CN114325164B - Multi-fault diagnosis method for single-phase three-level rectifier - Google Patents
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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
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 the core components of the 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 have actuator faults at the same time, the actuator faults generated in the actual transportation process can cause abnormal functions of a traction transmission system of the high-speed train, serious traffic accidents are caused, and meanwhile, 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 the corresponding fault diagnosis is realized by acquiring fault data information and analyzing and processing the data information; corresponding papers and patents such as "a data-drive a vehicle to an activator and sensor fault detection, isolation and estimation in discrete-time linear systems" and "a data-driven transmission sensor fault diagnosis method" (application publication No. CN 202011201104.0) do not need to establish an accurate mathematical model, but need a large amount of data bases, and need to perform complex data processing on the bases, and the algorithms are complex, and have large workload and high difficulty.
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:
a Simultaneous project activator and sensor fault evaluation for non-linear Lipschitz systems aims at performing complex fault decoupling on faults of an actuator and a sensor to form two subsystems and then respectively designing an observer for the two subsystems to perform 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, and further designs a self-adaptive approach rate, and the jitter characteristics in the control process are reduced by the self-adaptive switching approach rate, so that the accuracy of system fault diagnosis is further improved; 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 s Network side equivalent inductor L s And net side equivalent resistance R s Rectifier bridge, two identical support capacitors C d1 ，C d2 A DC side load and two identical voltage sensors; support capacitor C d1 And a support capacitor C d2 After being connected in series, the capacitor C is connected in parallel between a direct current positive bus P and a direct current negative bus Q1 of a direct current side load d1 And a support capacitor C d1 The 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 d1 At both ends of which the voltage sensor 2 is connected to the supporting capacitor C d2 Both 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; recording two-phase bridge arms as bridge arms k, wherein k is a bridge sequence, and k = 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 kγ γ denotes a serial number of the switching tube, γ =1,2,3,4, and 4 clamping diodes are denoted as clamping diodes D ckρ ρ is the serial number of the clamp diode, ρ =1,2; in each of the two-phase arms, a switching tube V k1 Switch tube V k2 Switch tube V k3 And a switch tube V k4 Are sequentially connected in series, wherein, the switch tube V k2 And a switching tube V k3 Is marked as the input point tau of the rectifier bridge k K = a, b; in each of the two-phase arms, a clamping diode D ck1 The cathode of the switch tube is connected with the switch tube V k1 And a switching tube V k2 Between, the clamping diode D ck1 Anode of (2) is connected to a clamping diode D ck2 Cathode of (2), clamping diode D ck2 Anode of the switch tube is connected with the switch tube V k3 And a switching tube V k4 And clamping diode D ck1 And a clamping diode D ck2 The connecting point of the direct current bus is connected with the midpoint O of the direct current bus;
the network side equivalent inductance L s One end of is connected with an input point tau of the rectifier bridge a The other end is connected with the equivalent resistance R of the network side in sequence s Grid side voltage source U s The 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:
Sampling the current of the network side and recording the current of the network side as the current i of the network side s Sampling support capacitor C d1 And a support capacitor C d2 And is denoted as DC voltage u 1 ，u 2 Sampling 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 ab Is estimated value of
The input end phase voltage U of the rectifier bridge ab For input point tau of rectifier bridge a And the input point tau of the rectifier bridge b A voltage in between;
the expression of the hybrid logic dynamic model of the single-phase three-level rectifier is as follows:
wherein the content of the first and second substances,
is an estimate of the voltage of the a-phase,
is an estimate of the b-phase voltage, T h Is a DC voltage u 1 Mixed logic dynamic function of, T l Is a DC voltage u 2 A hybrid logical dynamic function of (a);
the input end phase voltage U of the rectifier bridge ab Is estimated value of
The expression of (a) is:
wherein x (t) is a state variable of the multi-fault system 1 and is marked as a primary state variable x (t),
x (t) is n 1 Dimensional state variables, noted
t is a variable of time and is,
the first derivative of the primary state variable x (t),
wherein
Is a network side current i s The derivative of (a) is determined,
are respectively DC voltage u 1 ，u 2 A 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) = u s U (t) is n 2 Dimensional state variables, noted
f a (t) actuator failure for multiple failure System 1, denoted as actuator failure f a (t)，f a (t) is n 3 Dimension 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 n 4 Dimension 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 n 5 Dimension state variable, as
f s (t) Voltage sensor Fault for multiple Fault System 1, noted System Voltage sensor Fault f s (t)，f s (t) is n 6 Dimension 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 n 7 Dimensional state variables, noted
f u2 (t) is a voltage sensor 2 failure, denoted as voltage sensor 2 failure f u2 (t)，f u2 (t) is n 8 Dimensional state variables, noted
A 1 The state matrix for the multiple fault system 1, denoted as primary state matrix A 1 ，
Wherein L is equivalent inductance L at network side s R is the equivalent resistance R of the network side s Resistance value of C 1 ，C 2 Are respectively a support capacitor C d1 And a support capacitor C d2 The capacitance value of (a); b is 1 The input matrix for the multiple fault system 1 is marked as a primary input matrix B 1 ，
G 1 For actuator failure f a (t) the coefficient matrix is recorded as a primary actuator fault coefficient matrix,
N 1 the coefficient matrix of harmonic disturbance eta (t) is recorded as a primary disturbance coefficient matrix N 1 ，
C y1 For multiple fault systems1 output matrix, denoted primary output matrix
F 1 For system voltage sensor failure f s (t) coefficient matrix, which is recorded as primary voltage sensor fault coefficient matrix F 1 ，
System voltage sensor fault f s (t) actuator failure f a (t) and the harmonic disturbance η (t) are both continuous and bounded functions satisfying the time variable t, denoted | | f s (t)||≤r s ，||f a (t)||≤r a ，||η(t)||≤r η Wherein | | | f s (t) | | is f s Norm of (t, | f a (t) | | is f a The norm of (t), where | | | η (t) | | is the norm of η (t), r s For system voltage sensor fault f s Upper limit of (t), r a For actuator failure f a Upper limit of (t), r η Is the supremum of the harmonic disturbance eta (t), and r s 、r a And r η Are all normal numbers, and are recorded as r s ＞0，r a ＞0，r η ＞0；
