CN114825281B - A multi-fault estimation method for staggered parallel Boost PFC systems - Google Patents

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

A multi-fault estimation method for interleaved parallel Boost PFC systems

Technical Field

The invention relates to the field of fault diagnosis, and in particular to a multi-fault estimation method for an interleaved parallel Boost PFC system, wherein the multi-faults include actuator faults and sensor faults.

Background Art

With the development of power electronics technology, various power electronic devices are widely used in power, household appliances, mobile devices, transportation and other fields. Compared with linear power supplies, high-frequency switching power electronic converters have significant advantages of high efficiency, high power density and low cost, and have been widely used in many fields of power conversion. The power factor of traditional switching power supplies is low, which will generate a large amount of current harmonics and reactive power in the power grid, thereby polluting the power grid. The mainstream ways to improve the power factor are harmonic compensation and power factor correction. The harmonic compensation method is to compensate the reactive power and certain subharmonics of the equipment that has generated harmonic current, so that the total harmonics flowing into the power grid are reduced and the total reactive power of the system is reduced; the power factor correction method is to add a power factor correction converter to the front-stage power supply circuit of the electrical equipment, so that the electrical equipment does not inject harmonic current into the power grid. Relatively speaking, power factor correction technology (PFC) suppresses the generation of harmonics from the source.

In recent years, as people have higher and higher requirements for the safety and reliability performance indicators of the system, the control system has become increasingly complex and intelligent. But at the same time, because a large number of actuators, sensors and other devices are integrated, system components often fail due to various unexpected situations, which may reduce system performance and destroy the entire working system, or endanger personal and property safety and cause catastrophic accidents. Therefore, in order to improve the reliability and safety of the system, timely and effective fault diagnosis and fault-tolerant control technology are very important. Fault diagnosis technology includes three parts: fault detection, fault isolation and fault estimation. Compared with fault detection and fault isolation technology achieved by indirect residual methods, the research on fault estimation methods is more practical and more challenging, because it can directly obtain the amplitude of the fault, making people more intuitive in understanding the faults occurring in the system, and can serve for further fault-tolerant control.

Most control systems can be modeled by mathematical analysis. In actual control system applications, actuator failures and sensor failures may occur separately or simultaneously. In recent years, model-based methods for estimating actuator failures and synchronous sensor failures have attracted a large number of researchers to study them. Most of them use sliding mode observers or unknown input observers. In addition, switching power supplies dominate the power supply field due to their high power density and high efficiency. The main method to suppress the generation of harmonics in switching power supplies is to design high-performance rectifiers, which have the characteristics of sinusoidal input current, low harmonic content and high power factor, that is, they have power factor correction (PFC) function.

Reference 1, “A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions” (Xianghua Wang, Chee Pin Tan, Donghua Zhou, AUTOMATICA 79 (2017) 290-295) describes in detail the two main constraints of the currently proposed observer method: the minimum phase system condition and the observer matching condition. The authors proposed a new fault estimation method under relatively loose conditions, but the auxiliary output matrix designed by the authors also needs to satisfy the rank condition.

Reference 2, "Simultaneous Fault Estimation for Markovian Jump Systems WithGenerally Uncertain Transition Rates:A Reduced-Order Observer Approach" (Xiaohang Li, Weidong Zhang, Yueying Wang, IEEE TRANSACTIONS ON INDUSTRIALELECTRONICS 67 (2020) 7889-7897) (Simultaneous Fault Estimation for Markovian Jump Systems WithGenerally Uncertain Transition Rates: A Reduced-Order Observer Approach (Xiaohang Li, Weidong Zhang, Yueying Wang, IEEE Transactions on Industrial Electronics, Issue 67, 2020, Pages 7889-7897)) proposes a fault diagnosis method based on a reduced-order observer that needs to satisfy the system output dimension being greater than the number of system faults, the observer matching condition, and the minimum phase system condition.

Document 3, the fault estimation method designed in the patent document "Sliding Mode Fault-Tolerant Control Method for Multi-Agent Tracking System with Multiple Faults" with Chinese patent publication number CN109557818B needs to satisfy the conditions that (A, C) are observable and rank([B, F _a ]) = rank(B), that is, it needs to satisfy the minimum phase system condition and observer matching condition, and the observer designed by the author is a full-dimensional observer.

Reference 4, “A method for active fault-tolerant control of spacecraft with fault-disturbance decoupling” (Zong Qun et al., Journal of Harbin Institute of Technology, 2020, 52(09), 107-115 DOI: 10.11918/201909065), proposes that the design of the unknown input observer must meet the following assumptions: It is an observable, that is, it needs to satisfy the observer matching condition and the minimum phase system condition, and the observer designed by the author is a full-dimensional observer.

The adaptive sliding mode observer designed in the article "Asymptotic estimation of state and faults for linear systems with unknown perturbations" (Jianglin Lan, AUTOMATICA 118 (2020) June) must meet the assumptions of the minimum phase system condition, observer matching condition, and system dimension condition.

Reference 6, “A Novel Adaptive Observer-Based Fault Reconstruction and State Estimation Method for Markovian Jump Systems” (Hongyan Yang, Xianling Li, Zhaoxu Chen, Shen Yin, IEEE SYSTEMS JOURNAL, 15 (2021) 2305-2313) (A Novel Adaptive Observer-Based Fault Reconstruction and State Estimation Method for Markovian Jump Systems (Hongyan Yang, Xianling Li, Zhaoxu Chen, Shen Yin, IEEE Systems Magazine, Issue 15, 2021, Pages 2305-2313)) The adaptive sliding mode observer designed in the article must meet the assumptions of the minimum phase system condition, observer matching condition, and system dimension condition.

In summary, the PFC control system is crucial to the power supply. The existing fault diagnosis technology is subject to many constraints, and many constraints greatly limit the application scope of the currently proposed fault estimation method. Therefore, the research on the estimation technology of multi-fault systems containing actuator and sensor faults and solving the shortcomings of the existing technology are technical problems that need to be solved urgently in the entire research field.

Summary of the invention

In view of the shortcomings of the prior art mentioned above, the purpose of the present invention is to provide a multi-fault estimation method for an interleaved parallel Boost PFC system containing actuator faults and sensor faults. When actuator faults and sensor faults occur in the system, the invented fault estimation method can accurately estimate the form, amplitude, size and other information of the fault.

