CN114825281A - Multi-fault estimation method for interleaved parallel Boost PFC (Power factor correction) system - Google Patents
Multi-fault estimation method for interleaved parallel Boost PFC (Power factor correction) system Download PDFInfo
- Publication number
- CN114825281A CN114825281A CN202210429921.4A CN202210429921A CN114825281A CN 114825281 A CN114825281 A CN 114825281A CN 202210429921 A CN202210429921 A CN 202210429921A CN 114825281 A CN114825281 A CN 114825281A
- Authority
- CN
- China
- Prior art keywords
- matrix
- fault
- state variable
- block
- denoted
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 52
- 238000012937 correction Methods 0.000 title description 7
- 238000013461 design Methods 0.000 claims abstract description 10
- 230000001360 synchronised effect Effects 0.000 claims abstract description 6
- 238000001914 filtration Methods 0.000 claims abstract description 4
- 239000011159 matrix material Substances 0.000 claims description 249
- 239000000126 substance Substances 0.000 claims description 26
- 230000009466 transformation Effects 0.000 claims description 21
- 238000005192 partition Methods 0.000 claims description 9
- 238000000638 solvent extraction Methods 0.000 claims description 9
- 238000004364 calculation method Methods 0.000 claims description 3
- 230000001131 transforming effect Effects 0.000 claims description 3
- 238000005516 engineering process Methods 0.000 abstract description 9
- 238000003745 diagnosis Methods 0.000 abstract description 6
- 230000009467 reduction Effects 0.000 abstract description 3
- 238000004088 simulation Methods 0.000 description 19
- 238000010586 diagram Methods 0.000 description 16
- 238000011160 research Methods 0.000 description 5
- 230000003044 adaptive effect Effects 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 2
- 230000000903 blocking effect Effects 0.000 description 2
- 239000003990 capacitor Substances 0.000 description 2
- 238000001514 detection method Methods 0.000 description 2
- 238000002955 isolation Methods 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 239000003795 chemical substances by application Substances 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 230000002401 inhibitory effect Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
- 230000007704 transition Effects 0.000 description 1
Images
Classifications
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02H—EMERGENCY PROTECTIVE CIRCUIT ARRANGEMENTS
- H02H7/00—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions
- H02H7/10—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions for converters; for rectifiers
- H02H7/12—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions for converters; for rectifiers for static converters or rectifiers
- H02H7/125—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions for converters; for rectifiers for static converters or rectifiers for rectifiers
- H02H7/1255—Emergency protective circuit arrangements specially adapted for specific types of electric machines or apparatus or for sectionalised protection of cable or line systems, and effecting automatic switching in the event of an undesired change from normal working conditions for converters; for rectifiers for static converters or rectifiers for rectifiers responsive to internal faults, e.g. by monitoring ripple in output voltage
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/42—Circuits or arrangements for compensating for or adjusting power factor in converters or inverters
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Power Engineering (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Data Mining & Analysis (AREA)
- Mathematical Physics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Computational Mathematics (AREA)
- Algebra (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- Test And Diagnosis Of Digital Computers (AREA)
Abstract
The invention provides a multi-fault estimation method for a staggered parallel Boost PFC system, and belongs to the field of fault diagnosis. The method specifically comprises the steps of establishing a state space expression with actuator faults and sensor faults, carrying out primary filtering on output, expanding the filtered output into a state of a multi-fault system, carrying out order reduction on the multi-fault system, carrying out observer parameter design, and estimating state variables, actuator faults and sensor faults of the system on line. Compared with the prior art, the invention provides a novel synchronous fault estimation method based on the dimension reduction observer technology and the generalized observer technology under the condition of not being constrained by the minimum phase condition, the observer matching condition and the output dimension condition, and the designed sliding mode observer can ensure that an error system is converged 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 containing multiple faults.
Description
Technical Field
The invention relates to the field of fault diagnosis, in particular to a multi-fault estimation method for an interleaved parallel Boost PFC system.
Background
With the development of power electronic technology, various power electronic devices are widely applied to the fields of electric power, household appliances, mobile equipment, 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 is 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 a power grid, thereby polluting the power grid. The mainstream methods for improving the power factor include a harmonic compensation method and a power factor correction method. The harmonic compensation mode is to compensate the reactive power and some subharmonics of the equipment which has generated harmonic current, so that the total harmonic which flows into the power grid is reduced, and the total reactive power of the system is reduced; the power factor correction mode is that a power factor correction converter is added to a preceding stage power supply circuit of the electric equipment, and 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 a source.
In recent years, as the requirements on the safety and reliability performance indexes of the system are higher and higher, the control system is more and more 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 unexpected conditions, the system performance is reduced slightly, the whole working system is damaged, and the personal safety and property safety are endangered seriously, so that catastrophic accidents are caused. Therefore, in order to improve the reliability and safety of the system, a timely and effective fault diagnosis and fault-tolerant control technology is very important. The fault diagnosis technology comprises three parts of fault detection, fault isolation and fault estimation. Compared with the fault detection and fault isolation technology realized by an indirect residual error method, the method has more practical significance and more challenging research because the amplitude of the fault can be directly obtained, so that people can know the fault in the system more intuitively and can serve for further fault-tolerant control.
Most control systems can be modeled by way of mathematical analysis. In practical control system applications, actuator faults and sensor faults may occur individually or simultaneously. In recent years, synchronous fault estimation of actuator faults and sensors by a model-based method has attracted a great deal of research effort in recent years, and most of the methods adopt a sliding mode observer or an unknown input observer. In addition, the switching power supply is dominant in the power supply field because of its high power density and high efficiency. The main method for inhibiting the harmonic wave generated by the switching power supply is to design a high-performance rectifier, which has the characteristics of sine wave input current, low harmonic wave content, high power factor and the like, namely has the function of Power Factor Correction (PFC).
The Observer-based Fault diagnosis method proposed in document 2, the article "Simultaneous Fault timing for Markovian Jump Systems With general uncertainty evaluation sites: A Reduced-Order Observer Approach (7889) 7897) (Simultaneous Fault Estimation for Markov Jump Systems With general uncertainty Transition rate: a Reduced Observer method (Xiaohang Li, Weidong Zhang, YueyWang, Ieee Industrial ELECTRONICS Collection 2020, pp. 7889-7897 of the annual 67) is required to satisfy the condition that the system output dimension is larger than the system Fault number, matching condition, minimum phase system condition.