a new system after the multi-fault system 1 is subjected to system state variable amplification transformation can be obtained, and the new system is marked as a multi-fault system 2, wherein the expression of the state space of the new system is as follows:
wherein z is 1 (t) is the state variable of the multiple fault system 2, noted as the secondary state variable z 1 (t)，z 1 (t) is n 1 +n 3 +n 6 Dimensional space vector, denoted as
Is a quadratic state variable z 1 (ii) the derivative of (t),
wherein
Is a failure f of the voltage sensor 1 u1 (ii) the derivative of (t),
for failure of the voltage sensor 2
A derivative of (a); f. of 1 (t) is a fault variable of the multi-fault system 2, and is recorded as a system fault quantity f 1 (t)；
E 1 As the second state variable derivative
Is recorded as a first derivative coefficient matrix E 1 In a
In the expression (2) of (a),
represents n 1 The dimension-unit matrix is a matrix of the dimension units,
represents n 3 A dimension unit matrix;
A 2 the state matrix for the multiple fault system 2, denoted as the quadratic state matrix A 2 ；
B 2 The input matrix for the multiple fault system 2, denoted as the quadratic input matrix B 2 ；
F 2 Is the amount of system failure f 1 (t) coefficient matrix, denoted as quadratic failure coefficient matrix F 2 In a
In the expression of (a) in (b),
represents n 7 The dimension-unit matrix is a matrix of dimension units,
represents n 8 A dimension unit matrix;
N 2 the coefficient matrix of harmonic disturbance eta (t) in the multi-fault system 2 is recorded as a secondary disturbance coefficient matrix N 2 ；
Step 4.1, outputting the secondary output matrix
Transposing, recording the transposed output matrix as
Handle
The matrix decomposition into the product of an orthogonal matrix and an upper triangular matrix is recorded as
U is an orthogonal matrix and Q is an upper triangular matrix; let P = U again T ，J＝Q T ，U T Is the transpose of the orthogonal matrix U, Q T Is the transpose matrix of the upper triangular matrix Q, then the obtained
Wherein P satisfies P T ＝P -1 ，P T Is the transpose of the matrix P, P -1 Is the inverse matrix of the matrix P, and takes P as a primary coordinate transformation matrix;
step 4.2, introduce coordinate transformation z 2 (t)＝Pz 1 (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 is 2 (t) is the state variable of the multiple fault system 3, noted as the third state variable z 2 (t)；
Is a cubic state variable z 2 (t) a derivative of;
E 2 is a third state variable derivative
Coefficient matrix of (2), noted as second derivativeCoefficient matrix E 2 ，E 2 ＝E 1 P T ；A 3 The state matrix of the multi-fault system 3 is marked as a cubic state matrix A 3 ，A 3 ＝A 2 P T ；B 3 The input matrix of the multi-fault system 3 is recorded as a cubic input matrix B 3 ；F 3 For faults f of the multiple fault system 3 1 (t) coefficient matrix, denoted as cubic failure coefficient matrix F 3 ；N 3 The coefficient matrix of the harmonic disturbance eta (t) of the multi-fault system 3 is recorded as a third-order disturbance coefficient matrix N 3 (ii) a J is the output matrix of the multiple fault system 3, denoted as the cubic output matrix J, and is denoted as the block matrix, i.e., J = (J) 1 0), wherein J 1 Left blocking submatrix of J, J 1 Belongs to n 5 Dimensional space, is denoted as
And J 1 Is a non-singular matrix;
Step 5.1, the second derivative coefficient matrix E 2 Conversion into a block matrix, i.e. E 2 ＝(E 21 E 22 ) In which E 21 Is a coefficient matrix E of the second derivative 2 Left blocking submatrix of (E) 21 Is (n) 1 +n 3 +n 6 )×n 5 Dimensional space, is denoted as
E 22 Is a coefficient matrix E of the second derivative 2 Right blocking submatrix of (E) 22 Is (n) 1 +n 3 +n 6 )×(n 1 +n 3 +n 6 -n 5 ) Dimensional space, is denoted as
Then designing a transformation matrix xi, recording as the matrix transformation matrix xi,
wherein xi 11 Being the upper part of the submatrix xi of the transform matrix xi 11 Is n 5 ×(n 1 +n 3 +n 6 ) Dimensional space, is denoted as
Ξ 21 A lower blocking submatrix of the transform matrix xi, xi 21 Belong to (n) 1 +n 3 +n 6 -n 5 )×(n 1 +n 3 +n 6 ) Dimensional space, is denoted as
And xi 11 Satisfies E 22 T Ξ 11 T =0, solution formula E 22 T Ξ 11 T =0, then may be xi 11 Wherein the matrix E 22 T Is a coefficient matrix E of the second derivative 2 Right blocking submatrix E 22 Transpose of (2), matrix xi 11 T An upper blocking submatrix xi being a transform matrix xi 11 Transposing; xi 21 ＝E 22 T (E 22 E 22 T ) -1 Matrix (E) 22 E 22 T ) -1 Is a matrix E 22 E 22 T The 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 is 3 (t) is the state variable of the multiple fault system 4, noted as the quartile state variable z 3 (t)；
Is a quartic state variable z 3 (t) a derivative of;
E 3 is the fourth derivative of the state variable
Is recorded as a coefficient matrix of the third derivative E 3 ，
Wherein E 31 Is a coefficient matrix E of the third derivative 3 Upper left blocking sub-matrix of (E) 32 Is a coefficient matrix E of the third derivative 3 The lower left block sub-matrix of (a),
is n 1 +n 3 +n 6 -n 5 A dimension unit matrix; a. The 4 The state matrix for the multiple fault system 4, denoted as the fourth state matrix A 4 ，
Wherein A is 411 Is a four-times state matrix A 4 Upper left blocking sub-matrix of A 412 Is a four-times state matrix A 4 Upper right blocking sub-matrix of, A 421 Is a four-times state matrix A 4 Left lower blocking submatrix of, A 422 Is a four-times state matrix A 4 The lower right blocking submatrix; b is 4 The input matrix for the multiple fault system 4 is denoted as the fourth input matrix B 4 ，
Wherein B is 41 Is a four-input matrix B 4 Upper blocking matrix of, B 42 Is a four-input matrix B 4 A lower block matrix of (a); f 4 For faults f of the multiple fault system 4 1 (t) coefficient matrix, denoted as Quaternary failure coefficient matrix F 4 ，
Wherein F 41 Is a four-fault coefficient matrix F 41 Upper block matrix of F 42 Is a four-fault coefficient matrix F 4 A lower blocking matrix of (a); n is a radical of 4 For sensor failureThe coefficient matrix of harmonic disturbance eta (t) of the system 4 is recorded as a fourth disturbance coefficient matrix N 4 ，
Wherein N is 41 Is a four-times disturbance coefficient matrix N 41 Upper blocking submatrix of (2), N 42 Is a four-times disturbance coefficient matrix N 4 A 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 n 5 The dimension-unit matrix is a matrix of dimension units,
is n 1 +n 3 +n 6 -n 5 Dimension unit matrix, L is a free matrix, denoted as free matrix L, which belongs to (n) 1 +n 3 +n 6 -n 5 )×n 5 Dimensional space, as
Step 6.2 introduction of coordinate transformation z 4 (t)＝Tz 3 (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 is 4 (t) is the state variable of the multiple fault system 5, noted as the quintic state variable z 4 (t) for the fifth state variable z 4 (t) blocking, i.e.
z 41 (t) is a five-state variable z 4 (t) upper block subvector z 41 (t)，z 41 (t) is n 5 Dimension vector, z 42 (t) is a five-state variable z 4 (t) lower block subvector z 42 (t)，z 42 (t) is n 1 +n 3 +n 6 -n 5 A dimension vector;
is a quintic state variable z 4 Derivative of (t), i.e.