To achieve the above object, the present invention provides a multi-fault estimation method for an interleaved parallel Boost PFC system, wherein the multi-faults include actuator faults and sensor faults, and the estimation method comprises the following steps:

Step 1: Establish a state space model of a system with multiple faults

The interleaved parallel Boost PFC system is called the system;

The system with multiple faults is recorded as multi-fault system 1, and the state space model of the multi-fault system 1 is recorded as expression (1). Expression (1) is as follows:

Wherein, t is time; x(t) represents the state variable of the multi-fault system 1, denoted as the first state variable x(t), and x(t) belongs to the n-dimensional vector space, denoted as x(t)∈R ⁿ ; is the derivative of the first state variable x(t) with respect to time t, denoted as the first derivative u(t) represents the input of the multi-fault system 1, denoted as input u(t), u(t) belongs to the m-dimensional vector space, denoted as u(t)∈R ^m ; y(t) represents the output of the multi-fault system 1, denoted as the first output y(t), y(t) belongs to the p-dimensional vector space, denoted as y(t)∈R ^p ; f _a (t) represents the q-dimensional actuator fault of the multi-fault system 1, denoted as actuator fault f _a (t), f _a (t) belongs to the q-dimensional vector space, denoted as f _a (t)∈R ^q ; f _d (t) represents the 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, denoted as f _d (t)∈R ^d ; f _s (t) represents the w-dimensional sensor fault of the multi-fault system 1, denoted as sensor fault f _s (t), f _s (t) belongs to the w-dimensional vector space, 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 a row full rank matrix, D is the coefficient matrix of the actuator fault _fa (t), G is the coefficient matrix of the external disturbance _fd (t), F is the coefficient matrix of the sensor fault _fs (t), and F is a column full rank matrix;

The actuator fault _fa (t), sensor fault _fs (t) and external disturbance _fd (t) are bounded, and || _fa (t)|| _≤ηa , || _fs (t)|| _≤ηs , || _fd (t)|| _≤ηd , where || _fa (t)|| represents the 2-norm of the actuator fault _fa (t), || _fs (t)|| represents the 2-norm of the sensor fault _fs (t), || _fd (t)|| represents the 2-norm of the external disturbance _fd (t), _ηa is the bound of the actuator fault _fa (t), _ηs is the bound of the sensor fault _fs (t), _ηd is the bound of the external disturbance _fd (t), and _ηa , _ηs and _ηd are all known normal numbers;

Step 2: Expand multi-fault system 1 to obtain 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 _f (t) is the new output of the multi-fault system 1, denoted as the second output z _f (t), and z _f (t) belongs to the p-dimensional vector space, denoted as z _f (t)∈R ^p , is the derivative of the second output z _f (t) with respect to time t, A _f is the first coefficient matrix of the second output z _f (t), and is a positive definite matrix;

According to the state space model of the multi-fault system 1 obtained in step 1, the second output z _f (t) is expanded into a new state variable, that is, a new state variable is defined The expanded system is recorded as multi-fault system 2, and the state space model of multi-fault system 2 is recorded as expression (3). Expression (3) is as follows:

in, Represents the state variable of multi-fault system 2, denoted as the second state variable Belongs to n+p dimensional vector space, denoted as is the second state variable The derivative with respect to time t is recorded as the second derivative d(t) represents the fault vector of multi-fault system 2, denoted as fault vector d(t), is the second state variable The coefficient matrix of is the second coefficient matrix of the input u(t), is the first coefficient matrix of the fault vector d(t), is the second state variable The output coefficient matrix of Where I _p represents the p-dimensional identity matrix;

Step 3: coordinate transformation of multi-fault system 2

Step 3.1, perform the first coordinate transformation

Let the first coordinate transformation matrix include two matrices to be designed, which are respectively denoted as the first free matrix Φ and the second free matrix R. The first free matrix Φ belongs to the k×(n+p)-dimensional space, denoted as Φ∈R ^k×(n+p) , where k<(n+p), and the second free matrix R belongs to the 1×p-dimensional space, denoted as R∈R ^1×p ;

The first free matrix Φ and the second free matrix R satisfy expression (4), which is as follows:

Make the first coordinate transformation and The multi-fault system 2 is transformed into the multi-fault system 3, and the state space model of the multi-fault system 3 is recorded as expression (5). Expression (5) is as follows:

in, Represents the state variable of multi-fault system 3, denoted as the third state variable Belongs to the k-dimensional vector space, denoted as is the third state variable The derivative with respect to time t is recorded as the third derivative represents the output of multi-fault system 3, recorded as the third output Belongs to the 1-dimensional vector space, denoted as is the third state variable The first state coefficient matrix of

is the third coefficient matrix of input u(t), is the second coefficient matrix of the second output z _f (t), is the second coefficient matrix of the fault vector d(t), is the third state variable The output coefficient matrix of

Step 3.2, perform the second coordinate transformation

Let the second coordinate transformation matrix be T ₁ , T ₁ belongs to k×k dimensional space, denoted as T ₁ ∈R ^k×k ; the second coordinate transformation of multi-fault system 3 is performed The multi-fault system 4 is obtained, and the state space model of the multi-fault system 4 is recorded as expression (6). Expression (6) is as follows:

in, is the state variable of multi-fault system 4, recorded as the fourth state variable Belongs to the k-dimensional vector space, denoted as The fourth state variable The derivative with respect to time t is recorded as the fourth derivative

The fourth state variable The first state coefficient matrix, the fourth state variable The first state coefficient matrix Divided into four blocks, the upper left matrix block is recorded as the first upper left matrix The upper right matrix block is recorded as the first upper right matrix The lower left matrix block is recorded as the first lower left matrix The lower right matrix block is recorded as the first lower right matrix Right now is the fourth coefficient matrix of input u(t), and the fourth coefficient matrix of input u(t) Divide the upper and lower blocks, and the upper block matrix is recorded as the second upper block The next block is recorded as the second next block Right now is the third coefficient matrix of the second output z _f (t), and the third coefficient matrix of the second output z _f (t) is Divide the upper and lower blocks, and the upper block matrix is recorded as the third upper block The next block is recorded as the third next block Right now is the third coefficient matrix of the fault vector d(t), and the third coefficient matrix of the fault vector d(t) is Divide the upper and lower blocks, and the upper block matrix is recorded as the fourth upper block The next block matrix is recorded as the fourth next block Right now The fourth state variable The output coefficient matrix of the fourth state variable The output coefficient matrix Perform left and right block division, and the left block matrix is recorded as the fifth left block The right block matrix is recorded as the fifth right block