In document 3, a fault estimation method designed in the patent document "sliding mode fault-tolerant control method of multi-agent tracking system with multiple faults" with chinese patent publication No. CN109557818B needs to satisfy the condition that (a, C) is observable and rank ([ B, F) a ]) Rank (b), i.e. the minimum phase system condition and observer matching condition need to be met, and the observer designed by the authors is a full-dimensional observer.
In document 4, "active fault-tolerant control method for spacecraft with decoupling of fault and interference" (zong et al, university of harbin university, 2020,52(09), 107-:
is a observator, i.e. the observer matching conditions and minimum phase system conditions need to be met, and the observer designed by the authors is a full-dimensional observer.
In document 5, the assumed conditions to be satisfied by the adaptive sliding mode observer designed in the article of "systematic estimation of state and fault for linear systems with unknown properties" (Jianglin Lan, AUTOMATICA 118 (2020)) are minimum phase system conditions, observer matching conditions, and system dimension conditions.
The assumed conditions that 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, Xialing Li, Zhaoxu Chen, Shen Yin, IEEE SYSTEM JOURNAL,15 (2021)) 2305- "a new Adaptive Observer-Based Mark Jump System Fault Reconstruction and State Estimation Method (Hongyan Yang, Xialing Li, Zhaoxu Chen, Shen Yin, IEEE Systems JOURNAL, 2305 th and 2305 th pages 2313 of No. 15 of 2021) needs to satisfy are minimum phase System conditions, Observer matching conditions, System dimension conditions.
In summary, the PFC control system is crucial to the power supply, and the conventional fault diagnosis technology is constrained by many constraints, and the many constraints greatly limit the application range of the currently proposed fault estimation method. Therefore, aiming at the research of the estimation technology of the multi-fault system containing faults of the actuator and the sensor, the technical problems to be solved in the whole research field are solved.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide a multi-fault estimation method for an interleaved parallel Boost PFC system with an actuator fault and a sensor fault, wherein the invented fault estimation method can accurately estimate information such as the form, amplitude, size, etc. of the fault when the actuator fault and the sensor fault occur in the system.
In order to achieve the purpose, the invention provides a multi-fault estimation method of an interleaved parallel Boost PFC system, wherein the multi-fault comprises an actuator fault and a sensor fault, and the estimation method is characterized by comprising the following steps:
The interleaved parallel Boost PFC system is called a system;
the system with multiple faults is recorded as a multiple-fault system 1, and the state space model of the multiple-fault system 1 is recorded as an expression (1), wherein the expression (1) is as follows:
wherein t is time; x (t) represents the state variable of the multi-fault system 1, and is denoted as the first state variable x (t), x (t) belongs to the n-dimensional vector space, and is denoted as x (t) e R n ；
Is the derivative of the first state variable x (t) with respect to time t, noted as the first derivative
u (t) represents the input of the multiple fault system 1, denoted as input u (t), u (t) belongs to the m-dimensional vector space, denoted as u (t) e R m (ii) a y (t) represents the output of the multiple fault system 1 and is denoted as the first output y (t), y (t) belongs to the p-dimensional vector space and is denoted as y (t) e R p ；f a (t) represents a q-dimensional actuator fault of the multi-fault system 1 and is noted as actuator fault f a (t)，f a (t) belongs to a q-dimensional vector space, denoted as f a (t)∈R q ；f d (t) represents the d-dimensional disturbance of the multi-fault system 1, denoted as disturbance f d (t)，f d (t) belongs to a d-dimensional vector space, denoted as f d (t)∈R d ；f s (t) denotes a w-dimensional sensor fault of the multiple 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 the row full rank matrix, D is the actuator failure f a (t) coefficient matrix, G is an external disturbance f d (t) coefficient matrix, F is sensor failure F s (t) and F is a column full rank matrix;
actuator failure f 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 the actuator failure f a (t) 2-norm, | | f s (t) | | denotes sensor failure f s (t) 2-norm, | | f d (t) | | denotes an external disturbance f d (t) 2-norm, η a Is actuator failure f a Boundary of (t) (. eta.) s Is a sensor failure f s Boundary of (t), η d Is an external disturbance f d Boundary of (t) (. eta.) a 、η s And η d Are all known normal numbers;
Filtering the first output y (t) of the multi-fault system 1 once to obtain a new output, wherein the new output satisfies an expression (2), and the expression (2) is as follows:
wherein z is f (t) is the new output of the multiple fault system 1, denoted as second output z f (t)，z f (t) belongs to a 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 (t) and is a positive definite matrix;
according to the state space model of the multi-fault system 1 obtained in the step 1, outputting a second output z 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, the state space model of the multi-fault system 2 is recorded as an expression (3), and the expression (3) is as follows:
wherein the content of the first and second substances,
the state variable representing the multi-fault system 2, denoted as the second state variable
Belongs to a vector space of n + p dimensions, and is marked as
Is a second state variable
The derivative with respect to time t, denoted as the second derivative
d (t) represents the fault vector of the multiple fault system 2, denoted as fault vector d (t),
is a second state variable
The matrix of coefficients of (a) is,
is a second matrix of coefficients of input u (t),
is the first coefficient matrix of the fault vector d (t),
is a second state variable
The matrix of output coefficients of (a) is,
wherein I p Representing a p-dimensional identity matrix;
Step 3.1, a first coordinate transformation is performed
The first coordinate transformation matrix comprises two matrixes to be designed and respectively recorded as a first free matrix phi and a second free matrix R, wherein the first free matrix phi belongs to a k x (n + p) dimensional space and is recorded as phi belonging to R k×(n+p) Wherein k is<(n + p), the second free matrix R belongs to a space of dimension 1 × p, and is marked as R ∈ R 1×p ；
The first free matrix Φ and the second free matrix R satisfy expression (4), the expression (4) being as follows:
making a first coordinate transformation
And
transforming the multi-fault system 2 into a multi-fault system 3, and recording the state space model of the multi-fault system 3 as an expression (5), wherein the expression (5) is as follows:
wherein the content of the first and second substances,
state variables representing the multi-fault system 3, denoted as third state variables
Belong to a k-dimensional vector space, denoted as
Is a third state variable
