CN114914888B - Multi-fault estimation method for single-phase three-level rectifier - Google Patents
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Abstract
The invention provides a multi-fault estimation method for a single-phase three-level rectifier, and belongs to the field of fault diagnosis. The method specifically comprises the steps of establishing a state space expression with an actuator fault and a sensor fault, converting the system into two reduced-order subsystems through nonsingular transformation, designing a sliding mode observer for the subsystem with the actuator fault, and estimating the actuator fault by combining an equivalent output control principle. Meanwhile, through designing a generalized reduced-order self-adaptive sliding mode observer, the occurrence of buffeting can be effectively reduced, and partial state variables and sensor faults can be accurately estimated. Compared with the prior art, the generalized reduced-order self-adaptive sliding-mode observer reduces the dimension of the observer, achieves the purpose of reducing the design complexity of the observer, ensures the convergence rate, effectively eliminates the buffeting phenomenon when reaching the sliding-mode surface, and improves the accuracy of system estimation.
Description
Technical Field
The invention belongs to the field of power fault diagnosis, and particularly relates to a multi-fault estimation method for a single-phase three-level rectifier.
Background
As one of the key components in the electric traction drive system, the single-phase three-level rectifier has very high reliability requirements, but is extremely prone to faults in the long-time operation process and the complex and changeable working environment. For a single-phase three-level rectifier, when the power device has an open-circuit fault, if the open-circuit fault cannot be processed in time, the adjacent device can bear excessive voltage and current, so that secondary faults occur, and more power devices are damaged; when the voltage sensor at the output end is damaged due to some external factors, the measured data is abnormal, and serious loss is caused, so that the life safety of people is threatened. Therefore, both the actuator fault and the sensor fault can reduce the reliability of the system and even cause safety accidents, and it is important to diagnose the actuator fault and the sensor fault in time.
As the fault diagnosis method, there are mainly two types, a data-driven-based method and an analytical model-based method.
1. Based on a data driving method, the method collects, analyzes and processes input and output signals, so that fault diagnosis is realized according to the extracted characteristic value variable.
The electrical engineering theory report in 2020, "fault diagnosis of the three-level inverter based on energy spectrum entropy and active neutral point clamping of a wavelet neural network" (Li Bing, cui Jiebing, he Yigang, shi Loujiang, liu Xiaohui) researches that the voltage signal characteristic quantity of a three-level inverter bridge arm is extracted through wavelet packet energy spectrum entropy, optimizes the characteristic vector by utilizing a principal component analysis method, performs fault diagnosis through a wavelet neural network method, and finally verifies that the method has the advantages of high identification speed, high precision and the like through experiments.
Although the data driving-based method has the advantages of strong adaptability, high sensitivity and the like in the field of fault diagnosis, certain difficulty exists due to large calculated amount and complex algorithm in the data processing process; in addition, there are many problems such as difficulty in selecting parameters and high hardware requirements.
2. The method based on the analytical model still takes the dominant role in the fault diagnosis field at present, a proper state observer is designed by referring to a mathematical model of a system, the estimated quantity and the actual state quantity are compared, residual information is obtained, the information is analyzed, and a certain evaluation index is used for detecting faults.
The 2002 AUTOMATICA document "Sliding mode observers for detection and reconstruction of sensor faults" (TAN C P, EDWARDS C.) ("sliding mode observer for detecting and reconstructing sensor faults" (TAN C P, EDWARDS C.)) proposes two methods for detecting and reconstructing actuator faults with the sliding mode observer, but both of them must meet certain conditions, so the application scope is narrow;
the university of aviation aerospace in Beijing in 2013 reports "sensor fault detection and signal reconstruction method based on observer" (Xia Jie, xu Jing Beijing, etc.), and the sensor fault signal reconstruction is realized by a coordinate transformation and sliding mode observer method, but only the sensor fault of a linear system is detected.
The IEEE literature "Reduced-Order Sliding-Mode-unserver-Based Fault Estimation for Markov Jump Systems" (Hongyan Yang, shen Yin) ("Reduced Sliding-Mode Observer-based markov jump system fault estimation" (Hongyan Yang, shen Yin)), in 2019, for a markov jump system having both an actuator fault and a sensor fault, the actuator fault is directly reconstructed, and the estimated values of the actuator fault, the sensor fault and the state variables can be obtained through a designed novel Reduced Sliding-Mode Observer, thereby avoiding the problems of Sliding surface reachability analysis and Sliding surface switching.
In summary, the fault estimation method for the single-phase three-level rectifier with multiple faults currently has the following disadvantages:
1. for a single-phase three-level rectifier, only sensor faults are often researched, and researches on faults of an actuator and the sensor are less;
2. when fault estimation is achieved by a sliding mode observer-based method, the problems of low estimation speed, large buffeting and the like often exist
3. When an observer is designed for a fault system, the problems of high dimension, complex observer design and the like often exist.
Disclosure of Invention
The invention aims to provide a multi-fault synchronous estimation method for a single-phase three-level rectifier with an actuator fault and a sensor fault. Specifically, an original system is converted into two reduced-order subsystems through nonsingular transformation, a sliding mode observer is designed for the subsystem containing the actuator faults, and the reconstruction of the actuator faults is carried out by combining an equivalent output control principle; meanwhile, through designing a generalized reduced-order self-adaptive sliding mode observer, the occurrence of buffeting can be effectively reduced, and partial state variables and sensor faults can be accurately estimated. When the system has the fault of the actuator and the fault of the sensor, the fault estimation method can accurately estimate the information such as the amplitude, the size and the like of the fault.
