A fault-tolerant control method for a buck-boost DC-DC converter

Abstract

The present invention belongs to the technical field of fault-tolerant control of buck-boost DC-DC converters, and specifically discloses a fault-tolerant control method of buck-boost DC-DC converters. The present invention comprises the following steps: first, according to the characteristics of the buck-boost DC-DC converter, it is established as a type of switching affine system mathematical model with average dwell time switching characteristics; second, when the buck-boost DC-DC converter has a voltage source failure and is subjected to external disturbances, a suitable reduced-order observer is designed to estimate the size and shape of the fault, and a dynamic output feedback fault-tolerant controller is designed to achieve fault-tolerant control performance; the system is subjected to gain analysis using a modal-dependent Lyapunov function to obtain the conditions for the actual exponential stability of the system and obtain the observer gain matrix and the controller gain matrix. The method of the present invention can ensure that the system can still operate safely and stably when the system is subjected to external disturbances and there is a voltage source failure.

Description

Technical Field

[0001] The invention belongs to the technical field of DC-DC converter control and relates to a fault-tolerant control method for a buck-boost DC-DC converter. Background Art

[0002] DC-DC converters are widely used in transportation, automobile, computer communication, aerospace, biomedicine, physical and chemical engineering, and are also an important part of electrical systems. In order to ensure safer and higher-quality operation of the system, fault diagnosis and fault-tolerant control should be given full attention. Device wear caused by improper operation, device aging caused by environmental factors, and open circuit, short circuit, breakdown, and inaccurate measurement element accuracy caused by other reasons, these seemingly small faults will affect the control and safe operation of the DC-DC converter. In order to offset the impact of the fault, an alarm can be set when the fault occurs, and then the fault can be handled as soon as possible to restore the system to normal operation. DC-DC converters are widely used in power systems. Of course, DC-DC converters are not only used in the power industry, but also in the aerospace industry, biomedicine, etc. Therefore, for a power system, only the safe and stable operation of each small unit can guarantee the safe and stable operation of the power system. Therefore, it is extremely important to perform fault diagnosis and fault-tolerant control of DC-DC converters.

[0003] In dynamic systems, disturbances and actuator faults often exist simultaneously. Online fault estimation strategies are usually used to obtain the size and shape of the fault. Generally speaking, the estimated fault information can be used for fault-tolerant control, such as adding a fault compensation signal in the controller to compensate for the fault impact. Therefore, fault estimation is attractive once a fault occurs.

[0004] A large number of fault estimation methods have been proposed, among which observer-based methods are characterized by high efficiency and strong operability. In particular, several methods have been proposed to achieve the fault estimation goal, including adaptive observers, sliding mode observers, unknown input observers, etc. For example, some scholars have solved the sensor fault estimation problem of DC-DC converters using a sliding mode fault estimation strategy, which relies on a sliding mode observer under the maximum area function switching method. Some scholars have used sliding mode observers to study the sensor fault detection and fault estimation problems of DC-DC converters.

[0005] However, these methods only consider sensor failures, i.e., open circuits and disconnections of inductors, and do not consider the situation where a voltage source failure occurs. On the other hand, in the above-mentioned method based on the sliding mode observer, the mode-dependent sliding surface may switch between predefined surfaces, making it difficult to judge the strict accessibility of the sliding surface. Therefore, it cannot be analyzed by an equivalent output error injection signal. And the observer designed for DC-DC converter fault estimation studied above is a full-order observer. Compared with the full-order observer, the estimation cost can be reduced by using a reduced-order observer. In the existing DC-DC converter fault-tolerant control method, there is no effective solution to the fault-tolerant control problem of DC-DC converters under voltage source faults. Summary of the invention

[0006] The purpose of the present invention is to propose a fault-tolerant control method for a buck-boost DC-DC converter. The method takes into account the conditions under which the buck-boost DC-DC converter simultaneously has a voltage source fault and an external disturbance, designs a reduced-order observer to estimate the size of the fault, and designs a dynamic output feedback fault-tolerant controller, which is conducive to achieving the purpose of fault-tolerant control of the system.

