CN112947389A - Multi-fault synchronous estimation method of PFC (Power factor correction) control system - Google Patents

Multi-fault synchronous estimation method of PFC (Power factor correction) control system Download PDF

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CN112947389A
CN112947389A CN202110353536.1A CN202110353536A CN112947389A CN 112947389 A CN112947389 A CN 112947389A CN 202110353536 A CN202110353536 A CN 202110353536A CN 112947389 A CN112947389 A CN 112947389A
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许水清
任炜
王巨兴
戴浩松
陶松兵
丁力健
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Hefei University of Technology
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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    • G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention provides a multi-fault synchronous estimation method of a PFC (power factor correction) control system, belonging to the field of fault diagnosis. Specifically, the method comprises the steps of establishing a state space expression with actuator faults and sensor faults, expanding the actuator faults and the sensor faults into states of a multi-fault system, introducing intermediate variables, designing observer parameters, and estimating state variables, actuator faults and sensor faults of the system on line. Compared with the prior art, the invention provides a novel synchronous fault estimation method based on the dimension reduction observer technology and the generalized observer technology under the condition of not being constrained by the minimum phase condition, the observer matching condition and the output dimension condition, and the designed intermediate variable fault observer can ensure that an error system is converged to zero in an exponential mode so as to achieve online synchronous estimation of state variables, actuator faults and sensor faults of a control system containing multiple faults.

Description

Multi-fault synchronous estimation method of PFC (Power factor correction) control system
Technical Field
The invention relates to the field of fault diagnosis, in particular to a multi-fault synchronous estimation method of a PFC (power factor correction) control system.
Background
Switching power supplies are dominant in the power supply field because of their high power density and high efficiency. The conventional switching power supply has a low power factor (generally only 0.45-0.75), and generates a large amount of current harmonics and reactive power in the power grid, thereby polluting the power grid. The main method for inhibiting the harmonic wave generated by the switching power supply is to design a high-performance rectifier, which has the characteristics of sine wave input current, low harmonic wave content, high power factor and the like, namely has the function of Power Factor Correction (PFC).
Nowadays, control systems are increasingly complex and very expensive, and the requirements on safety and reliability performance of the systems are also increasing. A large number of engineering control systems, such as vehicle systems, aerospace systems, and chemical systems, are all related to safety, and once a system fails, the system performance may be degraded, the stability may be degraded, and the system may be crashed, which may result in disastrous consequences such as casualties and huge economic losses. Therefore, the fault diagnosis technology and the fault-tolerant control design are carried out in the control system in time, so that the system can keep a normal control effect under the condition of fault occurrence, the safety and the reliability of the system are improved, and the loss is reduced to the maximum extent, thereby having very important practical significance. The fault diagnosis technology comprises three parts of fault detection, fault isolation and fault estimation. The fault estimation can obtain more fault information than the fault detection, such as the size of the fault and the form of the fault, and the fault estimation is the basis of fault-tolerant control.
Most control systems can be modeled by way of mathematical analysis. In practical control system applications, actuator faults and sensor faults may occur individually or simultaneously. In recent years, synchronous fault estimation of actuator faults and sensors by a model-based method has attracted a great deal of research effort in recent years, and most of the methods adopt a sliding mode observer or an unknown input observer. In addition, the switching power supply is dominant in the power supply field because of its high power density and high efficiency. The conventional switching power supply has a low power factor (generally only 0.45-0.75), and generates a large amount of current harmonics and reactive power in the power grid, thereby polluting the power grid. The main method for inhibiting the harmonic wave generated by the switching power supply is to design a high-performance rectifier, which has the characteristics of sine wave input current, low harmonic wave content, high power factor and the like, namely has the function of Power Factor Correction (PFC).
An article of the document 1, "a novel fault reconstruction and estimation adaptation for a class of systems of actuator and sensor fault units reconstructed estimates" (Dimassi, Habib, ISA Transactions 02(2020 November) (a novel fault reconstruction and estimation method for a class of systems of actuator and sensor faults under the loose assumption) (Dimassi, Habib, ISA statement, 11 th 2/2020/year) describes in detail that there are three main constraints of the currently proposed observer method, namely, minimum phase system condition, observer matching condition and output dimension condition, and the author proposes a new fault estimation method under the relatively loose condition, but the auxiliary output matrix designed by the author also needs to satisfy the rank condition.
Document 2, a fault diagnosis method based on a Sliding mode observer proposed in an article of "Sliding mode observer based localized sensor fault detection with application to high-speed rail traction device" (long Zhang, Bin Jiang, Xing-gan, Zehui Mao, ISA transmission 63(2016)49-59) (micro sensor fault detection based on a Sliding mode observer applied to a high-speed railway traction device (long Zhang, Bin Jiang, Xing-gan Yan, Zehui Mao, ISA statement, 2016, pages 49-59) requires that a system output dimension is greater than a system fault number, an observer matching condition, a minimum phase system condition, the proposed fault method is based on residual error to identify faults, amplitude, size and form of the faults cannot be accurately obtained, and the designed observer is a full-dimensional observer.
Document 3, chinese patent publication No. CN109557818B, the sliding mode fault-tolerant control method for multi-agent tracking system with multiple faultsThe barrier estimation method requires that the condition (A, C) is observable and rank ([ B, F)a]) Rank (b), i.e. the minimum phase system condition and observer matching condition need to be met, and the observer designed by the authors is a full-dimensional observer.
In document 4, "active fault-tolerant control method for spacecraft with decoupling of fault and interference" (zong et al, university of harbin university, 2020, 52(09), 107-:
Figure BDA0003000643680000031
Figure BDA0003000643680000032
is a observator, i.e. the observer matching conditions and minimum phase system conditions need to be met, and the observer designed by the authors is a full-dimensional observer.
Document 5, "Descriptor reduced-order sliding mode observer design for switched systems with sensor and activator faults" (Shen Yin, Huijun Gao, Jianbin Qiu, Okyay Kaynak, automation 76(2017) 282) (generalized reduced order sliding mode observer design of switching system with sensor and actuator faults (Shen Yin, Huijun Gao, Jianbin Qiu, Okyay Kaynak, automation, 282-292 page of 2017, 76 th paragraph) the linear generalized reduced order observer designed in the article needs to satisfy the hypothetical conditions a1-A3, i.e., minimum phase system conditions, observer matching conditions, system dimension conditions, respectively.
The assumed condition a1 that the Reduced Order sliding Mode Observer designed in the article "Reduced-Order S1 identification-Mode-Observer-Based Estimation for Markov Jump Systems" (Hongyan Yang and Shen Yin, IEEE Transactions on automatic control, Vol 64, N0.20111, Novenmber 9) (for the Fault Estimation Based on the Reduced Order sliding Mode Observer of the Markov Jump system (Hongyan Yang, Shen Yin, institute of electrical and electronic engineers, 11 th month 11 th 2019)) needs to satisfy is the minimum phase system condition.
In summary, the PFC control system is crucial to the power supply, and the conventional fault diagnosis technology is constrained by many constraints, and the many constraints greatly limit the application range of the currently proposed fault estimation method. Therefore, aiming at the research of the synchronous estimation technology of the multi-fault system containing faults of the actuator and the sensor, the technical problems to be solved in the whole research field are solved by solving the defects of the prior art.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide a multi-fault synchronous estimation method of a PFC control system containing an actuator fault and a sensor fault, which can accurately estimate information of the form, amplitude, size, etc. of the fault when the actuator fault and the sensor fault occur in the system.