Is z 4 (t) an upper block vector z 41 (ii) the derivative of (t),
is z of the upper block vector 42 (t) derivative of; is transformed by the above coordinate z 4 (t)＝Tz 3 (t) it can be seen that,
E 4 fifth order state variable derivative
A coefficient matrix of (a), and
A 5 the state matrix for the multi-fault system 5 is denoted as the five-time state matrix A 5 ，
Wherein A is 511 Is a quintic state matrix A 5 Upper left blocking sub-matrix of A 512 Is a quintic state matrix A 5 Upper right blocking sub-matrix of (A) 521 Is a quintic state matrix A 5 Left lower blocking submatrix of (A) 522 Is a quintic state matrix A 5 The lower right blocking submatrix; t is -1 An inverse matrix which is a quadratic coordinate transformation matrix T; b is 5 The input matrix for the multiple fault system 5 is denoted as the quintic input matrix B 5 ，
Wherein B is 51 For five inputs of matrix B 5 Upper blocking submatrix of (2), B 52 For five inputs of matrix B 5 A lower block submatrix of (a); f 5 The coefficient matrix for the fault F (t) of the multiple fault system 5 is noted as the quintic fault coefficient matrix F 5 ，
Wherein F 51 Is a quintic fault coefficient matrix F 5 Upper blocking submatrix of F 52 Is a quintic fault coefficient matrix F 5 A lower block submatrix of (a); n is a radical of 5 The coefficient matrix of harmonic disturbance eta (t) of the multi-fault system 5 is recorded as a quintic disturbance coefficient matrix N 5 ，
Wherein N is 51 For a quintic disturbance coefficient matrix N 5 Upper blocking submatrix of (2), N 52 For a quintic disturbance coefficient matrix N 5 Lower blocking submatrix of (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＝(LE 31 +E 32 -L)z 41 (t)+z 42 (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 the content of the first and second substances,
is the derivative of the state quantity theta of the reduced-order system, and delta is the state expression z of the reduced-order system 41 The coefficient matrix of (t) is marked as a reduced system coefficient matrix delta, and the expression is as follows:
Δ＝-(LA 512 +A 522 )(LE 51 +E 52 -L)+L(A 511 -A 512 L)+A 511 -A 522 L
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, the first and the second end of the pipe are connected with each other,
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, Γ = (LF) 51 +F 52 ) And v is the approach law,
wherein, the first and the second end of the pipe are connected with each other,
in order to be able to vary the parameter 1,
tanh () is a hyperbolic tangent function,
is variable parameter 2, and
σ is a variable parameter 3, and σ is an element (0, 1), θ is a variable parameter 4, and θ > 1, ρ is a variable parameter 5, β > 0, Ψ is a positive definite symmetric matrix, χ is a diagonal matrix,
epsilon is a constant number term, epsilon > 1 Θ (t) is the error of the estimation,
let S = 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:
(LA 412 +A 422 ) T P+P(LA 412 +A 422 )＝-I
wherein (LA) 412 +A 422 ) T Is LA 412 +A 422 P 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 multiple fault system 1 in step 1 and substituting the sampled value into z in step 6.2 41 (t)＝z 31 (t)＝J 1 -1 y (t), the five state variables z can be obtained 4 (t) upper block subvector z 41 (t) value, again according to the known five state variable z 4 (t) upper block vector z 41 Value of (t), Θ = (LE) in step 7.1 31 +E 32 -L)z 41 (t)+z 42 (t), step 7.2
And the error e is estimated in step 7.2 Θ (t) =0, and z can be obtained 42 (t), the expression of which is:
then the five state variables z are obtained 4 (t) upper block subvector z 41 (t) value and quintic state variable z 4 (t) lower block subvector z 42 (t) value substituted into step 6.2
The state variable z can be calculated five times 4 (t) a value;
step 8.2, starting from the multiple fault system 2, according to a coordinate transformation z 2 (t)＝Pz 1 (t) and quadratic coordinate transformation z 4 (t)＝Tz 3 (t) and the matrix transformation does not change the cubic state variable z in the sensor failure system 3 in step 5 2 (t) obtaining z 3 (t)＝z 2 (t) thereby obtaining z 4 (t)＝TPz 1 (t) calculating a secondary state variable z by inverse operation of the matrix 1 (t)＝P T T -1 z 4 (t), and the five state variables z calculated in step 8.1 are further added 4 (t) substitution of formula z 1 (t)＝P T T -1 z 4 (t) obtaining a secondary state variable z 1 (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 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 Z 1 ，
And positioned as follows:
if Z is 1 =0, no actuator failure has occurred in the multiple fault system 1;
if Z is 1 =1, the multi-fault system 1 has an actuator fault;
defining fault location Z 2 ，
And positioned as follows:
if Z is 2 =0, no voltage sensor 1 fault occurred in the multiple fault system 1;
if Z is 2 =1, multiple fault system 1 has voltage sensor 1 fault;
defining fault location Z 3 ，
And positioned as follows:
if Z is 3 =0, no voltage sensor 2 failure occurred in the multiple fault system 1;
if Z is 3 =1, the multiple fault system 1 has a voltage sensor 2 fault.
Preferably, the DC voltage u in step 1 1 Hybrid logic dynamic function T of h And a DC voltage u 2 Hybrid logic dynamic function T of l The calculation process of (c) is as follows:
recording the switching function of the k-phase bridge arm as S k K = a, b, then:
recording the pulse control signal of the switching tube as v kγ K = a, b, γ =1,2,3,4, then the k-phase bridge arm switching function S k ＝v k1 v k2 -v k3 v k4 。
Preferably, the diagnostic adaptive threshold T of step 8.4 th The expressions are respectively as follows:
T th ＝E 1 +Γ 1 (ζ 1 +ζ 2 )
wherein E is 1 Is a constant 1, Γ 1 Is a constant number 2, and Γ 1 ∈(1，2)，ζ 1 ζ is a bounded external perturbation 2 Is 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 diagnostic method of the present invention;
FIG. 4 shows an actuator failure f in this embodiment a (t) actuator estimation value
And an adaptive threshold T th A simulation graph of (a);
FIG. 5 shows the failure of the voltage sensor 1 in this example
Voltage sensor 1 fault estimation
And an adaptive threshold T th A simulated oscillogram of (c);
FIG. 6 shows a failure f of the voltage sensor 2 in this example u2 (t), voltage sensor 2 Fault estimation value
And an adaptive threshold T th A simulated waveform diagram of (c).
Detailed Description
Fig. 1 is a topology diagram of a single phase three level rectifier in an embodiment of the present invention. It can be seen from the figure that the circuit topology according to the invention comprises a network-side voltage source U s Network side equivalent inductance s and network side equivalent resistance R s Rectifier bridge, two identical support capacitors C d1 ，C d2 A direct current side load and two identical voltage sensors; support capacitor C d1 And a support capacitor C d2 After being connected in series, the capacitor C is connected in parallel between a direct current positive bus P and a direct current negative bus Q1 of a direct current side load d1 And a support capacitor C d2 The 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 d1 At both ends of which the voltage sensor 2 is connected to the supporting capacitor C d2 At both ends of the same. In FIG. 1, S V1 Is a voltage sensor 1, S V2 For the voltage sensor 2, two sensors are used for the measurement of the voltage value.
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; recording two-phase bridge arms as bridge arms k, wherein k is a bridge sequence, and k = a, b; in two-phase bridge arms, each phase of bridge arm comprises 4 switching tubes with reverse-connection diodes, two clamping diodes, namely a rectifier bridge comprises 8 switching tubes with reverse-connection diodes and 4 clamping diodesThe 8 switching tubes form an actuator of the single-phase three-level rectifier; marking 8 switch tubes as switch tubes V kγ γ denotes a serial number of the switching tube, γ =1,2,3,4, and 4 clamping diodes are denoted as clamping diodes D ckρ ρ is the serial number of the clamp diode, ρ =1,2; in each of the two-phase arms, a switching tube V k1 And a switch tube V k1 Switch tube V k3 Switch tube V k4 Are sequentially connected in series, wherein, the switch tube V k2 And a switching tube V k3 Is recorded as the rectifier bridge input point tau k K = a, b; in each of the two-phase arms, a clamping diode D ck1 The cathode of the switch tube is connected with the switch tube V k1 And a switching tube V k2 Between, the clamping diode D ck1 Anode of (2) is connected to a clamping diode D ck2 Cathode of (2), clamping diode D ck2 Anode of the switch tube is connected with the switch tube V k3 And a switching tube V k4 And clamping diode D ck1 And a clamping diode D ck2 The connecting point of the direct current bus is connected with the midpoint O of the direct current bus.