The derivative with respect to time t, denoted as the third derivative
Represents the output of the multiple fault system 3, denoted as third output
Belongs to a 1-dimensional vector space, and is marked as
Is a third state variable
Of the first state coefficient matrix of (a),
step 3.2, second coordinate transformation is carried out
Let the second coordinate transform matrix be T 1 ，
T 1 Belongs to k × k dimensional space and is marked as T 1 ∈R k×k (ii) a Second coordinate transformation for multi-fault system 3
Obtaining a multi-fault system 4, and modeling a state space of the multi-fault system 4 as an expression (6), wherein the expression (6) is as follows:
wherein the content of the first and second substances,
is a state variable of the multi-fault system 4 and is recorded as a fourth state variable
Belongs to a k-dimensional vector space, and is marked as
Is a fourth state variable
The derivative with respect to time t, denoted as the fourth derivative
Step 3.3, carrying out third coordinate transformation
Let the third coordinate transform matrix be T 2 ，
Wherein L is a matrix to be designed and is marked as a third free matrix L, the third free matrix L belongs to a (k-1) multiplied by 1 dimensional space and is marked as L belonging to R (k-1)×1 ；
Third coordinate transformation for multi-fault system 4
Obtaining a multi-fault system 5, and modeling the state space of the multi-fault system 5 as an expression (7), wherein the expression (7) is as follows:
wherein the content of the first and second substances,
is a state variable of the multi-fault system 5 and is marked as a fifth state variable
Is the first component of the fifth state variable,
is the second component of the fifth state variable,
is composed of
The derivative with respect to time t;
is a fifth state variable
Coefficient matrix of, a fifth state variable
Is divided into four blocks, and the upper left matrix block is marked as the sixth upper left block
The upper right matrix block is marked as the sixth upper right partition
The lower left matrix block is denoted as the sixth lower left partition
The lower right matrix block is denoted as the sixth lower right partition
Namely, it is
Transforming the matrix T for the third coordinate 2 The inverse matrix of (d);
for inputting the fifth coefficient matrix of u (t), the fifth coefficient matrix of u (t) is divided into two blocks, and the upper matrix block is marked as the seventh upper block
The lower sub-block is denoted as a seventh lower sub-block
Namely that
Is the second output z f (t) a fourth coefficient matrix, and outputting a second output z f (t) dividing the fourth coefficient matrix into two blocks, and recording the upper matrix block as the eighth upper block
The lower matrix block is marked as the eighth lower block
Namely, it is
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 sub-block is marked as the ninth lower sub-block
Namely, it is
Is a fifth state variable
Output coefficient matrix of, a fifth state variable
Output coefficient matrix of
Performing left and right blocking, wherein the left block is marked as a tenth left block 0, and the right block is marked as a tenth right block
Namely that
Is a tenth right block
The inverse matrix of (d);
Step 4.1, design of fault observer
Definition of
Is a fifth state variable
Is measured in a time-domain manner by a time-domain,
is the first component of the fifth state variable
Is detected by the measured values of (a) and (b),
is the second component of the fifth state variable
The observed value of (1) to make the observed error
Error of observation
For the fifth state variable
Designing a sliding-mode observer to obtain a dynamic equation of the observer, and recording the dynamic equation as an expression (8), wherein the expression (8) is as follows:
wherein the content of the first and second substances,
is observed value of first component of fifth state variable
The derivative with respect to the time t,
is observed value of second component of fifth state variable
The derivative with respect to time t; v. of 1 Is the first component of the fifth state variable
Item of sliding form v 1 ＝(v 11 ,…,v 1(k-1) ，v 1i ＝sgn(e 1i )，v 2 Is the second component of the fifth state variable
Item of sliding form v 2 ＝sgn(e 2 )，
Is the first component of the fifth state variable
The sliding-mode gain matrix of (a),
wherein the content of the first and second substances,
is a symmetric positive definite matrix P 1 Inverse matrix of, P 1 For the matrix to be designed, it is marked as the fourth autonomous matrix P 1 ，k 1 Is the first constant to be designed, k 1 ∈R，k 2 For the observation error e 2 (t) sliding mode gain, k 2 Is the second constant to be designed, k 2 ∈R，k 3 Is the second component of the fifth state variable
Gain of sliding mode, 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, which is as follows:
wherein the content of the first and second substances,
for the observation error e 1 (t) the derivative with respect to time t,
for the observation error e 2 (t) a derivative over time t;
Step 5.1, estimating faults
Will actuator fail f a (t) the estimated value is recorded as
Will sensor fail f s (t) the estimated value is recorded as
Will disturb the outside f d (t) the estimated value is recorded as
The three estimates are calculated as follows:
wherein, I q Is a q-dimensional identity matrix, I d Is a d-dimensional identity matrix, I w Is a w-dimensional identity matrix.
Step 5.2, estimating the state
Defining a state variable x (of tThe estimated value is x (1) (t)、x (1) The derivative of (t) is
Estimating actuator fault
And external disturbance estimation value
Substituting expression (1) to obtain
The calculation formula (c) is as follows:
and finishing the multi-fault estimation of the interleaved parallel Boost PFC system containing the multi-fault.
Preferably, x in step 2 T (t) is the transpose of the first state variable x (t), z f T (t) is the second output z f (t) transferring,
Is composed of
The transposing of (1).
Preferably, the first constant k to be designed 1 Second to-be-designed constant k 2 Third to design constant k 3 Respectively satisfy the following formula:
k 2 >0，
wherein the content of the first and second substances,
the maximum value of the characteristic is represented,λ(. cndot.) represents the minimum eigenvalue.
Preferably, the third free matrix L, the fourth free matrix P 1 Respectively satisfy the following formula:
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 a minimum phase condition, an observer matching condition and an output dimension condition, the method provides a new fault estimation method, 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 expanded;
2. by adopting the dimension reduction observer technology, the estimated variable dimension is n + q + w + d, the actually required observer dimension is k, k is less than n + p, and p is less than q + w + d, so that the observer dimension is reduced, and the design complexity of the observer is reduced;
3. the state variable information of a multi-fault system and information such as fault of an actuator, fault of a sensor, external disturbance form and size can be accurately and synchronously estimated on line.