To achieve the above and other related objects, the present invention provides a multi-fault synchronous estimation method of a PFC control system, the multi-fault including an actuator fault and a sensor fault, the multi-fault synchronous estimation method including the steps of:
step 1, establishing a state space model of a PFC control system with multiple faults
The PFC control system with multiple faults is denoted as a multiple fault system 1, and a state space model of the multiple fault system 1 is denoted as an expression (1), where the expression (1) is as follows:
Figure BDA0003000643680000041
wherein t is time; x (t) represents the state variable of the multi-fault system 1, and is denoted as the first state variable x (t), x (t) belongs to the n-dimensional vector space, and is denoted as x (t) e Rn；
Figure BDA0003000643680000042
Is the derivative of the state variable x (t) with respect to time t, noted as the first derivative
Figure BDA0003000643680000043
u (t) represents the output of the multiple fault system 1In, denoted as input u (t), u (t) belongs to m-dimensional vector space, denoted as u (t) e Rm(ii) a y (t) represents the output of the multiple fault system 1, denoted as output y (t), which belongs to the p-dimensional vector space RpDenoted y (t) e Rp；fa(t) represents a q-dimensional actuator fault of the multi-fault system 1 and is noted as actuator fault fa(t)，fa(t) belongs to a q-dimensional vector space, denoted as fa(t)∈Rq；fs(t) denotes a w-dimensional sensor fault of the multiple fault system 1, denoted as sensor fault fs(t)，fs(t) belongs to the w-dimensional vector space, denoted as fs(t)∈Rw；
A is the state coefficient matrix of the first state variable x (t), B is the first coefficient matrix of the input u (t), C is the output coefficient matrix of the first state variable x (t), and C is the row full rank matrix, D is the actuator failure fa(t) coefficient matrix, F is sensor failure Fs(t) and F is a column full rank matrix;
actuator failure fa(t) and sensor failure fs(t) satisfies bounded and continuous derivative with respect to time, and | | | fa(t)||≤ηa，||fs(t)||≤ηsWherein | | | fa(t) | | represents the actuator failure fa(t) 2-norm, | | fs(t) | | denotes sensor failure fs2-norm, η of (t)aIs actuator failure faBoundary of (t) (. eta.)sIs a sensor failure fsBoundary of (t) (. eta.)aAnd ηsAre all known normal numbers;
step 2, expanding the multi-fault system 1 to obtain a multi-fault system 2
Expanding the actuator fault and the sensor fault into new state variables according to the state space model of the multi-fault system 1 obtained in the step 1, namely defining a new state variable
Figure BDA00030006436800000525
Figure BDA00030006436800000523
And the expanded strainCollectively referred to as a multiple fault system 2, the state space model of the multiple fault system 2 is referred to as expression (2), and expression (2) is as follows:
Figure BDA0003000643680000051
wherein the content of the first and second substances,
Figure BDA0003000643680000052
the state variable representing the multi-fault system 2, denoted as the second state variable
Figure BDA0003000643680000053
Figure BDA0003000643680000054
Belongs to the vector space of n + q + w dimensions and is marked as
Figure BDA0003000643680000055
Figure BDA0003000643680000056
Is a second state variable
Figure BDA0003000643680000057
The derivative with respect to time t, denoted as the second derivative
Figure BDA0003000643680000058
d (t) represents the fault vector of the multiple fault system 2, denoted as fault vector d (t),
Figure BDA0003000643680000059
Figure BDA00030006436800000510
for actuator failure fa(t) a derivative over time t;
Figure BDA00030006436800000511
is the second derivative
Figure BDA00030006436800000512
The matrix of coefficients of (a) is,
Figure BDA00030006436800000513
wherein InRepresenting an n-dimensional identity matrix, IqRepresenting a q-dimensional identity matrix;
Figure BDA00030006436800000514
is a second state variable
Figure BDA00030006436800000524
The matrix of coefficients of (a) is,
Figure BDA00030006436800000515
wherein IwRepresenting a w-dimensional identity matrix;
Figure BDA00030006436800000516
is a second matrix of coefficients of input u (t),
Figure BDA00030006436800000517
Figure BDA00030006436800000518
is the first coefficient matrix of the fault vector d (t),
Figure BDA00030006436800000519
Figure BDA00030006436800000520
is a second state variable
Figure BDA00030006436800000521
The matrix of output coefficients of (a) is,
Figure BDA00030006436800000522
step 3, carrying out coordinate transformation on the multi-fault system 2 and introducing an intermediate variable zeta (t)
Step 3.1, a first coordinate transformation is performed
Second state variable
Figure BDA0003000643680000061
Output coefficient matrix of
Figure BDA0003000643680000062
Transposing, and recording the transposed output series matrix as
Figure BDA0003000643680000063
To pair
Figure BDA0003000643680000064
Carrying out QR decomposition, i.e. reaction
Figure BDA0003000643680000065
Wherein Q is an orthogonal matrix and R is an upper triangular matrix; let W be QT，S＝RTThen, then
Figure BDA0003000643680000066
W is an orthogonal matrix;
making a first coordinate transformation
Figure BDA0003000643680000067
The multi-fault system 2 is transformed into a multi-fault system 3, the state space model of the multi-fault system 3 is expressed as an expression (3), and the expression (3) is as follows:
Figure BDA0003000643680000068
wherein the content of the first and second substances,
Figure BDA0003000643680000069
state variables representing the multi-fault system 3, denoted as third state variables
Figure BDA00030006436800000610
Figure BDA00030006436800000611
Is a third state variable
Figure BDA00030006436800000612
The derivative with respect to time t, denoted as the third derivative
Figure BDA00030006436800000613
Figure BDA00030006436800000614
Is the third derivative
Figure BDA00030006436800000615
The first state coefficient matrix of (a) is,
Figure BDA00030006436800000616
wherein WTIs a transposed matrix of the orthogonal matrix W,
Figure BDA00030006436800000617
is a third state variable
Figure BDA00030006436800000618
The first state coefficient matrix of (a) is,
Figure BDA00030006436800000619
Figure BDA00030006436800000620
a third coefficient matrix of input u (t),
Figure BDA00030006436800000621
Figure BDA00030006436800000622
a second matrix of coefficients for the fault vector d (t),
Figure BDA00030006436800000623
s is a third state variable
Figure BDA00030006436800000624
The output coefficient matrix of (1) left and right blocks S, and the left block is marked as a first left block matrix S1I.e. S ═ S10) First left block matrix S1Belongs to a space of dimension p × p, and is denoted as S1∈Rp×pAnd S1Is a reversible matrix;
step 3.2, introduce transformation matrix
The third derivative
Figure BDA00030006436800000625
First state coefficient matrix of
Figure BDA00030006436800000626
Performing left and right block division, and recording the left block as a left block matrix
Figure BDA00030006436800000627
The right block is marked as a right block matrix
Figure BDA00030006436800000628
Figure BDA00030006436800000629
Wherein the left block matrix
Figure BDA00030006436800000630
Belongs to the (n + q + w) x p dimensional space and is marked as
Figure BDA00030006436800000631
Right block matrix
Figure BDA00030006436800000632
Belongs to the (n + q + w) × (n + q + w-p) dimensional space and is marked as
Figure BDA00030006436800000633
Setting the transformation matrix to be designed as M, partitioning the transformation matrix to be designed into upper and lower blocks, and recording the upper blocks as an upper block matrix M1The lower block is marked as a lower block matrix M2I.e. by
Figure BDA0003000643680000071
Wherein M is1Belongs to a space of dimension p x (n + q + w) and is marked as M1∈Rp×(n+q+w)Wherein M is2Belongs to the (n + q + w) × (n + q + w-p) dimensional space and is marked as M2∈R(n+q+w-p)×(n+q+w)(ii) a Right block matrix
Figure BDA0003000643680000072
Transpose, note
Figure BDA0003000643680000073
Will go to the block matrix M1Transpose, denoted as M1 TSolving the equation
Figure BDA0003000643680000074
To obtain M1，
Figure BDA0003000643680000075
Wherein
Figure BDA0003000643680000076
Is composed of
Figure BDA0003000643680000077
The inverse matrix of (d);
multiplying the two sides of the multi-fault system (3) by the transformation matrix M to obtain a new system, recording the new system as a multi-fault system (4), recording a state space model of the multi-fault system (4) as an expression (4), wherein the expression (4) is as follows:
Figure BDA0003000643680000078
wherein the content of the first and second substances,
Figure BDA0003000643680000079
is the third derivative
Figure BDA00030006436800000710
The second state coefficient matrix of (2), the third derivative
Figure BDA00030006436800000711
The second state coefficient matrix of (2) is divided into four blocks, and the upper left matrix block is marked as the first upper left matrix
Figure BDA00030006436800000712
The lower left matrix block is marked as the first lower left matrix
Figure BDA00030006436800000713
Namely, it is
Figure BDA00030006436800000714
Wherein In+q+w-pIs an n + q + w-p dimensional unit matrix;
Figure BDA00030006436800000715
is a third state variable
Figure BDA00030006436800000716
A second state coefficient matrix of a third state variable
Figure BDA00030006436800000717
Second state coefficient matrix of
Figure BDA00030006436800000718
Divided into four blocks, the upper left matrix block is marked as the second upper left matrix
Figure BDA00030006436800000719
The upper right matrix block is marked as the second upper right matrix
Figure BDA00030006436800000720
The lower left matrix block is marked as the second lower left matrix
Figure BDA00030006436800000721
The lower right matrix block is marked as the second lower right matrix
Figure BDA00030006436800000722
Namely, it is
Figure BDA00030006436800000723
Figure BDA00030006436800000724
Is the fourth coefficient matrix of input u (t), the fourth coefficient matrix of input u (t)
Figure BDA00030006436800000725
Partitioning the block into upper and lower blocks, and recording the upper block matrix as a third upper block
Figure BDA00030006436800000726
The lower block matrix is marked as the third lower block
Figure BDA0003000643680000081
Namely, it is
Figure BDA0003000643680000082
Figure BDA0003000643680000083
Is a third coefficient matrix of the fault vector d (t), and the third coefficient matrix of the fault vector d (t)
