CN114825281B - Multi-fault estimation method of staggered parallel Boost PFC system - Google Patents

Multi-fault estimation method of staggered parallel Boost PFC system Download PDF

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CN114825281B
CN114825281B CN202210429921.4A CN202210429921A CN114825281B CN 114825281 B CN114825281 B CN 114825281B CN 202210429921 A CN202210429921 A CN 202210429921A CN 114825281 B CN114825281 B CN 114825281B
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CN114825281A (en
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许水清
张云龙
任炜
何怡刚
陶松兵
许晓凡
王乐静
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Hefei University of Technology
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Abstract

The invention provides a multi-fault estimation method of an interleaved Boost PFC system, and belongs to the field of fault diagnosis. The method specifically comprises the steps of establishing a state space expression with an actuator fault and a sensor fault, carrying out primary filtering on output, expanding the filtered output to the state of a multi-fault system, carrying out order reduction on the multi-fault system, carrying out observer parameter design, estimating state variables of the system on line, and carrying out actuator fault and sensor fault. Compared with the prior art, the invention provides a new synchronous fault estimation method based on the dimension reduction observer technology and the generalized observer technology under the condition that the minimum phase condition, the observer matching condition and the output dimension condition are not constrained, and the designed sliding mode observer can ensure that an error system converges to zero in an exponential form so as to achieve the online synchronous estimation of state variables, actuator faults and sensor faults of a control system with multiple faults.

Description

Multi-fault estimation method of staggered parallel Boost PFC system
Technical Field
The invention relates to the field of fault diagnosis, in particular to a multi-fault estimation method of an interleaved Boost PFC system, wherein the multi-faults comprise actuator faults and sensor faults.
Background
With the development of power electronics technology, various power electronics devices are widely used in the fields of power, home appliances, mobile devices, traffic, and the like. Compared with a linear power supply, the high-frequency switching power electronic converter has the remarkable advantages of high efficiency, high power density and low cost, and has been widely applied to various fields of power conversion. The traditional switching power supply has low power factor, and can generate a large amount of current harmonic waves and reactive power in the power grid, so that the power grid is polluted. The main ways of improving the power factor are a harmonic compensation way and a power factor correction way. The harmonic compensation mode is to perform reactive power and some subharmonic compensation on equipment which has generated harmonic current, so that the total harmonic flowing into the power grid is reduced, and the total reactive power of the system is reduced; the power factor correction mode is to add a power factor correction converter on a front-stage power supply circuit of the electric equipment, so that the electric equipment does not inject harmonic current into a power grid. In contrast, power Factor Correction (PFC) techniques suppress the generation of harmonics from the source.
In recent years, as the requirements of safety and reliability performance indexes of a system are higher and higher, a control system is increasingly complicated and intelligent. At the same time, because a large number of actuators, sensors and other devices are integrated, system components often fail due to various accidents, the system performance is reduced slightly, the whole working system is destroyed, and the personal and property safety is endangered seriously, so that catastrophic accidents are caused. Therefore, in order to improve the reliability and safety of the system, timely and effective fault diagnosis and fault-tolerant control techniques are very important. The fault diagnosis technology comprises three parts of fault detection, fault isolation and fault estimation. Compared with fault detection and fault isolation technology realized by an indirect residual error method, the research of the fault estimation method is more practical and more challenging, because the amplitude of the fault can be directly obtained, people can know the fault in the system more intuitively, and further fault-tolerant control service can be realized.
Most control systems can be modeled by means of mathematical analysis. In actual control system applications, actuator and sensor faults may occur separately or simultaneously. In recent years, model-based methods have attracted a great deal of researchers in recent years to study actuator faults and synchronous fault estimation of sensors, most of which are either sliding mode observers or unknown input observers. In addition, the switching power supply is dominant in the power supply field because of its high power density and high efficiency. The most important method for suppressing the generation of harmonic waves of the switching power supply is to design a high-performance rectifier, which has the characteristics of sine wave input current, low harmonic content, high power factor and the like, namely the Power Factor Correction (PFC) function.
Document 1, article "A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions" (Xianghua Wang, chenghua zapu, audiomatrix 79 (2017) 290-295), a new sliding mode observer for system status and fault estimation that does not meet matching and minimum phase conditions (Xianghua Wang, chenghin Tan, chenghua zapu, automation, 2017, 79 th pages 290-295), details that there are two main constraints on the observer approach currently proposed: the minimum phase system condition and the observer matching condition, the author proposes a new fault estimation method under a relatively loose condition, but the auxiliary output matrix designed by the author also needs to meet the rank condition.
The Reduced-observer-based fault diagnosis method proposed in article "Simultaneous Fault Estimation for Markovian Jump Systems With Generally Uncertain Transition Rates: a Reduced-Order Observer Approach" (Xiaohang Li, weidong Zhang, yueying Wang, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 67 (2020) 7889-7897) (simultaneous fault estimation of markov jump system with generally uncertain transition rate: a Reduced-order observer method (Xiaohang Li, weidong Zhang, yueying Wang, ieee industrial electronics complex, 2020, 67 th edition, pages 7889-7897)) needs to satisfy the system output dimension greater than the number of system faults, observer matching condition, minimum phase system condition.
Document 3, chinese patent publication No. CN109557818B, a fault estimation method designed in the patent document "sliding mode fault-tolerant control method of multi-agent tracking system with multiple faults" needs to satisfy the condition (a, C) that is observable and rank ([ B, F) a ]) =rank (B), i.e. need to be fullThe minimum phase system conditions and observer matching conditions are sufficient, and the observer designed by the author is a full-dimensional observer.
Document 4, "a method for active fault-tolerant control of a spacecraft with fault-interference decoupling" (Zong Qun et al, university of Harbin university of Industrial, 2020,52 (09), 107-115DOI: 10.11918/201909065), proposes a design-unknown input observer that satisfies the assumption condition: Is an observable, i.e., the observer matching condition and minimum phase system condition need to be satisfied, and the author-designed observer is a full-dimensional observer.
The assumption that an adaptive sliding-mode observer designed in document 5, "Asymptotic estimation of state and faults for linear systems with unknown perturbations" (Jianglin Lan, autonomous 118 (2020) June) (unknown perturbed linear system state and asymptotic estimation of faults (Jianglin Lan, automated, 2020, month 6, 118)) needs to meet is a minimum phase system condition, an observer matching condition, a system dimension condition.
The assumed conditions to be satisfied by the adaptive sliding-mode observer designed in the article of "A Novel Adaptive Observer-Based Fault Reconstruction and State Estimation Method for Markovian Jump Systems" (Hongyan Yang, xian ling Li, zhaxu Chen, shen Yin, IEEE SYSTEMS jou rnal,15 (2021) 2305-2313) (a new adaptive observer-based mahalanobis jump system fault reconstruction and status estimation method (Hongyan Yang, xian ling Li, zhaxu Chen, shen Yin, IEEE JOURNAL of systems, 2021, 15 th edition 2305-2313)) are minimum phase system conditions, observer matching conditions, system dimension conditions.