The network side equivalent inductor L s One end of is connected with an input point tau of the rectifier bridge a The other end is connected with the equivalent resistance R of the network side in sequence s Grid side voltage source U s The 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:
Sampling the current of the network side and recording the current of the network side as the current i of the network side s Sampling ofSupport capacitor C d1 And a support capacitor C d2 And is denoted as DC voltage u 1 ，u 2 Sampling 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 ab Is estimated value of
The input end phase voltage U of the rectifier bridge ab For input point tau of rectifier bridge a And the input point tau of the rectifier bridge b The voltage in between.
The expression of the hybrid logic dynamic model of the single-phase three-level rectifier is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is an estimate of the voltage of the a-phase,
is an estimate of the b-phase voltage, T h Is a direct current voltage u 1 Mixed logical dynamic function of (2), T l Is a DC voltage u 2 Mixed logical dynamic functions of (1).
The input end phase voltage U of the rectifier bridge ab Is estimated value of
The expression of (a) is:
in this embodiment, the straight lineCurrent voltage u 1 Hybrid logic dynamic function T of h And a DC voltage u 2 Mixed logic dynamic function T of l The calculation process of (2) is as follows:
recording the switching function of the k-phase bridge arm as S k K = a, b, then:
recording the pulse control signal of the switching tube as v kγ K = a, b, γ =1,2,3,4, then the k-phase bridge arm switching function S k ＝v k1 v k2 -v k3 v k4 。
wherein x (t) is a state variable of the multi-fault system 1 and is marked as a primary state variable x (t),
x (t) is n 1 Dimension state variable, as
t is a variable of time and is,
the first derivative of the primary state variable x (t),
wherein
Is a net side current i s The derivative of (a) of (b),
are respectively DC voltage u 1 ，u 2 A derivative of (a); u (t) is the input of the multiple fault system 1 and is recorded as one system input u (t), u (t) = u s U (t) is n 2 Dimensional state variables, noted
f a (t) actuator failure for multiple failure System 1, denoted as actuator failure f a (t)，f a (t) is n 3 Dimensional state variables, noted
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 n 4 Dimension state variable, as
y (t) is the output of the multi-fault system 1 and is denoted as the system output y (t), and y (t) is n 5 Dimensional state variables, noted
f s (t) Voltage sensor Fault for multiple Fault System 1, noted System Voltage sensor Fault f s (t)，f s (t) is n 6 Dimensional state variables, noted
Wherein
For a failure of voltage sensor 1, note as a failure f of voltage sensor 1 u1 (t)，f u1 (t) is n 7 Dimension 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 n 8 Dimension state variable, as
A 1 The state matrix for the multiple fault system 1, denoted as primary state matrix A 1 ，
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 η Wherein | | | f s (t) | | is f s Norm of (t, | f a (t) | | is f a The norm of (t), where | | | η (t) | | is the norm of η (t), r s For system voltage sensor fault f s Upper limit of (t), r a For actuator failure f a Upper limit of (t), r η Is a supremum of harmonic disturbance η (t), and r s 、r a And r η Are all normal numbers and are recorded as r s ＞0，r a ＞0，r η ＞0。
In the present embodiment, R =0.34 Ω, L =2.2 × 10 -3 H，C 1 ＝16×10 -3 F，C 2 ＝16×10 -3 F，
n 1 ＝3，n 2 ＝1，n 3 ＝1，n 4 ＝1，n 5 ＝5，n 6 ＝2，n 7 ＝1，n 8 ＝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 satisfied with respect toContinuous and bounded function of the amount of time t, denoted | | f s (t)||≤r s ，||f a (t)||≤r a ，||η(t)||≤r η Wherein | | | f s (t) | | is f s Norm of (t, | f a (t) | | is f a The norm of (t), where | | | η (t) | | is the norm of η (t), r s For system voltage sensor fault f s Upper limit of (t), r a For actuator failure f a Upper limit of (t), r η Is the supremum of the harmonic disturbance eta (t), and r s 、r a And r η Are all normal numbers, and are recorded as r s ＞0，r a ＞0，r η ＞0。
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 is 1 (t) is the state variable of the multiple fault system 2, noted as the secondary state variable z 1 (t)，z 1 (t) is n 1 +n 3 +n 6 Dimensional space vector, is
Is a quadratic state variable z 1 (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. of 1 (t) is a fault variable of the multi-fault system 2, and is recorded as a system fault quantity f 1 (t)；
E 1 As the second state variable derivative
Is recorded as a first derivative coefficient matrix E 1 In a
In the expression of (a) in (b),
represents n 1 The dimension-unit matrix is a matrix of dimension units,
represents n 3 A dimension unit matrix;
A 2 the state matrix for the multi-fault system 2 is denoted as a quadratic state matrix A 2 ；
B 2 The input matrix for the multiple fault system 2, denoted as the quadratic input matrix B 2 ；
F 2 Is the amount of system failure f 1 (t) coefficient matrix, denoted as quadratic failure coefficient matrix F 2 In a
In the expression of (a) in (b),
represents n 7 The dimension-unit matrix is a matrix of dimension units,
represents n 8 A dimension unit matrix;
N 2 the coefficient matrix of harmonic disturbance eta (t) in the multi-fault system 2 is marked as a secondary disturbance coefficient matrix N 2 ；
The parameters in this example are as follows:
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 = U again T ，J＝Q T ，U T Is the transpose of the orthogonal matrix U, Q T Is the transpose of the upper triangular matrix Q, then the result is
Wherein P satisfies P T ＝P -1 ，P T Is the transpose of the matrix P, P -1 Is the inverse of matrix P, which is denoted as the primary coordinate transformation matrix.
Step 4.2, introducing coordinate transformation z 2 (t)＝Pz 1 (t), the multi-fault system 2 can be transformed into a new system through coordinate transformation, the new system is recorded as a multi-fault system 3, and the state space expression is as follows:
wherein z is 2 (t) is the state variable of the multiple fault system 3, noted as the third state variable z 2 (t)；
Is a cubic state variable z 2 (t) derivative of;
E 2 is the third order state variable derivative
Is denoted as the second derivative coefficient matrix E 2 ，E 2 ＝E 1 P T ；A 3 The state matrix of the multi-fault system 3 is marked as a cubic state matrix A 3 ，A 3 ＝A 2 P T ；B 3 The input matrix of the multi-fault system 3 is recorded as a cubic input matrix B 3 ；F 3 For faults f of multiple-fault systems 3 1 (t) coefficient matrix, denoted as cubic failure coefficient matrix F 3 ；N 3 The coefficient matrix of the harmonic disturbance eta (t) of the multi-fault system 3 is recorded as a third-order disturbance coefficient matrix N 3 (ii) a J is the output matrix of the multiple fault system 3, denoted as the cubic output matrix J, and is denoted as the block matrix, i.e., J = (J) 1 0), wherein J 1 Left blocking submatrix of J, J 1 Belongs to n 5 Dimensional space, is denoted as
And J 1 Is a non-singular matrix.