Figure BDA0003000643680000084
Partitioning the block into upper and lower blocks, and recording the upper block matrix as a fourth upper block
Figure BDA0003000643680000085
The lower block matrix is recorded as the fourth lower block
Figure BDA0003000643680000086
Namely, it is
Figure BDA0003000643680000087
Step 3.3, second coordinate transformation is carried out
Let the second coordinate transformation matrix be T,
Figure BDA0003000643680000088
wherein L is a matrix to be designed and is marked as a first free matrix L, the first free matrix L belongs to a p x (n + q + w-p) dimensional space and is marked as L belonging to Rp×(n+q+w-p)；
Second coordinate transformation for multi-fault system 4
Figure BDA0003000643680000089
Obtaining a multi-fault system 5, and modeling the state space of the multi-fault system 5 as an expression (5), wherein the expression (5) is as follows:
Figure BDA00030006436800000810
wherein the content of the first and second substances,
Figure BDA00030006436800000811
is a state variable of the multi-fault system (5) and is recorded as a fourth state variable
Figure BDA00030006436800000812
Fourth state variable
Figure BDA00030006436800000813
The vector composed of the first p rows is recorded as
Figure BDA00030006436800000814
Fourth state variable
Figure BDA00030006436800000815
The vector formed by the last n + q + w-p lines is recorded as
Figure BDA00030006436800000816
Namely, it is
Figure BDA00030006436800000817
Is composed of
Figure BDA00030006436800000818
The derivative with respect to time t;
Figure BDA00030006436800000819
Figure BDA00030006436800000820
S1 -1is a first left block matrix S1The inverse of the matrix of (a) is,
Figure BDA00030006436800000821
is a third state variable
Figure BDA00030006436800000822
Is recorded as the vector composed of the first p rows of
Figure BDA00030006436800000823
Figure BDA0003000643680000091
Is a fourth state variable
Figure BDA0003000643680000092
Coefficient matrix of (2), the fourth state variable
Figure BDA0003000643680000093
Is divided into four blocks, the upper left matrix block of which is marked as the fifth upper left block
Figure BDA0003000643680000094
The upper right matrix block is denoted as the fifth upper right partition
Figure BDA0003000643680000095
The bottom left matrix block is denoted as the fifth bottom left partition
Figure BDA0003000643680000096
The lower right matrix block is denoted as the fifth lower right partition
Figure BDA0003000643680000097
Namely, it is
Figure BDA0003000643680000098
T-1An inverse matrix of the second coordinate transformation matrix T;
step 3.4, introduce the intermediate variable ζ (t)
Introducing an intermediate variable ζ (t), giving a dynamic equation of the intermediate variable ζ (t), and recording as an expression (6):
Figure BDA0003000643680000099
wherein the intermediate variable
Figure BDA00030006436800000910
Figure BDA00030006436800000911
Is the derivative of the intermediate variable ζ (t) with respect to time;
step 4, observer parameter design is carried out on the intermediate variable zeta (t)
Step 4.1, design of Fault observer
Definition of
Figure BDA00030006436800000912
For the observed value of the intermediate variable ζ (t), let the observed error
Figure BDA00030006436800000913
Designing a sliding-mode observer for the intermediate variable zeta (t), obtaining a dynamic equation of the observer, and recording the dynamic equation as an expression (7):
Figure BDA00030006436800000914
wherein, KsIs a sliding mode gain matrix and is a sliding mode gain matrix,
Figure BDA00030006436800000915
Usin order to form the item of the sliding mode,
Figure BDA00030006436800000916
the absolute value of | e (t) | is e (t), and is recorded as | e (t) |, ks1Is the first gain term, ks1＝ηa+ηs+ η, η is a first constant term, η is a positive constant, ε is a second constant term, 0 < ε < 1; p1Belongs to (w + q) x (n + w + q-P) -dimensional vector space and is marked as P1∈R(w+q)×(n+w+q-p)，P1Is a positive definite matrix; ks2Is a coefficient matrix of the observation error e (t) in the sliding mode term,
Figure BDA0003000643680000101
wherein diag () represents a diagonal matrix, δ is a third constant term, δ is greater than 0 and less than 1;
step 4.2, observing error e (t)
Solving the expression (6) and the expression (7) to obtain an error dynamic equation of the designed observer, which is as follows:
Figure BDA0003000643680000102
wherein the content of the first and second substances,
Figure BDA0003000643680000103
is the derivative of the observed error e (t) with respect to time;
design Lyapuloff function V (t), V (t) eT(t) Pe (t), wherein eT(t) is the transpose of the observation error e (t), P is a positive definite symmetric matrix, P is the Lyapunov equation
Figure BDA0003000643680000104
Where I is the identity matrix and the derivative of V (t) with respect to time is noted
Figure BDA0003000643680000105
Let the observation error e (t) converge to 0 for a finite time, then:
Figure BDA0003000643680000106
de lei punuo equation
Figure BDA0003000643680000107
The lyapunov equation is converted to the following linear matrix inequality (8):
Figure BDA0003000643680000108
solving a linear matrix inequality (8) by using an LMI tool kit in matlab to obtain a positive definite symmetric matrix P and a first free matrix L;
step 5, carrying out on-line synchronous fault estimation
Step 5.1, sampling the output y (t) to obtain the amplitude of the output y (t), which is recorded as y(1)(t)；
Step 5.2, the amplitude y of the output y (t) obtained in the step 5.1(1)(t) substitution into step 3.3
Figure BDA0003000643680000111
Get the fourth state variable
Figure BDA0003000643680000112
The first p row vectors
Figure BDA0003000643680000113
A value of (d);
step 5.3, according to the fourth state variable obtained in step 5.2
Figure BDA0003000643680000114
The first p row vectors
Figure BDA0003000643680000115
Value of (3), step 3.4
Figure BDA0003000643680000116
In step 4.1
Figure BDA0003000643680000117
And the observation error e (t) in the step 4.2 is 0, and the expression (9) is obtained:
Figure BDA0003000643680000118
solving the fourth state variable by the expression (7) and the expression (9)
Figure BDA0003000643680000119
Last n + q + w-p row vector
Figure BDA00030006436800001110
Step 5.4, the fourth state variable calculated in step 5.2 is used
Figure BDA00030006436800001111
The first p row vectors
Figure BDA00030006436800001112
Fourth State variable calculated in step 5.3
Figure BDA00030006436800001113
Last n + q + w-p row vector
Figure BDA00030006436800001114
Substituted in step 3.3
Figure BDA00030006436800001115
Calculating a fourth state variable
Figure BDA00030006436800001116
Step 5.5, transform by the second coordinate
Figure BDA00030006436800001117
And a first coordinate transformation
Figure BDA00030006436800001118
Obtaining a second state variable
Figure BDA00030006436800001119
The fourth state variable calculated in step 5.4
Figure BDA00030006436800001120
Substitution into
Figure BDA00030006436800001121
Obtaining a second state variable
Figure BDA00030006436800001122
Step 5.6, calculating to obtain an estimated value of the first state variable x (t) and an actuator fault fa(t) estimated value, sensor failure fs(t) estimated value, specifically, the estimated value of the state variable x (t) is denoted as x(1)(t), failing the actuator fa(t) the estimated value is recorded as
Figure BDA00030006436800001123
Will sensor fail fs(t) the estimated value is recorded as
Figure BDA00030006436800001124
The three estimates are calculated as follows:
Figure BDA00030006436800001125
Figure BDA00030006436800001126
Figure BDA0003000643680000121
at this point, the multi-fault synchronous estimation of the PFC control system having the multi-fault is finished.
Preferably, x in step 2T(t) is the transposition of the first state variable x (t), fa T(t) actuator failure fa(t) transposition, fs T(t) is sensor failure fs(t) transposition, [ x ]T(t) fa T(t) fs T(t)]TIs [ x (t) fa(t) fs(t)]The transposing of (1).
Preferably, the derivation process of expression (6) in step 3 is as follows:
an intermediate variable ζ (t) is introduced,
Figure BDA0003000643680000122
finishing to obtain:
Figure BDA0003000643680000123
introducing the derivative of the intermediate variable ζ (t) with respect to time
Figure BDA0003000643680000124
Figure BDA0003000643680000125
Order to
Figure BDA0003000643680000126
The dynamic equation for the intermediate variable ζ (t) is obtained and recorded as expression (6), as follows:
Figure BDA0003000643680000127
compared with the prior art, the invention has the beneficial effects that:
1. under the condition of not being constrained by a minimum phase condition, an observer matching condition and an output dimension condition, the novel fault estimation method is provided, the intermediate variable observer is designed, the designed intermediate fault observer can ensure that an error system converges to zero in an exponential form, and compared with the existing fault estimation method, the application range is greatly expanded;
2. by adopting the dimension reduction observer technology, the estimated variable dimension is n + q + w, the actually required observer dimension is n + q + w-p, the observer dimension is reduced, and the design complexity of the observer is reduced;
3. the state variable information of a multi-fault system and the fault form, size and other information of an actuator and a sensor can be accurately and synchronously estimated on line.
Drawings
FIG. 1 is a schematic diagram of a multi-fault synchronization estimation method according to the present invention;
FIG. 2 is a flow chart of a multi-fault synchronization estimation method of the present invention;
FIG. 3 shows an actuator failure f according to the present inventiona1(t) and its estimated value
Figure BDA0003000643680000131
A simulation diagram of (1);
FIG. 4 shows a sensor failure f in the present inventions(t) and its estimated value
Figure BDA0003000643680000132
A simulation diagram of (1);
FIG. 5 shows a system state variable x in the present invention1(t) and its estimated value x1 (1)(t) a simulation diagram;
FIG. 6 shows a system state variable x in the present invention2(t) and its estimated value x2 (1)(t) a simulation diagram;
FIG. 7 shows a system state variable x in the present invention3(t) and its estimated value x3 (1)(t) a simulation diagram;
FIG. 8 shows an actuator failure f in the present inventiona2(t) and its estimated value
Figure BDA0003000643680000133
A simulation diagram of (1);
FIG. 9 is a circuit topology diagram in a simulation of the present invention.
