(t)＝Tz₃(t) a transformed new system is obtained, and the new system is marked as a multi-fault system 5, and the state space expression of the new system is as follows:

wherein z is₄(t) is the state variable of the multiple fault system 5, noted as the quintic state variable z₄(t) for the fifth state variable z₄(t) blocking, i.e.

z₄₁(t) is a five-state variable z₄(t) upper block subvector z₄₁(t)，z₄₁(t) is n₅Dimension vector, z₄₂(t) is a five-state variable z₄(t) lower block subvector z₄₂(t)，z₄₂(t) is n₁+n₃+n₆-n₅A dimension vector;

is a five-fold state variable z₄Derivative of (t), i.e.

Is z₄(t) upper block vector z₄₁(ii) the derivative of (t),

is z of the upper block vector₄₂(t) derivative of; then z is transformed from the above coordinate₄(t)＝Tz₃(t) it can be seen that,

E₄fifth order state variable derivative

A coefficient matrix of (a), and

A₅the state matrix for the multi-fault system 5 is denoted as the five-time state matrix A₅，

Wherein A is₅₁₁Is a quintic state matrix A₅Upper left blocking sub-matrix of, A₅₁₂Is a quintic state matrix A₅Upper right blocking sub-matrix of, A₅₂₁Is a quintic state matrix A₅Left lower blocking submatrix of, A₅₂₂Is a quintic state matrix A₅The lower right blocking submatrix; t is^-1An inverse matrix of the quadratic coordinate transformation matrix T; b is₅The input matrix for the multiple fault system 5 is marked as five-times input matrix B₅，

Wherein B is₅₁For five inputs of matrix B₅Upper blocking submatrix of, B₅₂For five inputs of matrix B₅A lower block submatrix of (a); f₅The coefficient matrix of the fault F (t) of the multi-fault system 5 is marked as a five-fault coefficient matrix F₅，

Wherein F₅₁Is a quintic fault coefficient matrix F₅Upper blocking submatrix of F₅₂Is a quintic fault coefficient matrix F₅A lower block submatrix of (a); n is a radical of₅The coefficient matrix of harmonic disturbance eta (t) of the multi-fault system 5 is recorded as a quintic disturbance coefficient matrix N₅，

Wherein N is₅₁For a quintic disturbance coefficient matrix N₅Upper block submatrix of, N₅₂For a quintic disturbance coefficient matrix N₅Lower blocking submatrix, J^*Is the output matrix of the multiple fault system 5 and knows the following relationship:

step 7, designing a self-adaptive reduced-order sliding mode observer

Step 7.1, calculating the state quantity theta of the order-reduced system according to the multi-fault system 5, and recording the state quantity theta as the state quantity theta of the order-reduced system, wherein the calculation formula is as follows:

Θ＝(LE₃₁+E₃₂-L)z₄₁(t)+z₄₂(t)

and solving a state space expression of the reduced-order system according to the reduced-order system state quantity theta, wherein the state space expression is as follows:

wherein,

is the derivative of the state quantity theta of the reduced-order system, and delta is the state expression z of the reduced-order system₄₁The coefficient matrix of (t) is marked as a reduced system coefficient matrix delta, and the expression is as follows:

Δ＝-(LA₅₁₂+A₅₂₂)(LE₅₁+E₅₂-L)+L(A₅₁₁-A₅₁₂L)+A₅₁₁-A₅₂₂L

step 7.2, designing a self-adaptive reduced order sliding mode observer aiming at a state space expression of a reduced order system, wherein the expression is as follows:

wherein,

is the estimated value of the state quantity theta of the reduced order system and is recorded as the estimated value of the state quantity theta of the reduced order system

Is an estimate of the state quantity of the reduced order system

Is a sliding mode gain matrix, where Γ is (LF) ═ f₅₁+F₅₂) V is the approach law,

wherein,

zeta > 0 for variable parameter 1, tanh () is a hyperbolic tangent function,

is variable parameter 2, and

sigma is variable parameter 3, sigma belongs to (0, 1), theta is variable parameter 4, theta is more than 1, rho is variable parameter 5, beta is more than 0, psi is positive definite symmetrical matrix, chi is diagonal matrix,

e is a constant number, e > 1_Θ(t) is the error of the estimation,

let S be e_Θ(t), where S is the designed adaptive reduced-order sliding mode observationA slip form surface of the device;

step 7.3, obtaining a free matrix L by solving a Lyapunov equation, wherein the expression of the Lyapunov equation is as follows:

(LA₄₁₂+A₄₂₂)^TP+P(LA₄₁₂+A₄₂₂)＝-I

wherein (LA)₄₁₂+A₄₂₂)^TIs LA₄₁₂+A₄₂₂P is a positive definite symmetric matrix, and I is a unit matrix;

step 8, fault diagnosis of the actuator and the sensor is carried out

Step 8.1, sampling the value of the system output y (t) of the multi-fault system 1 in step 1, and substituting the sampled value into z in step 6.2₄₁(t)＝z₃₁(t)＝J₁ ^-1y (t), the state variable z can be obtained five times₄(t) upper block subvector z₄₁(t) value, again according to the known five state variable z₄(t) upper block vector z₄₁The value of (t), Θ in step 7.1 ═ (LE)₃₁+E₃₂-L)z₄₁(t)+z₄₂(t), step 7.2

And the error e is estimated in step 7.2_Θ(t) is 0, and z can be obtained₄₂(t), the expression of which is:

then the five state variables z are obtained₄(t) upper block subvector z₄₁(t) value and five state variables z₄(t) lower block subvector z₄₂(t) value substituted into step 6.2

The state variable z can be calculated five times₄(t) value;

step 8.2, starting from the multiple fault system 2, according to a coordinate transformationz₂(t)＝Pz₁(t) and quadratic coordinate transformation z₄(t)＝Tz₃(t) and the matrix transformation does not change the cubic state variable z in the sensor failure system 3 in step 5₂(t) obtaining z₃(t)＝z₂(t) thereby obtaining z₄(t)＝TPz₁(t) calculating a secondary state variable z by inverse operation of the matrix₁(t)＝P^TT^{- 1}z₄(t), and the five state variables z calculated in step 8.1 are further added₄(t) substitution of formula z₁(t)＝P^TT^-1z₄(t) obtaining a secondary state variable z₁(t)；

Step 8.3, mixing

Is recorded as a primary state variable estimation value,

is recorded as the estimated value of the actuator fault

Is recorded as the fault estimation value of the voltage sensor 1

Is recorded as the fault estimation value of the voltage sensor 2

Calculating a primary state variable estimate

Actuator fault estimation

Voltage sensor fault 1 estimation

And voltage sensor 2 fault estimation

The specific calculation formula is as follows:

step 8.4, diagnosing faults of the actuator, the voltage sensor 1 and the voltage sensor 2, and giving a self-adaptive diagnosis threshold value T_th；

Defining fault location quantity Z₁，

And positioned as follows:

if Z is₁When the fault is equal to 0, the multi-fault system 1 has no actuator fault;

if Z is₁1, the multi-fault system 1 has an actuator fault;

defining fault location quantity Z₂，

And positioned as follows:

if Z is₂When the voltage sensor 1 fails, the multi-fault system 1 is not failed;

if Z is₂1, the multi-fault system 1 has a fault in the voltage sensor 1;

defining fault location quantity Z₃，

And positioned as follows:

if Z is₃When the failure rate is 0, the multi-failure system 1 has no failure of the voltage sensor 2;

if Z is₃The multiple fault system 1 has a voltage sensor 2 fault 1.

2. The method according to claim 1, wherein the DC voltage u of step 1 is the DC voltage u₁Hybrid logic dynamic function T of_hAnd a DC voltage u₂Hybrid logic dynamic function T of_lThe calculation process of (2) is as follows:

recording the switching function of the k-phase bridge arm as S_kAnd k is a, b, then:

recording the pulse control signal of the switching tube as v_kγK is a, b, γ is 1, 2, 3, 4, then k-phase bridge arm switching function S_k＝v_k1v_k2-v_k3v_k4。

3. The single-phase three-level rectifier bridge multi-fault diagnostic method according to claim 1,diagnostic adaptive threshold T as described in step 8.4_thThe expressions are respectively as follows:

T_th＝E₁+Γ₁(ζ₁+ζ₂)

wherein E is₁Is a constant 1, Γ₁Is a constant number 2, and Γ₁∈(1，2)，ζ₁For a bounded external disturbance, ζ₂Is a bounded voltage perturbation.

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