In the present embodiment, it is preferred that,
Step 5.1, coefficient matrix E of second derivative 2 Conversion into a block matrix, i.e. E 2 ＝(E 21 E 22 ) In which E 21 Is a coefficient matrix E of the second derivative 2 Left blocking submatrix of (E) 21 Is (n) 1 +n 3 +n 6 )×n 5 Dimensional space, is denoted as
E 22 Is a coefficient matrix E of the second derivative 2 Right blocking submatrix, E 22 Is (n) 1 +n 3 +n 6 )×(n 1 +n 3 +n 6 -n 5 ) Dimensional space, is denoted as
Then designing a transformation matrix xi, which is recorded as a matrix transformation matrix xi,
wherein xi 11 Being an upper blocking submatrix of the transform matrix xi, xi 11 Is n 5 ×(n 1 +n 3 +n 6 ) Dimensional space, is denoted as
Ξ 21 Being a lower blocking submatrix of the transform matrix xi, xi 21 Belong to (n) 1 +n 3 +n 6 -n 5 )×(n 1 +n 3 +n 6 ) Dimensional space, as
And xi 11 Satisfies E 22 T Ξ 11 T =0, solution of formula E 22 T Ξ 11 T =0, then may be xi 11 Wherein the matrix E 22 T Is a coefficient matrix E of the second derivative 2 Right blocking submatrix E 22 Transpose of (2), matrix xi 11 T An upper blocking submatrix xi being a transform matrix xi 11 Transposing; xi 21 ＝E 22 T (E 22 E 22 T ) -1 Matrix (E) 22 E 22 T ) -1 Is a matrix E 22 E 22 T The 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 is 3 (t) is the state variable of the multiple fault system 4, noted as the quartile state variable z 3 (t)；
Is a quartic state variable z 3 (t) derivative of;
E 3 is the fourth derivative of the state variable
Is noted as a coefficient matrix of the third derivative E 3 ，
Wherein E 31 Is a coefficient matrix E of the third derivative 3 Upper left blocking sub-matrix of (E) 32 Is a coefficient matrix E of the third derivative 3 The lower left block sub-matrix of (a),
is n 1 +n 3 +n 6 -n 5 A dimension unit matrix; a. The 4 Is a state matrix of the multi-fault system 4,is denoted as a quartic state matrix A 4 ，
Wherein A is 411 Is a four-times state matrix A 4 Upper left blocking sub-matrix of, A 411 Is a four-times state matrix A 4 Upper right blocking sub-matrix of (A) 421 Is a four-times state matrix A 4 Left lower blocking submatrix of, A 422 Is a four-times state matrix A 4 The lower right blocking submatrix; b is 4 The input matrix for the multiple fault system 4 is denoted as the fourth input matrix B 4 ，
Wherein B is 41 Is a four-input matrix B 4 Upper block matrix of, B 42 Is a four-input matrix B 4 A lower block matrix of (a); f 4 For faults f of the multiple fault system 4 1 (t) coefficient matrix, denoted as Quaternary failure coefficient matrix F 4 ，
Wherein F 41 Is a four-fault coefficient matrix F 41 Upper block matrix of F 42 Is a four-fault coefficient matrix F 4 A lower block matrix of (a); n is a radical of 4 The coefficient matrix for the harmonic disturbance η (t) of the sensor fault system 4 is noted as the fourth-order disturbance coefficient matrix N 4 ，
Wherein N is 41 Is a four-times disturbance coefficient matrix N 41 Upper blocking submatrix of (2), N 42 Is a four-times disturbance coefficient matrix N 4 The 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 design coordinate transformation matrix T, record as quadratic coordinate transformation matrix T, and express T as block matrix, that is
Wherein therein
Is n 5 The dimension-unit matrix is a matrix of the dimension units,
is n 1 +n 3 +n 6 -n 5 Dimension unit matrix, L is a free matrix, denoted as free matrix L, which belongs to (n) 1 +n 3 +n 6 -n 5 )×n 5 Dimensional space, is denoted as
Step 6.2 introduction of coordinate transformation z 4 (t)＝Tz 3 (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 is 4 (t) is the state variable of the multiple fault system 5, noted as the quintic state variable z 4 (t) for the quintic state variable z 4 (t) Is divided into blocks, i.e.
z 41 (t) is a quintic state variable z 4 (t) upper block subvector z 41 (t)，z 41 (t) is n 5 Dimension vector, z 42 (t) is a five-state variable z 4 (t) lower block subvector z 42 (t)，z 42 (t) is n 1 +n 3 +n 6 -n 5 A dimension vector;
is a five-fold state variable z 4 Derivative of (t), i.e.
Is z 4 (t) upper block vector z 41 (ii) the derivative of (t),
is z of the upper block vector 42 (t) derivative of; is transformed by the above coordinate z 4 (t)＝Tz 3 (t) it can be seen that,
E 4 is the fifth derivative of the state variable
A coefficient matrix of (a), and
A 5 the state matrix for the multi-fault system 5 is denoted as the five-time state matrix A 5 ，
Wherein A is 511 Is a quintic state matrix A 5 Upper left blocking sub-matrix of, A 512 Is a quintic state matrix A 5 Upper right blocking sub-matrix of, A 521 Is a quintic state matrix A 5 Is divided into left lower blocksSub-matrix, A 522 Is a quintic state matrix A 5 The lower right blocking submatrix; t is -1 An inverse matrix of the quadratic coordinate transformation matrix T; b 5 The input matrix for the multiple fault system 5 is marked as five-times input matrix B 5 ，
Wherein B is 51 For five inputs of matrix B 5 Upper blocking submatrix of (2), B 52 For five inputs of matrix B 5 A lower block submatrix of (a); f 5 The coefficient matrix for the fault F (t) of the multiple fault system 5 is noted as the quintic fault coefficient matrix F 5 ，
Wherein F 51 Is a quintic fault coefficient matrix F 5 Upper blocking submatrix of F 52 Is a quintic fault coefficient matrix F 5 A lower blocking submatrix of (a); n is a radical of hydrogen 5 The coefficient matrix of harmonic disturbance eta (t) of the multi-fault system 5 is recorded as a quintic disturbance coefficient matrix N 5 ，
Wherein N is 51 For a quintic disturbance coefficient matrix N 5 Upper blocking submatrix of (2), N 52 For a quintic disturbance coefficient matrix N 5 Lower 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＝(LE 31 +E 32 -L)z 41 (t)+z 42 (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, the first and the second end of the pipe are connected with each other,
is the derivative of the state quantity theta of the reduced-order system, and delta is the state expression z of the reduced-order system 41 The coefficient matrix of (t) is marked as a reduced system coefficient matrix delta, and the expression is as follows:
Δ＝-(LA 512 +A 522 )(LE 51 +E 52 -L)+L(A 511 -A 512 L)+A 511 -A 522 L
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 the content of the first and second substances,
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, Γ = (LF) 51 +F 52 ) V is the approach law,
wherein the content of the first and second substances,
in order to be able to vary the parameter 1,
tanh () is a hyperbolic tangent function,
is variable parameter 2, and
σ is a variable parameter 3, and σ is an element (0, 1), θ is a variable parameter 4, and θ > 1, ρ is a variable parameter 5, β > 0, Ψ is a positive definite symmetric matrix, χ is a diagonal matrix,
epsilon is a constant number term, epsilon > 1 Θ (t) is the error of the estimation,
let S = 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:
(LA 412 +A 422 ) T P+P(LA 412 +A 422 )＝-I
wherein (LA) 412 +A 422 ) T Is LA 412 +A 422 P is a positive definite symmetric matrix, and I is a unit 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 multiple fault system 1 in step 1 and substituting the sampled value into z in step 6.2 41 (t)＝z 31 (t)＝J 1 -1 y (t), the state variable z can be obtained five times 4 (t) upper block subvector z 41 (t) value, again according to the known five state variable z 4 (t) upper block vector z 41 Value of (t), Θ = (LE) in step 7.1 31 +E 32 -L)z 41 (t)+z 42 (t), step 7.2
And the error e is estimated in step 7.2 Θ (t) =0, and z can be obtained 42 (t) the expression is:
then the five state variables z are obtained 4 (t) upper block subvector z 41 (t) value and quintic state variable z 4 (t) lower block subvector z 42 (t) value substituted into step 6.2
The five state variable z can be calculated 4 (t) a value;
step 8.2, starting from the multiple fault system 2, according to a coordinate transformation z 2 (t)＝Pz 1 (t) and quadratic coordinate transformation z 4 (t)＝Tz 3 (t) and the matrix transformation does not change the cubic state variable z in the sensor fault system 3 in step 5 2 (t) obtaining z 3 (t)＝z 2 (t) thereby obtaining z 4 (t)＝TPz 1 (t) calculating a secondary state variable z by inverse operation of the matrix 1 (t)＝P T T -1 z 4 (t), and the five state variables z calculated in step 8.1 are further added 4 (t) substitution of formula z 1 (t)＝P T T -1 z 4 (t) obtaining a secondary state variable z 1 (t)；
Step 8.3, mixing
Is recorded as a primary state variable estimation value,
recording 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 th The expressions are respectively as follows:
T th ＝E 1 +Γ 1 (ζ 1 +ζ 2 )
wherein E is 1 Is a constant 1, Γ 1 Is a constant number 2, and Γ 1 ∈(1，2)，ζ 1 For a bounded external disturbance, ζ 2 Is a bounded voltage perturbation. Specifically, in the present embodiment, E 1 ＝0.01，Γ 1 ＝1.01，ζ 1 ＝0.02sin(10t)，
Defining fault location quantity Z 1 ，
And positioned as follows:
if Z is 1 =0, no actuator failure occurred in the multiple fault system 1;
if Z is 1 =1, the multi-fault system 1 has an actuator fault;
defining fault location quantity Z 2 ，
And positioned as follows:
if Z is 2 =0, no voltage sensor 1 failure has occurred in the multiple fault system 1;
if Z is 2 =1, multiple fault system 1 has voltage sensor 1 fault;
defining fault location quantity Z 3 ，
And positioned as follows:
if Z is 3 =0, no voltage sensor 2 failure occurred in the multiple fault system 1;
if Z is 3 =1, the multiple fault system 1 has a voltage sensor 2 fault.
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 th A simulated waveform diagram of (c). 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 actuator failure estimation
Has exceeded adaptive diagnostic threshold T th I.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 th A simulated waveform diagram of (c). 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 th Namely, 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 value
And an adaptive threshold T th The 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
Has exceeded the adaptive diagnostic threshold T th I.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 s Network side equivalent inductor L s And net side equivalent resistance R s Rectifier bridge, two identical support capacitors C d1 ，C d2 A DC side load and two identical voltage sensors; support capacitor C d1 And a support capacitor C d2 A DC positive bus P and a DC negative bus Q connected in parallel with a DC side load after being connected in series 1 Between, support the capacitor C d1 And a support capacitor C d2 The 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 d1 At both ends of which the voltage sensor 2 is connected to the supporting capacitor C d2 Two 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; recording two-phase bridge arms as bridge arms k, wherein k is a bridge sequence, and k = 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 kγ γ denotes the serial number of the switching tube, γ =1,2,3,4, and 4 clamping diodes are denoted as clamping diodes D ckρ ρ is the number of the clamping diode, ρ =1,2; in each of the two-phase arms, a switching tube V k1 Switch tube V k2 Switch tube V k3 Switch tube V k4 Are sequentially connected in series, wherein, the switch tube V k2 And a switching tube V k3 Is recorded as the rectifier bridge input point tau k K = a, b; in each of the two-phase arms, a clamping diode D ck1 The cathode of the switch tube is connected with the switch tube V k1 And a switching tube V k2 Between, the clamping diode D ck1 Anode of (2) is connected to a clamping diode D ck2 Cathode of (2), clamping diode D ck2 Anode of the switch tube is connected with the switch tube V k3 And a switching tube V k4 And clamping diode D ck1 And a clamping diode D ck2 The connecting point of the direct current bus is connected with the midpoint O of the direct current bus;
the network side equivalent inductance L s One end of is connected with an input point tau of the rectifier bridge a The other end is connected with the equivalent resistance R of the network side in sequence s Grid side voltage source U s The 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 ab Is estimated by
The network side current is sampled and recorded as the network side current i s Sampling support capacitor C d1 And a support capacitor C d2 And is denoted as DC voltage u 1 ,u 2 Sampling 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 ab Is estimated value of
The input end phase voltage U of the rectifier bridge ab For the input point tau of the rectifier bridge a And the input point tau of the rectifier bridge b A voltage in between;
the expression of the hybrid logic dynamic model of the single-phase three-level rectifier is as follows:
wherein, the first and the second end of the pipe are connected with each other,
as an estimate of the voltage of the a-phase，
Is an estimate of the b-phase voltage, T h Is a DC voltage u 1 Mixed logic dynamic function of, T l Is a direct current voltage u 2 A hybrid logical dynamic function of (a);
the input end phase voltage U of the rectifier bridge ab Is 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 a state variable of the multi-fault system 1 and is marked as a primary state variable x (t),
x (t) is n 1 Dimension state variable, as
t is a variable of time and t is,
the first derivative of the primary state variable x (t),
wherein
Is a net side current i s The derivative of (a) of (b),
are respectively DC voltage u 1 ,u 2 A 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) = u s U (t) is n 2 Dimension state variable, as
f a (t) actuator failure for multiple failure System 1, denoted as actuator failure f a (t)，f a (t) is n 3 Dimensional state variables, noted
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 n 4 Dimension state variable, as
y (t) is the output of the multi-fault system 1 and is denoted as the system output y (t), and y (t) is n 5 Dimension state variable, as
f s (t) Voltage sensor Fault for multiple Fault System 1, noted System Voltage sensor Fault f s (t)，f s (t) is n 6 Dimension 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 n 7 Dimension 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 n 8 Dimension state variable, as
A 1 The state matrix for the multi-fault system 1 is marked as a primary state matrix A 1 ，
Wherein L is equivalent inductance L at network side s R is the equivalent resistance R of the network side s Resistance value of C 1 ,C 2 Are respectively a support capacitor C d1 And a support capacitor C d2 The capacitance value of (a); b 1 The input matrix for the multiple fault system 1 is marked as a primary input matrix B 1 ，
G 1 For actuator failure f a (t) the coefficient matrix is recorded as a primary actuator fault coefficient matrix,
N 1 the coefficient matrix of harmonic disturbance eta (t) is recorded as a primary disturbance coefficient matrix N 1 ，
C y1 The output matrix of the multi-fault system 1 is recorded as a primary output matrix
F 1 For system voltage sensor fault f s (t) coefficient matrix, memoryIs a primary voltage sensor fault coefficient matrix F 1 ，