In order to achieve the above objective, a multi-fault estimation method for a single-phase three-level rectifier involves a circuit topology structure including a network side voltage source U s Net side equivalent inductance L s And net side equivalent resistance R s The rectifier bridge, two identical supporting capacitors, a direct-current side load and two identical voltage sensors are respectively marked as supporting capacitor C d1 And a supporting capacitor C d2 Two identical voltage sensors are respectively denoted as voltage sensor S V1 And a voltage sensor S V2 Wherein the voltage sensor S V1 Connected to the supporting capacitor C d1 Voltage sensor S V2 Connected to the supporting capacitor C d2 Is provided; support capacitor C d1 And a supporting capacitor C d2 The series connection is connected in parallel between a direct current positive bus P and a direct current negative bus Q of the direct current side load, and supports a capacitor C d1 And a supporting capacitor C d2 The contact point of the (a) is marked as a midpoint O of the direct current bus;
the rectifier bridge comprises two-phase bridge arms, which are respectively marked as a bridge arm a and a bridge arm b; in two-phase bridge arms, each bridge arm comprises 4 switching tubes with reverse diodes, 2 clamping diodes, i.e. the rectifier bridge comprises 8 switching tubes with reverse diodesAnd 4 clamping diodes; the 8 switching tubes are denoted as switching tube V kγ K is bridge sequence, k=a, b, gamma represents the serial number of the switching tube, and gamma=1, 2,3,4; let 4 clamp diodes be denoted as clamp diode D ckl L represents the serial number of the clamp diode, l=1, 2; in each of the two phase legs, switching tube V k1 Switch tube V k2 Switch tube V k3 And a switching tube V k4 In series in turn, switch tube V k2 And a switching tube V k3 Is marked as the input point tau of the rectifier bridge k K=a, b; in each of the two-phase legs, a clamp diode D ck1 The cathode of (C) is connected with the switch tube V k1 And a switching tube V k2 Between, clamp diode D ck1 Is connected with the clamping diode D by the anode ck2 Clamping diode D ck2 The anode of (C) is connected with the switch tube V k3 And a switching tube V k4 Between, and clamp diode D ck1 And a clamp diode D ck2 The connecting point of the (a) is connected with the midpoint O of the direct current bus;
the net side equivalent inductance L s Is connected with the input point tau of the rectifier bridge a The other end is sequentially connected with the equivalent resistor R at the net side S Network side voltage source U s The other end of the network side voltage source is connected with the input point tau of the rectifier bridge in series b ；
The multi-fault estimation method is characterized by comprising the following steps of:
step 1, establishing a mixed logic dynamic model of a single-phase three-level rectifier
The mixed logic dynamic expression of the single-phase three-level rectifier is as follows:
Wherein,for the estimated value of the input phase voltage, +.>For the estimated value of the a-phase pole voltage, +.>An estimated value of b-phase pole voltage; u (u) 1 To support the capacitor C d1 The voltage at two sides is recorded as a first DC voltage u 1 ；u 2 To support the capacitor C d2 The voltage at two sides is recorded as a second DC voltage u 2 ；S 1 For the first direct current voltage u 1 Is a mixed logic dynamic function of S 2 At a second DC voltage u 2 Is a mixed logic dynamic function of (1);
step 2, establishing a state space model of the single-phase three-level rectifier system with multiple faults
The single-phase three-level rectifier system with multiple faults is recorded as a multiple fault system 1, and the state space model expression of the multiple fault system 1 is as follows:
wherein t is time; x (t) is a state variable of the multi-fault system 1, belonging to an n-dimensional space, denoted as a first state variable x (t),i s is the network side current; />Is the derivative of the first state variable x (t) with respect to time, belonging toIn the n-dimensional space, the first derivative is marked +.> For the net side current i s Derivative with respect to time, < >>For the first direct current voltage u 1 Derivative with respect to time, < >>At a second DC voltage u 2 Derivative with respect to time; u (t) represents input, belongs to m-dimensional space, u (t) ∈R m ；f a (t) is an actuator failure belonging to a-dimensional space, f a (t)∈R a ；f s (t) sensor faults, belonging to s-dimensional space, Wherein f u1 (t) is a voltage sensor S V1 Failure belongs to j-dimensional space, f u1 (t)∈R j ，f u2 (t) is a voltage sensor S V2 Failure belongs to k-dimensional space, f u2 (t)∈R k The method comprises the steps of carrying out a first treatment on the surface of the y (t) is the output of the multi-fault system 1, belonging to the p-dimensional space, denoted as the first output variable y (t), y (t) ∈R p ；
A i Is a state coefficient matrix of a first state variable x (t), and is recorded as a first state coefficient matrix A i ，Wherein L is the equivalent inductance L of the network side s R is the net side equivalent resistance R s Resistance value C of (C) 1 To support the capacitor C d1 Capacitance value C of (C) 2 To support the capacitor C d2 Capacitance value of (2)The method comprises the steps of carrying out a first treatment on the surface of the i is a normal number, and i=1, 2,..9; b is the coefficient matrix of input u (t), denoted as the first input matrix B, ">C is an output matrix of the multi-fault system 1 and is marked as a first output matrix C; f (F) s For sensor failure f s The coefficient matrix of (t) belongs to p x s dimension space and is marked as a first sensor fault matrix F s ，F s ∈R p×s ；F a For actuator failure f a The coefficient matrix of (t) belonging to n×a, denoted as first actuator failure matrix F a ，F a ∈R n×a ；
Failure f of actuator a (t), voltage sensor failure f s (t) is a continuous and bounded function with respect to the time variable t, satisfying ||f a (t) delta and f s (t) f is less than or equal to ω a (t) || represents an actuator failure f a The 2-norm of (t), I F s (t) || represents a sensor failure f s (t) 2-norm, delta representing actuator failure f a Upper bound of (t), ω represents voltage sensor fault f s The upper bound of (t), δ, ω are both known positive constants;
step 3, establishing a state space model of the multi-fault system 2
Introducing a first nonsingular transformation matrix T and a second nonsingular transformation matrix S, and carrying out coordinate transformation on the multi-fault system 1;
coordinate transformation z (t) =tx (t),transforming the multi-fault system 1 into the multi-fault system 2, the state space model expression of the multi-fault system 2 is as follows:
where z (t) is a state variable of the multi-fault system 2, denoted as a second state variable z (t),z 1 (t) the first state component of the second state variable, belonging to the l-dimensional space, denoted as the third state variable z 1 (t)，z 1 (t)∈R l ；z 2 (t) a second state component of the second state variable, belonging to the n-l dimensional space, denoted as a fourth state variable z 2 (t)，z 2 (t)∈R n-l ；/>The time derivative of the second state variable z (t) is denoted as second derivative +.> Is the third state variable z 1 (t) the derivative with respect to time, denoted as third derivative +.> Is the fourth state variable z 2 (t) derivative with respect to time, noted as fourth derivative +.> Is the output of the multiple fault system 2 belonging to the p-dimensional space, denoted second output variable +.> Wherein y is 1 (t) is the second output variable +. >The upper component of (2) belonging to the l-dimensional space, denoted as the third output variable y 1 (t)，y 1 (t)∈R l ；y 2 (t) is the second output variable +.>The lower component of (2) belonging to the p-l dimensional space, denoted as the fourth output variable y 2 (t)，/>Wherein y is 21 (t) is the upper component of the fourth output variable, belonging to e-dimensional space, i.e., y 21 (t)∈R e ，y 22 (t) is the upper component of the fourth output variable, belonging to the f-dimensional space, i.e., y 22 (t)∈R f ；
Is a coefficient matrix of the second state variable z (t), denoted as second state coefficient matrix +.> A i1 Is a second state coefficient matrix->The upper left matrix belonging to l×l dimensional space is denoted as the second upper left matrix A i1 ，A i1 ∈R l×l ；A i2 Is a second state coefficient matrix->The upper right matrix belonging to the l× (n-l) dimensional space is denoted as the second upper right matrix A i2 ，A i2 ∈R l×(n-l) ；A i3 Is a second state coefficient matrix->The lower left matrix belonging to the (n-l) x l dimensional space is denoted as the second lower left matrix A i3 ，A i3 ∈R (n-l)×l ；A i4 Is a second state coefficient matrix->The lower right matrix belonging to the (n-l) x (n-l) dimensional space is denoted as the second lower right matrix A i4 ，A i4 ∈R (n-l)×(n-l) ；/>Is the coefficient matrix of input u (t), denoted as second input matrix +.> Wherein B is 1 Is the second input matrix +.>Belongs to the l×m dimensional space and is marked as a second input upper matrix B 1 ，B 1 ∈R l×m ，B 2 Is the second input matrix +.>Belongs to (n-l) x m dimensional space and is denoted as a second input lower matrix B 2 ，B 2 ∈R (n-l)×m ；Is the failure f of the actuator a The coefficient matrix of (t) is marked as a second actuator failure matrix +.> Wherein F is a1 Is a second actuator failure matrix->Is a first upper matrix F of the second actuator fault, belonging to the l x a dimension space a1 ，F a1 ∈R l×a ；/>The output matrix of the multi-fault system 2 is denoted as second output matrix +.> Wherein C is 1 Is the second output matrix->Is denoted as the third output matrix C 1 ，C 4 Is the second output matrix->Is denoted as the fourth output matrix C 4 ；/>Is a sensor fault f s The coefficient matrix of (t) is denoted as second sensor failure matrix +.> Wherein F is s2 Is a second sensor failure matrix +.>Belongs to (p-l)) The x s dimension space is recorded as a matrix F under the fault of the second sensor s2 ，F s2 ∈R (p-l)×s ；
The multi-fault system 2 is decomposed into two reduced order subsystems as follows:
the state space model expression of subsystem 1 is:
the state space model expression of subsystem 2 is:
step 4, system expansion is carried out on the subsystem 2
The state space expression of the expanded subsystem 2 is:
wherein,the state variable of the expanded subsystem 2 belongs to the n-l+s dimension space and is marked as a fifth state variable +.> For the fifth state variable->The derivative with respect to time, denoted fifth derivative->
Is the fifth derivative->Is a coefficient matrix belonging to (n-l+s) x (n-l+s) dimensional space, Wherein I is n-l A unit matrix representing an (n-l) x (n-l) dimensional space; />For the fifth state variable->Is marked as a third state coefficient matrix +.> I s An identity matrix representing an s x s dimensional space; />Is the third state variable z 1 The coefficient matrix of (t) is denoted as the fourth state coefficient matrix +.> The coefficient matrix for input u (t) is denoted as the third input matrix +.> Is a sensor fault f s The coefficient matrix of (t) is marked as a third sensor failure matrix +.> Is the output matrix of the expanded subsystem 2, denoted fifth output matrix +.> I p-l A unit matrix representing a (p-l) x (p-l) dimensional space;
step 5, observer design
For subsystem 1, a sliding mode observer is designed as follows:
wherein,is the third state variable z 1 Estimate of (t)/(t)>Is the third state variable z 1 Estimate of (t)Derivative with respect to time; d (D) 1 Is a sliding mode gain matrix, taking D 1 ＝F a1 The method comprises the steps of carrying out a first treatment on the surface of the The v (t) is the approach rate,e 1 (t) is the first observation error, and +.>ρ is the sliding mode gain, ρ is less than or equal to δ - ρ 0 ，ρ 0 ＝0.2；L 1 For the first matrix to be designed, P 1 Is a first li-apunov matrix; />For the third output variable y 1 An estimate of (t);
for the expanded subsystem 2, an adaptive reduced order sliding mode observer is designed as follows:
wherein,is the fifth state variable +. >Is a function of the estimated value of (2); ζ (t) is a sixth state variable belonging to the n-l+s dimension space, ++>ξ 1 (t) is the first component, ζ, of the sixth state variable 2 (t) is the sixth state variable second component, ζ 3 (t) is the third component, ζ, of the sixth state variable 4 (t) a fourth component of a sixth state variable; />Is the derivative of the sixth state variable ζ (t) with respect to time, denoted sixth derivative +.>
For the sixth derivative->Is denoted as a fifth coefficient matrix-> Belongs to a nonsingular matrix, wherein ∈>For the intermediate matrix to be designed, < > for>Is an intermediate matrix to be designed->Belongs to the (p-l) x (p-l) dimension and is denoted as the second matrix to be designed +.>And is also provided with Is an intermediate matrix to be designed->Belongs to the (p-l) x (p-l) dimension and is denoted as the third matrix to be designed->And-> Coefficient matrix for the sixth state variable ζ (t), +.> Is a proportional gain matrix> For the fifth coefficient matrix->An inverse matrix of (a); />Is a sliding mode gain matrix>u s (t) is a sliding mode control item, < ->Wherein f(s) is a constant velocity approach factor, ++>e is a natural index, eta is a constant, 0 < eta < 1, epsilon is an index approach coefficient, epsilon=20, s (t) is a sliding mode surface, and->Wherein,for the fifth coefficient matrix->Is>Transposed matrix of>For the second Leidefenof matrix, < - > and- >Is the second observation error, and->
Step 6, solving the matrix to be designed
The matrix to be designed comprises a first matrix to be designed L 1 A second matrix to be designedAnd a third matrix to be designed->
Order theWherein (1)>To observe the total error; according to the expressions of the subsystem 1, the expanded subsystem 2, the sliding mode observer and the self-adaptive reduced order sliding mode observer, an error dynamic equation is obtained as follows:
wherein,is the first observed error e 1 (t) derivative with respect to time, < >>Is the second observation error->Derivative with respect to time;
for in the dynamic error equationPerforming pole allocation to obtain a first matrix L to be designed 1 ；
In the equation of known dynamic errorSensor failure f s The coefficient matrix of (t) is +.> Setting a second matrix to be designedAnd a third matrix to be designed->Wherein->
Step 7, performing fault estimation of the actuator and the sensor
Step 7.1, estimating the actuator failure
Will beRecorded as actuator failure f a An estimated value of (t), v eq (t) the equivalent output control signal of the approach ratio v (t), then the actuator failure estimation value +.>The method comprises the following steps:
wherein δ is a positive scalar, δ=0.1;
step 7.2, estimating the voltage sensor failure
Will beIs denoted as voltage sensor S V1 Failure f u1 Estimate of (t)/(t)>Is denoted as voltage sensor S V2 Failure f u2 Calculating the estimated value of (t) and calculating the voltage sensor S V1 Failure f u1 Estimate of (t)>Voltage sensor S V2 Failure f u2 Estimate of (t)>The specific calculation formula is as follows:
so far, the multi-fault estimation of the single-phase three-level rectifier is finished.
Preferably, the first DC voltage u in step 1 1 Is a mixed logic dynamic function S of 1 And a second DC voltage u 2 Is a mixed logic dynamic function S of 2 The calculation process of (2) is as follows:
wherein S is a Is a switching function of a phase bridge arm, S b Is the switching function of the b-phase bridge arm; switch tube V kγ The pulse control signal of (2) isk=a, b, γ=1, 2,3,4, then the switching function of the a-phase leg +.>Switching function of b-phase bridge arm>
Compared with the prior art, the invention has the beneficial effects that:
1. through designing the novel index approach rate, the system state variable is guaranteed to be converged to the sliding mode surface rapidly, the buffeting phenomenon when reaching the sliding mode surface is effectively eliminated, and the accuracy of system estimation is improved.
2. By designing the gain of the observer, the negative influence of faults on the system is reduced, the stability of the observer is improved, and the accuracy of state variable and fault information estimation is improved.
3. The generalized reduced order sliding mode observer is designed, and the dimension of the observer is reduced, so that the purpose of reducing the design complexity of the observer is achieved.
4. When the single-phase three-level rectifier has the actuator fault and the sensor fault at the same time, the method can accurately estimate the fault type and related information on line.
Drawings
FIG. 1 is a topology of a single phase three level rectifier in an example of the invention;
FIG. 2 is a schematic diagram of a multi-fault synchronization estimation method in an example of the invention;
FIG. 3 is a schematic representation of a design of a multiple fault synchronization estimation method in accordance with an example of the present invention;
FIG. 4 is an actuator failure f in the present embodiment a (t) and its estimateIs a simulation diagram of (1);
fig. 5 is a diagram of a sensor failure f in the present embodiment u1 (t) and its estimateIs a simulation diagram of (1);
FIG. 6 is a sensor failure f in the present embodiment u2 (t) and its estimateIs a simulation of the above.
Detailed description of the preferred embodiments
The present invention will be described in further detail with reference to the accompanying drawings.
FIG. 1 is a circuit topology of a single-phase three-level rectifier according to an embodiment of the invention, and as can be seen from FIG. 1, the circuit topology includes a network side voltage source U s Net side equivalent inductance L s And net side equivalent resistance R s The rectifier bridge, two identical supporting capacitors, a direct-current side load and two identical voltage sensors are respectively marked as supporting capacitor C d1 And a supporting capacitor C d2 Two identical voltage transmissionsThe sensors are respectively marked as voltage sensors S V1 And a voltage sensor S V2 Wherein the voltage sensor S V1 Connected to the supporting capacitor C d1 Voltage sensor S V2 Connected to the supporting capacitor C d2 Is provided; support capacitor C d1 And a supporting capacitor C d2 The series connection is connected in parallel between a direct current positive bus P and a direct current negative bus Q of the direct current side load, and supports a capacitor C d1 And a supporting capacitor C d2 The junction point of (2) is denoted as the midpoint O of the dc bus.
The rectifier bridge comprises two-phase bridge arms, which are respectively marked as a bridge arm a and a bridge arm b; in the two-phase bridge arm, each bridge arm comprises 4 switching tubes with reverse connection diodes and 2 clamping diodes, namely, the rectifier bridge totally comprises 8 switching tubes with reverse connection diodes and 4 clamping diodes; the 8 switching tubes are denoted as switching tube V kγ K is bridge sequence, k=a, b, gamma represents the serial number of the switching tube, and gamma=1, 2,3,4; let 4 clamp diodes be denoted as clamp diode D ckl L represents the serial number of the clamp diode, l=1, 2; in each of the two phase legs, switching tube V k1 Switch tube V k2 Switch tube V k3 And a switching tube V k4 In series in turn, switch tube V k2 And a switching tube V k3 Is marked as the input point tau of the rectifier bridge k K=a, b; in each of the two-phase legs, a clamp diode D ck1 The cathode of (C) is connected with the switch tube V k1 And a switching tube V k2 Between, clamp diode D ck1 Is connected with the clamping diode D by the anode ck2 Clamping diode D ck2 The anode of (C) is connected with the switch tube V k3 And a switching tube V k4 Between, and clamp diode D ck1 And a clamp diode D ck2 Is connected with the midpoint O of the DC bus.
The net side equivalent inductance L s Is connected with the input point tau of the rectifier bridge a The other end is sequentially connected with the equivalent resistor R at the net side S Network side voltage source U s The other end of the network side voltage source is connected with the input point tau of the rectifier bridge in series b 。
Fig. 2 is a schematic diagram of a multi-fault estimation method according to an embodiment of the present invention, and fig. 3 is a schematic diagram of a design mechanism of the multi-fault estimation method according to an embodiment of the present invention. As can be seen from fig. 2 and 3, the multi-fault estimation method comprises the steps of:
step 1, establishing a mixed logic dynamic model of a single-phase three-level rectifier
The mixed logic dynamic expression of the single-phase three-level rectifier is as follows:
wherein,for the estimated value of the input phase voltage, +.>For the estimated value of the a-phase pole voltage, +.>An estimated value of b-phase pole voltage; u (u) 1 To support the capacitor C d1 The voltage at two sides is recorded as a first DC voltage u 1 ；u 2 To support the capacitor C d2 The voltage at two sides is recorded as a second DC voltage u 2 ；S 1 For the first direct current voltage u 1 Is a mixed logic dynamic function of S 2 At a second DC voltage u 2 A hybrid logic dynamic function of (a).
Step 2, establishing a state space model of the single-phase three-level rectifier system with multiple faults
The single-phase three-level rectifier system with multiple faults is recorded as a multiple fault system 1, and the state space model expression of the multiple fault system 1 is as follows:
wherein t is time; x (t) is a state variable of the multi-fault system 1, belonging to an n-dimensional space, denoted as a first state variable x (t),i s is the network side current; />The derivative of the first state variable x (t) with respect to time, belonging to the n-dimensional space, is denoted as the first derivative +.> For the net side current i s Derivative with respect to time, < >>For the first direct current voltage u 1 Derivative with respect to time, < >>At a second DC voltage u 2 Derivative with respect to time; u (t) represents input, belongs to m-dimensional space, u (t) ∈R m ；f a (t) is an actuator failure belonging to a-dimensional space, f a (t)∈R a ；f s (t) sensor faults, belonging to s-dimensional space,wherein f u1 (t) is a voltage sensor S V1 Failure belongs to j-dimensional space, f u1 (t)∈R j ，f u2 (t) is a voltage sensor S V2 Failure belongs to k-dimensional space, f u2 (t)∈R k The method comprises the steps of carrying out a first treatment on the surface of the y (t) is the output of the multi-fault system 1, belonging to the p-dimensional space, denoted as the first output variable y (t), y (t) ∈R p ；
A i Is a state coefficient matrix of a first state variable x (t), and is recorded as a first state coefficient matrix A i ，Wherein L is the equivalent inductance L of the network side s R is the net side equivalent resistance R s Resistance value C of (C) 1 To support the capacitor C d1 Capacitance value C of (C) 2 To support the capacitor C d2 Is a capacitance value of (2); i is a normal number, and i=1, 2,..9; b is the coefficient matrix of input u (t), denoted as the first input matrix B, ">C is an output matrix of the multi-fault system 1 and is marked as a first output matrix C; f (F) s For sensor failure f s The coefficient matrix of (t) belongs to p x s dimension space and is marked as a first sensor fault matrix F s ，F s ∈R p×s ；F a For actuator failure f a The coefficient matrix of (t) belonging to n×a, denoted as first actuator failure matrix F a ，F a ∈R n×a ；
Failure f of actuator a (t), voltage sensor failure f s (t) is a continuous and bounded function with respect to the time variable t, satisfying ||f a (t) delta and f s (t) f is less than or equal to ω a (t) || represents an actuator failure f a The 2-norm of (t), I F s (t) || represents a sensor failure f s (t) 2-norm, delta representing actuator failure f a Upper bound of (t), ω represents voltage sensor fault f s The upper bound of (t), δ, ω are both known positive constants.
In the present embodiment, l=2.2×10 -3 H，R＝0.34Ω，C 1 ＝16×10 -3 Ω，C 2 ＝16×10 -3 Ω，n＝3，m＝1，a＝1，s＝2，p＝3，
Step 3, establishing a state space model of the multi-fault system 2
Introducing a first nonsingular transformation matrix T and a second nonsingular transformation matrix S, and carrying out coordinate transformation on the multi-fault system 1;
Coordinate transformation z (t) =tx (t),transforming the multi-fault system 1 into the multi-fault system 2, the state space model expression of the multi-fault system 2 is as follows:
where z (t) is a state variable of the multi-fault system 2, denoted as a second state variable z (t),z 1 (t) the first state component of the second state variable, belonging to the l-dimensional space, denoted as the third state variable z 1 (t)，z 1 (t)∈R l ；z 2 (t) a second state component of the second state variable, belonging to the n-l dimensional space, denoted as a fourth state variable z 2 (t)，z 2 (t)∈R n-l ；/>The time derivative of the second state variable z (t) is denoted as second derivative +.> Is the third state variable z 1 (t) the derivative with respect to time, denoted as third derivative +.> Is the fourth state variable z 2 (t) derivative with respect to time, noted as fourth derivative +.> Is the output of the multiple fault system 2 belonging to the p-dimensional space, denoted second output variable +.> Wherein y is 1 (t) is the second output variable +.>The upper component of (2) belonging to the l-dimensional space, denoted as the third output variable y 1 (t)，y 1 (t)∈R l ；y 2 (t) is the second output variable +.>The lower component of (2) belonging to the p-l dimensional space, denoted as the fourth output variable y 2 (t)，/>Wherein y is 21 (t) is the upper component of the fourth output variable, belonging to e-dimensional space, i.e., y 21 (t)∈R e ，y 22 (t) is the upper component of the fourth output variable, belonging to the f-dimensional space, i.e., y 22 (t)∈R f ；/>
Is a coefficient matrix of the second state variable z (t), denoted as second state coefficient matrix +. > A i1 Is a second state coefficient matrix->The upper left matrix belonging to l×l dimensional space is denoted as the second upper left matrix A i1 ，A i1 ∈R l×l ；A i2 Is a second state coefficient matrix->The upper right matrix belonging to the l× (n-l) dimensional space is denoted as the second upper right matrix A i2 ，A i2 ∈R l×(n-l) ；A i3 Is a second state coefficient matrix->The lower left matrix belonging to the (n-l) x l dimensional space is denoted as the second lower left matrix A i3 ，A i3 ∈R (n-l)×l ；A i4 Is a second state coefficient matrix->The lower right matrix belonging to the (n-l) x (n-l) dimensional space is denoted as the second lower right matrix A i4 ，A i4 ∈R (n-l)×(n-l) ；/>Is the coefficient matrix of input u (t), denoted as second input matrix +.> Wherein B is 1 Is the second input matrix +.>Belongs to the l×m dimensional space and is marked as a second input upper matrix B 1 ，B 1 ∈R l×m ，B 2 Is the second input matrix +.>Belongs to (n-l) x m dimensional space and is denoted as a second input lower matrix B 2 ，B 2 ∈R (n-l)×m ；Is the failure f of the actuator a The coefficient matrix of (t) is marked as a second actuator failure matrix +.> Wherein F is a1 Is a second actuator failure matrix->Is a first upper matrix F of the second actuator fault, belonging to the l x a dimension space a1 ，F a1 ∈R l×a ；/>The output matrix of the multi-fault system 2 is denoted as second output matrix +.> Wherein C is 1 Is the second output matrix->Is denoted as the third output matrix C 1 ，C 4 Is the second output matrix->Is denoted as the fourth output matrix C 4 ；/>Is a sensor fault f s The coefficient matrix of (t) is denoted as second sensor failure matrix +.> Wherein F is s2 Is a second sensor failure matrix +.>Belongs to the (p-l) x s dimensional space and is marked as a second sensor failure lower matrix F s2 ，F s2 ∈R (p-l)×s ；
The multi-fault system 2 is decomposed into two reduced order subsystems as follows:
the state space model expression of subsystem 1 is:
the state space model expression of subsystem 2 is:
the parameters in this example are as follows:
step 4, system expansion is carried out on the subsystem 2
The state space expression of the expanded subsystem 2 is:
wherein,the state variable of the expanded subsystem 2 belongs to the n-l+s dimension space and is marked as a fifth state variable +.> For the fifth state variable->The derivative with respect to time, denoted fifth derivative->
Is the fifth derivative->Is a coefficient matrix belonging to (n-l+s) x (n-l+s) dimensional space,wherein I is n-l A unit matrix representing an (n-l) x (n-l) dimensional space; />For the fifth state variable->Is marked as a third state coefficient matrix +.> I s An identity matrix representing an s x s dimensional space; />Is the third state variable z 1 The coefficient matrix of (t) is denoted as the fourth state coefficient matrix +.>/> The coefficient matrix for input u (t) is denoted as the third input matrix +.> Is a sensor fault f s The coefficient matrix of (t) is marked as a third sensor failure matrix +.> Is the output matrix of the expanded subsystem 2, denoted fifth output matrix +.> I p-l Representing the identity matrix of the (p-l) x (p-l) dimensional space.
In this embodiment:
step 5, observer design
For subsystem 1, a sliding mode observer is designed as follows:
wherein,is a third state variablez 1 Estimate of (t)/(t)>Is the third state variable z 1 Estimate of (t)Derivative with respect to time; d (D) 1 Is a sliding mode gain matrix, taking D 1 ＝F a1 The method comprises the steps of carrying out a first treatment on the surface of the The v (t) is the approach rate,e 1 (t) is the first observation error, and +.>ρ is the sliding mode gain, ρ is less than or equal to δ - ρ 0 ，ρ 0 ＝0.2；L 1 For the first matrix to be designed, P 1 Is a first li-apunov matrix; />For the third output variable y 1 An estimate of (t);
for the expanded subsystem 2, an adaptive reduced order sliding mode observer is designed as follows:
wherein,is the fifth state variable +.>Is a function of the estimated value of (2); ζ (t) is a sixth state variable belonging to the n-l+s dimension space, ++>ξ 1 (t) is the first component, ζ, of the sixth state variable 2 (t) is sixthSecond component of state variable, ζ 3 (t) is the third component, ζ, of the sixth state variable 4 (t) a fourth component of a sixth state variable; />Is the derivative of the sixth state variable ζ (t) with respect to time, denoted sixth derivative +. >
For the sixth derivative->Is denoted as a fifth coefficient matrix-> Belongs to a nonsingular matrix, wherein ∈>For the intermediate matrix to be designed,is an intermediate matrix to be designed->Belongs to the (p-l) x (p-l) dimension and is denoted as the second matrix to be designed +.>And is also provided with Is an intermediate matrix to be designed->Belongs to the (p-l) x (p-l) dimension and is denoted as the third matrix to be designed->And-> Coefficient matrix for the sixth state variable ζ (t), +.> Is a proportional gain matrix> For the fifth coefficient matrix->An inverse matrix of (a); />Is a sliding mode gain matrix>u s (t) is a sliding mode control item, < ->Wherein f(s) is a constant velocity approach factor, ++>e is a natural index, eta is a constant, 0 < eta < 1, epsilon is an index approach coefficient, epsilon=20, s (t) is a sliding mode surface, and->Wherein,for the fifth coefficient matrix->Is>Transposed matrix of>For the second Leidefenof matrix, < - > and->Is the second observation error, and->
In the present embodiment, in the case of the sliding mode control item u s (t) in the design, η=0.2 and ε=20.
Step 6, solving the matrix to be designed
The matrix to be designed comprises a first matrix to be designed L 1 A second matrix to be designedAnd a third matrix to be designed->
Order theWherein,/>to observe the total error; according to the expressions of the subsystem 1, the expanded subsystem 2, the sliding mode observer and the self-adaptive reduced order sliding mode observer, an error dynamic equation is obtained as follows:
Wherein,is the first observed error e 1 (t) derivative with respect to time, < >>Is the second observation error->Derivative with respect to time;
for in the dynamic error equationPerforming pole allocation to obtain a first matrix L to be designed 1 ；
In the equation of known dynamic errorSensor failure f s The coefficient matrix of (t) is +.> Setting a second matrix to be designedAnd a third matrix to be designed->Wherein->
In this embodiment:
to stabilize the observer of subsystem 1, take A i1 -L 1 C 1 = -3, the dynamic matrix L can be obtained 1 . Taking outThen->
Step 7, performing fault estimation of the actuator and the sensor
Step 7.1, estimating the actuator failure
Will beRecorded as actuator failure f a An estimated value of (t), v eq (t) the equivalent output control signal of the approach ratio v (t), then the actuator failure estimation value +.>The method comprises the following steps:
wherein δ is a positive scalar, δ=0.1;
step 7.2, estimating the voltage sensor failure
Will beIs denoted as voltage sensor S V1 Failure f u1 Estimate of (t)/(t)>Is denoted as voltage sensor S V2 Failure f u2 Calculating the estimated value of (t) and calculating the voltage sensor S V1 Failure f u1 Estimate of (t)>Voltage sensor S V2 Failure f u2 Estimate of (t)>The specific calculation formula is as follows: />
In this embodiment:
therefore, can obtain:
so far, the multi-fault estimation of the single-phase three-level rectifier is finished.
In order to demonstrate the technical effects of the present invention, simulations were performed on the present invention.
FIG. 4 is an example set up of actuator failure f a (t) and method of using the inventionEstimated actuator fault estimationIs a simulation waveform diagram of (1). Wherein, the solid line is the executor trouble of setting, and its mathematical expression is:
the dashed line is an estimated actuator failure. From this figure, it is clear that at 0-1.5s, the system has not failed, and at t=1.5 s, the system has failed, and the actuator failure estimate valueThe actuator fault f can be well estimated u (t)。
Fig. 5 is a voltage sensor S provided in the example V1 Failure f u1 (t) a voltage sensor S estimated by the method of the present invention V1 Estimated value of faultIs a simulation waveform diagram of (1). Wherein the solid line is a set sensor S V1 The mathematical expression of the voltage waveform when the complete failure fault occurs is as follows:
the dashed line is an estimated voltage sensor fault. From the figure, it can be seen that at 0-0.5S, no sensor failure occurs in the system, and at t=0.5S, the voltage sensor S V1 A complete failure fault occurs and the voltage sensor S V1 Estimated value of faultThe voltage sensor S can be well estimated V1 Failure f u1 (t)。
FIG. 6 is a real world The voltage sensor S provided in the example V2 Failure f u2 (t) a voltage sensor S estimated by the method of the present invention V2 Estimated value of faultIs a simulation waveform diagram of (1). Wherein the solid line is a set sensor S V2 The mathematical expression of the voltage waveform when drift fault occurs is as follows: />
The dashed line is an estimated voltage sensor fault. From this figure, it can be seen that at 0-1S, no voltage sensor failure occurs in the system, and at t=1S, sensor S V2 Drift failure occurs and the voltage sensor S V2 Estimated value of faultThe voltage sensor S can be well estimated V2 Failure f u2 (t)。/>
Claims (2)
1. A multi-fault estimation method for a single-phase three-level rectifier includes a network side voltage source U s Net side equivalent inductance L s And net side equivalent resistance R s The rectifier bridge, two identical supporting capacitors, a direct-current side load and two identical voltage sensors are respectively marked as supporting capacitor C d1 And a supporting capacitor C d2 Two identical voltage sensors are respectively denoted as voltage sensor S V1 And a voltage sensor S V2 Wherein the voltage sensor S V1 Connected to the supporting capacitor C d1 Voltage sensor S V2 Connected to the supporting capacitor C d2 Is provided; support capacitor C d1 And a supporting capacitor C d2 The series connection is connected in parallel between a direct current positive bus P and a direct current negative bus Q of the direct current side load, and supports a capacitor C d1 And a supporting capacitor C d2 Is marked as a contact point ofA direct current bus midpoint O;
the rectifier bridge comprises two-phase bridge arms, which are respectively marked as a bridge arm a and a bridge arm b; in the two-phase bridge arm, each bridge arm comprises 4 switching tubes with reverse connection diodes and 2 clamping diodes, namely, the rectifier bridge totally comprises 8 switching tubes with reverse connection diodes and 4 clamping diodes; the 8 switching tubes are denoted as switching tube V kγ K is bridge sequence, k=a, b, gamma represents the serial number of the switching tube, and gamma=1, 2,3,4; the 4 clamp diodes are denoted as clamp diodes Serial number representing clamp diode, +.>In each of the two phase legs, switching tube V k1 Switch tube V k2 Switch tube V k3 And a switching tube V k4 In series in turn, switch tube V k2 And a switching tube V k3 Is marked as the input point tau of the rectifier bridge k K=a, b; in each of the two-phase legs, a clamp diode D ck1 The cathode of (C) is connected with the switch tube V k1 And a switching tube V k2 Between, clamp diode D ck1 Is connected with the clamping diode D by the anode ck2 Clamping diode D ck2 The anode of (C) is connected with the switch tube V k3 And a switching tube V k4 Between, and clamp diode D ck1 And a clamp diode D ck2 The connecting point of the (a) is connected with the midpoint O of the direct current bus;
the net side equivalent inductance L s Is connected with the input point tau of the rectifier bridge a The other end is sequentially connected with the equivalent resistor R at the net side S Network side voltage source U s The other end of the network side voltage source is connected with the input point tau of the rectifier bridge in series b ；
The multi-fault estimation method is characterized by comprising the following steps of:
step 1, establishing a mixed logic dynamic model of a single-phase three-level rectifier
The mixed logic dynamic expression of the single-phase three-level rectifier is as follows:
wherein,for the estimated value of the input phase voltage, +.>For the estimated value of the a-phase pole voltage, +.>An estimated value of b-phase pole voltage; u (u) 1 To support the capacitor C d1 The voltage at two sides is recorded as a first DC voltage u 1 ；u 2 To support the capacitor C d2 The voltage at two sides is recorded as a second DC voltage u 2 ；S 1 For the first direct current voltage u 1 Is a mixed logic dynamic function of S 2 At a second DC voltage u 2 Is a mixed logic dynamic function of (1);
step 2, establishing a state space model of the single-phase three-level rectifier system with multiple faults
The single-phase three-level rectifier system with multiple faults is recorded as a multiple fault system 1, and the state space model expression of the multiple fault system 1 is as follows:
Wherein t is time; x (t) is a state variable of the multi-fault system 1, belonging to an n-dimensional space, denoted as a first state variable x (t),i s is the network side current; />The derivative of the first state variable x (t) with respect to time, belonging to the n-dimensional space, is denoted as the first derivative +.> For the net side current i s Derivative with respect to time, < >>For the first direct current voltage u 1 Derivative with respect to time, < >>At a second DC voltage u 2 Derivative with respect to time; u (t) represents input, belongs to m-dimensional space, u (t) ∈R m ；f a (t) is an actuator failure belonging to a-dimensional space, f a (t)∈R a ；f s (t) sensor faults, belonging to s-dimensional space,wherein f u1 (t) is a voltage sensor S V1 Failure belongs to j-dimensional space, f u1 (t)∈R j ，f u2 (t) is a voltage sensor S V2 Failure belongs to k-dimensional space, f u2 (t)∈R k The method comprises the steps of carrying out a first treatment on the surface of the y (t) is the output of the multi-fault system 1, belonging to the p-dimensional space, denoted as the first output variable y (t), y (t) ∈R p ；A i Is a state coefficient matrix of a first state variable x (t), and is recorded as a first state coefficient matrix A i ，/>Wherein L is the equivalent inductance L of the network side s R is the net side equivalent resistance R s Resistance value C of (C) 1 To support the capacitor C d1 Capacitance value C of (C) 2 To support the capacitor C d2 Is a capacitance value of (2); i is a normal number, and i=1, 2,..9; b is the coefficient matrix of input u (t), denoted as the first input matrix B, " >C is an output matrix of the multi-fault system 1 and is marked as a first output matrix C; f (F) s For sensor failure f s The coefficient matrix of (t) belongs to p x s dimension space and is marked as a first sensor fault matrix F s ，F s ∈R p×s ；F a For actuator failure f a The coefficient matrix of (t) belonging to n×a, denoted as first actuator failure matrix F a ，F a ∈R n×a ；
Failure f of actuator a (t), voltage sensor failure f s (t) is a continuous and bounded function with respect to the time variable t, satisfying ||f a (t) delta and f s (t) f is less than or equal to ω a (t) || represents an actuator failure f a The 2-norm of (t), I F s (t) || represents a sensor failure f s (t) 2-norm, delta representing actuator failure f a Upper bound of (t), ω represents voltage sensor fault f s The upper bound of (t), δ, ω are both known positive constants;
step 3, establishing a state space model of the multi-fault system 2
Introducing a first nonsingular transformation matrix T and a second nonsingular transformation matrix S, and carrying out coordinate transformation on the multi-fault system 1;
coordinate transformation z (t) =tx (t),transforming the multi-fault system 1 into the multi-fault system 2, the state space model expression of the multi-fault system 2 is as follows:
where z (t) is a state variable of the multi-fault system 2, denoted as a second state variable z (t),z 1 (t) the first state component of the second state variable, belonging to the l-dimensional space, denoted as the third state variable z 1 (t)，z 1 (t)∈R l ；z 2 (t) a second state component of the second state variable, belonging to the n-l dimensional space, denoted as a fourth state variable z 2 (t)，z 2 (t)∈R n-l ；/>The time derivative of the second state variable z (t) is denoted as second derivative +.> Is the third state variable z 1 (t) the derivative with respect to time, denoted as third derivative +.> Is a fourth state changeQuantity z 2 (t) derivative with respect to time, noted as fourth derivative +.> Is the output of the multiple fault system 2 belonging to the p-dimensional space, denoted second output variable +.>Wherein y is 1 (t) is the second output variable +.>The upper component of (2) belonging to the l-dimensional space, denoted as the third output variable y 1 (t)，y 1 (t)∈R l ；y 2 (t) is the second output variable +.>The lower component of (2) belonging to the p-l dimensional space, denoted as the fourth output variable y 2 (t)，/>Wherein y is 21 (t) is the upper component of the fourth output variable, belonging to e-dimensional space, i.e., y 21 (t)∈R e ，y 22 (t) is the upper component of the fourth output variable, belonging to the f-dimensional space, i.e., y 22 (t)∈R f ；
Is a coefficient matrix of the second state variable z (t), denoted as second state coefficient matrix +.> A i1 Is a second state coefficient matrix->The upper left matrix belonging to l×l dimensional space is denoted as the second upper left matrix A i1 ，A i1 ∈R l×l ；A i2 Is a second state coefficient matrix->The upper right matrix belonging to the l× (n-l) dimensional space is denoted as the second upper right matrix A i2 ，A i2 ∈R l ×(n-l) ；A i3 Is a second state coefficient matrix->The lower left matrix belonging to the (n-l) x l dimensional space is denoted as the second lower left matrix A i3 ，A i3 ∈R (n-l)×l ；A i4 Is a second state coefficient matrix->The lower right matrix belonging to the (n-l) x (n-l) dimensional space is denoted as the second lower right matrix A i4 ，A i4 ∈R (n-l)×(n-l) ；/>Is the coefficient matrix of input u (t), denoted as second input matrix +.> Wherein B is 1 Is the second input matrix +.>Is of the upper matrix of l m dimension spaceMarked as matrix B on the second input 1 ，B 1 ∈R l×m ，B 2 Is the second input matrix +.>Belongs to (n-l) x m dimensional space and is denoted as a second input lower matrix B 2 ，B 2 ∈R (n-l)×m ；/>Is the failure f of the actuator a The coefficient matrix of (t) is marked as a second actuator failure matrix +.>Wherein F is a1 Is a second actuator failure matrix->Is a first upper matrix F of the second actuator fault, belonging to the l x a dimension space a1 ，F a1 ∈R l ×a ；/>The output matrix of the multi-fault system 2 is denoted as second output matrix +.>Wherein C is 1 Is the second output matrix->Is denoted as the third output matrix C 1 ，C 4 Is the second output matrix->Is denoted as the fourth output matrix C 4 ；/>Is a sensor fault f s The coefficient matrix of (t) is denoted as second sensor failure matrix +.>Wherein F is s2 Is a second sensor failure matrix +.>Belongs to the (p-l) x s dimensional space and is marked as a second sensor failure lower matrix F s2 ，F s2 ∈R (p-l)×s ；
The multi-fault system 2 is decomposed into two reduced order subsystems as follows:
the state space model expression of subsystem 1 is:
The state space model expression of subsystem 2 is:
step 4, system expansion is carried out on the subsystem 2
The state space expression of the expanded subsystem 2 is:
wherein,the state variable of the expanded subsystem 2 belongs to an n-l+s dimensional space and is marked as a fifth state variable For the fifth state variable->The derivative with respect to time, denoted as the fifth derivative
Is the fifth derivative->Is a coefficient matrix belonging to (n-l+s) x (n-l+s) dimensional space,wherein I is n-l A unit matrix representing an (n-l) x (n-l) dimensional space; />For the fifth state variable->Is marked as a third state coefficient matrix +.> I s An identity matrix representing an s x s dimensional space; />Is the third state variable z 1 The coefficient matrix of (t) is denoted as a fourth state coefficient matrix The coefficient matrix for input u (t) is denoted as the third input matrix +.> Is a sensor fault f s The coefficient matrix of (t) is marked as a third sensor failure matrix +.> Is the output matrix of the expanded subsystem 2, denoted fifth output matrix +.>I p-l A unit matrix representing a (p-l) x (p-l) dimensional space;
step 5, observer design
For subsystem 1, a sliding mode observer is designed as follows:
wherein,is the third state variable z 1 Estimate of (t)/(t)>Is the third state variable z 1 Estimate of (t) >Derivative with respect to time; d (D) 1 Is a sliding mode gain matrix, taking D 1 ＝F a1 The method comprises the steps of carrying out a first treatment on the surface of the V (t) is the approach rate, and ∈10%>e 1 (t) is the first observation error, and +.>ρ is the sliding mode gain, ρ is less than or equal to δ - ρ 0 ，ρ 0 ＝0.2；L 1 For the first matrix to be designed, P 1 Is a first li-apunov matrix; />For the third output variable y 1 An estimate of (t);
for the expanded subsystem 2, an adaptive reduced order sliding mode observer is designed as follows:
wherein,is the fifth state variable +.>Is a function of the estimated value of (2); ζ (t) is a sixth state variable belonging to the n-l + s dimension space,ξ 1 (t) is a sixth state variableFirst component, ζ 2 (t) is the sixth state variable second component, ζ 3 (t) is the third component, ζ, of the sixth state variable 4 (t) a fourth component of a sixth state variable; />Is the derivative of the sixth state variable ζ (t) with respect to time, denoted sixth derivative +.>
For the sixth derivative->Is denoted as a fifth coefficient matrix-> Belongs to a nonsingular matrix, wherein ∈>For the intermediate matrix to be designed, < > for>Is an intermediate matrix to be designed->Belongs to the (p-l) x (p-l) dimension and is denoted as the second matrix to be designed +.>And-> Is an intermediate matrix to be designed->Belongs to the (p-l) x (p-l) dimension and is denoted as the third matrix to be designed->And-> Coefficient matrix for the sixth state variable ζ (t), +. > Is a proportional gain matrix> For the fifth coefficient matrix->An inverse matrix of (a); />Is a sliding mode gain matrix>u s (t) is a sliding mode control item,wherein f(s) is a constant velocity approach coefficient,e is a natural index, eta is a constant, 0 < eta < 1, epsilon is an index approach coefficient, epsilon=20, s (t) is a sliding mode surface, and->Wherein (1)>For the fifth coefficient matrix->Is>Transposed matrix of>For the second Leidefenof matrix, < - > and->Is the second observation error, and
step 6, solving the matrix to be designed
The matrix to be designed comprises a first matrix to be designed L 1 A second matrix to be designedAnd a third matrix to be designed->
Order theWherein (1)>To observe the total error; according to the expressions of the subsystem 1, the expanded subsystem 2, the sliding mode observer and the self-adaptive reduced order sliding mode observer, an error dynamic equation is obtained as follows:
wherein,is the first observed error e 1 (t) derivative with respect to time, < >>Is the second observation error->Derivative with respect to time;
for in the dynamic error equationPerforming pole allocation to obtain a first matrix L to be designed 1 ；
In the equation of known dynamic errorSensor failure f s The coefficient matrix of (t) is +.>Setting a second matrix to be designed->And a third matrix to be designed- >Wherein->
Step 7, performing fault estimation of the actuator and the sensor
Step 7.1, estimating the actuator failure
Will beRecorded as actuator failure f a An estimated value of (t), v eq (t) the equivalent output control signal of the approach ratio v (t), then the actuator failure estimation value +.>The method comprises the following steps:
wherein δ is a positive scalar, δ=0.1;
step 7.2, estimating the voltage sensor failure
Will beIs denoted as voltage sensor S V1 Failure f u1 Estimate of (t)/(t)>Recorded as voltage sensingDevice S V2 Failure f u2 Calculating the estimated value of (t) and calculating the voltage sensor S V1 Failure f u1 Estimate of (t)>Voltage sensor S V2 Failure f u2 Estimate of (t)>The specific calculation formula is as follows:
so far, the multi-fault estimation of the single-phase three-level rectifier is finished.
2. The method for multi-fault estimation of a single-phase three-level rectifier according to claim 1, wherein the first dc voltage u of step 1 1 Is a mixed logic dynamic function S of 1 And a second DC voltage u 2 Is a mixed logic dynamic function S of 2 The calculation process of (2) is as follows:
wherein S is a Is a switching function of a phase bridge arm, S b Is the switching function of the b-phase bridge arm; switch tube V kγ The pulse control signal of (2) isThe switching function of the a-phase leg>Switching function of b-phase bridge arm >
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| CN114325164A (en) * | 2021-11-24 | 2022-04-12 | 合肥工业大学 | Multi-fault diagnosis method for single-phase three-level rectifier |
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