Drawings
FIG. 1 is a schematic diagram of a multi-fault synchronization estimation method according to the present invention;
FIG. 2 is a flow chart of a multi-fault synchronization estimation method of the present invention;
FIG. 3 shows an actuator failure f according to the present invention a (t) and its estimated value
A simulation diagram of (1);
FIG. 4 shows a sensor failure f in the present invention s (t) and its estimated value
A simulation diagram of (1);
FIG. 5 shows a system state variable x in the present invention 1 (t) and its estimated value x 1 (1) (t) a simulation diagram;
FIG. 6 shows a system state variable x in the present invention 2 (t) and its estimated value x 2 (1) (t) a simulation diagram;
FIG. 7 shows a system state variable x in the present invention 3 (t) and its estimated value x 3 (1) (t) a simulation diagram;
FIG. 8 shows an actuator failure f in the present invention d (t) and its estimated value
A simulation diagram of (2);
FIG. 9 is a circuit topology diagram in a simulation of the present invention.
Detailed Description
The technical solution of the present invention is further described in detail below with reference to the accompanying drawings.
In embodiment 1, the invention provides a multi-fault estimation method for an interleaved parallel Boost PFC system, where the multi-fault includes an actuator fault and a sensor fault. Fig. 1 is a schematic diagram of a multi-fault estimation method of the present invention, and fig. 2 is a flowchart of the multi-fault estimation method of the present invention, as can be seen from fig. 1 and 2, the multi-fault estimation method includes the following steps:
The interleaved parallel Boost PFC system is called a system;
the system with multiple faults is recorded as a multiple-fault system 1, and the state space model of the multiple-fault system 1 is recorded as an expression (1), wherein the expression (1) is as follows:
wherein t is time; x (t) represents the state variable of the multi-fault system 1, and is denoted as the first state variable x (t), x (t) belongs to the n-dimensional vector space, and is denoted as x (t) e R n ；
Is the derivative of the first state variable x (t) with respect to time t, noted as the first derivative
u (t) represents the input of the multiple fault system 1, denoted as input u (t), u (t) belongs to the m-dimensional vector space, denoted as u (t) e R m (ii) a y (t) represents the output of the multiple fault system 1 and is denoted as the first output y (t), y (t) belongs to the p-dimensional vector space and is denoted as y (t) e R p ；f a (t) represents a q-dimensional actuator fault of the multi-fault system 1 and is noted as actuator fault f a (t)，f a (t) belongs to a q-dimensional vector space, denoted as f a (t)∈R q ；f d (t) represents the d-dimensional disturbance of the multi-fault system 1, denoted as disturbance f d (t)，f d (t) belongs to a d-dimensional vector space, denoted as f d (t)∈R d ；f s (t) denotes a w-dimensional sensor fault of the multiple 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 the row full rank matrix, D is the actuator failure f a (t) coefficient matrix, G is an external disturbance f d (t) coefficient matrix, F is sensor failure F s (t) and F is a column full rank matrix;
actuator failure f 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 the actuator failure f a (t) 2-norm, | | f s (t) | | denotes sensor failure f s (t) 2-norm, | | f d (t) | | denotes an external disturbance f d 2-norm, η of (t) a Is actuator failure f a Boundary of (t) (. eta.) s Is a sensor failure f s Boundary of (t) (. eta.) d Is an external disturbance f d Boundary of (t) (. eta.) a 、η s And η d Are all known normal numbers;
Filtering the first output y (t) of the multi-fault system 1 once to obtain a new output, wherein the new output satisfies an expression (2), and the expression (2) is as follows:
wherein z is f (t) is the new output of the multiple fault system 1, denoted as second output z f (t)，z f (t) belongs to a 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 (t) and is a positive definite matrix;
according to the state space model of the multi-fault system 1 obtained in the step 1, outputting a second output z f (t) expanding to a new state variable, i.e. defining a new state variable
And the expanded system is marked as a multi-fault system 2, and the multi-fault system 2The state space model is noted as expression (3), and expression (3) is as follows:
wherein the content of the first and second substances,
the state variable representing the multi-fault system 2, denoted as the second state variable
Belongs to a vector space of n + p dimensions, and is marked as
Is a second state variable
The derivative with respect to time t, denoted as the second derivative
d (t) represents the fault vector of the multiple fault system 2, denoted as fault vector d (t),
is a second state variable
The matrix of coefficients of (a) is,
is a second matrix of coefficients of input u (t),
is the first coefficient matrix of the fault vector d (t),
is a second state variable
The matrix of output coefficients of (a) is,
wherein I p Representing a p-dimensional identity matrix;
Step 3.1, a first coordinate transformation is performed
The first coordinate transformation matrix comprises two matrixes to be designed and respectively recorded as a first free matrix phi and a second free matrix R, wherein the first free matrix phi belongs to a k x (n + p) dimensional space and is recorded as phi belonging to R k×(n+p) Wherein k is<(n + p), the second free matrix R belongs to a space of dimension 1 × p, and is marked as R ∈ R 1×p ；
The first free matrix Φ and the second free matrix R satisfy expression (4), the expression (4) being as follows:
making a first coordinate transformation
And
the multi-fault system 2 is transformed into a multi-fault system 3, the state space model of the multi-fault system 3 is expressed as an expression (5), and the expression (5) is as follows:
wherein the content of the first and second substances,
state variables representing the multi-fault system 3, denoted as third state variables
Belongs to a k-dimensional vector space, and is marked as
Is a third state variable
The derivative with respect to time t, denoted as the third derivative
Represents the output of the multiple fault system 3, denoted as the third output
Belongs to the 1-dimensional directionVolume space, is marked as
Is a third state variable
The first state coefficient matrix of (a) is,
a third coefficient matrix of input u (t),
is the second output z f (t) a second matrix of coefficients of,
a second matrix of coefficients for the fault vector d (t),
is a third state variable
The matrix of output coefficients of (a) is,
step 3.2, second coordinate transformation is carried out
Let the second coordinate transform matrix be T 1 ，
T 1 Belongs to k × k dimensional space and is marked as T 1 ∈R k×k (ii) a Second coordinate transformation for multi-fault system 3
Obtaining a multi-fault system 4, and modeling a state space of the multi-fault system 4 as an expression (6), wherein the expression (6) is as follows:
wherein the content of the first and second substances,
is a state variable of the multi-fault system 4 and is recorded as a fourth state variable
Belongs to a k-dimensional vector space, and is marked as
Is a fourth state variable
The derivative with respect to time t, denoted as the fourth derivative
Step 3.3, carrying out third coordinate transformation
Let the third coordinate transform matrix be T 2 ，
Wherein L is a matrix to be designed and is marked as a third free matrix L, the third free matrix L belongs to a (k-1) multiplied by 1 dimensional space and is marked as L belonging to R (k-1)×1 ；