System voltage sensor fault f s (t) actuator failure f a (t) and the harmonic disturbance η (t) are both continuous and bounded functions satisfying the time variable t, denoted | | f s (t)||≤r s ，||f a (t)||≤r a ，||η(t)||≤r η Wherein | | | f s (t) | | is f s Norm of (t, | f a (t) | | is f a The norm of (t), where | | | η (t) | | is the norm of η (t), r s For system voltage sensor fault f s Upper limit of (t), r a For actuator failure f a Upper limit of (t), r η Is a supremum of harmonic disturbance η (t), and r s 、r a And r η Are 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 is 1 (t) is the state variable of the multiple fault system 2, noted as the secondary state variable z 1 (t)，z 1 (t) is n 1 +n 3 +n 6 Dimensional space vector, is
Is a quadratic state variable z 1 (ii) the derivative of (t),
wherein
Is a failure f of the voltage sensor 1 u1 (ii) the derivative of (t),
for failure of the voltage sensor 2
A derivative of (a); f. of 1 (t) is a fault variable of the multi-fault system 2, and is recorded as a system fault quantity f 1 (t)；
E 1 As derivatives of state variables of second order
Is denoted as the first derivative coefficient matrix E 1 In a
In the expression of (a) in (b),
represents n 1 Dimension unitThe matrix is a matrix of a plurality of pixels,
represents n 3 A dimension unit matrix;
A 2 the state matrix for the multi-fault system 2 is denoted as a quadratic state matrix A 2 ；
B 2 The input matrix of the multi-fault system 2 is marked as a secondary input matrix B 2 ；
F 2 Is the amount of system failure f 1 (t) coefficient matrix, denoted as quadratic failure coefficient matrix F 2 In a
In the expression of (a) in (b),
represents n 7 The dimension-unit matrix is a matrix of the dimension units,
represents n 8 A dimension unit matrix;
N 2 the coefficient matrix of harmonic disturbance eta (t) in the multi-fault system 2 is recorded as a secondary disturbance coefficient matrix N 2 ；
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 = U again T ,J＝Q T ，U T Is the transpose of the orthogonal matrix U, Q T Is the transpose of the upper triangular matrix Q, then the result is
Wherein P satisfies P T ＝P -1 ,P T Is the transpose of the matrix P, P -1 Is the inverse matrix of the matrix P, and takes P as a primary coordinate transformation matrix;
step 4.2, introduce coordinate transformation z 2 (t)＝Pz 1 (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 is 2 (t) is the state variable of the multi-fault system 3, and is recorded as a cubic state variable z 2 (t)；
Is a cubic state variable z 2 (t) derivative of;
E 2 is a third state variable derivative
Is denoted as the second derivative coefficient matrix E 2 ，E 2 ＝E 1 P T ；A 3 The state matrix for the multi-fault system 3, denoted as the cubic state matrix A 3 ,A 3 ＝A 2 P T ；B 3 The input matrix of the multi-fault system 3 is recorded as a cubic input matrix B 3 ；F 3 For faults f of the multiple fault system 3 1 (t) coefficient matrix, denoted as cubic failure coefficient matrix F 3 ；N 3 The coefficient matrix of the harmonic disturbance eta (t) of the multi-fault system 3 is recorded as a third-order disturbance coefficient matrix N 3 (ii) a J is the output matrix of the multiple fault system 3, denoted as the cubic output matrix J, and is denoted as the block matrix, i.e., J = (J) 1 0), wherein J 1 Left blocking submatrix of J, J 1 Belong to n 5 Dimensional space, is denoted as
And J 1 Is 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 E 2 Conversion into a block matrix, i.e. E 2 ＝(E 21 E 22 ) In which E 21 Is a coefficient matrix E of the second derivative 2 Left blocking submatrix of (E) 21 Is (n) 1 +n 3 +n 6 )×n 5 Dimensional space, is denoted as
E 22 Is a coefficient matrix E of the second derivative 2 Right blocking submatrix, E 22 Is (n) 1 +n 3 +n 6 )×(n 1 +n 3 +n 6 -n 5 ) Dimensional space, is denoted as
Then designing a transformation matrix xi, which is recorded as a matrix transformation matrix xi,
wherein xi 11 Being an upper blocking submatrix of the transform matrix xi, xi 11 Is n 5 ×(n 1 +n 3 +n 6 ) Dimensional space, as
Ξ 21 Being a lower blocking submatrix of the transform matrix xi, xi 21 Belong to (n) 1 +n 3 +n 6 -n 5 )×(n 1 +n 3 +n 6 ) Dimensional space, is denoted as
And xi 11 Satisfies E 22 T Ξ 11 T =0, solution of formula E 22 T Ξ 11 T =0, then may be xi 11 Wherein the matrix E 22 T Is a coefficient matrix E of the second derivative 2 Right blocking submatrix E 22 Transpose of (2), matrix xi 11 T An upper blocking submatrix xi being a transform matrix xi 11 Transposing; xi 21 ＝E 22 T (E 22 E 22 T ) -1 Matrix (E) 22 E 22 T ) -1 Is a matrix E 22 E 22 T The 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 is 3 (t) is the state variable of the multiple fault system 4, noted as the quartic state variable z 3 (t)；
Is a quartic state variable z 3 (t) derivative of;
E 3 is the fourth derivative of the state variable
Is recorded as a coefficient matrix of the third derivative E 3 ，
Wherein E 31 Is a coefficient matrix E of the third derivative 3 Upper left blocking sub-matrix of (E) 32 Is a coefficient matrix E of the third derivative 3 The lower left block sub-matrix of (a),
is n 1 +n 3 +n 6 -n 5 A dimension unit matrix; a. The 4 The state matrix of the multi-fault system 4 is marked as a fourth state matrix A 4 ，
Wherein A is 411 Is a four-times state matrix A 4 Upper left blocking sub-matrix of, A 412 Is a four-times state matrix A 4 Upper right blocking sub-matrix of, A 421 Is a four-times state matrix A 4 Left lower blocking submatrix of, A 422 Is a four-times state matrix A 4 The lower right blocking submatrix; b is 4 An input matrix for the multiple fault system 4, denoted as a quadruple input matrix B 4 ，
Wherein B is 41 Is a four-input matrix B 4 Upper block matrix of, B 42 Is a four-input matrix B 4 A lower block matrix of (a); f 4 For faults f of the multiple fault system 4 1 (t) coefficient matrix, denoted as Quaternary failure coefficient matrix F 4 ，
Wherein F 41 Is a four-fault coefficient matrix F 41 Upper block matrix of F 42 Is a four-fault coefficient matrix F 4 A lower block matrix of (a); n is a radical of 4 The coefficient matrix for the harmonic disturbance η (t) of the sensor fault system 4 is noted as the fourth-order disturbance coefficient matrix N 4 ，
Wherein N is 41 Is a four-times disturbance coefficient matrix N 41 Upper blocking submatrix of (2), N 42 Is a four-times disturbance coefficient matrix N 4 A lower blocking submatrix of (a);
step 6, carrying out secondary coordinate transformation on the multi-fault system 4
Step 6.1 design coordinate transformation matrix T, record as quadratic coordinate transformation matrix T, and express T as block matrix, that is
Wherein
Is n 5 The dimension-unit matrix is a matrix of dimension units,
is n 1 +n 3 +n 6 -n 5 Dimension unit matrix, L is a free matrix, denoted as free matrix L, which belongs to (n) 1 +n 3 +n 6 -n 5 )×n 5 Dimensional space, is denoted as
Step 6.2 introduction of coordinate transformation z 4 (t)＝Tz 3 (t) obtaining a transformed new system, and marking the new system as a multi-fault system 5, wherein the expression of the state space of the new system is as follows:
wherein z is 4 (t) is the state variable of the multiple fault system 5, noted as the quintic state variable z 4 (t) for the fifth state variable z 4 (t) blocking, i.e.
z 41 (t) is a quintic state variable z 4 (t) upper block subvector z 41 (t)，z 41 (t) is n 5 Dimension vector, z 42 (t) is a five-state variable z 4 (t) lower block subvector z 42 (t)，z 42 (t) is n 1 +n 3 +n 6 -n 5 A dimension vector;
is a five-fold state variable z 4 Derivative of (t), i.e.