Step 3.3, perform the third coordinate transformation

Let the third coordinate transformation matrix be T ₂ , Wherein, L is the matrix to be designed, denoted as the third free matrix L, and the third free matrix L belongs to the (k-1)×1 dimensional space, denoted as L∈R ^(k-1)×1 ;

Perform the third coordinate transformation on the multi-fault system 4 The multi-fault system 5 is obtained, and the state space model of the multi-fault system 5 is recorded as expression (7). Expression (7) is as follows:

in, is the state variable of multi-fault system 5, recorded as the fifth state variable is the first component of the fifth state variable, is the second component of the fifth state variable, for The derivative with respect to time t; The fifth state variable The coefficient matrix of the fifth state variable The coefficient matrix is divided into four blocks, and the upper left matrix block is recorded as the sixth upper left block The upper right matrix block is recorded as the sixth upper right block The lower left matrix block is recorded as the sixth lower left block The lower right matrix block is recorded as the sixth lower right sub-block Right now is the inverse matrix of the third coordinate transformation matrix T ₂ ; The fifth coefficient matrix of input u(t) is divided into two blocks, and the upper matrix block is recorded as the seventh upper block. The next block is recorded as the seventh next block Right now is the fourth coefficient matrix of the second output z _f (t), the fourth coefficient matrix of the second output z _f (t) is divided into two blocks, and the upper matrix block is recorded as the eighth upper block The lower matrix block is recorded as the eighth lower block Right now is the fourth coefficient matrix of the fault vector d(t), the fourth coefficient matrix of the fault vector d(t) is divided into two blocks, and the upper block is recorded as the ninth upper block The next sub-block is recorded as the ninth sub-block Right now The fifth state variable The output coefficient matrix of the fifth state variable The output coefficient matrix Divide the blocks into left and right blocks, the left block is recorded as the tenth left block 0, and the right block is recorded as the tenth right block Right now The tenth right block The inverse matrix of

Step 4: Design observer for multi-fault system 5

Step 4.1, Fault Observer Design

definition The fifth state variable The observed value of is the first component of the fifth state variable The observed value of is the second component of the fifth state variable The observed value, let the observation error Observation Error For the fifth state variable The sliding mode observer is designed to obtain the dynamic equation of the observer, which is recorded as expression (8). Expression (8) is as follows:

in, is the observed value of the first component of the fifth state variable The derivative with respect to time t, is the observed value of the second component of the fifth state variable The derivative with respect to time t; v ₁ is the first component of the fifth state variable The sliding mode term, v ₁ = (v ₁₁ ,…,v _1(k-1) , v _1i = sgn(e _1i ), v ₂ is the second component of the fifth state variable The sliding mode term, v ₂ =sgn(e ₂ ), is the first component of the fifth state variable The sliding mode gain matrix, in, is the inverse matrix of the symmetric positive definite matrix P ₁ , P ₁ is the matrix to be designed, denoted as the fourth free matrix P ₁ , k ₁ is the first constant to be designed, k ₁ ∈ R, k ₂ is the sliding mode gain of the observation error e ₂ (t), k ₂ is the second constant to be designed, k ₂ ∈ R, k ₃ is the second component of the fifth state variable The sliding mode gain, k ₃ is the third constant to be designed, k ₃ ∈R;

Step 4.2, observation error e(t)

Solving expressions (7) and (8) yields the error dynamic equation of the designed observer, as follows:

in, is the derivative of the observation error e ₁ (t) with respect to time t, is the derivative of the observation error e ₂ (t) with respect to time t;

Step 5: Perform online synchronization estimation

Step 5.1: Estimate the fault

The estimated value of the actuator fault _fa (t) is denoted as The estimated value of the sensor fault _fs (t) is denoted as The estimated value of the external disturbance f _d (t) is denoted as The calculation formulas for the three estimated values are as follows:

Among them, _Iq is the q-dimensional identity matrix, _Id is the d-dimensional identity matrix, and _Iw is the w-dimensional identity matrix.

Step 5.2, estimate the state

Define the estimated value of the state variable x(t) as x ⁽¹⁾ (t) and the derivative of x ⁽¹⁾ (t) as The actuator fault estimate and external disturbance estimates Substituting into expression (1), we get The calculation formula is:

At this point, the multi-fault estimation of the interleaved parallel Boost PFC system with multiple faults is completed.

Preferably, x ^T (t) in step 2 is the transposition of the first state variable x(t), z _f ^T (t) is the transposition of the second output z _f (t), for The transpose of .

Preferably, the first constant to be designed k ₁ , the second constant to be designed k ₂ , and the third constant to be designed k ₃ respectively satisfy the following formulas:

k ₂ > 0,

in, represents the maximum eigenvalue, and λ (·) represents the minimum eigenvalue.

Preferably, the third free matrix L and the fourth free matrix _P1 satisfy the following formulas respectively:

Where I is the identity matrix.

Compared with the prior art, the beneficial effects of the present invention include:

1. Without being constrained by the minimum phase condition, observer matching condition and output dimension condition, a new fault estimation method is proposed and a sliding mode observer is designed. The designed sliding mode observer can ensure that the error system converges to zero in an exponential form. Compared with the existing fault estimation methods, it greatly broadens the scope of application;

2. Using the dimension reduction observer technology, the estimated variable dimension is n+q+w+d, and the actual required observer dimension is k, k<n+p, where p<q+w+d, which reduces the observer dimension and the design complexity of the observer;

3. It can accurately and synchronously estimate the state variable information of the multi-fault system and the actuator fault, sensor fault and external disturbance form and size information online.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a multi-fault synchronous estimation method according to the present invention;

FIG2 is a flow chart of a multi-fault synchronous estimation method according to the present invention;

FIG3 shows the actuator fault _fa (t) and its estimated value in the present invention. Simulation diagram of

Figure 4 shows the sensor fault _fs (t) and its estimated value in the present invention. Simulation diagram of

FIG5 is a simulation diagram of the system state variable x ₁ (t) and its estimated value x ₁ ⁽¹⁾ (t) in the present invention;

FIG6 is a simulation diagram of the system state variable x ₂ (t) and its estimated value x ₂ ⁽¹⁾ (t) in the present invention;

FIG7 is a simulation diagram of the system state variable x ₃ (t) and its estimated value x ₃ ⁽¹⁾ (t) in the present invention;

Figure 8 shows the actuator fault f _d (t) and its estimated value in the present invention. Simulation diagram of

FIG. 9 is a circuit topology diagram in the simulation of the present invention.