[0007] In order to achieve the above object, the present invention adopts the following technical scheme:

[0008] A fault-tolerant control method for a buck-boost DC-DC converter comprises the following steps:

[0009] Step 1. Build a mathematical model of the buck-boost DC-DC converter test simulation system;

[0010] When the buck-boost DC-DC converter has both voltage source fault and disturbance, the buck-boost DC-DC converter with switching characteristics is considered as a switching affine system with average dwell time switching property.

[0011] Step 2. Design a reduced-order observer for the system under voltage source fault and disturbance conditions to estimate the fault;

[0012] Step 3. Design a dynamic output feedback fault-tolerant controller for the system under voltage source fault and disturbance conditions, and use the dynamic output feedback fault-tolerant controller to achieve stable and safe operation of the buck-boost DC-DC converter;

[0013] Step 4. Use the modal dependent Lyapunov function to perform gain analysis on the system, obtain the conditions for the actual exponential stability of the system and obtain the reduced-order observer gain matrix and the dynamic output feedback fault-tolerant controller gain matrix.

[0014] In addition, based on the above-mentioned buck-boost DC-DC converter fault-tolerant control method, the present invention also proposes a corresponding buck-boost DC-DC converter fault-tolerant control system, which adopts the following technical solution:

[0015] A buck-boost DC-DC converter fault-tolerant control system, comprising the following modules:

[0016] Model building module, used to build the mathematical model of the buck-boost DC-DC converter test simulation system;

[0017] When the buck-boost DC-DC converter has both voltage source fault and disturbance, the buck-boost DC-DC converter with switching characteristics is considered as a switching affine system with average dwell time switching property.

[0018] The observer module is used to design a reduced-order observer for the system in the presence of voltage source faults and disturbances to estimate the faults;

[0019] Fault-tolerant control module, used to design a dynamic output feedback fault-tolerant controller for the system under the conditions of voltage source faults and disturbances, so as to achieve stable and safe operation of the buck-boost DC-DC converter;

[0020] And the gain analysis module is used to perform gain analysis on the system using the mode-dependent Lyapunov function, obtain the conditions for the actual exponential stability of the system and obtain the reduced-order observer gain matrix and the dynamic output feedback fault-tolerant controller gain matrix.

[0021] In addition, based on the above-mentioned buck-boost DC-DC converter fault-tolerant control method, the present invention also proposes a computer device, which includes a memory and one or more processors. An executable code is stored in the memory. When the processor executes the executable code, the steps of the buck-boost DC-DC converter fault-tolerant control method are implemented.

[0022] In addition, based on the above-mentioned buck-boost DC-DC converter fault-tolerant control method, the present invention also proposes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the above-mentioned buck-boost DC-DC converter fault-tolerant control method.

[0023] The present invention has the following advantages:

[0024] As described above, the present invention relates to a fault-tolerant control method for a buck-boost DC-DC converter. The method of the present invention takes into account the existence of voltage source faults and external disturbances in the buck-boost DC-DC converter, designs a reduced-order observer to estimate the fault, and thus obtains the size and shape of the fault. The present invention provides an average dwell time switching signal constraint and adopts a modal dependent Lyapunov function method to perform stability analysis on the estimation error system and the closed-loop system, respectively, to obtain system stability and implementation The present invention also provides a dynamic output feedback fault-tolerant controller. After the dynamic output feedback fault-tolerant controller of the present invention is applied, the system can still operate stably even when the system suffers from voltage source failure and external disturbance. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flow chart of a fault-tolerant control method for a buck-boost DC-DC converter according to an embodiment of the present invention;

[0026] Figure 2 It is a structural diagram of a buck-boost DC-DC converter. DETAILED DESCRIPTION

[0027] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0028] Example 1

[0029] like Figure 1 As shown, the buck-boost DC-DC converter fault-tolerant control method in this embodiment includes the following steps:

[0030] Step 1. Build a mathematical model of the buck-boost DC-DC converter test simulation system.