Is z 4 (t) an upper block vector z 41 (ii) the derivative of (t),
is z of the upper block vector 42 (t) a derivative of; is transformed by the above coordinate z 4 (t)＝Tz 3 (t) it can be known that,
E 4 fifth order state variable derivative
A coefficient matrix of (a), and
A 5 the state matrix for the multi-fault system 5 is denoted as the five-time state matrix A 5 ，
Wherein A is 511 Is a quintic state matrix A 5 Upper left blocking sub-matrix of, A 512 Is a quintic state matrix A 5 Upper right blocking sub-matrix of, A 521 Is a quintic state matrix A 5 Left lower blocking submatrix of, A 522 Is a quintic state matrix A 5 The lower right blocking submatrix; t is a unit of -1 An inverse matrix of the quadratic coordinate transformation matrix T; b is 5 The input matrix for the multiple fault system 5 is marked as five-times input matrix B 5 ,
Wherein B is 51 For five inputs of matrix B 5 Upper blocking submatrix of (2), B 52 For five inputs of matrix B 5 A lower block submatrix of (a); f 5 The coefficient matrix for the fault F (t) of the multiple fault system 5 is noted as the quintic fault coefficient matrix F 5 ，
Wherein F 51 Is a quintic fault coefficient matrix F 5 Upper blocking submatrix of F 52 Is a quintic fault coefficient matrix F 5 A lower block submatrix of (a); n is a radical of hydrogen 5 The coefficient matrix of the harmonic disturbance eta (t) of the multi-fault system 5 is recorded as a quintic disturbance coefficient matrix N 5 ，
Wherein N is 51 For a quintic disturbance coefficient matrix N 5 Upper block submatrix of, N 52 For a quintic disturbance coefficient matrix N 5 Lower 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＝(LE 31 +E 32 -L)z 41 (t)+z 42 (t)
and solving a state space expression of the reduced-order system according to the state quantity theta of the reduced-order system, wherein the state space expression is as follows:
wherein the content of the first and second substances,
is the derivative of the state quantity theta of the reduced-order system, and delta is the state expression z of the reduced-order system 41 The coefficient matrix of (t) is marked as a reduced system coefficient matrix delta, and the expression is as follows:
Δ＝-(LA 512 +A 522 )(LE 51 +E 52 -L)+L(A 511 -A 512 L)+A 511 -A 522 L
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 the content of the first and second substances,
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 of the reduced order system
Is an estimate of the state quantity of the reduced order system
Is a sliding mode gain matrix, Γ = (LF) 51 +F 52 ) And v is the approach law,
wherein the content of the first and second substances,
in order to be able to vary the parameter 1,
tanh () is a hyperbolic tangent function,
is variable parameter 2, and
sigma is a variable parameter 3, sigma belongs to (0, 1), theta is a variable parameter 4, theta is more than 1, rho is a variable parameter 5, beta is more than 0, psi is a positive definite symmetrical matrix, and chi is a diagonal matrix,
epsilon is a constant number term, epsilon > 1 Θ (t) is the error of the estimation,
let S = 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:
(LA 412 +A 422 ) T P+P(LA 412 +A 422 )＝-I
wherein (LA) 412 +A 422 ) T Is LA 412 +A 422 P 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 multiple fault system 1 in step 1 and substituting the sampled value into z in step 6.2 41 (t)＝z 31 (t)＝J 1 -1 y (t), the state variable z can be obtained five times 4 (t) upper block subvector z 41 (t) value, again according to the known five state variable z 4 (t) an upper block vector z 41 Value of (t), Θ = (LE) in step 7.1 31 +E 32 -L)z 41 (t)+z 42 (t), step 7.2
And the error e is estimated in step 7.2 Θ (t) =0, and z can be obtained 42 (t) the expression is:
then the five state variables z are obtained 4 (t) an upper block subvector z 41 (t) value and quintic state variable z 4 (t) lower block subvector z 42 (t) value is substituted into step 6.2
The state variable z can be calculated five times 4 (t) a value;
step 8.2, starting from the multiple fault system 2, according to a coordinate transformation z 2 (t)＝Pz 1 (t) and quadratic coordinate transformation z 4 (t)＝Tz 3 (t) and the matrix transformation does not change the cubic state variable z in the sensor failure system 3 in step 5 2 (t) obtaining z 3 (t)＝z 2 (t) to obtain z 4 (t)＝TPz 1 (t) calculating a secondary state variable z by inverse operation of the matrix 1 (t)＝P T T - 1 z 4 (t), and the five state variables z calculated in step 8.1 are further added 4 (t) substitution of formula z 1 (t)＝P T T -1 z 4 (t) obtaining a secondary state variable z 1 (t)；
Step 8.3, mixing
Is recorded as a primary state variable estimation value,
recording 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 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 Z 1 ，
And positioned as follows:
if Z is 1 =0, no actuator failure occurred in the multiple fault system 1;
if Z is 1 =1, the multi-fault system 1 has an actuator fault;
defining fault location quantity Z 2 ，
And positioned as follows:
if Z is 2 =0, no voltage sensor 1 fault occurred in the multiple fault system 1;
if Z is 2 =1, multiple fault system 1 has voltage sensor 1 fault;
defining fault location quantity Z 3 ，
And positioned as follows:
if Z is 3 =0, no voltage sensor 2 failure occurred in the multiple fault system 1;
if Z is 3 =1, the multiple fault system 1 has a voltage sensor 2 fault.
2. The method according to claim 1, wherein the DC voltage u of step 1 is the DC voltage u 1 Hybrid logic dynamic function T of h And a DC voltage u 2 Mixed logic dynamic function T of l The calculation process of (2) is as follows:
recording the switching function of the k-phase bridge arm as S k K = a, b, then:
recording the pulse control signal of the switching tube as v kγ K = a, b, γ =1,2,3,4, then the k-phase bridge arm switching function S k ＝v k1 v k2 -v k3 v k4 。
3. Method for multiple fault diagnosis of a single-phase three-level rectifier according to claim 1, characterized in that the diagnosis adaptive threshold T of step 8.4 is defined th The expressions are respectively as follows:
T th ＝E 1 +Γ 1 (ζ 1 +ζ 2 )
wherein E is 1 Is a constant 1, Γ 1 Is a constant number 2, and Γ 1 ∈(1，2)，ζ 1 For a bounded external disturbance, ζ 2 Is a bounded voltage perturbation.
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