DETAILED DESCRIPTION

The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings.

Embodiment 1, the present invention provides a multi-fault estimation method for an interleaved parallel Boost PFC system, wherein the multi-faults include actuator faults and sensor faults. FIG1 is a schematic diagram of the multi-fault estimation method of the present invention, and FIG2 is a flow chart of the multi-fault estimation method of the present invention. As can be seen from FIG1 and FIG2, the multi-fault estimation method includes the following steps:

Step 1: Establish a state space model of a system with multiple faults

The interleaved parallel Boost PFC system is called a system;

The system with multiple faults is recorded as multi-fault system 1, and the state space model of the multi-fault system 1 is recorded as expression (1). Expression (1) is as follows:

Wherein, t is time; x(t) represents the state variable of the multi-fault system 1, denoted as the first state variable x(t), and x(t) belongs to the n-dimensional vector space, denoted as x(t)∈R ⁿ ; is the derivative of the first state variable x(t) with respect to time t, denoted as the first derivative u(t) represents the input of the multi-fault system 1, denoted as input u(t), u(t) belongs to the m-dimensional vector space, denoted as u(t)∈R ^m ; y(t) represents the output of the multi-fault system 1, denoted as the first output y(t), y(t) belongs to the p-dimensional vector space, denoted as y(t)∈R ^p ; f _a (t) represents the q-dimensional actuator fault of the multi-fault system 1, denoted as actuator fault f _a (t), f _a (t) belongs to the q-dimensional vector space, denoted as f _a (t)∈R ^q ; f _d (t) represents the 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, denoted as f _d (t)∈R ^d ; f _s (t) represents the w-dimensional sensor fault of the multi-fault system 1, denoted as sensor fault f _s (t), f _s (t) belongs to the w-dimensional vector space, 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 a row full rank matrix, D is the coefficient matrix of the actuator fault _fa (t), G is the coefficient matrix of the external disturbance _fd (t), F is the coefficient matrix of the sensor fault _fs (t), and F is a column full rank matrix;

The actuator fault _fa (t), sensor fault _fs (t) and external disturbance _fd (t) are bounded, and || _fa (t)|| _≤ηa , || _fs (t)|| _≤ηs , || _fd (t)|| _≤ηd , where || _fa (t)|| represents the 2-norm of the actuator fault _fa (t), || _fs (t)|| represents the 2-norm of the sensor fault _fs (t), || _fd (t)|| represents the 2-norm of the external disturbance _fd (t), _ηa is the bound of the actuator fault _fa (t), _ηs is the bound of the sensor fault _fs (t), _ηd is the bound of the external disturbance _fd (t), and _ηa , _ηs and _ηd are all known normal numbers;

Step 2: Expand multi-fault system 1 to obtain 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 _f (t) is the new output of the multi-fault system 1, denoted as the second output z _f (t), and z _f (t) belongs to the p-dimensional vector space, denoted as z _f (t)∈R ^p , is the derivative of the second output z _f (t) with respect to time t, A _f is the first coefficient matrix of the second output z _f (t), and is a positive definite matrix;

According to the state space model of the multi-fault system 1 obtained in step 1, the second output z _f (t) is expanded into a new state variable, that is, a new state variable is defined The expanded system is recorded as multi-fault system 2, and the state space model of multi-fault system 2 is recorded as expression (3). Expression (3) is as follows:

in, Represents the state variable of multi-fault system 2, denoted as the second state variable Belongs to n+p dimensional vector space, denoted as is the second state variable The derivative with respect to time t is recorded as the second derivative d(t) represents the fault vector of multi-fault system 2, denoted as fault vector d(t), is the second state variable The coefficient matrix of is the second coefficient matrix of the input u(t), is the first coefficient matrix of the fault vector d(t), is the second state variable The output coefficient matrix of Where I _p represents the p-dimensional identity matrix;

Step 3: coordinate transformation of multi-fault system 2

Step 3.1, perform the first coordinate transformation

Let the first coordinate transformation matrix include two matrices to be designed, which are respectively denoted as the first free matrix Φ and the second free matrix R. The first free matrix Φ belongs to the k×(n+p)-dimensional space, denoted as Φ∈R ^k×(n+p) , where k<(n+p), and the second free matrix R belongs to the 1×p-dimensional space, denoted as R∈R ^1×p ;

The first free matrix Φ and the second free matrix R satisfy expression (4), which is as follows:

Make the first coordinate transformation and The multi-fault system 2 is transformed into the multi-fault system 3, and the state space model of the multi-fault system 3 is recorded as expression (5). Expression (5) is as follows:

in, Represents the state variable of multi-fault system 3, denoted as the third state variable Belongs to the k-dimensional vector space, denoted as is the third state variable The derivative with respect to time t is recorded as the third derivative represents the output of multi-fault system 3, recorded as the third output Belongs to the 1-dimensional vector space, denoted as is the third state variable The first state coefficient matrix of is the third coefficient matrix of input u(t), is the second coefficient matrix of the second output z _f (t), is the second coefficient matrix of the fault vector d(t), is the third state variable The output coefficient matrix of

Step 3.2, perform the second coordinate transformation

Let the second coordinate transformation matrix be T ₁ , T ₁ belongs to k×k dimensional space, denoted as T ₁ ∈R ^k×k ; the second coordinate transformation of multi-fault system 3 is performed The multi-fault system 4 is obtained, and the state space model of the multi-fault system 4 is recorded as expression (6). Expression (6) is as follows:

in, is the state variable of multi-fault system 4, recorded as the fourth state variable Belongs to the k-dimensional vector space, denoted as The fourth state variable The derivative with respect to time t is recorded as the fourth derivative

The fourth state variable The first state coefficient matrix, the fourth state variable The first state coefficient matrix Divided into four blocks, the upper left matrix block is recorded as the first upper left matrix The upper right matrix block is recorded as the first upper right matrix The lower left matrix block is recorded as the first lower left matrix The lower right matrix block is recorded as the first lower right matrix Right now is the fourth coefficient matrix of input u(t), and the fourth coefficient matrix of input u(t) Divide the upper and lower blocks, and the upper block matrix is recorded as the second upper block The next block is recorded as the second next block Right now is the third coefficient matrix of the second output z _f (t), and the third coefficient matrix of the second output z _f (t) is Divide the upper and lower blocks, and the upper block matrix is recorded as the third upper block The next block is recorded as the third next block Right now is the third coefficient matrix of the fault vector d(t), and the third coefficient matrix of the fault vector d(t) is Divide the upper and lower blocks, and the upper block matrix is recorded as the fourth upper block The next block matrix is recorded as the fourth next block Right now The fourth state variable The output coefficient matrix of the fourth state variable The output coefficient matrix Perform left and right block division, and the left block matrix is recorded as the fifth left block The right block matrix is recorded as the fifth right block

Step 3.3, perform the third coordinate transformation

Let the third coordinate transformation matrix be T ₂ , Wherein, L is the matrix to be designed, denoted as the third free matrix L, and the third free matrix L belongs to the (k-1)×1 dimensional space, denoted as L∈R ^(k-1)×1 ;

Perform the third coordinate transformation on the multi-fault system 4 The multi-fault system 5 is obtained, and the state space model of the multi-fault system 5 is recorded as expression (7). Expression (7) is as follows:

in, is the state variable of multi-fault system 5, recorded as the fifth state variable is the first component of the fifth state variable, is the second component of the fifth state variable, for The derivative with respect to time t; The fifth state variable The coefficient matrix of the fifth state variable The coefficient matrix is divided into four blocks, and the upper left matrix block is recorded as the sixth upper left block The upper right matrix block is recorded as the sixth upper right block The lower left matrix block is recorded as the sixth lower left block The lower right matrix block is recorded as the sixth lower right sub-block Right now is the inverse matrix of the third coordinate transformation matrix T ₂ ; is the fifth coefficient matrix of the input u(t), the fifth coefficient matrix of the input u(t) is divided into two blocks, and the upper matrix block is recorded as the seventh upper block The next block is recorded as the seventh next block Right now is the fourth coefficient matrix of the second output z _f (t), the fourth coefficient matrix of the second output z _f (t) is divided into two blocks, and the upper matrix block is recorded as the eighth upper block The lower matrix block is recorded as the eighth lower block Right now is the fourth coefficient matrix of the fault vector d(t), the fourth coefficient matrix of the fault vector d(t) is divided into two blocks, and the upper block is recorded as the ninth upper block The next sub-block is recorded as the ninth sub-block Right now The fifth state variable The output coefficient matrix of the fifth state variable The output coefficient matrix Divide the blocks into left and right blocks, the left block is recorded as the tenth left block 0, and the right block is recorded as the tenth right block Right now The tenth right block The inverse matrix of

Step 4: Design observer for multi-fault system 5

Step 4.1, Fault Observer Design

definition The fifth state variable The observed value of is the first component of the fifth state variable The observed value of is the second component of the fifth state variable The observed value, let the observation error Observation Error For the fifth state variable The sliding mode observer is designed to obtain the dynamic equation of the observer, which is recorded as expression (8). Expression (8) is as follows:

in, is the observed value of the first component of the fifth state variable The derivative with respect to time t, is the observed value of the second component of the fifth state variable The derivative with respect to time t; v ₁ is the first component of the fifth state variable The sliding mode term, v ₁ = (v ₁₁ ,…,v _1(k-1) , v _1i = sgn(e _1i ), v ₂ is the second component of the fifth state variable The sliding mode term, v ₂ =sgn(e ₂ ), is the first component of the fifth state variable The sliding mode gain matrix, in, is the inverse matrix of the symmetric positive definite matrix P ₁ , P ₁ is the matrix to be designed, denoted as the fourth free matrix P ₁ , k ₁ is the first constant to be designed, k ₁ ∈ R, k ₂ is the sliding mode gain of the observation error e ₂ t, k ₂ is the second constant to be designed, k ₂ ∈ R, k ₃ is the second component of the fifth state variable The sliding mode gain, k ₃ is the third constant to be designed, k ₃ ∈R;

Step 4.2, observation error e(t)

Solving expressions (7) and (8) yields the error dynamic equation of the designed observer, as follows:

in, is the derivative of the observation error e ₁ (t) with respect to time t, is the derivative of the observation error e ₂ (t) with respect to time t;

Step 5: Perform online synchronization estimation

Step 5.1: Estimate the fault

The estimated value of the actuator fault _fa (t) is denoted as The estimated value of the sensor fault _fs (t) is denoted as The estimated value of the external disturbance f _d (t) is denoted as The calculation formulas for the three estimated values are as follows:

Among them, _Iq is the q-dimensional identity matrix, _Id is the d-dimensional identity matrix, and _Iw is the w-dimensional identity matrix.

Step 5.2, estimate the state

Define the estimated value of the state variable x(t) as x ⁽¹⁾ (t) and the derivative of x ⁽¹⁾ (t) as The actuator fault estimate and external disturbance estimates Substituting into expression (1), we get The calculation formula is:

At this point, the multi-fault estimation of the interleaved parallel Boost PFC system with multiple faults is completed.

In the present embodiment 1, x ^T (t) in step 2 is the transposition of the first state variable x(t), z _f ^T (t) is the transposition of the second output z _f (t), for The transpose of .

In the present embodiment 1, the first constant to be designed k ₁ , the second constant to be designed k ₂ , and the third constant to be designed k ₃ respectively satisfy the following formulas:

k ₂ > 0,

in, represents the maximum eigenvalue, and λ (·) represents the minimum eigenvalue.

In this embodiment 1, the third free matrix L and the fourth free matrix _P1 respectively satisfy the following equations:

Where I is the identity matrix.

Example 2, an interleaved parallel Boost PFC circuit is implemented, and its topology is shown in FIG9. As can be seen from FIG9, the interleaved parallel Boost The PFC circuit includes an AC power supply, a full-wave rectifier circuit, a Boost circuit, an output filter capacitor and a load resistor; at the same time, the PFC system also contains actuator faults and sensor faults; an industrial survey report points out that power semiconductor switching devices are one of the devices most prone to failure in power electronic converters; the switch tube failures of the PFC system are mainly divided into short-circuit faults and open-circuit faults. The short-circuit fault of the switch tube is protected by a hardware protection circuit. When a short-circuit fault occurs, the hardware protection circuit will be quickly cut off, and eventually the short-circuit fault of the switch tube will be converted into an open-circuit fault, so only the open-circuit fault of the PFC system is considered for fault estimation; in addition to the power switch tube failure, sensor failure is also one of the common faults of the PFC system; the sensor provides real-time current and voltage information for the closed-loop controller, and the accuracy of the feedback information output by the sensor has an important impact on the control performance of the system; the DC voltage sensor failure is mainly divided into short-circuit fault, open-circuit fault, time-varying fault and intermittent fault. Since the output of the analog-to-digital converter has maximum and minimum value limits, short-circuit faults and open-circuit faults can also be regarded as special cases of intermittent faults, so only intermittent faults and time-varying faults of the DC voltage sensor are considered; the present invention studies KS _1. The switch tube is open circuit fault, and the output voltage sensor V _o is intermittent fault;

The AC voltage of the AC power supply is V _ac ;

The full-wave rectifier circuit includes four identical rectifier diodes, which are respectively denoted as rectifier diode BD ₁ , rectifier diode BD ₂ , rectifier diode BD ₃ and rectifier diode BD _4. Rectifier diode BD ₁ is connected in series with rectifier diode BD _{3, and the cathode of rectifier diode BD 3} is connected to the anode of rectifier diode BD _1. Rectifier diode BD ₂ is connected in series with rectifier diode BD ₄ , and the cathode of rectifier diode BD ₄ is connected to the anode of rectifier diode BD _2. One end of the AC power supply is connected to the common connection point of rectifier diode BD ₁ and rectifier diode BD ₃ , and the other end of the AC power supply is connected to the common connection point of rectifier diode BD ₂ and rectifier diode _{BD 4} .

The Boost circuit includes two identical inductors, two identical boost diodes and two identical switch tubes, the two identical inductors are respectively recorded as PFC inductor _L1 and PFC inductor _L2 , the two identical boost diodes are respectively recorded as boost diode _KD1 and boost diode _KD2 , the two passing switch tubes are respectively recorded as switch tube _KS1 and switch tube _KS2 , the PFC inductor _L1 and boost diode _KD1 are connected in series and then connected in parallel with the circuit in which the PFC inductor _L2 and boost diode _D2 are connected in series, the switch tube _KS1 is connected between the common connection point of the PFC inductor _L1 and the boost diode _D1 and the ground, and the switch tube _KS2 is connected between the common connection point of the PFC inductor _L2 and the boost diode _KD2 and the ground;

The output filter capacitor is recorded as capacitor CL ₀ , and capacitor CL ₀ is connected between the common connection point of boost diode KD ₁ and boost diode KD ₂ and the ground;

The load resistance is recorded as resistance RL ₀ , and the resistance RL ₀ is connected in parallel across the capacitor CL ₀ ;

The specific parameters of the staggered parallel Boost PFC circuit are as follows: the voltage value of the AC power supply is 220V, the inductance of the PFC inductor _L1 is 300uH, the inductance of the PFC inductor _L2 is 300uH, the capacitance value of the capacitor _CL0 is 1000uF, the resistance value of the resistor _RL0 is 40Ω, and the conduction voltage drop of _KD1 and _KD2 is not considered.

The first state variable x(t) belongs to the three-dimensional vector space, that is, n=3, and the output y(t) belongs to the one-dimensional vector space, that is, p=1. The PFC control system contains actuator faults and sensor faults, and the total number of faults is q+w=2.

In this embodiment, the steps are the same as those in Embodiment 1, and the matrices involved in the estimation process are 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), eta _a =(1.5), k ₃ =(150), eta _s =(2.5), eta _d =(0.5).

In order to verify the technical effect of the present invention, simulation was also carried out.

FIG3 shows the actuator fault set in the simulation experiment and the actuator fault estimated by the method of the present invention. The solid line in the figure is the actuator fault set, and its mathematical expression is:

in, and

The dotted line in the figure is the estimation result obtained by Matlab simulation. It can be seen that there is no actuator failure in the 0-2s. The actuator failure just occurred at 2s, and the estimation result has a short-term small error, and then the estimation error is close to 0. The sensor failure just occurred at 4s, and the estimation result has a short-term error, and then the estimation error is close to 0.

FIG4 shows the sensor failure set in the simulation experiment and the sensor failure estimated by the method of the present invention. The solid line in the figure is the set sensor failure, and its mathematical expression is:

in, And h(t)≤1.

The dotted line in the figure is the estimated result obtained by Matlab simulation. It can be seen that there is no sensor failure in the 0-4s. The sensor failure just occurred at 4s, and the estimated result has a short-term slight error, and then the estimated error is close to 0.

FIG5 is a simulation diagram of the system state variable _x1 (t) and its estimated value _x1 ⁽¹⁾ (t) in the present invention, FIG6 is a simulation diagram of the system state variable _x2 (t) and its estimated value _x2 ⁽¹⁾ (t) in the present invention, and FIG7 is a simulation diagram of the system state variable _x3 (t) and its estimated value _x3 ⁽¹⁾ (t) in the present invention. That is, FIG5-7 are simulation diagrams of the three state variables of the PFC system and their estimated results after the actuator failure and sensor failure set in the specific embodiment. It can be seen from FIG5-7 that after the actuator failure occurs in the 2nd second, the estimated result has a small error, and the sensor failure just occurs in the 4th second, the estimated result has a short-term error, and then the estimated error is close to 0.

FIG8 shows the external disturbance set in the simulation experiment in a specific example and the external disturbance estimated by the method of the present invention. The solid line in the figure is the external disturbance set, and its mathematical expression is:

f _d (t) = 0.05 sin t

The dotted line in the figure is the estimation result obtained by Matlab simulation. It can be seen that at 0s, when the external disturbance just occurred, the estimation result had a short-term error, and then the estimation error was close to 0. At 4s, when the sensor failure just occurred, the estimation result had a short-term error, and then the estimation error was close to 0.

In addition, the three main constraints summarized in document 1: minimum phase system condition, observer matching condition and output dimension condition. The PFC model established in the example of the present invention is verified according to the constraints provided in the document, and the verification is as follows:

1. Since n = 3, take the Laplace operator s = 0, then

because Therefore, this system does not satisfy the minimum phase condition.

2.

because The observer matching condition is not met.

3. The established interleaved parallel Boost PFC system contains actuator faults and sensor faults. The total number of faults is q+w=2. The output dimension of the system is p=1. Since q+w>p, the system dimension condition is not met.

It can be seen from this that the interleaved parallel Boost PFC system established in the present invention does not meet the minimum phase system conditions, observer matching conditions and output dimension conditions. The simulation results of Figures 3 to 8 verify that the present invention is capable of performing fault estimation on multiple faults of the interleaved parallel Boost PFC system without meeting the minimum phase system conditions, observer matching conditions and output dimension conditions, further verifying the beneficial effects of the present invention.

Claims (4)

1. A multi-fault estimation method for an interleaved parallel Boost PFC system, wherein the multi-faults include actuator faults and sensor faults, wherein the estimation method comprises the following steps: Step 1: Establish a state space model of a system with multiple faults The interleaved parallel Boost PFC system is called a system; The system with multiple faults is recorded as multi-fault system 1, and the state space model of the multi-fault system 1 is recorded as expression (1). Expression (1) is as follows: Wherein, t is time; x(t) represents the state variable of the multi-fault system 1, denoted as the first state variable x(t), and x(t) belongs to the n-dimensional vector space, denoted as x(t)∈R ⁿ ; is the derivative of the first state variable x(t) with respect to time t, denoted as the first derivative u(t) represents the input of the multi-fault system 1, denoted as input u(t), and u(t) belongs to the m-dimensional vector space, denoted as u(t)∈R ^m ; y(t) represents the output of the multi-fault system 1, denoted as the first output y(t), and y(t) belongs to the p-dimensional vector space, denoted as y(t)∈R ^p ; f _a (t) represents the q-dimensional actuator fault of the multi-fault system 1, denoted as actuator fault f _a (t), and f _d (t) belongs to the q-dimensional vector space, denoted as f _a (t)∈R ^q ; f _d (t) represents the d-dimensional external disturbance of the multi-fault system 1, denoted as external disturbance f _d (t), and f _d (t) belongs to the d-dimensional vector space, denoted as f _d (t)∈R ^d ; f _s (t) represents the w-dimensional sensor fault of the multi-fault system 1, denoted as sensor fault f _s (t), and f _s (t) belongs to the w-dimensional vector space, 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 a row full rank matrix, D is the coefficient matrix of the actuator fault _fa (t), G is the coefficient matrix of the external disturbance _fd (t), F is the coefficient matrix of the sensor fault _fs (t), and F is a column full rank matrix; The actuator fault _fa (t), sensor fault _fs (t) and external disturbance _fd (t) are bounded, and || _fa (t)|| _≤ηa , || _fs (t)||≤ηs, || _fd (t)|| _{≤ηd ,} where || _fa (t)|| represents the 2-norm of the actuator fault _fa (t), || _fs (t)|| represents the 2-norm of the sensor fault _fs (t), || _fd (t)|| represents the 2-norm of the external disturbance _fd (t), _ηa is the bound of the actuator fault _fa (t), _ηs is the bound of the sensor fault _fs (t), _ηd is the bound of the external disturbance _fd (t), and _ηa , _ηs and _ηd are all known normal numbers; Step 2: Expand multi-fault system 1 to obtain 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 _f (t) is the new output of the multi-fault system 1, denoted as the second output z _f (t), and z _f (t) belongs to the p-dimensional vector space, denoted as z _f (t)∈R ^p , is the derivative of the second output z _f (t) with respect to time t, A _f is the first coefficient matrix of the second output z _f (t), and is a positive definite matrix; According to the state space model of the multi-fault system 1 obtained in step 1, the second output z _f (t) is expanded into a new state variable, that is, a new state variable is defined The expanded system is recorded as multi-fault system 2, and the state space model of multi-fault system 2 is recorded as expression (3). Expression (3) is as follows: in, Represents the state variable of multi-fault system 2, denoted as the second state variable Belongs to n+p dimensional vector space, denoted as is the second state variable The derivative with respect to time t is recorded as the second derivative d(t) represents the fault vector of multi-fault system 2, denoted as fault vector d(t), is the second state variable The coefficient matrix of is the second coefficient matrix of the input u(t), is the first coefficient matrix of the fault vector d(t), is the second state variable The output coefficient matrix of Where I _p represents the p-dimensional identity matrix; Step 3: coordinate transformation of multi-fault system 2 Step 3.1, perform the first coordinate transformation Let the first coordinate transformation matrix include two matrices to be designed, which are respectively denoted as the first free matrix Φ and the second free matrix R. The first free matrix Φ belongs to the k×(n+p)-dimensional space, denoted as Φ∈R ^k×(n+p) , where k＜(n+p), and the second free matrix R belongs to the 1×p-dimensional space, denoted as R∈R ^1×p ; The first free matrix Φ and the second free matrix R satisfy expression (4), which is as follows: Make the first coordinate transformation and The multi-fault system 2 is transformed into the multi-fault system 3, and the state space model of the multi-fault system 3 is recorded as expression (5). Expression (5) is as follows: in, Represents the state variable of multi-fault system 3, denoted as the third state variable Belongs to the k-dimensional vector space, denoted as is the third state variable The derivative with respect to time t is recorded as the third derivative represents the output of multi-fault system 3, recorded as the third output Belongs to the 1-dimensional vector space, denoted as is the third state variable The first state coefficient matrix of is the third coefficient matrix of input u(t), is the second coefficient matrix of the second output z _f (t), is the second coefficient matrix of the fault vector d(t), is the third state variable The output coefficient matrix of Step 3.2, perform the second coordinate transformation Let the second coordinate transformation matrix be T ₁ , T ₁ belongs to k×k dimensional space, denoted as T ₁ ∈R ^{k ×k} ; the second coordinate transformation of multi-fault system 3 is performed The multi-fault system 4 is obtained, and the state space model of the multi-fault system 4 is recorded as expression (6). Expression (6) is as follows: in, is the state variable of multi-fault system 4, recorded as the fourth state variable Belongs to the k-dimensional vector space, denoted as The fourth state variable The derivative with respect to time t is recorded as