Third coordinate transformation for multi-fault system 4
Obtaining a multi-fault system 5, and recording a state space model of the multi-fault system 5 as an expression (7), wherein the expression (7) is as follows:
wherein the content of the first and second substances,
is a state variable of the multi-fault system 5 and is marked as a fifth state variable
Is the first component of the fifth state variable,
is the second component of the fifth state variable,
is composed of
The derivative with respect to time t;
is a fifth state variable
Coefficient matrix of, a fifth state variable
Is divided into four blocks, and the upper left matrix block is marked as the sixth upper left block
The upper right matrix block is marked as the sixth upper right partition
The lower left matrix block is denoted as the sixth lower left partition
The lower right matrix block is denoted as the sixth lower right partition
Namely, it is
Transforming the matrix T for the third coordinate 2 The inverse matrix of (d);
dividing the fifth coefficient matrix of input u (t) into two blocks, and recording the upper matrix block as the seventh upper block
The lower sub-block is denoted as a seventh lower sub-block
Namely, it is
Is the second output z f (t) a fourth coefficient matrix, and outputting a second output z f (t) dividing the fourth coefficient matrix into two blocks, and recording the upper matrix block as the eighth upper block
The lower matrix block is marked as the eighth lower block
Namely, it is
Dividing the fourth coefficient matrix of the fault vector d (t) into two blocks, and marking the upper block as a ninth upper block
The lower sub-block is marked as the ninth lower sub-block
Namely, it is
Is a fifth state variable
Output coefficient matrix of, a fifth state variable
Output coefficient matrix of
Performing left and right blocking, wherein the left block is marked as a tenth left block 0, and the right block is marked as a tenth right block
Namely that
Is a tenth right block
The inverse matrix of (d);
Step 4.1, design of fault observer
Definition of
Is a fifth state variable
Is measured in a time-domain manner by a time-domain,
is the first component of the fifth state variable
Is measured in a time-domain manner by a time-domain,
is the second component of the fifth state variable
The observed value of (1) to make the observed error
Error of observation
For the fifth state variable
Designing a sliding-mode observer to obtain a dynamic equation of the observer, and recording the dynamic equation as an expression (8), wherein the expression (8) is as follows:
wherein the content of the first and second substances,
is observed value of first component of fifth state variable
The derivative with respect to the time t,
is observed value of second component of fifth state variable
The derivative with respect to time t; v. of 1 Is the first component of the fifth state variable
Item of sliding form v 1 ＝(v 11 ,…,v 1(k-1) ，v 1i ＝sgn(e 1i )，v 2 Is the second component of the fifth state variable
Item of sliding form v 2 ＝sgn(e 2 )，
Is the first component of the fifth state variable
The sliding-mode gain matrix of (a),
wherein the content of the first and second substances,
is a symmetric positive definite matrix P 1 Inverse matrix of, P 1 For the matrix to be designed, it is marked as the fourth autonomous matrix P 1 ，k 1 Is the first constant to be designed, k 1 ∈R，k 2 For the observation error e 2 t sliding mode gain, k 2 Is the second constant to be designed, k 2 ∈R，k 3 Is the second component of the fifth state variable
Gain of sliding mode, 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, which is as follows:
wherein the content of the first and second substances,
for the observation error e 1 (t) the derivative with respect to time t,
for the observation error e 2 (t) a derivative over time t;
Step 5.1, estimating faults
Will actuator fail f a (t) the estimated value is recorded as
Will sensor fail f s (t) the estimated value is recorded as
Will disturb the outside f d (t) the estimated value is recorded as
The three estimates are calculated as follows:
wherein, I q Is a q-dimensional identity matrix, I d Is a 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) is
Estimating actuator fault
And external disturbance estimation value
Substituting expression (1) to obtain
The calculation formula (c) is as follows:
and finishing the multi-fault estimation of the interleaved parallel Boost PFC system containing the multi-fault.
In this example 1, x in step 2 T (t) is the transpose of the first state variable x (t), z f T (t) is a second output z f (t) transferring,
Is composed of
The transposing of (1).
In this embodiment 1, the first constant k to be designed 1 Second to-be-designed constant k 2 Third to be designed constant k 3 Respectively satisfy the following formula:
k 2 >0，
wherein the content of the first and second substances,
the maximum value of the characteristic is represented,λ(. cndot.) represents the minimum eigenvalue.
In this embodiment 1, the third free matrix L, the fourth free matrix P 1 Respectively satisfy the following formula:
wherein I is an identity matrix.
the alternating voltage of the alternating current power supply is V ac ；
The full-wave rectification circuit comprises four same rectifying diodes which are respectively marked as rectifying diodes BD 1 And a rectifier diode BD 2 And a rectifier diode BD 3 And a rectifier diode BD 4 Diode BD of rectifier 1 And a rectifier diode BD 3 Series connected, rectifying diodes BD 3 Is connected to the rectifier diode BD 1 Anode of (2), rectifier diode BD 2 And a rectifier diode BD 4 Series connected, rectifying diodes BD 4 Is connected to the rectifier diode BD 2 One end of an alternating current power supply is connected to the rectifier diode BD 1 And a rectifier diode BD 3 The other end of the alternating current power supply is connected to a rectifier diode BD 2 And a rectifier diode BD 4 A common connection point of (a);
the Boost circuit comprises two same inductors, two same Boost diodes and two same switching tubes, wherein the two same inductors are respectively marked as PFC inductors L 1 And a PFC inductor L 2 The two same boost diodes are respectively recorded as boost diodes KD 1 And boost diode KD 2 The two passing switch tubes are respectively marked as a switch tube KS 1 And a switching tube KS 2 PFC inductance L 1 And boost diode KD 1 Connected in series and then connected with a PFC inductor L 2 And a boost diode D 2 The series circuit is connected in parallel, and a switch tube KS 1 Connected to the PFC inductor L 1 And a boost diode D 1 Between the common connection point of (2) and ground, a switching tube KS 2 Connected to the PFC inductor L 2 And boost diode KD 2 Between the common connection point of (a) and ground;
the output filteringThe capacitance is denoted as the capacitance CL 0 Capacitance CL 0 Connected to the boost diode KD 1 And boost diode KD 2 Between the common connection point of (a) and ground;
the load resistance is noted as resistance RL 0 Resistance RL 0 Connected in parallel to the capacitor CL 0 Two ends;
the specific parameters of the interleaved parallel Boost PFC circuit are as follows: the voltage value of the alternating current power supply is 220V, and the PFC inductor L 1 Inductance of 300uH, PFC inductance L 2 The inductance of (1) is 300uH, and the capacitance CL is 0 Has a capacitance value of 1000uF and a resistance RL 0 Has a resistance value of 40 Ω irrespective of KD 1 And KD 2 The conduction voltage drop of (1).