In summary, the PFC control system is critical to the power supply, and the existing fault diagnosis technology is constrained by a plurality of constraint conditions, and the application range of the currently proposed fault estimation method is greatly limited by the plurality of constraint conditions. Therefore, for the research of the estimation technology of the multi-fault system containing the faults of the actuator and the sensor, the technical problem to be solved is urgent to solve in the whole research field.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, an object of the present invention is to provide a multi-fault estimation method for an interleaved parallel Boost PFC system with an actuator fault and a sensor fault, where the fault estimation method according to the present invention can accurately estimate information such as form, amplitude, magnitude, etc. of the fault when the actuator fault and the sensor fault occur in the system.
In order to achieve the above object, the present invention provides a multi-fault estimation method for an interleaved Boost PFC system, where the multi-fault includes an actuator fault and a sensor fault, and the estimation method includes the following steps:
step 1, establishing a state space model of a system with multiple faults
The staggered parallel Boost PFC system is called a system;
The system containing multiple failures is denoted as a multiple failure system 1, and a state space model of the multiple failure system 1 is denoted as expression (1), expression (1) is as follows:
wherein t is time; x (t) represents a state variable of the multi-fault system 1, denoted as a first state variable x (t), x (t) belonging to an n-dimensional vector space, denoted as x (t) ∈R n ；The derivative of the first state variable x (t) with respect to time t is denoted as the first derivativeu (t) represents the input of the multi-fault system 1, denoted as input u (t), which belongs to the m-dimensional vector space, denoted as u (t) ∈R m The method comprises the steps of carrying out a first treatment on the surface of the y (t) represents the output of the multi-fault system 1, denoted as the first outputy (t), which belongs to the p-dimensional vector space, is denoted as y (t) ∈R p ；f a (t) represents a q-dimensional actuator failure of the multi-failure system 1, denoted as actuator failure f a (t)，f a (t) belongs to the q-dimensional vector space and is denoted as f a (t)∈R q ；f d (t) represents d-dimensional external disturbance of the multi-fault system 1, denoted as external disturbance f d (t)，f d (t) belongs to the d-dimensional vector space and is denoted as f d (t)∈R d ；f s (t) represents a w-dimensional sensor failure of the multi-failure system 1, denoted as sensor failure f s (t)，f s (t) belongs to the w-dimensional vector space and is denoted as f s (t)∈R w ；
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 line-full order matrix, D is the actuator fault f a The coefficient matrix of (t), G is the external disturbance f d The coefficient matrix of (t), F is the sensor fault F s A coefficient matrix of (t), and F is a column full order matrix;
failure f of actuator a (t), sensor failure f s (t) and external disturbance f d (t) is bounded and f a (t)||≤η a ，||f s (t)||≤η s ，||f d (t)||≤η d Wherein f a (t) || represents an actuator failure f a The 2-norm of (t), I F s (t) || represents a sensor failure f s The 2-norm of (t), I F d (t) || represents the external disturbance f d 2-norm, η of (t) a Is the failure f of the actuator a The boundary, eta, of (t) s Is a sensor fault f s The boundary, eta, of (t) d Is an external disturbance f d The boundary, eta, of (t) a 、η s And eta d Are all known positive constants;
step 2, expanding the multi-fault system 1 to obtain a multi-fault system 2
The first output y (t) of the multi-fault system 1 is filtered once to obtain a new output, which satisfies expression (2), expression (2) is as follows:
wherein z is f (t) is the new output of the multi-fault system 1, denoted as the second output z f (t)，z f (t) belongs to the p-dimensional vector space, denoted as z f (t)∈R p ，Is the second output z f (t) derivative with respect to time t, A f Is the second output z f A first coefficient matrix of (t) and being a positive definite matrix;
according to the state space model of the multi-fault system 1 obtained in the step 1, a second output z is obtained f (t) expanding to a new state variable, i.e. defining a new state variable And the expanded system is recorded as a multi-fault system 2, a state space model of the multi-fault system 2 is recorded as an expression (3), and the expression (3) is as follows:
wherein,the state variable representing the multi-fault system 2 is denoted second state variable +.> Belongs to n+p dimension vector space and is marked as +.> Is the second state variable +.>The derivative of time t, noted as the second derivatived (t) represents a fault vector of the multi-fault system 2, denoted as fault vector d (t),> is the second state variable +.>Coefficient matrix of> Is a second coefficient matrix of input u (t), a second coefficient matrix of input u (t)> Is the first coefficient matrix of the fault vector d (t), is> Is the second state variable +.>Output coefficient matrix, ">Wherein I is p Representing a p-dimensional identity matrix;
step 3, coordinate transformation is carried out on the multi-fault system 2
Step 3.1, performing a first coordinate transformation
The first coordinate transformation matrix comprises two matrices to be designed, namely a first free matrix phi and a second free matrix R, wherein the first free matrix phi belongs to a k× (n+p) dimensional space and is marked as phi epsilon R k×(n+p) Wherein k is<(n+p), the second free matrix R belongs to a 1 Xp dimensional space, denoted R.epsilon.R 1×p ；
The first free matrix Φ and the second free matrix R satisfy expression (4), and expression (4) is as follows:
make a first coordinate transformation And->Transforming the multi-fault system 2 into the multi-fault system 3, and the state space model of the multi-fault system 3 is expressed as expression (5), wherein expression (5) is as follows:
wherein,the state variable representing the multi-fault system 3 is denoted third state variable +.> Belongs to k-dimensional vector space and is marked as +.> For the third state variable->The derivative of time t, denoted third derivative +.> The output of the multiple fault system 3 is denoted as third output +.> Belongs to a 1-dimensional vector space and is marked as +.> For the third state variable->Is provided with a first state coefficient matrix of (c),
third for input u (t)Coefficient matrix, < >> For a second output z f A second coefficient matrix of (t), +.>A second coefficient matrix for the fault vector d (t)> For the third state variable->Output coefficient matrix, ">
Step 3.2, performing a second coordinate transformation
Let the second coordinate transformation matrix be T 1 ，T 1 Belonging to k x k dimensional space, denoted T 1 ∈R k×k The method comprises the steps of carrying out a first treatment on the surface of the Second coordinate transformation of the multiple fault system 3>Obtaining a multi-fault system 4, wherein a state space model of the multi-fault system 4 is expressed as an expression (6), and the expression (6) is as follows:
wherein,the state variable of the multi-fault system 4 is denoted fourth state variable +.> Belongs to k-dimensional vector space and is marked as +.> For the fourth state variable->The derivative of time t, denoted fourth derivative +. >
For the fourth state variable->Fourth state variable +.>Is>Divided into four blocks, the upper left matrix block is marked as the first upper left matrix +.>The upper right matrix block is marked as a first upper right matrixThe lower left matrix block is marked as the first lower left matrix +.>The lower right matrix block is marked as the first lower right matrix +.>I.e. For the fourth coefficient matrix of input u (t), the fourth coefficient matrix of input u (t) is +.>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a second upper partitioning +.>The lower partition is marked as the second lower partition +.>I.e. < -> For a second output z f A third coefficient matrix of (t) outputting a second output z f Third coefficient matrix of (t)>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a third upper partitioning +.>The lower partition is marked as a third lower partition +.>I.e. < -> For the third coefficient matrix of the fault vector d (t), the third coefficient matrix of the fault vector d (t) is +.>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a fourth upper partitioning +.>The lower block matrix is marked as a fourth lower block +.>I.e. < -> Is a fourth state variableOutput coefficient matrix of (2) for the fourth state variable +.>Output coefficient matrix +.>Performing left and right block division, wherein the left block matrix is marked as a fifth left block +.>The right block matrix is marked as fifth right block +.>
Step 3.3, performing a third coordinate transformation
Let the third coordinate transformation matrix be T 2 ，Wherein L is a matrix to be designed, and is marked as a third free matrix L, and the third free matrix L belongs to (k-1) x 1-dimensional space and is marked as L epsilon R (k-1)×1 ；
Third coordinate transformation of multiple fault system 4Obtaining a multi-fault system 5, wherein a state space model of the multi-fault system 5 is expressed as an expression (7), and the expression (7) is as follows:
wherein,the state variable of the multi-fault system 5 is denoted as fifth state variable +.> For the first component of the fifth state variable, +.>Is the firstFive state variable second component,/->Is->Derivative with respect to time t;For the fifth state variable->Is to add a fifth state variable to the coefficient matrix of (2)>The coefficient matrix of (2) is divided into four blocks, the upper left matrix block is marked as the sixth upper left block +.>The upper right matrix block is marked as a sixth upper right partition block +.>The lower left matrix block is marked as a sixth lower left block +.>The lower right matrix block is marked as a sixth lower right partition block +.>I.e. For a third coordinate transformation matrix T 2 An inverse matrix of (a);For the fifth coefficient matrix of input u (t, willThe fifth coefficient matrix of input u (t) is divided into two blocks, the upper matrix block is marked as the seventh upper block +.>The lower partition is denoted as seventh lower partition +.>I.e. < -> For a second output z f A fourth coefficient matrix of (t) outputting a second output z f The fourth coefficient matrix of (t) is divided into two blocks, the upper matrix block is marked as the eighth upper block +. >The lower matrix block is denoted as eighth lower block +.>I.e. < -> For the fourth coefficient matrix of the fault vector d (t), dividing the fourth coefficient matrix of the fault vector d (t) into two blocks, wherein the upper block is marked as a ninth upper block +.>The lower block is marked as a ninth lower block +.>I.e. < -> For the fifth state variable->Output coefficient matrix of (2) for the fifth state variable +.>Output coefficient matrix +.>Performing left and right block division, wherein the left block is marked as a tenth left block 0, and the right block is marked as a tenth right block +.>I.e. < -> For the tenth right block->An inverse matrix of (a);
step 4, observer design is carried out on the multi-fault system 5
Step 4.1, fault observer design
Definition of the definitionFor the fifth state variable->Is>First component of the fifth state variable +.>Is>Second component for the fifth state variable +.>Is to let observation error +.>Observation error->For the fifth state variable->Designing a sliding mode observer to obtain a dynamic equation of the observer, and recording as an expression (8), wherein the expression (8) is as follows:
wherein,first component observations for a fifth state variable +.>Derivative of time t>Second component observation for the fifth state variable +.>Derivative with respect to time t; v 1 First component of the fifth state variable +.>V of the sliding mode item 1 ＝(v 11 ,…,v 1(k-1) ，v 1i ＝sgn(e 1i )，v 2 Second component for the fifth state variable +.>V of the sliding mode item 2 ＝sgn(e 2 )，First component of the fifth state variable +.>Is a sliding mode gain matrix, ">Wherein (1)>Is a symmetrical positive definite matrix P 1 Inverse matrix of P 1 For the matrix to be designed, the matrix is marked as a fourth free matrix P 1 ，k 1 Is a first constant to be designed, k 1 ∈R，k 2 To observe error e 2 (t) sliding mode gain, k 2 Is the second constant to be designed, k 2 ∈R，k 3 Second component for the fifth state variableThe sliding mode gain, k 3 Is the third to-be-designed constant, k 3 ∈R；
Step 4.2, observing error e (t)
Solving the expression (7) and the expression (8) to obtain an error dynamic equation of the designed observer is as follows:
wherein,to observe error e 1 (t) derivative with respect to time t, < >>To observe error e 2 (t) a derivative of time t;
step 5, online synchronous estimation is carried out
Step 5.1, estimating the fault
Failure of actuator f a The estimated value of (t) is recorded asFailure of sensor f s The estimated value of (t) is recorded asDisturbance f of the outside d The estimated value of (t) is marked +.>The calculation formulas of the three estimated values are as follows:
wherein I is q For q-dimensional identity matrix, I d For d-dimensional identity matrix, I w Is a w-dimensional identity matrix.
Step 5.2, estimating the state
Defining a state variable x (t has an estimated value of x (1) (t)、x (1) The derivative of (t) isError estimation value of actuator- >And external disturbance estimation +.>Carrying out expression (1) to obtain +.>Is calculated by the formula:
so far, the multi-fault estimation of the staggered parallel Boost PFC system containing the multi-faults is finished.
Preferably, x in step 2 T (t) is the transpose, z, of the first state variable x (t) f T (t) is the second output z f Transpose of (t),Is->Is a transpose of (a).
Preferably, the first constant k to be designed 1 A second constant k to be designed 2 A third constant k to be designed 3 Respectively satisfies the following formulas:
k 2 >0，
wherein,the maximum characteristic value is indicated to be the maximum characteristic value,λ(. Cndot.) represents the minimum eigenvalue.
Preferably, the third free matrix L and the fourth free matrix P 1 Respectively satisfies the following formulas:
wherein I is an identity matrix.
Compared with the prior art, the invention has the beneficial effects that:
1. under the condition of not being constrained by the minimum phase condition, the observer matching condition and the output dimension condition, a new fault estimation method is provided, a sliding mode observer is designed, the designed sliding mode 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 widened;
2. by adopting a dimension reduction observer technology, the estimated variable dimension is n+q+w+d, the actually required observer dimension is k, k is smaller than n+p, wherein p is smaller than q+w+d, the observer dimension is reduced, and the design complexity of the observer is reduced;
3. The state variable information of the multi-fault system and the information of the fault of the actuator, the fault of the sensor, the external disturbance form, the external disturbance size and the like can be synchronously estimated on line.
Drawings
FIG. 1 is a schematic diagram of a multi-fault synchronous estimation method according to the present invention;
FIG. 2 is a flow chart of a multi-fault synchronous estimation method of the present invention;
FIG. 3 shows an actuator failure f in the present invention a (t) and its estimateIs a simulation diagram of (1);
FIG. 4 shows a sensor failure f in the present invention s (t) and its estimateIs a simulation diagram of (1);
FIG. 5 is a system state variable x in the present invention 1 (t) and its estimate x 1 (1) A simulation diagram of (t);
FIG. 6 is a system state variable x in the present invention 2 (t) and its estimate x 2 (1) A simulation diagram of (t);
FIG. 7 is a system state variable x in the present invention 3 (t) and its estimate x 3 (1) A simulation diagram of (t);
FIG. 8 shows an actuator failure f in the present invention d (t) and its estimateIs a simulation diagram of (1);
fig. 9 is a circuit topology diagram in a simulation of the present invention.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings.
Embodiment 1 the present invention provides a method of multi-fault estimation for interleaved parallel Boost PFC systems, the multi-faults including actuator faults and sensor faults. Fig. 1 is a schematic diagram of a multi-fault estimation method according to the present invention, fig. 2 is a flowchart of the multi-fault estimation method according to the present invention, and as can be seen from fig. 1 and 2, the multi-fault estimation method includes the following steps:
Step 1, establishing a state space model of a system with multiple faults
The staggered parallel Boost PFC system is called a system;
the system containing multiple failures is denoted as a multiple failure system 1, and a state space model of the multiple failure system 1 is denoted as expression (1), expression (1) is as follows:
wherein t is time; x (t) represents a state variable of the multi-fault system 1,denoted as first state variable x (t), x (t) belonging to an n-dimensional vector space, denoted as x (t) ∈R n ；The derivative of the first state variable x (t) with respect to time t is denoted as the first derivativeu (t) represents the input of the multi-fault system 1, denoted as input u (t), which belongs to the m-dimensional vector space, denoted as u (t) ∈R m The method comprises the steps of carrying out a first treatment on the surface of the y (t) represents the output of the multi-fault system 1, denoted as first output y (t), y (t) belonging to the p-dimensional vector space, denoted as y (t) ∈R p ；f a (t) represents a q-dimensional actuator failure of the multi-failure system 1, denoted as actuator failure f a (t)，f a (t) belongs to the q-dimensional vector space and is denoted as f a (t)∈R q ；f d (t) represents d-dimensional external disturbance of the multi-fault system 1, denoted as external disturbance f d (t)，f d (t) belongs to the d-dimensional vector space and is denoted as f d (t)∈R d ；f s (t) represents a w-dimensional sensor failure of the multi-failure system 1, denoted as sensor failure f s (t)，f s (t) belongs to the w-dimensional vector space and is denoted as f s (t)∈R w ；
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 line-full order matrix, D is the actuator fault f a The coefficient matrix of (t), G is the external disturbance f d The coefficient matrix of (t), F is the sensor fault F s A coefficient matrix of (t), and F is a column full order matrix;
failure f of actuator a (t), sensor failure f s (t) and external disturbance f d (t) is bounded and f a (t)||≤η a ，||f s (t)||≤η s ，||f d (t)||≤η d Wherein f a (t) || represents an actuator failure f a The 2-norm of (t), I F s (t) || represents a sensor failure f s The 2-norm of (t), I F d (t) || represents the external disturbance f d (t) 2-norm, eta of (2) a Is the failure f of the actuator a The boundary, eta, of (t) s Is a sensor fault f s The boundary, eta, of (t) d Is an external disturbance f d The boundary, eta, of (t) a 、η s And eta d Are all known positive constants;
step 2, expanding the multi-fault system 1 to obtain a multi-fault system 2
The first output y (t) of the multi-fault system 1 is filtered once to obtain a new output, which satisfies expression (2), expression (2) is as follows:
wherein z is f (t) is the new output of the multi-fault system 1, denoted as the second output z f (t)，z f (t) belongs to the p-dimensional vector space, denoted as z f (t)∈R p ，Is the second output z f (t) derivative with respect to time t, A f Is the second output z f A first coefficient matrix of (t) and being a positive definite matrix;
according to the state space model of the multi-fault system 1 obtained in the step 1, a second output z is obtained f (t) expanding to a new state variable, i.e. defining a new state variable And the expanded system is recorded as a multi-fault system 2, a state space model of the multi-fault system 2 is recorded as an expression (3), and the expression (3) is as follows:
wherein,the state variable representing the multi-fault system 2 is denoted second state variable +.> Belongs to n+p dimension vector space and is marked as +.> Is the second state variable +.>The derivative of time t, noted as the second derivatived (t) represents a fault vector of the multi-fault system 2, denoted as fault vector d (t),> is the second state variable +.>Coefficient matrix of> Is a second coefficient matrix of input u (t), a second coefficient matrix of input u (t)> Is the first coefficient matrix of the fault vector d (t), is> Is the second state variable +.>Output coefficient matrix, ">Wherein I is p Representing a p-dimensional identity matrix;
step 3, coordinate transformation is carried out on the multi-fault system 2
Step 3.1, performing a first coordinate transformation
The first coordinate transformation matrix comprises two matrices to be designed, namely a first free matrix phi and a second free matrix R, wherein the first free matrix phi belongs to a k× (n+p) dimensional space and is marked as phi epsilon R k×(n+p) Wherein k is<(n+p), the second free matrix R belongs to a 1 Xp dimensional space, denoted R.epsilon.R 1×p ；
The first free matrix Φ and the second free matrix R satisfy expression (4), and expression (4) is as follows:
make a first coordinate transformation And->Transforming the multi-fault system 2 into the multi-fault system 3, and recording a state space model of the multi-fault system 3 as an expression (5), wherein the expression is(5) The following are provided:
wherein,the state variable representing the multi-fault system 3 is denoted third state variable +.> Belongs to k-dimensional vector space and is marked as +.> For the third state variable->The derivative of time t, denoted third derivative +.> The output of the multiple fault system 3 is denoted as third output +.> Belongs to a 1-dimensional vector space and is marked as +.> For the third state variable->Is a first state coefficient matrix of-> A third coefficient matrix for input u (t), a third coefficient matrix for input u (t)> For a second output z f A second coefficient matrix of (t), +.>A second coefficient matrix for the fault vector d (t)> For the third state variable->Output coefficient matrix, ">
Step 3.2, performing a second coordinate transformation
Let the second coordinate transformation matrix be T 1 ，T 1 Belonging to k x k dimensional space, denoted T 1 ∈R k×k The method comprises the steps of carrying out a first treatment on the surface of the Second coordinate transformation of multi-fault system 3Exchange->Obtaining a multi-fault system 4, wherein a state space model of the multi-fault system 4 is expressed as an expression (6), and the expression (6) is as follows:
wherein,the state variable of the multi-fault system 4 is denoted fourth state variable +.> Belongs to k-dimensional vector space and is marked as +.> For the fourth state variable->The derivative of time t, denoted fourth derivative +. >
For the fourth state variable->Fourth state variable +.>Is>Divided into four blocks, the upper left matrix block is marked as the first upper left matrix +.>The upper right matrix block is marked as a first upper right matrixThe lower left matrix block is marked as the first lower left matrix +.>The lower right matrix block is marked as the first lower right matrix +.>I.e. For the fourth coefficient matrix of input u (t), the fourth coefficient matrix of input u (t) is +.>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a second upper partitioning +.>The lower partition is marked as the second lower partition +.>I.e. For a second output z f A third coefficient matrix of (t) outputting a second output z f Third coefficient matrix of (t)>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a third upper partitioning +.>The lower partition is marked as a third lower partition +.>I.e. For the third coefficient matrix of the fault vector d (t), the third coefficient matrix of the fault vector d (t) is +.>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a fourth upper partitioning +.>The lower block matrix is marked as a fourth lower block +.>I.e. For the fourth state variable->Output coefficient matrix of (2) for the fourth state variable +.>Output coefficient matrix +.>Performing left and right block division, wherein the left block matrix is marked as a fifth left block +.>The right block matrix is marked as a fifth right block
Step 3.3, performing a third coordinate transformation
Let the third coordinate transformation matrix be T 2 ，Wherein L is a matrix to be designed, and is marked as a third free matrix L, and the third free matrix L belongs to (k-1) x 1-dimensional space and is marked as L epsilon R (k-1)×1 ；
Third coordinate transformation of multiple fault system 4Obtaining a multi-fault system 5, wherein a state space model of the multi-fault system 5 is expressed as an expression (7), and the expression (7) is as follows:
wherein,the state variable of the multi-fault system 5 is denoted as fifth state variable +.> For the first component of the fifth state variable, +.>For the fifth state variable second component, +.>Is->Derivative with respect to time t;For the fifth state variable->Is to add a fifth state variable to the coefficient matrix of (2)>The coefficient matrix of (2) is divided into four blocks, the upper left matrix block is marked as the sixth upper left block +.>The upper right matrix block is marked as a sixth upper right partition block +.>The lower left matrix block is marked as a sixth lower left block +.>The lower right matrix block is marked as a sixth lower right partition block +.>I.e. For a third coordinate transformation matrix T 2 An inverse matrix of (a);For the fifth coefficient matrix of input u (t), dividing the fifth coefficient matrix of input u (t) into two blocks, wherein the upper matrix block is marked as a seventh upper block->The lower partition is denoted as seventh lower partition +.>I.e. For a second output z f A fourth coefficient matrix of (t) outputting a second output z f The fourth coefficient matrix of (t) is divided into two blocks, the upper matrix block is marked as the eighth upper block +. >The lower matrix block is denoted as eighth lower block +.>I.e. < -> For the fourth coefficient matrix of the fault vector d (t), dividing the fourth coefficient matrix of the fault vector d (t) into two blocks, wherein the upper block is marked as a ninth upper block +.>The lower block is marked as a ninth lower block +.>I.e. For the fifth state variable->Output coefficient matrix of (2) for a fifth state variableOutput coefficient matrix +.>The left and right blocks are divided, wherein the left block is marked as a tenth left block 0, and the right block is marked as a tenth right blockI.e. < -> For the tenth right block->An inverse matrix of (a);
step 4, observer design is carried out on the multi-fault system 5
Step 4.1, fault observer design
Definition of the definitionFor the fifth state variable->Is>First component of the fifth state variable +.>Is>Second component for the fifth state variable +.>Is to let observation error +.>Observation error->For the fifth state variable->Designing a sliding mode observer to obtain a dynamic equation of the observer, and recording as an expression (8), wherein the expression (8) is as follows:
wherein,first as a fifth state variableComponent observations +.>Derivative of time t>Second component observation for the fifth state variable +.>Derivative with respect to time t; v 1 First component of the fifth state variable +.>V of the sliding mode item 1 ＝(v 11 ,…,v 1(k-1) ，v 1i ＝sgn(e 1i )，v 2 Second component for the fifth state variable +. >V of the sliding mode item 2 ＝sgn(e 2 )，First component of the fifth state variable +.>Is a sliding mode gain matrix, ">Wherein (1)>Is a symmetrical positive definite matrix P 1 Inverse matrix of P 1 For the matrix to be designed, the matrix is marked as a fourth free matrix P 1 ，k 1 Is a first constant to be designed, k 1 ∈R，k 2 To observe error e 2 t sliding mode gain, k 2 Is the second constant to be designed, k 2 ∈R，k 3 Second component for the fifth state variableThe sliding mode gain, k 3 Is the third to-be-designed constant, k 3 ∈R；
Step 4.2, observing error e (t)
Solving the expression (7) and the expression (8) to obtain an error dynamic equation of the designed observer is as follows:
wherein,to observe error e 1 (t) derivative with respect to time t, < >>To observe error e 2 (t) a derivative of time t;
step 5, online synchronous estimation is carried out
Step 5.1, estimating the fault
Failure of actuator f a The estimated value of (t) is recorded asFailure of sensor f s The estimated value of (t) is marked +.>Disturbance f of the outside d The estimated value of (t) is marked +.>The calculation formulas of the three estimated values are as follows:
wherein I is q For q-dimensional identity matrix, I d For d-dimensional identity matrix，I w Is a w-dimensional identity matrix.
Step 5.2, estimating the state
Defining the estimated value of the state variable x (t) as x (1) (t)、x (1) The derivative of (t) isError estimation value of actuator->And external disturbance estimation +. >Carrying out expression (1) to obtain +.>Is calculated by the formula:
so far, the multi-fault estimation of the staggered parallel Boost PFC system containing the multi-faults is finished.
In this example 1, x in step 2 T (t) is the transpose, z, of the first state variable x (t) f T (t) is the second output z f Transpose of (t),Is->Is a transpose of (a).
In this embodiment 1, the first design constant k 1 A second constant k to be designed 2 A third constant k to be designed 3 Respectively satisfies the following formulas:
k 2 >0，
wherein,the maximum characteristic value is indicated to be the maximum characteristic value,λ(. Cndot.) represents the minimum eigenvalue.
In this embodiment 1, the third free matrix L and the fourth free matrix P 1 Respectively satisfies the following formulas:
wherein I is an identity matrix.
In embodiment 2, an interleaved Boost PFC circuit is implemented, and the topology diagram 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 rectifying circuit, a Boost circuit, an output filter capacitor, and a load resistor; meanwhile, the PFC system also comprises an actuator fault and a sensor fault; industry investigations have shown that power semiconductor switching devices are one of the most prone to failure in power electronic converters; the switching tube faults of the PFC system are mainly divided into short-circuit faults and open-circuit faults, the short-circuit faults of the switching tube are protected by a hardware protection circuit, when the short-circuit faults occur, the hardware protection circuit is rapidly cut off, and finally the short-circuit faults of the switching tube are converted into open-circuit faults, so that only the open-circuit faults of the PFC system are considered to be subjected to fault estimation; in addition to power switching tube faults, sensor faults are also one of the common faults of PFC systems; the sensor provides real-time current and voltage information for the closed-loop controller, and the accuracy of feedback information output by the sensor has important influence on the control performance of the system; The faults of the direct current voltage sensor are mainly divided into short circuit faults, open circuit faults, time-varying faults and intermittent faults, and the short circuit faults and the open circuit faults can be regarded as special conditions of the intermittent faults because the output of the analog-to-digital converter has the limit of the maximum value and the minimum value, so that only the intermittent faults and the time-varying faults of the direct current voltage sensor are considered; the invention is studied for KS 1 Open-circuit fault of switching tube and output voltage sensor V o Intermittent failure;
the alternating voltage of the alternating current power supply is V ac ；
The full-wave rectifying circuit comprises four identical rectifying diodes, which are respectively denoted as rectifying diodes BD 1 Rectifier diode BD 2 Rectifier diode BD 3 And a rectifying diode BD 4 Rectifier diode BD 1 And rectifier diode BD 3 Series connection of rectifier diodes BD 3 Is connected to the rectifying diode BD 1 Anode of rectifier diode BD 2 And a rectifying diode BD 4 Series connection of rectifier diodes BD 4 Is connected to the rectifying diode BD 2 An AC power source is connected to the rectifying diode BD 1 And rectifier diode BD 3 Is connected to the rectifying diode BD at the other end 2 And rectifier diode BD 4 Is a common connection point of (2);
The Boost circuit comprises two identical inductors, two identical Boost diodes and two identical switching tubes, wherein the two identical inductors are respectively marked as PFC inductance L 1 And PFC inductance L 2 The two identical boost diodes are respectively denoted as boost diode KD 1 And boost diode KD 2 The two passing switching tubes are respectively denoted as switching tubes KS 1 And a switching tube KS 2 PFC inductance L 1 And boost diode KD 1 After being connected in series, the Power Factor Correction (PFC) inductor L 2 And boost diode D 2 The circuits after being connected in series are connected in parallel, and the switching tube KS 1 Connected to PFC inductance L 1 And boost diode D 1 Is connected between the common connection point of (c) and ground, switch tube KS 2 Connected to PFC inductance L 2 And boost diode KD 2 Is connected between the common connection point of (c) and ground;
the output filter capacitance is denoted as capacitance CL 0 Capacitance CL 0 Connected to the boost diode KD 1 And boost diode KD 2 Is connected between the common connection point of (c) and ground;
the load resistance is denoted as resistance RL 0 Resistance RL 0 Connected in parallel with the capacitor CL 0 Both ends;
specific parameters of the staggered parallel Boost PFC circuit are as follows: the voltage value of the alternating current power supply is 220V, PFC inductance L 1 The inductance of (2) is 300uH, PFC inductance L 2 The inductance of (C) is 300uH, and the capacitance CL 0 The capacitance value of (2) is 1000uF, resistance RL 0 The resistance value of (2) is 40Ω, irrespective of KD 1 And KD 2 Is provided.
Taking that the first state variable x (t) belongs to a three-dimensional vector space, namely n=3, the output y (t) belongs to a one-dimensional vector space, namely p=1, and the PFC control system comprises an actuator fault and a sensor fault, and the total fault quantity q+w=2.
In this embodiment, the steps are as in embodiment 1, and the matrix involved in the estimation process is as follows:
C＝(0 0 1)，F＝(1)，A f ＝(1)，
R＝(0.5022)，
J＝(-0.7031 -0.4419 -0.2411)，
k 1 ＝(20)，k 2 ＝(20)，η a ＝(1.5)，k 3 ＝(150)，η s ＝(2.5)，η d ＝(0.5)。
in order to prove the technical effect of the invention, simulation is also carried out.
Fig. 3 is a diagram showing an actuator failure set in a simulation experiment and an actuator failure estimated by the method of the present invention, wherein a solid line is the set actuator failure, and a mathematical expression is as follows:
wherein,and->
The dashed line in the figure is the estimated result graph obtained by matlab simulation. It can be seen that no actuator failure occurs in the 0 th to the 2 nd s, a short and small error occurs in the estimation result just after the actuator failure occurs in the 2s, then the estimation error is close to 0, a short error occurs in the estimation result just after the sensor failure occurs in the 4s, and then the estimation error is close to 0.
Fig. 4 is a diagram showing a sensor fault set in a simulation experiment and a sensor fault estimated by the method of the present invention, wherein a solid line is a set sensor fault, and a mathematical expression is as follows:
Wherein,and h (t) is less than or equal to 1.
The dashed line in the figure is the estimated result graph obtained by matlab simulation. It can be seen that no sensor failure occurred in the 0 th to 4 th s, a short and small error occurred in the estimated result just after the sensor failure occurred in the 4 th s, and then the estimated error was close to 0.
FIG. 5 is a system state variable x in the present invention 1 (t) and its estimate x 1 (1) (t) A simulation diagram, FIG. 6 is a system state variable x in the present invention 2 (t) and its estimate x 2 (1) (t) simulation diagram, FIG. 7 is a system state variable x in the present invention 3 (t) and its estimate x 3 (1) A simulation diagram of (t). Fig. 5-7 are simulation graphs of three state variables and estimation results of the PFC system after the failure of the actuator and the failure of the sensor in the embodiment. As can be seen from fig. 5-7, after the actuator failure occurs at the 2 nd s, there is a small error in the estimation result, the sensor failure occurs just at the 4 th s, there is a short error in the estimation result, and then the estimation error approaches 0.
FIG. 8 is a graph showing the external disturbance set in the simulation experiment and the external disturbance estimated by the method of the present invention, wherein the solid line is the set external disturbance, and the mathematical expression is:
f d (t)＝0.05sin t
the dashed line in the figure is the estimated result graph obtained by matlab simulation. It can be seen that the external disturbance just occurs at 0s, the estimation result has a short error, then the estimation error approaches 0, the sensor fault just occurs at 4s, the estimation result has a short error, and then the estimation error approaches 0.
In addition, three main constraints exist for the summary of document 1: minimum phase system conditions, observer matching conditions, and output dimension conditions. The PFC model built in the example of the present invention was validated according to the constraints provided in this document as follows:
1. since n=3, taking the laplace operator s=0, then
Due toThe system does not meet the minimum phase condition.
2.
Due toThe observer matching condition is not satisfied.
3. The built staggered parallel Boost PFC system comprises actuator faults and sensor faults, the total fault quantity is q+w=2, the output dimension p=1 of the system, and the q+w > p does not meet the dimension condition of the system.
Therefore, the staggered parallel Boost PFC system established in the invention can be seen to not meet the minimum phase system condition, the observer matching condition and the output dimension condition, and the simulation results of the figures 3-8 prove that the staggered parallel Boost PFC system can perform fault estimation on multiple faults of the staggered parallel Boost PFC system under the condition that the minimum phase system condition, the observer matching condition and the output dimension condition are not met, so that the beneficial effects of the staggered parallel Boost PFC system are further verified.

Claims (4)

1. A method of multi-fault estimation for an interleaved parallel Boost PFC system, the multi-fault including an actuator fault and a sensor fault, the method comprising the steps of:
Step 1, establishing a state space model of a system with multiple faults
The staggered parallel Boost PFC system is called a system;
the system containing multiple failures is denoted as a multiple failure system 1, and a state space model of the multiple failure system 1 is denoted as expression (1), expression (1) is as follows:
wherein t is time; x (t) represents a state variable of the multi-fault system 1, denoted as a first state variable x (t), x (t) belonging to an n-dimensional vector space, denoted as x (t) ∈R n ；The derivative of the first state variable x (t) with respect to time t is denoted as first derivative +.>u (t) represents the input of the multi-fault system 1, denoted as input u (t), which belongs to the m-dimensional vector space, denoted as u (t) ∈R m The method comprises the steps of carrying out a first treatment on the surface of the y (t) represents the output of the multi-fault system 1, denoted as first output y (t), y (t) belonging to the p-dimensional vector space, denoted as y (t) ∈R p ；f a (t) represents a q-dimensional actuator failure of the multi-failure system 1, denoted as actuator failure f a (t)，f d (t) belongs to the q-dimensional vector space and is denoted as f a (t)∈R q ；f d (t) represents d-dimensional external disturbance of the multi-fault system 1, denoted as external disturbance f d (t)，f d (t) belongs to the d-dimensional vector space and is denoted as f d (t)∈R d ；f s (t) represents a w-dimensional sensor failure of the multi-failure system 1, denoted as sensor failure f s (t)，f s (t) belongs to the w-dimensional vector space and is denoted as f s (t)∈R w ；
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 line-full order matrix, D is the actuator fault f a The coefficient matrix of (t), G is the external disturbance f d The coefficient matrix of (t), F is the sensor fault F s A coefficient matrix of (t), and F is a column full order matrix;
failure f of actuator a (t), sensor failure f s (t) and external disturbance f d (t) is bounded and f a (t)||≤η a ，||f s (t)||≤η s ，||f d (t)||≤η d Wherein f a (t) || represents an actuator failure f a The 2-norm of (t), I F s (t) || represents a sensor failure f s The 2-norm of (t), I F d (t) || represents the external disturbance f d 2-norm, η of (t) a Is the failure f of the actuator a The boundary, eta, of (t) s Is a sensor fault f s The boundary, eta, of (t) d Is an external disturbance f d The boundary, eta, of (t) a 、η s And eta d Are all known positive constants;
step 2, expanding the multi-fault system 1 to obtain a multi-fault system 2
The first output y (t) of the multi-fault system 1 is filtered once to obtain a new output, which satisfies expression (2), expression (2) is as follows:
wherein z is f (t) is the new output of the multi-fault system 1, denoted as the second output z f (t)，z f (t) belongs to the p-dimensional vector space, denoted as z f (t)∈R p ，Is the second output z f (t) derivative with respect to time t, A f Is the second output z f A first coefficient matrix of (t) and being a positive definite matrix;
according to the state space model of the multi-fault system 1 obtained in the step 1, a second output z is obtained f (t) expanding to a new state variable, i.e. defining a new state variable And will pass throughThe expanded system is denoted as a multi-fault system 2, and the state space model of the multi-fault system 2 is denoted as expression (3), expression (3) is as follows:
wherein,the state variable representing the multi-fault system 2 is denoted second state variable +.> Belongs to n+p dimension vector space and is marked as +.> Is the second state variable +.>The derivative of time t, denoted second derivative +.>d (t) represents a fault vector of the multi-fault system 2, denoted as fault vector d (t),> is the second state variable +.>Coefficient matrix of> Is a second coefficient matrix of input u (t), a second coefficient matrix of input u (t)> Is the first coefficient matrix of the fault vector d (t), is> Is the second state variable +.>Output coefficient matrix, ">Wherein I is p Representing a p-dimensional identity matrix;
step 3, coordinate transformation is carried out on the multi-fault system 2
Step 3.1, performing a first coordinate transformation
The first coordinate transformation matrix comprises two matrices to be designed, namely a first free matrix phi and a second free matrix R, wherein the first free matrix phi belongs to a k× (n+p) dimensional space and is marked as phi epsilon R k×(n+p) Wherein k < (n+p), the second free matrix R belongs to a 1 x p dimensional space, denoted R.epsilon.R 1×p ；
The first free matrix Φ and the second free matrix R satisfy expression (4), and expression (4) is as follows:
make a first coordinate transformation And->Transforming the multi-fault system 2 into the multi-fault system 3, and the state space model of the multi-fault system 3 is expressed as expression (5), wherein expression (5) is as follows:
wherein,the state variable representing the multi-fault system 3 is denoted third state variable +.> Belongs to k-dimensional vector space and is marked as +.> For the third state variable->The derivative of time t, denoted third derivative +.> The output of the multiple fault system 3 is denoted as third output +.> Belongs to a 1-dimensional vector space and is marked as +.> For the third state variable->Is a first state coefficient matrix of-> A third coefficient matrix for input u (t), a third coefficient matrix for input u (t)> For a second output z f A second coefficient matrix of (t), +.>A second coefficient matrix for the fault vector d (t)> For the third state variable->Output coefficient matrix, ">
Step 3.2, performing a second coordinate transformation
Let the second coordinate transformation matrix be T 1 ，T 1 Belonging to k x k dimensional space, denoted T 1 ∈R k ×k The method comprises the steps of carrying out a first treatment on the surface of the Second coordinate transformation of the multiple fault system 3>Obtaining a multi-fault system 4, wherein a state space model of the multi-fault system 4 is expressed as an expression (6), and the expression (6) is as follows:
wherein,the state variable of the multi-fault system 4 is denoted fourth state variable +.> Belongs to k-dimensional vector space and is marked as +.> For the fourth state variable->The derivative of time t, denoted fourth derivative +. >
For the fourth state variable->Fourth state variable +.>Is>Divided into four blocks, the upper left matrix block is marked as the first upper left matrix +.>The upper right matrix block is marked as the first upper right matrix +.>The lower left matrix block is marked as the first lower left matrix +.>The lower right matrix block is marked as the first lower right matrix +.>I.e. < -> For the fourth coefficient matrix of input u (t), the fourth coefficient matrix of input u (t) is +.>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a second upper partitioning +.>The lower partition is marked as the second lower partition +.>I.e. < -> For a second output z f A third coefficient matrix of (t) outputting a second output z f Third coefficient matrix of (t)>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a third upper partitioning +.>The lower partition is marked as a third lower partition +.>I.e. < -> For the third coefficient matrix of the fault vector d (t), the third coefficient matrix of the fault vector d (t) is +.>Performing upper and lower partitioning, wherein the upper partitioning matrix is marked as a fourth upper partitioning +.>The lower block matrix is marked as a fourth lower block +.>I.e. < -> For the fourth state variable->Output coefficient matrix of (2) for the fourth state variable +.>Output coefficient matrix +.>Performing left and right block division, wherein the left block matrix is marked as a fifth left block +.>The right block matrix is marked as fifth right block +.>
Step 3.3, performing a third coordinate transformation
Let the third coordinate transformation matrix be T 2 ，Wherein L is a matrix to be designed, and is marked as a third free matrix L, and the third free matrix L belongs to (k-1) x 1-dimensional space and is marked as L epsilon R (k-1)×1 ；
Third coordinate transformation of multiple fault system 4Obtaining a multi-fault system 5, wherein a state space model of the multi-fault system 5 is expressed as an expression (7), and the expression (7) is as follows:
wherein,the state variable of the multi-fault system 5 is denoted as fifth state variable +.> For the first component of the fifth state variable, +.>For the fifth state variable second component, +.>Is->Derivative with respect to time t;For the fifth state variable->Is to add a fifth state variable to the coefficient matrix of (2)>The coefficient matrix of (2) is divided into four blocks, the upper left matrix block is marked as the sixth upper left block +.>The upper right matrix block is marked as a sixth upper right partition block +.>The lower left matrix block is marked as a sixth lower left block +.>The lower right matrix block is marked as a sixth lower right partition block +.>
I.e. For a third coordinate transformation matrix T 2 An inverse matrix of (a);For the fifth coefficient matrix of input u (t), dividing the fifth coefficient matrix of input u (t) into two blocks, wherein the upper matrix block is marked as a seventh upper block->The lower partition is denoted as seventh lower partition +.>I.e. For a second output z f A fourth coefficient matrix of (t) outputting a second output z f The fourth coefficient matrix of (t) is divided into two blocks, the upper matrix block is marked as the eighth upper block +. >The lower matrix block is denoted as eighth lower block +.>I.e. For this reasonThe fourth coefficient matrix of the fault vector d (t) is divided into two blocks, and the upper block is marked as a ninth upper block +.>The lower block is marked as a ninth lower block +.>I.e. For the fifth state variable->Output coefficient matrix of (2) for a fifth state variableOutput coefficient matrix +.>The left and right blocks are divided, wherein the left block is marked as a tenth left block 0, and the right block is marked as a tenth right blockI.e. < -> For the tenth right block->An inverse matrix of (a);
step 4, observer design is carried out on the multi-fault system 5
Step 4.1, fault observer design
Definition of the definitionFor the fifth state variable->Is>First component of the fifth state variable +.>Is>Second component for the fifth state variable +.>Is to let observation error +.>Observation error->For the fifth state variable->Designing a sliding mode observer to obtain a dynamic equation of the observer, and recording as an expression (8), wherein the expression (8) is as follows:
wherein,first component observations for a fifth state variable +.>Derivative of time t>Second component observation for the fifth state variable +.>Derivative of time t; v 1 First component of the fifth state variable +.>V of the sliding mode item 1 ＝(v 11 ，...，v 1(k-1) ，v 1i ＝sgn(e 1i )，v 2 Second component for the fifth state variable +. >V of the sliding mode item 2 ＝sgn(e 2 )，First component of the fifth state variable +.>Is a sliding mode gain matrix, ">Wherein (1)>Is a symmetrical positive definite matrix P 1 Inverse matrix of P 1 For the matrix to be designed, the matrix is marked as a fourth free matrix P 1 ，k 1 Is a first constant to be designed, k 1 ∈R，k 2 To observe error e 2 (t) sliding mode gain, k 2 Is the second to be designedConstant, k 2 ∈R，k 3 Second component for the fifth state variableThe sliding mode gain, k 3 Is the third to-be-designed constant, k 3 ∈R；
Step 4.2, observing error e (t)
Solving the expression (7) and the expression (8) to obtain an error dynamic equation of the designed observer is as follows:
wherein,to observe error e 1 (t) derivative with respect to time t, < >>To observe error e 2 (t) a derivative of time t;
step 5, online synchronous estimation is carried out
Step 5.1, estimating the fault
Failure of actuator f a The estimated value of (t) is recorded asFailure of sensor f s The estimated value of (t) is marked +.>Disturbance f of the outside d The estimated value of (t) is marked +.>The calculation formulas of the three estimated values are as follows:
wherein I is q For q-dimensional identity matrix, I d For d-dimensional identity matrix, I w Is a w-dimensional identity matrix;
step 5.2, estimating the state
Defining the estimated value of the state variable x (t) as x (1) (t)、x (1) The derivative of (t) isEstimating actuator failure valuesAnd external disturbance estimation +. >Carrying out expression (1) to obtain +.>Is calculated by the formula:
so far, the multi-fault estimation of the staggered parallel Boost PFC system containing the multi-faults is finished.
2. The method of claim 1, wherein x in step 2 is T (t) is the transpose, z, of the first state variable x (t) f T (t) is the second output z f Transpose of (t),Is->Is a transpose of (a).
3. The multiple of interleaved parallel Boost PFC systems according to claim 1The fault estimation method is characterized in that the first constant k to be designed 1 A second constant k to be designed 2 A third constant k to be designed 3 Respectively satisfies the following formulas:
k 2 ＞0，
wherein,the maximum characteristic value is indicated to be the maximum characteristic value,λ(. Cndot.) represents the minimum eigenvalue.
4. The method for multiple fault estimation of an interleaved parallel Boost PFC system according to claim 1 wherein the third free matrix L, the fourth free matrix P 1 Respectively satisfies the following formulas:
wherein I is an identity matrix.
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