Detailed Description
The technical solution of the present invention is further described in detail below with reference to the accompanying drawings.
In embodiment 1, the present invention provides a method for synchronously estimating multiple faults of a PFC control system, where the multiple faults include an actuator fault and a sensor fault. Fig. 1 is a schematic diagram of a multi-fault synchronous estimation method of the present invention, and fig. 2 is a flowchart of the multi-fault synchronous estimation method of the present invention, as can be seen from fig. 1 and fig. 2, the multi-fault synchronous estimation method includes the following steps:
step 1, establishing a state space model of a PFC control system with multiple faults
The PFC control system with multiple faults is denoted as a multiple fault system 1, and a state space model of the multiple fault system 1 is denoted as an expression (1), where the expression (1) is as follows:
Figure BDA0003000643680000134
wherein t is time; x (t) represents the state variable of the multi-fault system 1, and is denoted as the first state variable x (t), x (t) belongs to the n-dimensional vector space, and is denoted as x (t) e Rn；
Figure BDA0003000643680000141
Is the derivative of the state variable x (t) with respect to time t, noted as the first derivative
Figure BDA0003000643680000142
u (t) represents the input of the multiple fault system 1, denoted as input u (t), u (t) belongs to the m-dimensional vector space, denoted as u (t) e Rm(ii) a y (t) represents the output of the multiple fault system 1, denoted as output y (t), which belongs to the p-dimensional vector space RpDenoted y (t) e Rp；fa(t) represents a q-dimensional actuator fault of the multi-fault system 1 and is noted as actuator fault fa(t)，fa(t) belongs to a q-dimensional vector space, denoted as fa(t)∈Rq；fs(t) denotes a w-dimensional sensor fault of the multiple fault system 1, denoted as sensor fault fs(t)，fs(t) belongs to the w-dimensional vector space, denoted as fs(t)∈Rw；
A is the state coefficient matrix of the first state variable x (t), B is the first coefficient matrix of the input u (t), C is the output coefficient matrix of the first state variable x (t),and C is the row full rank matrix and D is the actuator failure fa(t) coefficient matrix, F is sensor failure Fs(t) and F is a column full rank matrix;
actuator failure fa(t) and sensor failure fs(t) satisfies bounded and continuous derivative with respect to time, and | | | fa(t)||≤ηa，||fs(t)||≤ηsWherein | | | fa(t) | | represents the actuator failure fa(t) 2-norm, | | fs(t) | | denotes sensor failure fs2-norm, η of (t)aIs actuator failure faBoundary of (t) (. eta.)sIs a sensor failure fsBoundary of (t) (. eta.)aAnd ηsAre all known normal numbers.
Step 2, expanding the multi-fault system 1 to obtain a multi-fault system 2
Expanding the actuator fault and the sensor fault into new state variables according to the state space model of the multi-fault system 1 obtained in the step 1, namely defining a new state variable
Figure BDA0003000643680000143
Figure BDA0003000643680000144
And the expanded system is recorded as a multi-fault system 2, the state space model of the multi-fault system 2 is recorded as an expression (2), and the expression (2) is as follows:
Figure BDA0003000643680000145
wherein the content of the first and second substances,
Figure BDA0003000643680000146
the state variable representing the multi-fault system 2, denoted as the second state variable
Figure BDA0003000643680000147
Figure BDA0003000643680000148
Belongs to the vector space of n + q + w dimensions and is marked as
Figure BDA0003000643680000151
Figure BDA0003000643680000152
Is a second state variable
Figure BDA0003000643680000153
The derivative with respect to time t, denoted as the second derivative
Figure BDA0003000643680000154
d (t) represents the fault vector of the multiple fault system 2, denoted as fault vector d (t),
Figure BDA0003000643680000155
Figure BDA0003000643680000156
for actuator failure fa(t) a derivative over time t;
Figure BDA0003000643680000157
is the second derivative
Figure BDA0003000643680000158
The matrix of coefficients of (a) is,
Figure BDA0003000643680000159
wherein InRepresenting an n-dimensional identity matrix, IqRepresenting a q-dimensional identity matrix;
Figure BDA00030006436800001510
is a second state variable
Figure BDA00030006436800001526
The matrix of coefficients of (a) is,
Figure BDA00030006436800001511
wherein IwRepresenting a w-dimensional identity matrix;
Figure BDA00030006436800001512
is a second matrix of coefficients of input u (t),
Figure BDA00030006436800001513
Figure BDA00030006436800001514
is the first coefficient matrix of the fault vector d (t),
Figure BDA00030006436800001515
Figure BDA00030006436800001516
is a second state variable
Figure BDA00030006436800001517
The matrix of output coefficients of (a) is,
Figure BDA00030006436800001518
xT(t) is the transposition of the first state variable x (t), fa T(t) actuator failure fa(t) transposition, fs T(t) is sensor failure fs(t) transposition, [ x ]T(t) fa T(t) fs T(t)]TIs [ x (t) fa(t) fs(t)]The transposing of (1).
Step 3, carrying out coordinate transformation on the multi-fault system 2 and introducing an intermediate variable zeta (t)
Step 3.1, a first coordinate transformation is performed
Second state variable
Figure BDA00030006436800001519
Output coefficient matrix of
Figure BDA00030006436800001520
Transposing, and transferring the transposed productGo out the series matrix and record
Figure BDA00030006436800001521
To pair
Figure BDA00030006436800001522
Carrying out QR decomposition, i.e. reaction
Figure BDA00030006436800001523
Wherein Q is an orthogonal matrix and R is an upper triangular matrix; let W be QT，S＝RTThen, then
Figure BDA00030006436800001524
W is an orthogonal matrix;
making a first coordinate transformation
Figure BDA00030006436800001525
The multi-fault system 2 is transformed into a multi-fault system 3, the state space model of the multi-fault system 3 is expressed as an expression (3), and the expression (3) is as follows:
Figure BDA0003000643680000161
wherein the content of the first and second substances,
Figure BDA0003000643680000162
state variables representing the multi-fault system 3, denoted as third state variables
Figure BDA0003000643680000163
Figure BDA0003000643680000164
Is a third state variable
Figure BDA0003000643680000165
The derivative with respect to time t, denoted as the third derivative
Figure BDA0003000643680000166
Figure BDA0003000643680000167
Is the third derivative
Figure BDA0003000643680000168
The first state coefficient matrix of (a) is,
Figure BDA0003000643680000169
wherein WTIs a transposed matrix of the orthogonal matrix W,
Figure BDA00030006436800001610
is a third state variable
Figure BDA00030006436800001611
The first state coefficient matrix of (a) is,
Figure BDA00030006436800001612
Figure BDA00030006436800001613
a third coefficient matrix of input u (t),
Figure BDA00030006436800001614
Figure BDA00030006436800001615
a second matrix of coefficients for the fault vector d (t),
Figure BDA00030006436800001616
s is a third state variable
Figure BDA00030006436800001617
The output coefficient matrix of (1) left and right blocks S, and the left block is marked as a first left block matrix S1I.e. S ═ S10) First left block matrix S1Belongs to a space of dimension p × p, and is denoted as S1∈Rp×pAnd S1Is an invertible matrix.
Step 3.2, introduce transformation matrix
Will be thirdDerivative of
Figure BDA00030006436800001618
First state coefficient matrix of
Figure BDA00030006436800001619
Performing left and right block division, and recording the left block as a left block matrix
Figure BDA00030006436800001620
The right block is marked as a right block matrix
Figure BDA00030006436800001621
Figure BDA00030006436800001622
Wherein the left block matrix
Figure BDA00030006436800001623
Belongs to the (n + q + w) x p dimensional space and is marked as
Figure BDA00030006436800001624
Right block matrix
Figure BDA00030006436800001625
Belongs to the (n + q + w) × (n + q + w-p) dimensional space and is marked as
Figure BDA00030006436800001626
Setting the transformation matrix to be designed as M, partitioning the transformation matrix to be designed into upper and lower blocks, and recording the upper blocks as an upper block matrix M1The lower block is marked as a lower block matrix M2I.e. by
Figure BDA00030006436800001627
Wherein M is1Belongs to a space of dimension p x (n + q + w) and is marked as M1∈Rp×(n+q+w)Wherein M is2Belongs to the (n + q + w) × (n + q + w-p) dimensional space and is marked as M2∈R(n+q+w-p)×(n+q+w)(ii) a Right block matrix
Figure BDA00030006436800001628
Transpose, note
Figure BDA00030006436800001629
Will go to the block matrix M1Transpose, denoted as M1 TSolving the equation
Figure BDA00030006436800001630
To obtain M1，
Figure BDA00030006436800001631
Wherein
Figure BDA00030006436800001632
Is composed of
Figure BDA00030006436800001633
The inverse matrix of (c).