Taking the first state variable x (t) belonging to a three-dimensional vector space, i.e. n equals 3, the output y (t) belonging to a one-dimensional vector space, i.e. p equals 1, the PFC control system contains actuator faults and sensor faults, and the total fault number q + w equals 2.
In this embodiment, the procedure is as in embodiment 1, and the involved matrices in the estimation process are as follows:
C＝(0 0 1)，F＝(1)，A f ＝(1)，
in order to prove the technical effect of the invention, simulation is also carried out.
Fig. 3 shows the actuator fault set in the simulation experiment and the actuator fault estimated by the method of the present invention, where the solid line shows the set actuator fault, and the mathematical expression is:
wherein the content of the first and second substances,
and is
The dotted line in the figure is a graph of the estimation result obtained by matlab simulation. It can be seen that no actuator fault occurs in the 0 th to 2 th seconds, an actuator fault occurs just at 2s, the estimation result has a short and slight error, then the estimation error is close to 0, a sensor fault occurs just at 4s, the estimation result has a short error, and then the estimation error is close to 0.
Fig. 4 shows a set sensor fault in a simulation experiment and a sensor fault estimated by using the method of the present invention, in which a solid line shows the set sensor fault and a mathematical expression thereof is:
wherein the content of the first and second substances,
and h (t) is less than or equal to 1.
The dotted line in the figure is a diagram of the estimation result obtained by matlab simulation. It can be seen that no sensor failure occurred in 0-4s, and that a short slight error occurred in the estimation result at 4s, and then the estimation error is close to 0.
FIG. 5 shows a system state variable x in the present invention 1 (t) andestimate x 1 (1) (t) simulation diagram, FIG. 6 is a system state variable x in the present invention 2 (t) and its estimated value x 2 (1) (t) simulation diagram, FIG. 7 is a system state variable x in the present invention 3 (t) and its estimated value x 3 (1) (t) simulation diagram. That is, fig. 5 to 7 are simulation diagrams of three state variables and estimation results thereof of the PFC system after an actuator failure and a sensor failure are set in the specific embodiment. As can be seen from fig. 5-7, the estimation result has a small error after the actuator failure occurs in the 2 nd s, and the estimation result has a short error just after the sensor failure occurs in the 4 th s, and then the estimation error is close to 0.
Fig. 8 shows the external disturbance set in the simulation experiment and the external disturbance estimated by the method of the present invention in the specific example, where the solid line is the set external disturbance and the mathematical expression is:
f d (t)＝0.05sin t
the dotted line in the figure is a diagram of the estimation result obtained by matlab simulation. It can be seen that the external disturbance occurs at 0s, the estimation result has a short error, and then the estimation error is close to 0, and the sensor failure occurs at 4s, and then the estimation result has a short error, and then the estimation error is close to 0.
In addition, there are three main constraints for what is summarized in document 1: minimum phase system conditions, observer matching conditions, and output dimension conditions. The PFC model established in the example of the present invention was verified according to the constraints provided in this document, as follows:
1. since n is 3 and s is 0, then
Due to the fact that
This system does not satisfy the minimum phase condition.
2.
Due to the fact that
The observer matching condition is not satisfied.
3. The established interleaving parallel Boost PFC system contains actuator faults and sensor faults, the total quantity of the faults is q + w equals to 2, the output dimension p of the system equals to 1, and the dimension condition of the system is not met due to the fact that q + w equals to p.
Therefore, the established interleaved parallel Boost PFC system does not meet the minimum phase system condition, the observer matching condition and the output dimension condition, and the simulation results of the graphs in the figures 3-8 verify that the fault estimation method can carry out fault estimation on multiple faults of the interleaved 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 fault estimation method are further verified.
Claims (4)
1. A multi-fault estimation method of an interleaved parallel Boost PFC system is disclosed, wherein the multi-fault comprises an actuator fault and a sensor fault, and the estimation method comprises the following steps:
step 1, establishing 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 a multiple-fault system 1, and the state space model of the multiple-fault system 1 is recorded as an expression (1), wherein the expression (1) is as follows:
wherein t is time; x (t) represents the state variable of the multi-fault system 1, and is denoted as the first state variable x (t), x (t) belongs to the n-dimensional vector space, and is denoted as x (t) e 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 multiple fault system 1, denoted as input u (t), u (t) belongs to the m-dimensional vector space, denoted as u (t) e R m (ii) a y (t) represents the output of the multiple fault system 1 and is denoted as the first output y (t), y (t) belongs to the p-dimensional vector space and is denoted as y (t) e R p ；f a (t) represents a q-dimensional actuator fault of the multi-fault system 1 and is noted as actuator fault f a (t)，f d (t) belongs to a q-dimensional vector space, denoted as f a (t)∈R q ；f d (t) represents the d-dimensional disturbance of the multi-fault system 1, denoted as disturbance f d (t)，f d (t) belongs to a d-dimensional vector space, denoted as f d (t)∈R d ；f s (t) denotes a w-dimensional sensor fault of the multiple 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 the row full rank matrix, D is the actuator failure f a (t) coefficient matrix, G is an external disturbance f d (t) coefficient matrix, F is sensor failure F s (t) and F is a column full rank matrix;
failure of the actuator f 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 the actuator failure f a (t) 2-norm, | | f s (t) | | denotes sensor failure f s (t) 2-norm, | | f d (t) | | denotes an external disturbance f d 2-norm, η of (t) a Is actuator failure f a Boundary of (t) (. eta.) s Is a sensor failure f s Boundary of (t) (. eta.) d Is an external disturbance f d Boundary of (t) (. eta.) a 、η s And η d Are all known normal numbers;
step 2, expanding the multi-fault system 1 to obtain a multi-fault system 2
Filtering the first output y (t) of the multi-fault system 1 once to obtain a new output, wherein the new output satisfies an expression (2), and the expression (2) is as follows:
wherein z is f (t) is the new output of the multiple fault system 1, denoted as second output z f (t)，z f (t) belongs to a 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 (t) and is a positive definite matrix;
according to the state space model of the multi-fault system 1 obtained in the step 1, outputting a second output z f (t) expanding to a new state variable, i.e. defining a new state variable
And the expanded system is marked as a multi-fault system 2, and the multi-fault system 2The state space is modeled as expression (3), and expression (3) is as follows:
wherein the content of the first and second substances,
the state variable representing the multiple fault system 2, denoted as the second state variable
Belongs to a vector space of n + p dimensions, and is marked as