[0031] The present invention establishes a state space model of a buck-boost DC-DC converter based on Kirchhoff's voltage law and current law, and due to the affine characteristics of the state space model, and considering that the buck-boost DC-DC converter has both voltage source failure and external disturbance, the buck-boost DC-DC converter with switching characteristics is considered as a type of average dwell time switching problem, thereby obtaining a mathematical model of a switching affine system. According to the switching characteristics of the buck-boost DC-DC converter system, the corresponding switching affine system mathematical model is established, and the mathematical model of the switching affine system is as follows:

[0032]

[0033] in, Indicates the system status. represents the control input, Indicates the measurement output, is the affine term, Indicates a voltage source failure. represents disturbance, belonging to in represents the infinite norm; the switching signal σ(t) selects among K available subsystems, B σ(t) 、E σ(t) denote the system constant matrices with appropriate dimensions, A σ(t) , C σ(t)They represent the control input matrix and output matrix of the system respectively.

[0034] By Kirchhoff's voltage law, Figure 2 The circuit dynamics model shown can be described by the switching signal σ(t): Choose between 2 available subsystems.

[0035] The state space model of the circuit is described as shown in equation (1), and the system state is In this embodiment, K is set to 2, for example, Figure 2 There are 2 subsystems shown, and the coefficient matrix is ​​as follows:

[0036]

[0037] C1=C2=[1 0];

[0038] Among them, R e Represents resistance, C a Represents capacitance, E in Represents the input voltage source, L e represents inductance, i L represents the inductor current, v c In order to simplify the representation, σ(t) is represented by σ in the following steps.

[0039] σ is the subsystem index, which is the subsystem index at the switching time t d and t d+1 Activate between.

[0040] Assumption 1: The first-order derivative of the fault and disturbance Satisfy

[0041] Where ∈>0,∈2>0.

[0042] Assumption 2: For any complex number s, it has a non-negative real part:

[0043]

[0044] Where n is the dimension of the system state and rank(·) represents the rank of (·).

[0045] Assumption 3: Output matrix C1=C2=C K It is of full rank.

[0046] Step 2. Design a reduced-order observer for the system under voltage source fault and disturbance conditions to estimate the fault.

[0047] To design a reduced-order observer, first make variable substitutions as follows:

[0048]

[0049] Among them, T σ represents a given constant matrix, A vector representing the transformation.

[0050] The matrix is ​​chosen to be:

[0051] C i T i =[I q×q O q×(a-q) ] (3)

[0052] Among them C i represents the output matrix of the system, T i Represents a given constant matrix, and the subscript i represents the index of the currently active subsystem.

[0053] From formula (2), we know that based on the variable The state is represented as:

[0054]

[0055] in, represents a given equilibrium point, is a given constant vector, and f(t) represents a voltage source fault.

[0056] variable In formula (4), the separation is as follows:

[0057]

[0058] A wwσ express The component at the matrix (2, 2), A ywσ express The component at the matrix (1, 2), A wyσ express The component at the position of the matrix (2, 1), A yyσ express The component at the (1,1) position of the matrix, B yσ express The first component, B wσ express The second component, E σ1 express The first component, E σ2 express The second component, l yσ Indicates l σ The first component, lwσ Indicates l σ The second component of .

[0059] Here, assuming the state is measurable. Formula (5) can be organized as:

[0060]

[0061] Next, you need to design a system that relies on the unavailable state. and the new vector φ of the voltage source fault f(t) s (t).

[0062] Therefore, the first equation of formula (6) can be rewritten as:

[0063]

[0064] in represents the output vector, which is equal to equation (7).

[0065] Then, the new equation is established as follows:

[0066]

[0067] Based on equation (8), a reduced-order observer is designed to obtain the state and voltage source fault information.

[0068] state The estimator of is expressed as:

[0069]

[0070] Here, L σ is the gain matrix to be designed. In addition, formula (9) is rewritten as:

[0071]

[0072] Obviously, Depends on To avoid the existence of Introduce the variable q(t):

[0073]

[0074] therefore, The estimate is rewritten as:

[0075]

[0076] Similarly, the fault estimator can be designed as:

[0077]

[0078] Among them, Q σ is the gain matrix to be determined. Then equation (14) can be rewritten as:

[0079]

[0080] By variable substitution Replace the above formula into the following form:

[0081]

[0082] Finally, the reduced-order fault observer is given as follows:

[0083]

[0084] The system state error is used to describe the degree to which the system state and fault estimation values ​​deviate from the actual state and fault values. The system state estimation error and fault estimation error are now defined as:

[0085]

[0086] in represents the system state estimation error, e f (t) represents the fault estimation error.

[0087] Then we get the following description of system state and fault estimation error:

[0088]

[0089] In step 2, the system state and voltage source fault are estimated by designing a reduced-order observer, thereby providing necessary fault information for the dynamic output feedback fault-tolerant control in step 3.

[0090] Step 3. Design a dynamic output feedback fault-tolerant controller for the system under voltage source fault and disturbance conditions, and use the dynamic output feedback fault-tolerant controller to achieve stable and safe operation of the buck-boost DC-DC converter.

[0091] Specifically, the dynamic output feedback fault-tolerant controller designed by the present invention is as follows:

[0092]

[0093] Where u(t) is the controller input, represents the state of the dynamic output feedback fault-tolerant controller, A dσ , B dσ , C dσ and l dσ are the gain matrices of the dynamic output feedback fault-tolerant controller to be designed.

[0094] The closed-loop equation of the system is as follows:

[0095]

[0096] in,

[0097] in, and represents the augmented matrix.

[0098]

[0099] Step 4. Use the modal dependent Lyapunov function to perform gain analysis on the system, obtain the conditions for the actual exponential stability of the system and obtain the reduced-order observer gain matrix and the dynamic output feedback fault-tolerant controller gain matrix.

[0100] Step 4.1. The observer gain matrix is ​​calculated as follows:

[0101] Given a scalar γ i ≥0,κ>0, if there exists a positive definite matrix P wσ , P yσ , the matrix W σ , H σ and scalar ρ1>0,μ i ≥1β>0, so that Established.

[0102] The matrix is ​​specifically expressed as follows:

[0103]

[0104] Among them, the MDADT constraints for the switching signal are as follows:

[0105]

[0106] Then, the error system and is exponentially stable.

[0107] The reduced-order observer gain matrix is ​​obtained as:

[0108]

[0109] in addition, Gain from To e f (t) is determined to be:

[0110]

[0111] in, It is calculated by formula (25), and v(ψ(0)) is calculated by (26). λmax represents the maximum eigenvalue, K is a positive integer, and the subsystem is from the set Take the value from.

[0112] Step 4.2. The controller gain matrix is ​​calculated as follows:

[0113] Given a scalar γ i ≥0,κ>0, if there exists a positive definite matrix Θ i ,matrix and scalars μ>0, ρ>0, c0>0, such that: Established.

[0114] The matrix is ​​specifically expressed as follows:

[0115]

[0116]

[0117] Then, the closed-loop system When , it is calmed by the index to the following area:

[0118]

[0119] in, represents the convergence region, λ′ min (P i ) represents the matrix P i The minimum eigenvalue of represents the square of the bound of the fault estimation error. The switching signal satisfies the MDADT switching constraint as follows:

[0120]

[0121] in:

[0122]

[0123] where Θ i and W i is a symmetric matrix, V i and M i is an arbitrary non-singular matrix.

[0124] The corresponding controller gains are obtained as:

[0125]

[0126] in, and M i is the matrix to be determined,

[0127] and μ i ≥1 satisfies:

[0128]

[0129] have:

[0130]

[0131] also, Gain from to y q (t) is given as:

[0132]

[0133] in, for Gain The previous coefficients are calculated by formula (28): represents the initial state of the closed-loop system, express The initial state of the gain can be calculated using equation (29).

[0134] After obtaining the dynamic output feedback fault-tolerant controller and the reduced-order observer gain, the designed reduced-order observer is used to obtain fault estimation information, and then the fault estimation information is brought into the dynamic output feedback fault-tolerant controller to compensate for the fault, thereby facilitating the buck-boost DC-DC converter to operate stably and safely in the presence of a fault.

[0135] The buck-boost DC-DC converter fault-tolerant control method provided by the present invention can ensure that the system can still operate safely and stably when the system is disturbed by the outside world and there is a voltage source fault (i.e., an actuator fault).

[0136] Example 2

[0137] This embodiment 2 describes a buck-boost DC-DC converter fault-tolerant control system, which is based on the same inventive concept as the buck-boost DC-DC converter fault-tolerant control method described in the above embodiment 1.

[0138] The buck-boost DC-DC converter fault-tolerant control system in this embodiment includes the following modules:

[0139] Model building module, used to build the mathematical model of the buck-boost DC-DC converter test simulation system;

[0140] When the buck-boost DC-DC converter has both voltage source fault and disturbance, the buck-boost DC-DC converter with switching characteristics is considered as a switching affine system with average dwell time switching property.

[0141] The observer module is used to design a reduced-order observer for the system in the presence of voltage source faults and disturbances to estimate the faults;

[0142] Fault-tolerant control module, used to design dynamic output feedback fault-tolerant controller for the system under the conditions of voltage source fault and disturbance, so as to realize stable and safe operation of buck-boost DC-DC converter;

[0143] And the gain analysis module is used to perform gain analysis on the system using the mode-dependent Lyapunov function, obtain the conditions for the actual exponential stability of the system and obtain the reduced-order observer gain matrix and the dynamic output feedback fault-tolerant controller gain matrix.

[0144] It should be noted that in the buck-boost DC-DC converter fault-tolerant control system of this embodiment 2, the implementation process of the functions and effects of each functional module is specifically described in the implementation process of the corresponding steps in the method in the above embodiment 1, and will not be repeated here.

[0145] Example 3

[0146] This embodiment 3 describes a computer device, which includes a memory and one or more processors. The memory stores executable code. When the processor executes the executable code, it is used to implement the steps of the buck-boost DC-DC converter fault-tolerant control method in the above embodiment 1.

[0147] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0148] Example 4

[0149] This embodiment 4 describes a computer-readable storage medium on which a program is stored. When the program is executed by a processor, it is used to implement the steps of the buck-boost DC-DC converter fault-tolerant control method in the above embodiment 1.

[0150] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card, etc. equipped on the device.

[0151] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with the field under the guidance of this specification fall within the essential scope of this specification and should be protected by the present invention.

Claims

1. A fault-tolerant control method for a buck-boost DC-DC converter, characterized in that: The steps include: Step 1. Build a mathematical model of the buck-boost DC-DC converter test simulation system; When the buck-boost DC-DC converter has voltage source fault and disturbance at the same time, the buck-boost DC-DC converter with switching characteristics is considered as a switching affine system with average dwell time switching property. Step 2. Design a reduced-order observer for the system under voltage source fault and disturbance conditions to estimate the fault; Step 3. Design a dynamic output feedback fault-tolerant controller for the system under voltage source fault and disturbance conditions, and use the dynamic output feedback fault-tolerant controller to achieve stable and safe operation of the buck-boost DC-DC converter; Step 4. Use the modal dependent Lyapunov function to perform gain analysis on the system, obtain the conditions for the actual exponential stability of the system and obtain the reduced-order observer gain matrix and the dynamic output feedback fault-tolerant controller gain matrix; In step 1, according to the switching characteristics of the buck-boost DC-DC converter system, a corresponding switching affine system mathematical model is established. The mathematical model of the switching affine system is as follows: in, Indicates the system status. represents the control input, Indicates the measurement output, is the affine term, Indicates voltage source failure; represents disturbance, belonging to represents the infinite norm; the switching signal σ(t) selects among K available subsystems, B σ(t) 、E σ(t) Respectively represent the system constant matrix; A σ(t) , C σ(t) Respectively represent the control input matrix and output matrix of the system; to simplify the representation, σ is used to represent σ(t); In step 2, the process of establishing a reduced-order observer is as follows: First, replace the variables as follows: Among them, T σ represents a given constant matrix, The vector representing the transformation, σ at the switching time t d and t d+1 Activate between; The matrix is ​​chosen to be: C σ T σ =[I q×q 0 q×(a-q) ] (3) From the above formula, we know that based on the variable The state is represented as: in, represents a given equilibrium point, is a given constant vector, variable In formula (4), it is separated as follows: in, for Component, f(t) is the voltage source fault, A wwσ , A ywσ , A wyσ , A yyσ for The weight, B yσ , B wσ for The weight, E σ1 、E σ2 for The weight, l yσ , l wσ for l σ The amount of Here, assuming the state is measurable, then formula (5) can be organized as: Next, design a system that depends on the unavailable state. and the new vector φ of the voltage source fault f(t) s (t); where superscripts a and q are letters used to represent the matrix dimensions, then the first equation of formula (7) can be rewritten as: in represents the output vector, which is equal to equation (8); Then, establish the new equation as follows: Based on the above formula (9), a reduced-order observer is designed to obtain the state and voltage source fault information; state Estimation of It is expressed as: in, express The estimated value of represents the fault estimate, Denotes the new vector φ s The estimated value of (t), L σ is the gain matrix of the reduced-order observer to be designed; Rewrite (10) as: To avoid the existence of Introduce the variable q(t): therefore, Estimation of Rewritten as: The fault estimator is designed as: Among them, Q σ represents the reduced-order observer gain matrix; Then formula (14) can be rewritten as: By variable substitution Replace formula (15) with the following form: Finally, the reduced-order fault observer is given as follows:

2. The buck-boost DC-DC converter fault-tolerant control method according to claim 1, characterized in that: In step 2, the system state error is used to describe the degree to which the system state and the fault estimation value deviate from the actual state and fault value. The system state estimation error and the fault estimation error are now defined as: in represents the system state estimation error, e f (t) represents the fault estimation error; Then we get the following description of system state and fault estimation error:

3. The fault-tolerant control method for a buck-boost DC-DC converter according to claim 2, characterized in that: In step 3, the designed dynamic output feedback fault-tolerant controller is as follows: in, represents the state of the dynamic output feedback fault-tolerant controller, A dσ , B dσ , C dσ and l dσ are the gain matrices of the dynamic output feedback fault-tolerant controller to be designed.

4. The fault-tolerant control method for a buck-boost DC-DC converter according to claim 3, characterized in that: In step 3, the closed-loop equation of the system is as follows: in, and represents the augmented matrix; 5. The fault-tolerant control method for a buck-boost DC-DC converter according to claim 4, characterized in that: In step 4, the calculation expression of the gain matrix of the reduced-order observer and the dynamic output feedback fault-tolerant controller is: The calculation expression of the gain matrix of the reduced-order observer is: Among them, W σ and H σ is the matrix to be solved, P wσ , P yσ is a positive definite matrix; The calculation expressions of the gain matrix of the dynamic output feedback fault-tolerant controller are shown in formulas (26) to (29): Among them, A dσ , B dσ , C dσ and l dσ By solving the linear matrix inequality conditions, V σ is a non-singular matrix, Θ σ , Υ σ , and is the matrix to be solved, M σ pass Please solve.

6. A buck-boost DC-DC converter fault-tolerant control system for implementing the buck-boost DC-DC converter fault-tolerant control method according to claim 1, characterized in that: The buck-boost DC-DC converter fault-tolerant control system comprises the following modules: Model building module, used to build the mathematical model of the buck-boost DC-DC converter test simulation system; When the buck-boost DC-DC converter has both voltage source fault and disturbance, the buck-boost DC-DC converter with switching characteristics is considered as a switching affine system with average dwell time switching property. The observer module is used to design a reduced-order observer for the system in the presence of voltage source faults and disturbances to estimate the faults; Fault-tolerant control module, used to design a dynamic output feedback fault-tolerant controller for the system under the conditions of voltage source faults and disturbances, so as to achieve stable and safe operation of the buck-boost DC-DC converter; And the gain analysis module is used to perform gain analysis on the system using the mode-dependent Lyapunov function, obtain the conditions for the actual exponential stability of the system and obtain the reduced-order observer gain matrix and the dynamic output feedback fault-tolerant controller gain matrix.

7. A computer device comprising a memory and one or more processors; an executable code is stored in the memory; characterized in that: When the processor executes the executable code, it is used to implement the steps of the buck-boost DC-DC converter fault-tolerant control method described in any one of claims 1 to 5.

8. A computer-readable storage medium having a program stored thereon; characterized in that: When the program is executed by a processor, it is used to implement the steps of the buck-boost DC-DC converter fault-tolerant control method described in any one of claims 1 to 5.

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