Multiplying the two sides of the multi-fault system (3) by the transformation matrix M to obtain a new system, recording the new system as a multi-fault system (4), recording a state space model of the multi-fault system (4) as an expression (4), wherein the expression (4) is as follows:
Figure BDA0003000643680000171
wherein the content of the first and second substances,
Figure BDA0003000643680000172
is the third derivative
Figure BDA0003000643680000173
The second state coefficient matrix of (2), the third derivative
Figure BDA0003000643680000174
The second state coefficient matrix of (2) is divided into four blocks, and the upper left matrix block is marked as the first upper left matrix
Figure BDA0003000643680000175
The lower left matrix block is marked as the first lower left matrix
Figure BDA0003000643680000176
Namely, it is
Figure BDA0003000643680000177
Wherein In+q+w-pIs an n + q + w-p dimensional unit matrix;
Figure BDA0003000643680000178
is a third state variable
Figure BDA00030006436800001726
A second state coefficient matrix of a third state variable
Figure BDA0003000643680000179
Second state coefficient matrix of
Figure BDA00030006436800001710
Divided into four blocks, the upper left matrix block is marked as the second upper left matrix
Figure BDA00030006436800001711
The upper right matrix block is marked as the second upper right matrix
Figure BDA00030006436800001712
The lower left matrix block is marked as the second lower left matrix
Figure BDA00030006436800001713
The lower right matrix block is marked as the second lower right matrix
Figure BDA00030006436800001714
Namely, it is
Figure BDA00030006436800001715
Figure BDA00030006436800001716
Is the fourth coefficient matrix of input u (t), the fourth coefficient matrix of input u (t)
Figure BDA00030006436800001717
Partitioning the block into upper and lower blocks, and recording the upper block matrix as a third upper block
Figure BDA00030006436800001718
The lower block matrix is marked as the third lower block
Figure BDA00030006436800001719
Namely, it is
Figure BDA00030006436800001720
Figure BDA00030006436800001721
Is a third coefficient matrix of the fault vector d (t), and the third coefficient matrix of the fault vector d (t)
Figure BDA00030006436800001722
Partitioning the block into upper and lower blocks, and recording the upper block matrix as a fourth upper block
Figure BDA00030006436800001723
The lower block matrix is recorded as the fourth lower block
Figure BDA00030006436800001724
Namely, it is
Figure BDA00030006436800001725
Step 3.3, second coordinate transformation is carried out
Let the second coordinate transformation matrix be T,
Figure BDA0003000643680000181
wherein L is a matrix to be designed and is marked as a first free matrix L, the first free matrix L belongs to a p x (n + q + w-p) dimensional space and is marked as L belonging to Rp×(n+q+w-p)；
Second coordinate transformation for multi-fault system 4
Figure BDA0003000643680000182
Obtaining multiple fault systemsIn the system 5, the state space model of the multi-fault system 5 is expressed as an expression (5), and the expression (5) is as follows:
Figure BDA0003000643680000183
wherein the content of the first and second substances,
Figure BDA0003000643680000184
is a state variable of the multi-fault system (5) and is recorded as a fourth state variable
Figure BDA0003000643680000185
Fourth state variable
Figure BDA0003000643680000186
The vector composed of the first p rows is recorded as
Figure BDA0003000643680000187
Fourth state variable
Figure BDA0003000643680000188
The vector formed by the last n + q + w-p lines is recorded as
Figure BDA0003000643680000189
Namely, it is
Figure BDA00030006436800001810
Is composed of
Figure BDA00030006436800001811
The derivative with respect to time t;
Figure BDA00030006436800001812
Figure BDA00030006436800001813
S1 -1is a first left block matrix S1The inverse of the matrix of (a) is,
Figure BDA00030006436800001814
is a third state variable
Figure BDA00030006436800001815
Is recorded as the vector composed of the first p rows of
Figure BDA00030006436800001816
Figure BDA00030006436800001817
Is a fourth state variable
Figure BDA00030006436800001818
Coefficient matrix of (2), the fourth state variable
Figure BDA00030006436800001819
Is divided into four blocks, the upper left matrix block of which is marked as the fifth upper left block
Figure BDA00030006436800001820
The upper right matrix block is denoted as the fifth upper right partition
Figure BDA00030006436800001821
The bottom left matrix block is denoted as the fifth bottom left partition
Figure BDA00030006436800001822
The lower right matrix block is denoted as the fifth lower right partition
Figure BDA00030006436800001823
Namely, it is
Figure BDA00030006436800001824
T-1Is the inverse of the second coordinate transformation matrix T.
Step 3.4, introduce the intermediate variable ζ (t)
Introducing an intermediate variable ζ (t), giving a dynamic equation of the intermediate variable ζ (t), and recording as an expression (6):
Figure BDA0003000643680000191
wherein the intermediate variable
Figure BDA0003000643680000192
Figure BDA0003000643680000193
The derivative of the intermediate variable ζ (t) over time.
Specifically, the derivation process of expression (6) is as follows:
an intermediate variable ζ (t) is introduced,
Figure BDA0003000643680000194
finishing to obtain:
Figure BDA0003000643680000195
introducing the derivative of the intermediate variable ζ (t) with respect to time
Figure BDA0003000643680000196
Figure BDA0003000643680000197
Order to
Figure BDA0003000643680000198
The dynamic equation for the intermediate variable ζ (t) is obtained and recorded as expression (6), as follows:
Figure BDA0003000643680000199
step 4, observer parameter design is carried out on the intermediate variable zeta (t)
Step 4.1, design of Fault observer
Definition of
Figure BDA00030006436800001910
As observed value of intermediate variable ζ (t)Let observation errors
Figure BDA00030006436800001911
Designing a sliding-mode observer for the intermediate variable zeta (t), obtaining a dynamic equation of the observer, and recording the dynamic equation as an expression (7):
Figure BDA00030006436800001912
wherein, KsIs a sliding mode gain matrix and is a sliding mode gain matrix,
Figure BDA0003000643680000201
Usin order to form the item of the sliding mode,
Figure BDA0003000643680000202
the absolute value of | e (t) | is e (t), and is recorded as | e (t) |, ks1Is the first gain term, ks1＝ηa+ηs+ η, η is a first constant term, η is a positive constant, ε is a second constant term, 0 < ε < 1; p1Belongs to (w + q) x (n + w + q-P) -dimensional vector space and is marked as P1∈R(w+q)×(n+w+q-p)，P1Is a positive definite matrix; ks2Is a coefficient matrix of the observation error e (t) in the sliding mode term,
Figure BDA0003000643680000203
wherein diag () represents a diagonal matrix, δ is a third constant term, 0 < δ < 1.
Step 4.2, observing error e (t)
Solving the expression (6) and the expression (7) to obtain an error dynamic equation of the designed observer, which is as follows:
Figure BDA0003000643680000204
wherein the content of the first and second substances,
Figure BDA0003000643680000205
is the derivative of the observed error e (t) with respect to time;
design Lyapuloff function V (t), V (t) eT(t) Pe (t), wherein eT(t) is the transpose of the observation error e (t), P is a positive definite symmetric matrix, P is the Lyapunov equation
Figure BDA0003000643680000206
Where I is the identity matrix and the derivative of V (t) with respect to time is noted
Figure BDA0003000643680000207
Let the observation error e (t) converge to 0 for a finite time, then:
Figure BDA0003000643680000208
de lei punuo equation
Figure BDA0003000643680000209
The lyapunov equation is converted to the following linear matrix inequality (8):
Figure BDA0003000643680000211
and solving the linear matrix inequality (8) by using an LMI tool kit in matlab to obtain a positive definite symmetric matrix P and a first free matrix L.
Step 5, carrying out on-line synchronous fault estimation
Step 5.1, sampling the output y (t) to obtain the amplitude of the output y (t), which is recorded as y(1)(t)。
Step 5.2, the amplitude y of the output y (t) obtained in the step 5.1(1)(t) substitution into step 3.3
Figure BDA0003000643680000212
Get the fourth state variable
Figure BDA0003000643680000213
The first p row vectors
Figure BDA0003000643680000214
The value of (c).