Is a second state variable
The derivative with respect to time t, denoted as the second derivative
d (t) represents the fault vector of the multiple fault system 2, denoted as fault vector d (t),
is a second state variable
The matrix of coefficients of (a) is,
is a second matrix of coefficients of input u (t),
is the first coefficient matrix of the fault vector d (t),
is a second state variable
The matrix of output coefficients of (a) is,
wherein I p Representing a p-dimensional identity matrix;
step 3, coordinate transformation is carried out on the multi-fault system 2
Step 3.1, a first coordinate transformation is performed
The first coordinate transformation matrix comprises two matrixes to be designed and respectively recorded as a first free matrix phi and a second free matrix R, wherein the first free matrix phi belongs to a k x (n + p) dimensional space and is recorded as phi belonging to R k×(n+p) Where k < (n + p), the second free matrix R belongs to a space of dimension 1 xp, denoted as R ∈ R 1×p ；
The first free matrix Φ and the second free matrix R satisfy expression (4), the expression (4) being as follows:
making a first coordinate transformation
And
transforming the multi-fault system 2 into a multi-fault system 3, and recording the state space model of the multi-fault system 3 as an expression (5), wherein the expression (5) is as follows:
wherein the content of the first and second substances,
state variables representing the multi-fault system 3, denoted as third state variables
Belongs to a k-dimensional vector space, and is marked as
Is a third state variable
The derivative with respect to time t, denoted as the third derivative
Represents the output of the multiple fault system 3, denoted as third output
Belongs to a 1-dimensional vector space, and is marked as
Is a third state variable
The first state coefficient matrix of (a) is,
a third coefficient matrix of input u (t),
is the second output z f (t) a second matrix of coefficients of,
a second matrix of coefficients for the fault vector d (t),
is a third state variable
The matrix of output coefficients of (a) is,
step 3.2, second coordinate transformation is carried out
Let the second coordinate transform matrix be T 1 ，
T 1 Belongs to k × k dimensional space and is marked as T 1 ∈R k ×k (ii) a Second coordinate transformation for multi-fault system 3
Obtaining a multi-fault system 4, and modeling a state space of the multi-fault system 4 as an expression (6), wherein the expression (6) is as follows:
wherein the content of the first and second substances,
is a state variable of the multi-fault system 4 and is recorded as a fourth state variable
Belong to a k-dimensional vector space, denoted as
Is a fourth state variable
The derivative with respect to time t, denoted as the fourth derivative
Step 3.3, carrying out third coordinate transformation
Let the third coordinate transform matrix be T 2 ，
Wherein L is a matrix to be designed and is marked as a third free matrix L, the third free matrix L belongs to a (k-1) multiplied by 1 dimensional space and is marked as L belonging to R (k-1)×1 ；
Third coordinate transformation for multi-fault system 4
Obtaining a multi-fault system 5, and modeling the state space of the multi-fault system 5 as an expression (7), wherein the expression (7) is as follows:
wherein the content of the first and second substances,
is a state variable of the multi-fault system 5 and is marked as a fifth state variable
Is the first component of the fifth state variable,
is the second component of the fifth state variable,
is composed of
The derivative with respect to time t;
is a fifth state variable
Coefficient matrix of, a fifth state variable
Is divided into four blocks, and the upper left matrix block is marked as the sixth upper left block
The upper right matrix block is marked as the sixth upper right partition
The lower left matrix block is denoted as the sixth lower left partition
The lower right matrix block is denoted as the sixth lower right partition
Namely, it is
Transforming the matrix T for the third coordinate 2 The inverse matrix of (d);
dividing the fifth coefficient matrix of input u (t) into two blocks, and marking the upper matrix block as the seventh upper block
Lower section is marked asThe seventh lower sub-block
Namely, it is
Is the second output z f (t) a fourth coefficient matrix, and outputting a second output z f (t) dividing the fourth coefficient matrix into two blocks, and recording the upper matrix block as the eighth upper block
The lower matrix block is marked as the eighth lower block
Namely, it is
Dividing the fourth coefficient matrix of the fault vector d (t) into two blocks, and marking the upper block as a ninth upper block
The lower sub-block is marked as the ninth lower sub-block
Namely, it is
Is a fifth state variable
Output coefficient matrix of, a fifth state variable
Output coefficient matrix of
Performing left and right block division, wherein the left block division is marked as tenth left block division 0, and the right block division is marked as tenth right block division
Namely, it is
Is a tenth right block
The inverse matrix of (d);
step 4, observer design is carried out on the multi-fault system 5
Step 4.1, design of fault observer
Definition of
Is a fifth state variable
Is detected by the measured values of (a) and (b),
is the first component of the fifth state variable
Is detected by the measured values of (a) and (b),
is the second component of the fifth state variable
The observed value of (1) to make the observed error
Error of observation
For the fifth state variable
Designing a sliding-mode observer to obtain a dynamic equation of the observer, and recording the dynamic equation as an expression (8), wherein the expression (8) is as follows:
wherein the content of the first and second substances,
is observed value of first component of fifth state variable
The derivative with respect to the time t,
is observed value of second component of fifth state variable
The derivative of time t; v. of 1 Is the first component of the fifth state variable
Item of sliding form v 1 ＝(v 11 ，...，v 1(k-1) ，v 1i ＝sgn(e 1i )，v 2 Is the second component of the fifth state variable
Item of sliding form v 2 ＝sgn(e 2 )，
Is the first component of the fifth state variable
The sliding-mode gain matrix of (a),
wherein the content of the first and second substances,
is a symmetric positive definite matrix P 1 Inverse matrix of, P 1 For the matrix to be designed, it is marked as the fourth autonomous matrix P 1 ，k 1 Is the first constant to be designed, k 1 ∈R，k 2 For the observation error e 2 (t) sliding mode gain, k 2 Is the second constant to be designed, k 2 ∈R，k 3 Is the second component of the fifth state variable
Gain of sliding mode, 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, which is as follows:
wherein the content of the first and second substances,
for the observation error e 1 (t) the derivative with respect to time t,
for the observation error e 2 (t) a derivative over time t;
step 5, carrying out on-line synchronous estimation
Step 5.1, estimating faults
Will actuator fail f a (t) the estimated value is recorded as
Will sensor fail f s (t) the estimated value is recorded as
Will disturb the outside f d (t) the estimated value is recorded as
The three estimates are calculated as follows:
wherein, I q Is a q-dimensional identity matrix, I d Is a 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) is
Estimating actuator fault
And external disturbance estimation
Substituting expression (1) to obtain
The calculation formula (c) is as follows:
and finishing the multi-fault estimation of the interleaved parallel Boost PFC system containing the multi-fault.