the fourth derivative The fourth state variable The first state coefficient matrix, the fourth state variable The first state coefficient matrix Divided into four blocks, the upper left matrix block is recorded as the first upper left matrix The upper right matrix block is recorded as the first upper right matrix The lower left matrix block is recorded as the first lower left matrix The lower right matrix block is recorded as the first lower right matrix Right now is the fourth coefficient matrix of input u(t), and the fourth coefficient matrix of input u(t) Divide the upper and lower blocks, and the upper block matrix is recorded as the second upper block The next block is recorded as the second next block Right now is the third coefficient matrix of the second output z _f (t), and the third coefficient matrix of the second output z _f (t) is Divide the upper and lower blocks, and the upper block matrix is recorded as the third upper block The next block is recorded as the third next block Right now is the third coefficient matrix of the fault vector d(t), and the third coefficient matrix of the fault vector d(t) is Divide the upper and lower blocks, and the upper block matrix is recorded as the fourth upper block The next block matrix is recorded as the fourth next block Right now The fourth state variable The output coefficient matrix of the fourth state variable The output coefficient matrix Perform left and right block division, and the left block matrix is recorded as the fifth left block The right block matrix is recorded as the fifth right block Step 3.3, perform the third coordinate transformation Let the third coordinate transformation matrix be T ₂ , Wherein, L is the matrix to be designed, denoted as the third free matrix L, and the third free matrix L belongs to the (k-1)×1 dimensional space, denoted as L∈R ^(k-1)×1 ; Perform the third coordinate transformation on the multi-fault system 4 The multi-fault system 5 is obtained, and the state space model of the multi-fault system 5 is recorded as expression (7). Expression (7) is as follows: in, is the state variable of multi-fault system 5, recorded as the fifth state variable is the first component of the fifth state variable, is the second component of the fifth state variable, for The derivative with respect to time t; The fifth state variable The coefficient matrix of the fifth state variable The coefficient matrix is divided into four blocks, and the upper left matrix block is recorded as the sixth upper left block The upper right matrix block is recorded as the sixth upper right block The lower left matrix block is recorded as the sixth lower left block The lower right matrix block is recorded as the sixth lower right sub-block Right now is the inverse matrix of the third coordinate transformation matrix T ₂ ; is the fifth coefficient matrix of the input u(t), the fifth coefficient matrix of the input u(t) is divided into two blocks, and the upper matrix block is recorded as the seventh upper block The next block is recorded as the seventh next block Right now is the fourth coefficient matrix of the second output z _f (t), the fourth coefficient matrix of the second output z _f (t) is divided into two blocks, and the upper matrix block is recorded as the eighth upper block The lower matrix block is recorded as the eighth lower block Right now is the fourth coefficient matrix of the fault vector d(t), the fourth coefficient matrix of the fault vector d(t) is divided into two blocks, and the upper block is recorded as the ninth upper block The next sub-block is recorded as the ninth sub-block Right now The fifth state variable The output coefficient matrix of the fifth state variable The output coefficient matrix Divide the blocks into left and right blocks, the left block is recorded as the tenth left block 0, and the right block is recorded as the tenth right block Right now The tenth right block The inverse matrix of Step 4: Design observer for multi-fault system 5 Step 4.1, Fault Observer Design definition The fifth state variable The observed value of is the first component of the fifth state variable The observed value of is the second component of the fifth state variable The observed value, let the observation error Observation Error For the fifth state variable The sliding mode observer is designed to obtain the dynamic equation of the observer, which is recorded as expression (8). Expression (8) is as follows: in, is the observed value of the first component of the fifth state variable The derivative with respect to time t, is the observed value of the second component of the fifth state variable The derivative at time t; v ₁ is the first component of the fifth state variable The sliding mode term, v ₁ =(v ₁₁ , ..., v _1(k-1) , v _1i =sgn(e _1i ), v ₂ is the second component of the fifth state variable The sliding mode term, v ₂ =sgn(e ₂ ), is the first component of the fifth state variable The sliding mode gain matrix, in, is the inverse matrix of the symmetric positive definite matrix P ₁ , P ₁ is the matrix to be designed, denoted as the fourth free matrix P ₁ , k ₁ is the first constant to be designed, k ₁ ∈ R, k ₂ is the sliding mode gain of the observation error e ₂ (t), k ₂ is the second constant to be designed, k ₂ ∈ R, k ₃ is the second component of the fifth state variable The sliding mode gain, k ₃ is the third constant to be designed, k ₃ ∈R; Step 4.2, observation error e(t) Solving expressions (7) and (8) yields the error dynamic equation of the designed observer, as follows: in, is the derivative of the observation error e ₁ (t) with respect to time t, is the derivative of the observation error e ₂ (t) with respect to time t; Step 5: Perform online synchronization estimation Step 5.1: Estimate the fault The estimated value of the actuator fault _fa (t) is denoted as The estimated value of the sensor fault _fs (t) is denoted as The estimated value of the external disturbance f _d (t) is denoted as The calculation formulas for the three estimated values are as follows: Among them, _Iq is the q-dimensional identity matrix, _Id is the d-dimensional identity matrix, and _Iw is the w-dimensional identity matrix; Step 5.2, estimate the state Define the estimated value of the state variable x(t) as x ⁽¹⁾ (t) and the derivative of x ⁽¹⁾ (t) as The actuator fault estimate and external disturbance estimates Substituting into expression (1), we get The calculation formula is: At this point, the multi-fault estimation of the interleaved parallel Boost PFC system with multiple faults is completed. 2. The multi-fault estimation method for an interleaved parallel Boost PFC system according to claim 1, wherein x ^T (t) in step 2 is the transpose of the first state variable x(t), z _f ^T (t) is the transpose of the second output z _f (t), for The transpose of . 3. The multi-fault estimation method of the staggered parallel Boost PFC system according to claim 1, characterized in that the first constant to be designed k ₁ , the second constant to be designed k ₂ , and the third constant to be designed k ₃ respectively satisfy the following formulas: k ₂ ＞0, in, represents the maximum eigenvalue, and λ (·) represents the minimum eigenvalue. 4. The multi-fault estimation method of the staggered parallel Boost PFC system according to claim 1, characterized in that the third free matrix L and the fourth free matrix _P1 respectively satisfy the following formulas: Where I is the identity matrix.