Step 5.3, according to the fourth state variable obtained in step 5.2
Figure BDA0003000643680000215
The first p row vectors
Figure BDA0003000643680000216
Value of (3), step 3.4
Figure BDA0003000643680000217
In step 4.1
Figure BDA0003000643680000218
And the observation error e (t) in the step 4.2 is 0, and the expression (9) is obtained:
Figure BDA0003000643680000219
solving the fourth state variable by the expression (7) and the expression (9)
Figure BDA00030006436800002110
Last n + q + w-p row vector
Figure BDA00030006436800002111
Step 5.4, the fourth state variable calculated in step 5.2 is used
Figure BDA00030006436800002112
The first p row vectors
Figure BDA00030006436800002113
Fourth State variable calculated in step 5.3
Figure BDA00030006436800002114
Last n + q + w-p row vector
Figure BDA00030006436800002115
Substituted in step 3.3
Figure BDA00030006436800002116
Calculating a fourth state variable
Figure BDA00030006436800002117
Step 5.5, transform by the second coordinate
Figure BDA00030006436800002118
And a first coordinate transformation
Figure BDA00030006436800002119
Obtaining a second state variable
Figure BDA00030006436800002120
The fourth state variable calculated in step 5.4
Figure BDA00030006436800002121
Substitution into
Figure BDA00030006436800002122
Obtaining a second state variable
Figure BDA00030006436800002123
Step 5.6, calculating to obtain an estimated value of the first state variable x (t) and an actuator fault fa(t) estimated value, sensor failure fs(t) estimated value, specifically, the estimated value of the state variable x (t) is denoted as x(1)(t), failing the actuator fa(t) the estimated value is recorded as
Figure BDA0003000643680000221
Will sensor fail fs(t) the estimated value is recorded as
Figure BDA0003000643680000222
The three estimates are calculated as follows:
Figure BDA0003000643680000223
Figure BDA0003000643680000224
Figure BDA0003000643680000225
at this point, the multi-fault synchronous estimation of the PFC control system having the multi-fault is finished.
Embodiment 2 is implemented by using an interleaved parallel Boost PFC circuit, and the topological diagram thereof is shown in fig. 9. As can be seen from fig. 9, the interleaved parallel Boost PFC circuit includes an ac power supply, a full-wave rectification circuit, a Boost circuit, an output filter capacitor, and a load resistor;
the alternating voltage of the alternating current power supply is Vac；
The full-wave rectification circuit comprises four same rectifying diodes which are respectively marked as rectifying diodes BD1And a rectifier diode BD2And a rectifier diode BD3And a rectifier diode BD4Diode BD of rectifier1And a rectifier diode BD3Series connected, rectifying diodes BD3Is connected to the rectifier diode BD1Anode of (2), rectifier diode BD2And a rectifier diode BD4Series connected, rectifying diodes BD4Is connected to the rectifier diode BD2One end of an alternating current power supply is connected to the rectifier diode BD1And a rectifier diode BD3The other end of the alternating current power supply is connected to a rectifier diode BD2And a rectifier diode BD4A common connection point of (a);
the Boost circuit comprises two same inductors, two same Boost diodes and two same switching tubes, wherein the two same inductors are respectively marked as PFC inductors L1And a PFC inductor L2The two same boost diodes are respectively recorded as boost diodes KD1And boost diode KD2The two passing switch tubes are respectively marked as a switch tube KS1And a switching tube KS2PFC inductance L1And boost diode KD1Connected in series and then connected with a PFC inductor L2And a boost diode D2The series circuit is connected in parallel, and a switching tube KS1Connected to the PFC inductor L1And a boost diode D1Between the common connection point of (2) and ground, a switching tube KS2Connected to the PFC inductor L2And boost diode KD2Between the common connection point of (a) and ground;
the output filter capacitor is recorded as a capacitor CL0Capacitance CL0Connected to the boost diode KD1And boost diode KD2Between the common connection point of (a) and ground;
the load resistance is noted as resistance RL0Resistance RL0Connected in parallel to the capacitor CL0Two ends;
the specific parameters of the interleaved parallel Boost PFC circuit are as follows: the voltage value of the alternating current power supply is 220V, and the PFC inductor L1Inductance of 300uH, PFC inductance L2The inductance of (1) is 300uH, and the capacitance CL is0Has a capacitance value of 1000uF and a resistance RL0Has a resistance value of 40 Ω irrespective of KD1And KD2The conduction voltage drop of (1).
Taking the first state variable x (t) belonging to a three-dimensional vector space, i.e. n equals 3, the output y (t) belonging to a one-dimensional vector space, i.e. p equals 1, the PFC control system contains actuator faults and sensor faults, and the total fault number q + w equals 2.
In this embodiment, the procedure is as in embodiment 1, and the involved matrices in the estimation process are as follows:
Figure BDA0003000643680000231
C＝(0 0 1)，
F＝(1)，
Figure BDA0003000643680000232
Figure BDA0003000643680000233
Figure BDA0003000643680000241
Figure BDA0003000643680000242
Figure BDA0003000643680000243
Figure BDA0003000643680000244
Figure BDA0003000643680000245
Figure BDA0003000643680000246
M1＝(0 0 0 0 1)，
Figure BDA0003000643680000251
Figure BDA0003000643680000252
Figure BDA0003000643680000253
Figure BDA0003000643680000254
Figure BDA0003000643680000255
Figure BDA0003000643680000261
wherein
Figure BDA0003000643680000262
Figure BDA0003000643680000263
Figure BDA0003000643680000264
Wherein k iss1＝ηa+ηs+η，ε＝0.01，η＝10，ηa＝1.5，ηs＝2.1；
Figure BDA0003000643680000265
Wherein delta is 0.1, the total delta is,
Figure BDA0003000643680000266
Figure BDA0003000643680000267
in order to prove the technical effect of the invention, simulation is also carried out.
Fig. 3 shows an actuator fault 1 set in a simulation experiment and an actuator fault 1 estimated by using the method of the present invention, where a solid line in the diagram is the set actuator fault 1, and a mathematical expression thereof is:
Figure BDA0003000643680000268
wherein the content of the first and second substances,
Figure BDA0003000643680000271
and is
Figure BDA0003000643680000272
The dotted line in the figure is a diagram of the estimation result obtained by matlab simulation. It can be seen that no actuator fault occurs in 0-10s, an actuator fault occurs just before 10s, the estimation result has a transient error, and then the estimation error is close to 0;
fig. 4 shows a set sensor fault in a simulation experiment and a sensor fault estimated by using the method of the present invention, in which a solid line shows the set sensor fault and a mathematical expression thereof is:
Figure BDA0003000643680000273
wherein
Figure BDA0003000643680000274
And h (t) is less than or equal to 2.
The dotted line in the figure is a diagram of the estimation result obtained by matlab simulation. It can be seen that no sensor failure occurred in 0-15s, a sensor failure occurred just 10s, the estimation result has a short error, and then the estimation error is close to 0.
FIG. 5 shows a system state variable x in the present invention1(t) and its estimated value x1 (1)(t) simulation diagram, FIG. 6 is a system state variable x in the present invention2(t) and its estimated value x2 (1) (t) simulation diagram, FIG. 7 is a system state variable x in the present invention3(t) and its estimated value x3 (1)(t) simulation diagram. That is, fig. 5 to 7 are simulation diagrams of three state variables of the PFC system and estimation results thereof after the actuator 1 and the sensor fail in the specific embodiment. As can be seen from the figures 5-7,after the sensor failure occurred in the 10 th s, the estimation result has a small error, and immediately after the actuator failure occurred in the 15 th s, the estimation result has a short error, and then the estimation error approaches to 0.
Fig. 8 shows an actuator fault 2 set in a simulation experiment in a specific example and an actuator fault 2 estimated by using the method of the present invention, where a solid line in the diagram is the set actuator fault 2 and a mathematical expression thereof is:
Figure BDA0003000643680000281
wherein
Figure BDA0003000643680000282
And is
Figure BDA0003000643680000283
The dotted line in the figure is a diagram of the estimation result obtained by matlab simulation. It can be seen that no actuator failure occurred from 0 th to 10 th s, and that the actuator failure occurred just 10s, the estimation result has a short error, and then the estimation error is close to 0.
In addition, there are three main constraints for what is summarized in document 1: minimum phase system conditions, observer matching conditions, and output dimension conditions. The PFC model established in the example of the present invention was verified according to the constraints provided in this document, as follows:
1. since n is 3 and s is 0, then
Figure BDA0003000643680000284
Figure BDA0003000643680000285
Due to the fact that
Figure BDA0003000643680000286
This system does not satisfy the minimum phase condition.
2.
Figure BDA0003000643680000287
Figure BDA0003000643680000288
Due to the fact that
Figure BDA0003000643680000291
The observer matching condition is not satisfied.
3. The established PFC control system contains actuator faults and sensor faults, the total quantity of the faults is q + w is 2, the output dimension p of the system is 1, and the system dimension condition is not met due to the fact that q + w is larger than p.
Therefore, the established PFC control system does not meet the minimum phase system condition, the observer matching condition and the output dimension condition, and the simulation results of the graphs in the figures 3-8 verify that the synchronous fault estimation method can carry out synchronous fault estimation on multiple faults of the PFC control system under the condition of meeting the minimum phase system condition, the observer matching condition and the output dimension condition, thereby further verifying the beneficial effects of the synchronous fault estimation method.

Claims (3)

1. A multiple fault synchronous estimation method for a PFC control system, the multiple faults comprising an actuator fault and a sensor fault, the multiple fault synchronous estimation method comprising the steps of:
step 1, establishing a state space model of a PFC control system with multiple faults
The PFC control system with multiple faults is denoted as a multiple fault system 1, and a state space model of the multiple fault system 1 is denoted as an expression (1), where the expression (1) is as follows:
Figure FDA0003000643670000011
wherein t is time; x (t) represents the state variable of the multi-fault system 1, and is denoted as the first state variable x (t), x (t) belongs to the n-dimensional vector space, and is denoted as x (t) e Rn；
Figure FDA0003000643670000012
Is the derivative of the state variable x (t) with respect to time t, noted as the first derivative
Figure FDA0003000643670000013
u (t) represents the input of the multiple fault system 1, denoted as input u (t), u (t) belongs to the m-dimensional vector space, denoted as u (t) e Rm(ii) a y (t) represents the output of the multiple fault system 1, denoted as output y (t), which belongs to the p-dimensional vector space RpDenoted y (t) e Rp；fa(t) represents a q-dimensional actuator fault of the multi-fault system 1 and is noted as actuator fault fa(t)，fa(t) belongs to a q-dimensional vector space, denoted as fa(t)∈Rq；fs(t) denotes a w-dimensional sensor fault of the multiple fault system 1, denoted as sensor fault fs(t)，fs(t) belongs to the w-dimensional vector space, denoted as fa(t)∈Rw；
A is the state coefficient matrix of the first state variable x (t), B is the first coefficient matrix of the input u (t), C is the output coefficient matrix of the first state variable x (t), and C is the row full rank matrix, D is the actuator failure fa(t) coefficient matrix, F is sensor failure Fs(t) and F is a column full rank matrix;
actuator failure fa(t) and sensor failure fs(t) satisfies bounded and continuous derivative with respect to time, and | | | fa(t)||≤ηa，||fs(t)||≤ηsWherein | | | fa(t) | | represents the actuator failure fa(t) 2-norm, | | fs(t) | | denotes sensor failure fs2-norm, η of (t)aIs actuator failure faBoundary of (t) (. eta.)sIs to transmitSensor failure fsBoundary of (t) (. eta.)aAnd ηsAre all known normal numbers;
step 2, expanding the multi-fault system 1 to obtain a multi-fault system 2
Expanding the actuator fault and the sensor fault into new state variables according to the state space model of the multi-fault system 1 obtained in the step 1, namely defining a new state variable
Figure FDA00030006436700000224
Figure FDA0003000643670000021
And the expanded system is recorded as a multi-fault system 2, the state space model of the multi-fault system 2 is recorded as an expression (2), and the expression (2) is as follows:
Figure FDA0003000643670000022
wherein the content of the first and second substances,
Figure FDA0003000643670000023
the state variable representing the multi-fault system 2, denoted as the second state variable
Figure FDA0003000643670000024
Figure FDA0003000643670000025
Belongs to the vector space of n + q + w dimensions and is marked as
Figure FDA0003000643670000026
Figure FDA0003000643670000027
Is a second state variable
Figure FDA0003000643670000028
The derivative with respect to time t, denoted as the second derivative
Figure FDA0003000643670000029
d (t) represents the fault vector of the multiple fault system 2, denoted as fault vector d (t),
Figure FDA00030006436700000210
Figure FDA00030006436700000211
for actuator failure fa(t) a derivative over time t;
Figure FDA00030006436700000212
is the second derivative
Figure FDA00030006436700000213
The matrix of coefficients of (a) is,
Figure FDA00030006436700000214
wherein InRepresenting an n-dimensional identity matrix, IqRepresenting a q-dimensional identity matrix;
Figure FDA00030006436700000215
is a second state variable
Figure FDA00030006436700000225
The matrix of coefficients of (a) is,
Figure FDA00030006436700000216
wherein IwRepresenting a w-dimensional identity matrix;
Figure FDA00030006436700000217
is a second matrix of coefficients of input u (t),
Figure FDA00030006436700000218
Figure FDA00030006436700000219
is the first coefficient matrix of the fault vector d (t),
Figure FDA00030006436700000220
Figure FDA00030006436700000221
is a second state variable
Figure FDA00030006436700000222
The matrix of output coefficients of (a) is,
Figure FDA00030006436700000223
step 3, carrying out coordinate transformation on the multi-fault system 2 and introducing an intermediate variable zeta (t)
Step 3.1, a first coordinate transformation is performed
Second state variable
Figure FDA0003000643670000031
Output coefficient matrix of
Figure FDA0003000643670000032
Transposing, and recording the transposed output series matrix as
Figure FDA0003000643670000033
To pair
Figure FDA0003000643670000034
Carrying out QR decomposition, i.e. reaction
Figure FDA0003000643670000035
Wherein Q is an orthogonal matrix and R is an upper triangular matrix; let W be QT，S＝RTThen, then
Figure FDA0003000643670000036
W is an orthogonal matrix;
making a first coordinate transformation
Figure FDA0003000643670000037
The multi-fault system 2 is transformed into a multi-fault system 3, the state space model of the multi-fault system 3 is expressed as an expression (3), and the expression (3) is as follows:
Figure FDA0003000643670000038
wherein the content of the first and second substances,
Figure FDA0003000643670000039
state variables representing the multi-fault system 3, denoted as third state variables
Figure FDA00030006436700000310
Figure FDA00030006436700000311
Is a third state variable
Figure FDA00030006436700000312
The derivative with respect to time t, denoted as the third derivative
Figure FDA00030006436700000313
Figure FDA00030006436700000314
Is the third derivative
Figure FDA00030006436700000315
The first state coefficient matrix of (a) is,
Figure FDA00030006436700000316
wherein WTIs a rotation of an orthogonal matrix WThe position of the matrix is determined,
Figure FDA00030006436700000317
is a third state variable
Figure FDA00030006436700000318
The first state coefficient matrix of (a) is,
Figure FDA00030006436700000319
Figure FDA00030006436700000320
a third coefficient matrix of input u (t),
Figure FDA00030006436700000321
Figure FDA00030006436700000322
a second matrix of coefficients for the fault vector d (t),
Figure FDA00030006436700000323
s is a third state variable
Figure FDA00030006436700000324
The output coefficient matrix of (1) left and right blocks S, and the left block is marked as a first left block matrix S1I.e. S ═ S10) First left block matrix S1Belongs to a space of dimension p × p, and is denoted as S1∈Rp×pAnd S1Is a reversible matrix;
step 3.2, introduce transformation matrix
The third derivative
Figure FDA00030006436700000325
First state coefficient matrix of
Figure FDA00030006436700000326
Performing left and right block division, and recording the left block division as a left blockMatrix array
Figure FDA00030006436700000327
The right block is marked as a right block matrix
Figure FDA00030006436700000328
Figure FDA00030006436700000329
Wherein the left block matrix
Figure FDA00030006436700000330
Belongs to the (n + q + w) x p dimensional space and is marked as
Figure FDA00030006436700000331
Right block matrix
Figure FDA00030006436700000332
Belongs to the (n + q + w) × (n + q + w-p) dimensional space and is marked as
Figure FDA00030006436700000333
Setting the transformation matrix to be designed as M, partitioning the transformation matrix to be designed into upper and lower blocks, and recording the upper blocks as an upper block matrix M1The lower block is marked as a lower block matrix M2I.e. by
Figure FDA00030006436700000334
Wherein M is1Belongs to a space of dimension p x (n + q + w) and is marked as M1∈Rp ×(n+q+w)Wherein M is2Belongs to the (n + q + w) × (n + q + w-p) dimensional space and is marked as M2∈R(n+q+w-p)×(n+q+w)(ii) a Right block matrix
Figure FDA0003000643670000041
Transpose, note
Figure FDA0003000643670000042
Will go to the block matrix M1Transpose, denoted as M1 TSolving the equation
Figure FDA0003000643670000043
To obtain M1，
Figure FDA0003000643670000044
Wherein
Figure FDA0003000643670000045
Is composed of
Figure FDA00030006436700000429
The inverse matrix of (d);
multiplying the two sides of the multi-fault system (3) by the transformation matrix M to obtain a new system, recording the new system as a multi-fault system (4), recording a state space model of the multi-fault system (4) as an expression (4), wherein the expression (4) is as follows:
Figure FDA0003000643670000046
wherein the content of the first and second substances,
Figure FDA0003000643670000047
is the third derivative
Figure FDA0003000643670000048
The second state coefficient matrix of (2), the third derivative
Figure FDA0003000643670000049
The second state coefficient matrix of (2) is divided into four blocks, and the upper left matrix block is marked as the first upper left matrix
Figure FDA00030006436700000410
The lower left matrix block is marked as the first lower left matrix
Figure FDA00030006436700000411
Namely, it is
Figure FDA00030006436700000412
Wherein In+q+w-pIs an n + q + w-p dimensional unit matrix;
Figure FDA00030006436700000413
is a third state variable
Figure FDA00030006436700000414
A second state coefficient matrix of a third state variable
Figure FDA00030006436700000415
Second state coefficient matrix of
Figure FDA00030006436700000416
Divided into four blocks, the upper left matrix block is marked as the second upper left matrix
Figure FDA00030006436700000417
The upper right matrix block is marked as the second upper right matrix
Figure FDA00030006436700000418
The lower left matrix block is marked as the second lower left matrix
Figure FDA00030006436700000419
The lower right matrix block is marked as the second lower right matrix
Figure FDA00030006436700000420
Namely, it is
Figure FDA00030006436700000421
Figure FDA00030006436700000422
Is the fourth coefficient matrix of input u (t), the fourth coefficient matrix of input u (t)
Figure FDA00030006436700000423
Partitioning the block into upper and lower blocks, and recording the upper block matrix as a third upper block
Figure FDA00030006436700000424
The lower block matrix is marked as the third lower block
Figure FDA00030006436700000425
Namely, it is
Figure FDA00030006436700000426
Figure FDA00030006436700000427
Is a third coefficient matrix of the fault vector d (t), and the third coefficient matrix of the fault vector d (t)
Figure FDA00030006436700000428
Partitioning the block into upper and lower blocks, and recording the upper block matrix as a fourth upper block
Figure FDA0003000643670000051
The lower block matrix is recorded as the fourth lower block
Figure FDA0003000643670000052
Namely, it is
Figure FDA0003000643670000053
Step 3.3, second coordinate transformation is carried out
Let the second coordinate transformation matrix be T,
Figure FDA0003000643670000054
wherein L is a matrix to be designed and is marked as a first free matrix L, the first free matrix L belongs to a p x (n + q + w-p) dimensional space and is marked as L belonging to Rp×(n+q+w-p)；
For multiple faultsSystem 4 performs a second coordinate transformation
Figure FDA0003000643670000055
Obtaining a multi-fault system 5, and modeling the state space of the multi-fault system 5 as an expression (5), wherein the expression (5) is as follows:
Figure FDA0003000643670000056
wherein the content of the first and second substances,
Figure FDA0003000643670000057
is a state variable of the multi-fault system (5) and is recorded as a fourth state variable
Figure FDA0003000643670000058
Fourth state variable
Figure FDA0003000643670000059
The vector composed of the first p rows is recorded as
Figure FDA00030006436700000510
Fourth state variable
Figure FDA00030006436700000511
The vector formed by the last n + q + w-p lines is recorded as
Figure FDA00030006436700000512
Namely, it is
Figure FDA00030006436700000513
Is composed of
Figure FDA00030006436700000514
The derivative with respect to time t;
Figure FDA00030006436700000515
Figure FDA00030006436700000516
S1 -1is a first left block matrix S1The inverse of the matrix of (a) is,
Figure FDA00030006436700000517
is a third state variable
Figure FDA00030006436700000518
Is recorded as the vector composed of the first p rows of
Figure FDA00030006436700000519
Figure FDA00030006436700000520
Is a fourth state variable
Figure FDA00030006436700000521
Coefficient matrix of (2), the fourth state variable
Figure FDA00030006436700000522
Is divided into four blocks, the upper left matrix block of which is marked as the fifth upper left block
Figure FDA00030006436700000523
The upper right matrix block is denoted as the fifth upper right partition
Figure FDA00030006436700000524
The bottom left matrix block is denoted as the fifth bottom left partition
Figure FDA00030006436700000525
The lower right matrix block is denoted as the fifth lower right partition
Figure FDA00030006436700000526
Namely, it is
Figure FDA0003000643670000061
T-1An inverse matrix of the second coordinate transformation matrix T;
step 3.4, introduce the intermediate variable ζ (t)
Introducing an intermediate variable ζ (t), giving a dynamic equation of the intermediate variable ζ (t), and recording as an expression (6):
Figure FDA0003000643670000062
wherein the intermediate variable
Figure FDA0003000643670000063
Figure FDA0003000643670000064
Is the derivative of the intermediate variable ζ (t) with respect to time;
step 4, observer parameter design is carried out on the intermediate variable zeta (t)
Step 4.1, design of Fault observer
Definition of
Figure FDA0003000643670000065
For the observed value of the intermediate variable ζ (t), let the observed error
Figure FDA0003000643670000066
Designing a sliding-mode observer for the intermediate variable zeta (t), obtaining a dynamic equation of the observer, and recording the dynamic equation as an expression (7):
Figure FDA0003000643670000067
wherein, KsIs a sliding mode gain matrix and is a sliding mode gain matrix,
Figure FDA0003000643670000068
Usin order to form the item of the sliding mode,
Figure FDA0003000643670000069
the absolute value of | e (t) | is e (t), and is recorded as | e (t) |, ks1Is the first gain term, ks1＝ηa+ηs+ η, η is a first constant term, η is a positive constant, ε is a second constant term, 0 < ε < 1; p1Belongs to (w + q) x (n + w + q-P) -dimensional vector space and is marked as P1∈R(w+q)×(n+w+q-p)，P1Is a positive definite matrix; ks2Is a coefficient matrix of the observation error e (t) in the sliding mode term,
Figure FDA00030006436700000610
wherein diag () represents a diagonal matrix, δ is a third constant term, δ is greater than 0 and less than 1;
step 4.2, observing error e (t)
Solving the expression (6) and the expression (7) to obtain an error dynamic equation of the designed observer, which is as follows:
Figure FDA0003000643670000071
wherein the content of the first and second substances,
Figure FDA0003000643670000072
is the derivative of the observed error e (t) with respect to time;
design Lyapuloff function V (t), V (t) eT(t) Pe (t), wherein eT(t) is the transpose of the observation error e (t), P is a positive definite symmetric matrix, P is the Lyapunov equation
Figure FDA0003000643670000073
Where I is the identity matrix and the derivative of V (t) with respect to time is noted
Figure FDA0003000643670000074
Let the observation error e (t) converge to 0 for a finite time, then:
Figure FDA0003000643670000075
de lei punuo equation
Figure FDA0003000643670000076
The lyapunov equation is converted to the following linear matrix inequality (8):
Figure FDA0003000643670000077
solving a linear matrix inequality (8) by using an LMI tool kit in matlab to obtain a positive definite symmetric matrix P and a first free matrix L;
step 5, carrying out on-line synchronous fault estimation
Step 5.1, sampling the output y (t) to obtain the amplitude of the output y (t), which is recorded as y(1)(t)；
Step 5.2, the amplitude y of the output y (t) obtained in the step 5.1(1)(t) substitution into step 3.3
Figure FDA0003000643670000078
Get the fourth state variable
Figure FDA0003000643670000079
The first p row vectors
Figure FDA00030006436700000710
A value of (d);
step 5.3, according to the fourth state variable obtained in step 5.2
Figure FDA00030006436700000711
The first p row vectors
Figure FDA00030006436700000712
Value of (3), step 3.4
Figure FDA0003000643670000081
In step 4.1
Figure FDA0003000643670000082
And the observation error e (t) in the step 4.2 is 0, and the expression (9) is obtained:
Figure FDA0003000643670000083
solving the fourth state variable by the expression (7) and the expression (9)
Figure FDA0003000643670000084
Last n + q + w-p row vector
Figure FDA0003000643670000085
Step 5.4, the fourth state variable calculated in step 5.2 is used
Figure FDA0003000643670000086
The first p row vectors
Figure FDA0003000643670000087
Fourth State variable calculated in step 5.3
Figure FDA0003000643670000088
Last n + q + w-p row vector
Figure FDA0003000643670000089
Substituted in step 3.3
Figure FDA00030006436700000810
Calculating a fourth state variable
Figure FDA00030006436700000811
Step 5.5, transform by the second coordinate
Figure FDA00030006436700000812
And a first coordinate transformation
Figure FDA00030006436700000813
Obtaining a second state variable
Figure FDA00030006436700000814
The fourth state variable calculated in step 5.4
Figure FDA00030006436700000815
Substitution into
Figure FDA00030006436700000816
Obtaining a second state variable
Figure FDA00030006436700000817
Step 5.6, calculating to obtain an estimated value of the first state variable x (t) and an actuator fault fa(t) estimated value, sensor failure fs(t) estimated value, specifically, the estimated value of the state variable x (t) is denoted as x(1)(t), failing the actuator fa(t) the estimated value is recorded as
Figure FDA00030006436700000818
Will sensor fail fs(t) the estimated value is recorded as
Figure FDA00030006436700000819
The three estimates are calculated as follows:
Figure FDA00030006436700000820
Figure FDA00030006436700000821
Figure FDA00030006436700000822
at this point, the multi-fault synchronous estimation of the PFC control system having the multi-fault is finished.
2. The multi-fault synchronous estimation method of the PFC control system of claim 1, wherein x in step 2T(t) is the transposition of the first state variable x (t), fa T(t) actuator failure fa(t) transposition, fs T(t) is sensor failure fs(t) transposition, [ x ]T(t) fa T(t) fs T(t)]TIs [ x (t) fa(t) fs(t)]The transposing of (1).
3. The multi-fault synchronous estimation method of the PFC control system according to claim 1, wherein the derivation procedure of the expression (6) in the step 3 is as follows:
an intermediate variable ζ (t) is introduced,
Figure FDA0003000643670000091
finishing to obtain:
Figure FDA0003000643670000092
introducing the derivative of the intermediate variable ζ (t) with respect to time
Figure FDA0003000643670000093
Figure FDA0003000643670000094
Order to
Figure FDA0003000643670000095
The dynamic equation for the intermediate variable ζ (t) is obtained and recorded as expression (6), as follows:
Figure FDA0003000643670000096
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