2. The method as claimed in claim 1, wherein x in step 2 is x T (t) is the transpose of the first state variable x (t), z f T (t) is the second output z f (t) transferring,
Is composed of
The transposing of (1).
3. The method of claim 1, wherein the first constant k to be designed is a constant k to be designed 1 Second to-be-designed constant k 2 Third to be designed constant k 3 Respectively satisfy the following formula:
k 2 ＞0，
wherein the content of the first and second substances,
the maximum value of the characteristic is represented,λ(. cndot.) represents the minimum eigenvalue.
4. The method as claimed in claim 1, wherein the third free matrix L, the fourth free matrix P is a multi-fault estimation method for interleaved parallel Boost PFC system 1 Respectively satisfy the following formula:
wherein I is an identity matrix.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210429921.4A CN114825281B (en) | 2022-04-22 | 2022-04-22 | Multi-fault estimation method of staggered parallel Boost PFC system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210429921.4A CN114825281B (en) | 2022-04-22 | 2022-04-22 | Multi-fault estimation method of staggered parallel Boost PFC system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114825281A true CN114825281A (en) | 2022-07-29 |
| CN114825281B CN114825281B (en) | 2024-03-26 |
Family
ID=82505756
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210429921.4A Active CN114825281B (en) | 2022-04-22 | 2022-04-22 | Multi-fault estimation method of staggered parallel Boost PFC system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114825281B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102695332A (en) * | 2011-01-17 | 2012-09-26 | 辐射研究有限公司 | Hybrid power control system |
| CN112947389A (en) * | 2021-03-31 | 2021-06-11 | 合肥工业大学 | Multi-fault synchronous estimation method of PFC (Power factor correction) control system |
| KR20210075479A (en) * | 2019-12-13 | 2021-06-23 | 한밭대학교 산학협력단 | Sensor fault diagnosis system for converter |
| CN113031570A (en) * | 2021-03-18 | 2021-06-25 | 哈尔滨工业大学 | Rapid fault estimation method and device based on self-adaptive unknown input observer |
| CN114325164A (en) * | 2021-11-24 | 2022-04-12 | 合肥工业大学 | Multi-fault diagnosis method for single-phase three-level rectifier |
-
2022
- 2022-04-22 CN CN202210429921.4A patent/CN114825281B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102695332A (en) * | 2011-01-17 | 2012-09-26 | 辐射研究有限公司 | Hybrid power control system |
| KR20210075479A (en) * | 2019-12-13 | 2021-06-23 | 한밭대학교 산학협력단 | Sensor fault diagnosis system for converter |
| CN113031570A (en) * | 2021-03-18 | 2021-06-25 | 哈尔滨工业大学 | Rapid fault estimation method and device based on self-adaptive unknown input observer |
| CN112947389A (en) * | 2021-03-31 | 2021-06-11 | 合肥工业大学 | Multi-fault synchronous estimation method of PFC (Power factor correction) control system |
| CN114325164A (en) * | 2021-11-24 | 2022-04-12 | 合肥工业大学 | Multi-fault diagnosis method for single-phase three-level rectifier |
Non-Patent Citations (1)
| Title |
|---|
| 文传博;邓露;吴兰;: "基于滑模观测器和广义观测器的故障估计方法", 自动化学报, no. 09, 30 September 2018 (2018-09-30), pages 1698 - 1705 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114825281B (en) | 2024-03-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107093955B (en) | A kind of continuous sliding formwork Current Sensorless control method of DC-DC down-converter | |
| CN102411396B (en) | Method and arrangement for tracking maximum power point of photovoltaic module | |
| CN107196534B (en) | A kind of single-phase inverter finite-time control method based on interference observer | |
| CN107040138A (en) | A kind of DC-DC down-converter recombination current about beam control method | |
| CN112947389B (en) | Multi-fault synchronous estimation method of PFC (Power factor correction) control system | |
| CN104393756A (en) | Advanced control method for direct-current boost converter system | |
| CN105610162A (en) | Adaptive fuzzy sliding mode RBF neural network control method for active power filter | |
| Ren et al. | Modified hybrid model of boost converters for parameter identification of passive components | |
| Liu et al. | Extended state observer based interval type-2 fuzzy neural network sliding mode control with its application in active power filter | |
| CN108539975A (en) | A kind of DC-DC down-converter system control method based on extended state observer and sliding formwork control technology | |
| Yang et al. | Investigation on the small signal characteristic based on the LLC hybrid hysteretic charge control | |
| CN104393775B (en) | Method of controlling three-phase PWM inverter based on second-order sliding mode and disturbance observer | |
| CN113555891B (en) | Method for estimating stability domain of AC/DC system containing uncertain parameters based on square sum | |
| CN114825281A (en) | Multi-fault estimation method for interleaved parallel Boost PFC (Power factor correction) system | |
| CN113285593A (en) | Direct-current buck converter system control method based on composite integral sliding mode control | |
| CN111817558A (en) | Composite sliding mode control method of buck type direct current converter system | |
| CN116522773A (en) | WPT system modeling method based on data driving | |
| CN110676880B (en) | Three-phase inverter stability analysis method based on SISO system theory | |
| CN114243933A (en) | PWM wave generation method, device and equipment of wireless power transmission system | |
| CN110429834B (en) | Three-phase rectifier sliding mode control method based on extended state observer | |
| CN113676037A (en) | Novel passive power factor correction device | |
| CN114914888B (en) | Multi-fault estimation method for single-phase three-level rectifier | |
| Mao et al. | Parameter identification of bidirectional converter based on improved BPNN | |
| Dupont et al. | Reduced order model of the boost converter with voltage multiplier cell | |
| Wang et al. | Research on fault prediction method of power electronic circuits based on particle swarm optimization RBF neural network |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |