CN111614343B - SP type ICPT system filter design method and system - Google Patents

SP type ICPT system filter design method and system Download PDF

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CN111614343B
CN111614343B CN202010517369.5A CN202010517369A CN111614343B CN 111614343 B CN111614343 B CN 111614343B CN 202010517369 A CN202010517369 A CN 202010517369A CN 111614343 B CN111614343 B CN 111614343B
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CN111614343A (en
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朱爽鑫
田恩刚
石玉成
李唐
王镇
梁国钰
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University of Shanghai for Science and Technology
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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Abstract

The invention discloses a design method of a SP type ICPT system filter, which comprises the following steps: the method comprises the steps of establishing a generalized state space average equation of the SP type ICPT system, establishing a filtering error amplification system model of the SP type ICPT system under external disturbance and random sensor faults, determining a sufficient condition of robust mean square progressive stability of the filtering error amplification system model by establishing a Lyapunov function, and solving gains of the filter according to the sufficient condition.

Description

SP type ICPT system filter design method and system
Technical Field
The invention relates to the technical field of wireless charging, in particular to a novel filter design method based on an SP type ICPT system.
Background
An SP (Series/Parallel) type ICPT (Inductively Coupled Power Transmission) system realizes non-contact Transmission of electric energy by using an alternating magnetic field and mainly comprises an electric energy transmitting device and an electric energy receiving device. Compared with the traditional wired charging mode, the ICPT system still has the advantages of safety, convenience, reliability and the like even under the severe working environment, so that the ICPT system is widely applied to the charging systems of equipment such as electric vehicles, smart homes and organ transplantation.
Considering that the ICPT system is a high frequency resonant system, although the harmonic components of the alternating voltage and the current generated during the operation of the system can be ignored, the fundamental components of the two are difficult to obtain an accurate measurement result in real time. Therefore, in practical engineering applications, the ICPT system generally measures the dc voltage and current output by the system through a voltage sensor and a current sensor, however, in the actual operation and measurement process of the ICPT system, not only the influence of external disturbances such as signal fluctuation, electromagnetic interference, energy bounded noise, etc. on the system performance cannot be completely eliminated, but also the adverse influence of sensor failure caused by long-term operation of the sensor in a severe environment on the system performance cannot be neglected. In the prior art, the influence of external disturbance and sensor fault on real-time tracking of a system signal is not considered, so that under the condition that the external disturbance and the sensor fault are considered in an SP-type ICPT system, how to design an H infinite filter enables the system to accurately obtain the variation trend and the amplitude of all state variables of the system even if the system suffers from adverse factors such as the external disturbance and the sensor fault, and the like, so that the problem to be solved at present is to improve the fault tolerance and the robustness of the SP-type ICPT system.
Disclosure of Invention
The invention aims to solve the technical problem of how to effectively inhibit the influence of external disturbance and random sensor faults on an SP type ICPT system, and provides an H infinite filter design method for improving the fault tolerance of the SP type ICPT system.
The invention solves the technical problems through the following technical scheme:
a design method of a SP type ICPT system filter comprises the following steps:
establishing a generalized state space average equation of the SP type ICPT system;
establishing a filtering error augmentation system model of the SP type ICPT system under the external disturbance and the random sensor fault;
determining a sufficient condition of robust mean square progressive stability of the filtering error augmentation system model by constructing a Lyapunov function;
and solving the gain of the filter according to the sufficient condition.
Preferably, the establishing a generalized state space average equation of the SP type ICPT system includes:
establishing a state space model of the SP type ICPT system according to kirchhoff's law;
quantizing variables in the state space model through Fourier transform;
establishing the generalized state space average equation of the SP-type ICPT system.
Preferably, the establishing a filtering error augmentation system model of the SP type ICPT system under the external disturbance and the random sensor fault includes:
establishing an external disturbance generalized state space model of the SP type ICPT system;
establishing a filter model of the SP type ICPT system;
establishing a sensor fault model of the SP type ICPT system;
and constructing the filtering error augmentation system model by the external disturbance generalized state space model, the filter model and the sensor fault model.
Further, the external perturbation generalized state space model may be:
Figure GDA0004092008360000031
wherein x (t) ∈ R 10 Is a vector of the states of the system,
Figure GDA0004092008360000032
is the derivative of the system state vector x (t); y (t) is belonged to R 2 Measuring an output vector for a system, the system measured output vector comprising measurements of system load voltage and load current, z (t) e R 10 For the system output vector, ω (t) is equal to R 1 And v (t) is epsilon to R 1 Respectively process noise and measurement noise of the system, S A 、S B 、S C 、S D And S L Is a matrix of known coefficients with appropriate dimensions, wherein S is A Can be obtained by the generalized state space-average equation;
the filter model may be:
Figure GDA0004092008360000033
wherein the gain H of the filter A 、H B And H L For a matrix of coefficients to be determined of suitable dimensions, x h (t)∈R 10 In order to be a vector of the filter states,
Figure GDA0004092008360000034
for the filter state vector x h Derivative of (t), z h (t)∈R 10 Is a filter output vector comprising an estimate of the system output vector z (t), is/are selected>
Figure GDA0004092008360000035
For a filter input vector, the filter input vector and the system measurement output vector y (t) may be expressed as:
Figure GDA0004092008360000036
where Ψ is a sensor failure random matrix, which can be expressed as:
Figure GDA0004092008360000037
wherein the random variable is
Figure GDA0004092008360000038
For describing the failure condition of the jth sensor: when the random variable is changed
Figure GDA0004092008360000039
When the sensor j is in a complete fault state, the jth system measures an output vector y j (t) is 0, when
Figure GDA00040920083600000310
When the sensor j is in a partial fault state, the jth system measures an output vector y j (t) the result does not exactly correspond to the actual value of the system when->
Figure GDA00040920083600000311
When the sensor j is in a normal working state, the jth system measures an output vector y j (t) the result is completely consistent with the actual value;
under the external disturbance and the random sensor fault, the filtering error augmentation system model may be:
Figure GDA0004092008360000041
wherein ε (t) e R 20 For the augmented system state vector, the augmented system state vector is composed of the system state vector x (t) and the filter state vector x h (t) the compound is formed by increasing,
Figure GDA0004092008360000042
for the derivative of the augmented system state vector ε (t), θ (t) e R 2 A noise vector for the augmented system, the noise vector being augmented by the process noise ω (t) and the measurement noise v (t), δ (t) e R 10 To augment a system output vector, the vector representing the system output vector z (t) and the filter output vector z h The error between (t), i.e. δ (t) = z (t) -z h (t)，Γ Am 、Γ Bm And gamma L Is a coefficient matrix with suitable dimensions, and the specific form is as follows:
Figure GDA0004092008360000043
wherein, gamma is L T Is a coefficient matrix gamma L Transpose of (d), coefficient matrix Γ Am And Γ Bm Contains the random matrix Ψ, so both can also be expressed as
Figure GDA0004092008360000044
Here, the first and second liquid crystal display panels are,
Figure GDA0004092008360000045
Figure GDA0004092008360000046
here, the first and second liquid crystal display panels are,
Figure GDA0004092008360000047
is the expectation of the random matrix Ψ.
Preferably, the sufficient condition for the robust mean square progressive stabilization of the filtering error augmentation system may be:
Figure GDA0004092008360000048
wherein the content of the first and second substances,
Figure GDA0004092008360000049
and &>
Figure GDA00040920083600000410
Respectively in said matrix>
Figure GDA00040920083600000411
And &>
Figure GDA00040920083600000412
Transposing; gamma ray>0 is the disturbance attenuation level; q ∫ A positive definite symmetric matrix is more than 0, and an identity matrix with proper dimension is I.
Preferably, solving for the gain of the filter comprises:
for the positive definite matrix Q ∫ Decompose and define a matrix N ∫ The specific form of (a);
the two sides of the robust mean square progressive sufficient condition of the filtering error augmentation system are respectively subjected to left multiplication and right multiplication diagonal matrix J = diag { N } ∫ I, I } and
Figure GDA0004092008360000051
and solving the filter gain.
Further, determining the matrix Q positively ∫ The decomposition is carried out, and the specific form can be as follows:
Figure GDA0004092008360000052
wherein Q s1 ＞0，Q s3 Greater than 0 is positive definite symmetric matrix, Q s2 In the form of a symmetrical matrix, the matrix is,
Figure GDA0004092008360000053
for said symmetric matrix Q s2 And satisfies >>
Figure GDA0004092008360000054
The matrix N ∫ The specific form of (b) may be:
Figure GDA0004092008360000055
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0004092008360000056
for said positive definite symmetric matrix Q s3 The inverse matrix of (d);
multiplying both sides of the sufficient condition by the diagonal matrices J and J at the same time T The resulting linear matrix inequality is of the form:
Figure GDA0004092008360000057
wherein the content of the first and second substances,
Figure GDA0004092008360000058
Figure GDA0004092008360000059
and &>
Figure GDA00040920083600000510
Are respectively a matrix S A 、S B 、S C 、S D 、H Am And H Bm Transpose of (3), matrix Y, H Am 、H Bm And H Lm Can be defined as:
Figure GDA00040920083600000511
here, the first and second liquid crystal display panels are,
Figure GDA00040920083600000512
for said positive definite symmetric matrix Q s3 Is inverted matrix of->
Figure GDA00040920083600000513
Is the symmetric matrix Q s2 Transposed matrix of (H) A 、H B And H C Is the filter gain;
the filter gain may be:
Figure GDA0004092008360000061
and tracking all state variable change conditions of the SP type ICPT system in real time by obtaining the filter gain.
Preferably, the filter is an H-infinity filter.
An ICPT system of the SP type for implementing the filter design method, the system comprising: the device comprises a direct current chopping module, an electric energy transmitting device module, an electric energy receiving device module, a voltage and current detection module, a wireless communication module and an H infinite filtering module; the output end of the direct current chopping module is connected to the electric energy transmitting device module, an air gap is formed between the electric energy transmitting device module and the electric energy receiving device module, the electric energy transmitting device module and the electric energy receiving device module are connected through mutual inductance, the output end of the electric energy receiving device module is connected to the input end of the voltage and current detection module, the output end of the voltage and current detection module is connected to the input end of the wireless communication module, and the output end of the wireless communication module is connected to the H infinite filtering module.
Preferably, the power transmission device module includes: the direct-current power supply module, the high-frequency inverter, the primary side resonance compensation network, the direct-current power supply module, the high-frequency inverter and the primary side resonance compensation network are electrically connected in sequence; the power receiving device includes: the secondary side resonance compensation network, the rectifier and the load are electrically connected in sequence; the voltage current detection module includes: a voltage sensor and a current sensor.
On the basis of the common knowledge in the field, the above preferred conditions can be combined randomly to obtain the preferred embodiments of the invention.
The positive progress effects of the invention are as follows: the H infinite filter design method and the system provided by the invention take the external disturbance and random sensor fault factors into consideration, obviously improve the fault tolerance and robustness of the SP type ICPT system, can estimate state variables which are difficult to measure according to measured values, and can ensure that the measured values of the load voltage and the load current of the system can still track the real-time change condition of all the state variables of the system even if the measured values are influenced by the external disturbance and/or the sensor fault.
Drawings
FIG. 1 is a flow chart of a design method in an embodiment of a method and system for designing a SP-type ICPT system filter of the present invention;
FIG. 2 is a system diagram of an embodiment of a method and system for designing a SP-type ICPT system filter according to the present invention;
FIG. 3 is a schematic diagram illustrating simulation of random distribution of sensor faults in an embodiment of the method and system for designing a SP-type ICPT system filter of the present invention;
FIG. 4 is a diagram illustrating simulation results of actual and estimated values of output voltage under external disturbance in an embodiment of the method and system for designing a SP-type ICPT system filter of the present invention;
FIG. 5 is a diagram illustrating simulation results of actual and estimated values of output current under external disturbance in an embodiment of the method and system for designing a SP-type ICPT system filter of the present invention;
FIG. 6 is a diagram illustrating simulation results of estimation errors of all state variables of a system under external disturbance in an embodiment of the method and system for designing a filter of an SP-type ICPT system according to the present invention;
FIG. 7 is a diagram illustrating simulation results of actual and estimated output voltages under external disturbances and random sensor faults in an embodiment of the method and system for designing a SP-type ICPT system filter of the present invention;
FIG. 8 is a schematic diagram showing simulation results of actual values and estimated values of output currents under external disturbance and random sensor failure in an embodiment of the filter design method and system for the SP-type ICPT system of the present invention;
fig. 9 is a schematic diagram of simulation results of estimation errors of all state variables of the system under external disturbance and random sensor failure in the method and system for designing the filter of the SP type ICPT system according to the present invention.
Detailed Description
To facilitate an understanding of the present application, the present application will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present application are shown in the drawings. This application may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
It will be understood that when an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. The terms "mounted," "one end," "the other end," and the like are used herein for illustrative purposes only.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the description of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
As shown in fig. 1, the present invention provides a filter design method suitable for an SP type ICPT system, the filter design method includes the following steps:
step S01: establishing a generalized state space average equation of the SP type ICPT system;
step S02: establishing a filtering error augmentation system model of the SP type ICPT system under the external disturbance and the random sensor fault;
step S03: determining a sufficient condition of robust mean square progressive stability of the filtering error augmentation system model by constructing a Lyapunov function;
step S04: and solving the gain of the filter according to the sufficient condition.
In an alternative example, the generalized state space average equation of the SP type ICPT system can be constructed by:
establishing a state space model of the SP type ICPT system according to kirchhoff's law;
Figure GDA0004092008360000091
wherein u is ac (t) an output voltage of the high frequency inverter; c p And C s Respectively representing primary and secondary resonance compensation capacitance values, L p And L s Respectively representing the inductance of the primary side coupling coil and the secondary side coupling coil; r is p And R s Respectively representing the internal resistance of the primary side coupling coil and the secondary side coupling coil; m represents the mutual inductance between the primary side coupling coil and the secondary side coupling coil; l is d 、C d And R d Respectively representing filter inductance, filter capacitance and load resistance；u cp (t) and i p (t) representing the voltage across the load resistor and the current through the load resistor, respectively; logic function s i (t) and s r (t) are respectively used for representing the working characteristics of the alternating transformation of the high-frequency inverter and the power rectifier, and the positive and negative conditions of the amplitudes of the two are represented by u ac (t) and u cs (t) direction determination.
Carrying out quantization processing on variables in the state space model through Fourier transform;
Figure GDA0004092008360000092
wherein<·> 1 Representing the first harmonic component of the alternating state variable, re<·> 1 And Im<·> 1 Respectively representing the real and imaginary parts of the first harmonic component,<·> 0 representing the fundamental component of the dc state variable.
Establishing the generalized state space average equation of the SP type ICPT system:
Figure GDA0004092008360000101
in an alternative example, a filtering error augmentation system model of the SP type ICPT system under the external disturbance and the random sensor fault is established, and the filtering error augmentation system model can be established through the following method:
establishing an external disturbance generalized state space model of the SP type ICPT system;
in order to analyze the characteristics of the system, the dynamic process under the condition of zero input of the system needs to be analyzed, so that under the condition of external disturbance, the GSSA (Generalized State-Space) model of the system based on the condition of zero input can be described as follows:
Figure GDA0004092008360000102
wherein x (t) ∈ R 10 Is in a stateA spatial vector, whose corresponding expression is:
Figure GDA0004092008360000103
here, x i (t) (i =1, …, 10) represents the i-th state variable of the system.
y(t)∈R 2 For measuring the output vector, its corresponding expression is
y(t)＝[y 1 (t) y 2 (t)] T (6)
Here, y j (t) (j =1,2) represents the measurement of sensor j, where y 1 (t) represents the system load voltage u d (t) measurement, y, by a voltage sensor 402 as shown in FIG. 2 2 (t) represents the system load current i d (t) measurement values obtained by the current sensor 401 shown in fig. 2.
z(t)∈R 10 For the system output vector, the matrix consists of all the state variables to be estimated for the system, considering that the filter designed by the invention can estimate all the state variables of the system.
ω(t)∈R 1 And v (t) is epsilon to R 1 Respectively process noise and measurement noise of the system, S A 、S B 、S C 、S D And S L Is a known matrix of suitable dimensions, in which S A Can be obtained by the formula (3).
Establishing a filter model of the SP type ICPT system;
the proposed H infinite filter can ensure that the system can still dynamically track the real-time data and the variation trend of the system output signal even if the system is subjected to external disturbance, and the form of the filter can be described as follows:
Figure GDA0004092008360000111
wherein the filter gain H A 、H B And H L A matrix to be determined of suitable dimensions; x is a radical of a fluorine atom h (t)∈R 10 Is the state space vector of the filter; z is a radical of h (t)∈R 10 Is the output vector of the filter, which represents the estimation of z (t);
Figure GDA0004092008360000112
is the input vector to the filter, which represents the actual case where y (t) is transmitted to the filter, and the corresponding form can be described as:
Figure GDA0004092008360000113
establishing a sensor fault model of the SP type ICPT system;
considering that random sensor faults have inevitable effects on the measurement results of the system, the invention reflects the random condition of the sensor faults by a random variable. Thus the input vector of the H-infinity filter under random sensor failure
Figure GDA0004092008360000114
Can be defined as:
Figure GDA0004092008360000115
wherein the random matrix Ψ ∈ R 2×2 For describing the degree of failure of the sensor, and an expanded form of the matrix may be defined as:
Figure GDA0004092008360000121
random variable here
Figure GDA0004092008360000122
For describing the fault condition of the jth sensor, the basic characteristics of this variable are as follows:
Figure GDA0004092008360000123
/>
wherein the random variable is
Figure GDA0004092008360000124
Is denoted as iota and variance, respectively j And &>
Figure GDA0004092008360000125
Both are used to characterize the failure level of sensor j.
According to given desired iota j Sum variance
Figure GDA0004092008360000126
The expectation and variance of the obtainable random matrix Ψ are:
Figure GDA0004092008360000127
Figure GDA0004092008360000128
constructing the filtering error augmentation system model by the external disturbance generalized state space model, the filter model and the sensor fault model:
by simultaneous formula (4), formula (7) and formula (9), the filtering error amplification system model of the system under external disturbance is obtained as follows:
Figure GDA0004092008360000129
wherein the augmented state vector ε (t) and the augmented noise vector θ (t) are represented as:
Figure GDA00040920083600001210
δ (t) is the error vector of the system (14) representing the deviation between the actual and estimated values of the system output, i.e., δ (t) = z (t) -z h (t)。Γ Am 、Γ Bm And gamma L A coefficient matrix with suitable dimensions, which is in the following specific form:
Figure GDA00040920083600001211
wherein, gamma is L T Is a coefficient matrix gamma L Transpose of (d), coefficient matrix Γ Am And Γ Bm Contains the random matrix Ψ, so both can also be expressed as
Figure GDA0004092008360000131
Here, the number of the first and second electrodes,
Figure GDA0004092008360000132
Figure GDA0004092008360000133
here, the number of the first and second electrodes,
Figure GDA0004092008360000134
is the expectation of the random matrix Ψ. In an alternative example, the sufficient condition for robust mean square asymptotic stabilization of the filtering error augmentation system model may be:
Figure GDA0004092008360000135
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0004092008360000136
and &>
Figure GDA0004092008360000137
Are respectively the matrix->
Figure GDA0004092008360000138
And &>
Figure GDA0004092008360000139
Transposing; gamma ray>0 is the disturbance attenuation level; q ∫ A positive definite symmetric matrix is more than 0, and an identity matrix with proper dimension is I.
The step of proving the sufficient condition (19) of robust mean square progressive stability of the filtering error augmentation system model is as follows:
constructing a Lyapunov function of an SP type ICPT filtering error augmentation system (14);
constructing a Lyapunov function F (t) based on the augmentation system (14);
F(ε(t))＝ε T (t)Q ∫ ε(t) (20)
introducing a basic definition of an infinite small operator, and solving the expectation of the Lyapunov function F (t) infinite small operator;
the infinitesimal operator of an arbitrary function F (t) can be defined as:
Figure GDA00040920083600001310
considering that the system (14) has a random matrix Ψ for describing the sensor failure, the desired infinitesimal operator corresponding to the Lyapunov function F (t) can be solved by equation (21).
Ε{LF(ε(t))}＝Ε{Σ 1 (t)-δ T (t)δ(t)+γ 2 θ T (t)θ(t)} (22)
Wherein γ represents the noise attenuation level of the system, which is used to suppress the effect of the amplified noise θ (t) on the robust performance of the system, and
Figure GDA0004092008360000141
wherein, sigma 1 It can also be described as:
Figure GDA0004092008360000142
obtaining a sufficient condition of gradual and stable mean square of the system (14) according to the schur complement theory;
in view of
Figure GDA0004092008360000143
It is therefore easy to infer the matrix +>
Figure GDA0004092008360000144
And
Figure GDA0004092008360000145
the expected values of (a) are: />
Figure GDA0004092008360000146
Therefore ∑ 1 The expectation of (a) is:
Figure GDA0004092008360000147
according to the Schur supplement theorem, sigma 1 The expectation of (c) is converted to the following form:
Figure GDA0004092008360000148
thereby obtaining a specific form of LMI (Linear Matrix inequality) as shown in equation (19).
Verifying that LMI shown in formula (19) is a sufficient condition for the mean square asymptotic stability of the system (14);
and (3) introducing a judgment basis for the progressive stabilization of the mean square of the system, namely:
if the system is asymptotically stable in mean square, the system satisfies:
Figure GDA0004092008360000149
wherein the augmented system noise θ (t) is an energy bounded noise; γ is a noise attenuation level for suppressing the system noise θ (t).
Integrating the two sides of the formula (22) simultaneously to obtain
Figure GDA00040920083600001410
Substituting equation (19) into equation (27) yields:
Figure GDA0004092008360000151
considering the requirement for the asymptotic stabilization of the mean square of the system as Ε { F (e (+ ∞)) } < Ε { F (e (0)) }, it can be deduced from the formula (28):
Figure GDA0004092008360000152
since equation (29) is consistent with equation (26), equation (19) is a sufficient condition for the mean-square asymptotic stability of the system (14).
In an alternative example, the specific steps of solving the gain of the filter according to the sufficient condition are:
to a definite matrix Q ∫ Decompose and define a matrix N ∫ The specific form of (a);
positive definite matrix Q ∫ The decomposition is carried out, and the specific form can be as follows:
Figure GDA0004092008360000153
wherein Q is s1 ＞0，Q s3 Greater than 0 is positive definite symmetric matrix, Q s2 In the form of a symmetrical matrix, the matrix is,
Figure GDA0004092008360000154
for said symmetric matrix Q s2 And satisfies->
Figure GDA0004092008360000155
The matrix N ∫ In particularThe form may be:
Figure GDA0004092008360000156
wherein the content of the first and second substances,
Figure GDA0004092008360000157
for said positive definite symmetric matrix Q s3 The inverse matrix of (d);
multiplying both sides of the sufficient condition by the diagonal matrices J and J at the same time T The resulting linear matrix inequality is of the form:
Figure GDA0004092008360000158
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0004092008360000159
Figure GDA0004092008360000161
and &>
Figure GDA0004092008360000162
Are respectively a matrix S A 、S B 、S C 、S D 、H Am And H Bm Transpose of (3), matrix Y, H Am 、H Bm And H Lm Can be defined as: />
Figure GDA0004092008360000163
Here, the first and second liquid crystal display panels are,
Figure GDA0004092008360000164
for said positive definite symmetric matrix Q s3 Is inverted matrix of->
Figure GDA0004092008360000165
Is the symmetric matrix Q s2 Transposed matrix of (H) A 、H B And H C Is the filter gain;
the filter gain may be:
Figure GDA0004092008360000166
and tracking all state variable change conditions of the SP type ICPT system in real time by obtaining the filter gain.
As shown in fig. 2, a block diagram of the structure of the SP type ICPT system of the present invention is shown, and the specific structure is as follows:
in one example, the dc chopper circuit module 100, the power transmitting device module 200, the power receiving device module 300, the voltage and current detection module 400, the wireless communication module 500, and the H infinite filter module 600 are connected, and the dc chopper circuit module 100 is connected to the power transmitting device module 200, an air gap with a certain interval exists between the power transmitting device module 200 and the power receiving device module 300, the voltage and current detection module 400 is connected to the power receiving device module 300, and the voltage and current detection module 400 and the H infinite filter module 600 are connected in a non-contact manner through the wireless communication module 500.
In an alternative example, in an SP-type ICPT system, the power transmission device module 200 includes: the direct-current chopper circuit module comprises a direct-current power supply 201, a high-frequency inverter 202 and a primary side resonance compensation network 203, wherein the direct-current power supply 201 is respectively connected with the output end of the direct-current chopper circuit module 100 and the input end of the high-frequency inverter 202, and the output end of the high-frequency inverter 202 is connected with the input end of the primary side resonance compensation network 203.
In an optional example, in the above SP type ICPT system, the high frequency inverter 202 further includes: full-control switch S 1 、S 2 、S 3 And S 4 Wherein, the circuit topology formed by four fully-controlled switches is a full-bridge inverter circuit, and the topology is realized by periodically transforming switch pairs (S) 1 /S 4 ,S 2 /S 3 ) Worker's toolObtaining the output voltage u of the high frequency inverter 202 in a state-of-operation manner ac (t)。
In an alternative example, in the above SP type ICPT system, the primary resonant compensation network 203 further includes: with internal resistance R p Primary side coupling coil L p And primary side compensation capacitor C p Wherein the primary side of the compensating capacitor C p And primary side coupling coil L p Connected in series and having a primary compensation capacitor C p The voltage at both ends and the current flowing through the primary side coupling coil L p Respectively is denoted as u cp (t) and i p (t)。
In an optional example, in the above SP type ICPT system, the power receiving device module 300 further includes: the secondary side resonance compensation network 301, the rectifier 302 and the load 303 are formed, wherein the input end of the rectifier 302 is connected with the output end of the secondary side resonance compensation network 301, and the output end of the rectifier 302 is connected with the input end of the load 303.
In an optional example, in the above SP type ICPT system, the secondary side resonance compensation network 301 further includes: with internal resistance R s Secondary side coupling coil L of s And secondary side compensation capacitor C s Wherein the secondary side compensates the capacitance C s Coil L coupled with secondary side s Connected in parallel and secondary side compensating capacitor C s Voltage at two ends and secondary side compensation inductor L flowing through s Respectively is denoted as u cs (t) and i s (t)。
In one example, in the above-mentioned SP type ICPT system, the primary side coupling coil L p Coil L coupled with secondary side s The wireless transmission of electric energy is realized through the electromagnetic induction law, and the mutual inductance of the two is M.
In an alternative example, in the above SP type ICPT system, the rectifier 302 further includes: diode D 1 、D 2 、D 3 And D 4 Wherein the bridge rectifier circuit composed of the four diodes realizes the conversion of alternating current to direct current and obtains a load voltage u d (t) and load current i d (t)。
In an alternative example, in the aboveIn the SP type ICPT system of (1), the load 303 further includes: filter inductance L d Filter capacitor C d And a load resistance R d Wherein the filter inductance L d And a filter capacitor C d Common for removing load voltage u d (t) and load current i d (t) unnecessary ripples.
In one example, in the above-described SP-type ICPT system, the voltage current detection module 400 further includes: a current sensor 401 and a voltage sensor 402, wherein the current sensor 401 and the voltage sensor 402 are respectively used for measuring the load voltage u d (t) and load current i d (t), and transmits the corresponding measurement result to the H ∞ filter module 600 through the wireless communication module 500.
In one example, the sampling time of the SP type ICPT system during the simulation is l μ s, and the electrical parameters of the SP type ICPT system are as follows:
electrical parameter summarization for SP-type ICPT system
Parameter name Parameter value Parameter name Parameter value
Primary side coupling coil inductance L p (μH) 126 Secondary side coupling inductance L s (μH) 126
Internal resistance R of primary side coupling coil p (Ω) 0.0017 Secondary side coupling coil resistor R p (Ω) 0.0017
Primary side resonance compensation capacitor C p (μF) 2.4 Secondary side resonance compensation capacitor C s (μF) 2
Load inductance L d (mH) 3 Load capacitance C d (μF) 220
Load resistance R d (Ω) 15 Mutual inductance M (mu H) 44.1
Resonant frequency f o (kHZ) 10 Switching angular frequency omega 0 (rad/s) 62800
Based on the GSSA model of the SP type ICPT system and the electrical parameters, a corresponding coefficient matrix form is obtained as follows:
Figure GDA0004092008360000191
S B ＝[1111111111] T
Figure GDA0004092008360000192
S D ＝[11] T
S L ＝I 10×10
assuming that the amplitude of the external disturbance of the system increases with time and shows a trend of continuous attenuation, the corresponding expression of the disturbance is as follows:
Figure GDA0004092008360000193
FIG. 3 shows the random variation of the system sensor fault, in which the sensor 1 is used to measure the load voltage u d (t) a voltage sensor, the sensor 2 being for measuring a load current i d (t) current sensors, and the random fault conditions of both passing through random variables
Figure GDA0004092008360000194
And &>
Figure GDA0004092008360000195
A description is made. Random variable>
Figure GDA0004092008360000196
And &>
Figure GDA0004092008360000197
The expectation and variance of (c) are:
Figure GDA0004092008360000198
according to the method provided by the invention, the SP-type ICPT system which is only subjected to external disturbance and simultaneously subjected to external disturbance and random sensor fault is subjected to H-infinity filter, and corresponding simulation result schematic diagrams are shown in FIGS. 4-9.
Fig. 4 to 6 are schematic diagrams of simulation results of an SP-type ICPT system affected by external disturbance, where:
FIGS. 4 and 5 are graphs of load voltage u d (t) and load current i d (t) comparing the actual value with the estimated value. It can be seen from the figure that the deviation between the actual value and the estimated value in the system operation process is not only completely within the allowable deviation range, but also the deviation between the actual value and the estimated value shows a continuously declining trend. Therefore, the H-infinity filter designed by the simulation result verification not only can inhibit the influence of external disturbance on the system, but also can accurately estimate the actual change condition of the measurement output.
FIG. 6 shows the real-time error estimation results of all state variables of the system, where d i (t) (i =1, …, 10) respectively represent an estimation error of the i-th state variable, and d i (t)＝z i (t)-z hi (t) of (d). As can be seen from the figure, the estimation error of all state variables of the system in the running process is less than 10 -3 And the estimation error of each state variable shows the trend of continuously attenuating along with time, which shows that the H-infinity filter designed by the invention not only can accurately estimate the actual change condition of the measurement output, but also can accurately estimate the real-time change condition of other state variables of the system according to the measurement result influenced by the external disturbance.
Fig. 7 to 9 are schematic diagrams of simulation results of an SP-type ICPT system affected by external disturbance and random sensor fault:
FIGS. 7 and 8 are graphs of load voltage u d (t) and load current i d (t) comparing the actual value with the estimated value. It can be seen from the figure that the deviation between the actual value and the estimated value during the operation of the system is still completely within the allowable deviation range, although it is larger than the deviation value under the condition of only external disturbance at the same time. Although the sensor fault condition of the system is switched once every 0.12s, the system can still be recovered to a normal tracking state in a short time during the switching process. According to the simulation result, the influence of the random sensor fault on the estimation error of the system measurement output can be found to be large, but the H-infinity filter designed by the invention can effectively inhibit the influence of the fault change condition of the random sensor on the system, so that the change trend base of the obtained estimation result and the actual measurement outputThe method is consistent.
FIG. 9 shows the real-time error estimation results for all state variables of the system, where d i (t) (i =1, …, 10) respectively represent an estimation error of the i-th state variable, and d i (t)＝z i (t)-z hi (t) of (d). As can be seen from the figure, the estimation errors of all state variables of the system immediately increase in the switching transient state of the sensor fault condition and recover to the allowable error range in a short time, which shows that the H infinity filter designed by the invention can accurately estimate the real-time change conditions of other state variables of the system according to the external disturbance and the measurement result under the random sensor fault condition, thereby verifying the accuracy of the design method provided by the invention.
While specific embodiments of the invention have been described above, it will be appreciated by those skilled in the art that this is by way of example only, and that the scope of the invention is defined by the appended claims. Various changes or modifications to these embodiments may be made by those skilled in the art without departing from the principle and spirit of this invention, and these changes and modifications are within the scope of this invention.

Claims (8)

  1. A design method of a SP type ICPT system filter is characterized by comprising the following steps:
    establishing a generalized state space average equation of the SP type ICPT system;
    establishing a filtering error augmentation system model of the SP type ICPT system under the external disturbance and the random sensor fault;
    determining a sufficient condition of robust mean square progressive stability of the filtering error augmentation system model by constructing a Lyapunov function;
    solving the gain of the filter according to the sufficient condition;
    the establishing of the generalized state space average equation of the SP type ICPT system comprises the following steps:
    establishing a state space model of the SP type ICPT system according to kirchhoff's law;
    quantizing variables in the state space model through Fourier transform;
    establishing the generalized state space average equation of the SP type ICPT system;
    the establishing of the filtering error augmentation system model of the SP type ICPT system under the external disturbance and the random sensor fault comprises the following steps:
    establishing an external disturbance generalized state space model of the SP type ICPT system;
    establishing a filter model of the SP type ICPT system;
    establishing a sensor fault model of the SP type ICPT system;
    and constructing the filtering error augmentation system model by the external disturbance generalized state space model, the filter model and the sensor fault model.
  2. 2. A method of filter design for an SP-type ICPT system as claimed in claim 1 wherein the external perturbation generalized state space model is:
    Figure FDA0004092008350000011
    wherein x (t) ∈ R 10 Is a vector of the states of the system,
    Figure FDA0004092008350000012
    is the derivative of the system state vector x (t); y (t) is belonged to R 2 Measuring an output vector for a system, the system measured output vector comprising measurements of system load voltage and load current, z (t) e R 10 For the system output vector, ω (t) is equal to R 1 And v (t) is epsilon to R 1 Respectively, the process noise and the measurement noise of the system, S A 、S B 、S C 、S D And S L Is a matrix of known coefficients with suitable dimensions, wherein S is A Can be obtained by the generalized state space average equation;
    the filter model is:
    Figure FDA0004092008350000021
    wherein the gain H of the filter A 、H B And H L For a matrix of coefficients to be determined of suitable dimensions, x h (t)∈R 10 In order to be a vector of the filter states,
    Figure FDA0004092008350000022
    for the filter state vector x h Derivative of (t), z h (t)∈R 10 Outputting a vector for a filter, said filter output vector comprising an estimate of said system output vector z (t), based on a predetermined criterion>
    Figure FDA0004092008350000023
    For a filter input vector, the filter input vector and the system measurement output vector y (t) may be expressed as:
    Figure FDA0004092008350000024
    where Ψ is a sensor failure random matrix, which can be expressed as:
    Figure FDA0004092008350000025
    wherein the random variable is
    Figure FDA0004092008350000026
    For describing the fault condition of the jth sensor: when the random variable->
    Figure FDA0004092008350000027
    When the sensor j is in a complete fault state, the jth system measures an output vector y j (t) is 0, when
    Figure FDA0004092008350000028
    When the sensor j is in a partial fault state, the jth system measures an output vector y j (t) the result does not exactly correspond to the actual value of the system when->
    Figure FDA0004092008350000029
    When the sensor j is in a normal working state, the jth system measures an output vector y j (t) the result is completely consistent with the actual value;
    under the external disturbance and the random sensor fault, the filtering error augmentation system model is as follows:
    Figure FDA00040920083500000210
    wherein ε (t) e R 20 To augment a system state vector, the augmented system state vector is formed from the system state vector x (t) and the filter state vector x h (t) the compound is formed by increasing,
    Figure FDA00040920083500000211
    for the derivative of the augmented system state vector ε (t), θ (t) E R 2 A noise vector for the augmentation system, the noise vector being augmented by the process noise ω (t) and the measurement noise v (t), δ (t) e R 10 To augment the system output vector, the vector represents the system output vector z (t) and the filter output vector z h The error between (t), i.e. δ (t) = z (t) -z h (t)，Γ Am 、Γ Bm And Γ L A coefficient matrix with suitable dimensions, which is in the following specific form:
    Figure FDA0004092008350000031
    wherein, gamma is L T Is a coefficient matrix gamma L Transpose of (2), coefficientMatrix gamma Am And Γ Bm Contains the random matrix Ψ, so that both are also expressed as
    Figure FDA0004092008350000032
    Here, the first and second liquid crystal display panels are,
    Figure FDA0004092008350000033
    Figure FDA0004092008350000034
    here, the first and second liquid crystal display panels are,
    Figure FDA0004092008350000035
    is the expectation of the random matrix Ψ.
  3. 3. The design method of the SP type ICP T system filter as recited in claim 1, wherein the sufficient conditions for the robust mean square progressive stabilization of the filtering error augmentation system are as follows:
    Figure FDA0004092008350000036
    wherein the content of the first and second substances,
    Figure FDA0004092008350000037
    and &>
    Figure FDA0004092008350000038
    Are respectively matrix->
    Figure FDA0004092008350000039
    And &>
    Figure FDA00040920083500000310
    Transposing; gamma ray>0 is disturbance attenuationReducing the level; q ∫ A positive definite symmetric matrix is more than 0, and an identity matrix with proper dimension is I.
  4. 4. The method of designing a filter for an SP-type ICPT system as defined in claim 1 wherein solving for the gain of the filter comprises:
    alignment of a symmetric matrix Q ∫ Decompose and define a matrix N ∫ A specific form of (a);
    and respectively multiplying the two sides of the robust mean square progressive sufficient condition of the filtering error augmentation system by the diagonal matrix J = diag { N { (N) } in a left-hand manner and a right-hand manner ∫ I, I } and
    Figure FDA00040920083500000311
    and solving the filter gain.
  5. 5. The method of claim 4, wherein said positive definite symmetric matrix Q is designed as a filter of an SP-type ICPT system ∫ Decomposing in the specific form:
    Figure FDA00040920083500000312
    wherein Q s1 ＞0，Q s3 Greater than 0 is positive definite symmetric matrix, Q s2 In the form of a symmetrical matrix, the matrix is,
    Figure FDA0004092008350000041
    for said symmetric matrix Q s2 And satisfies->
    Figure FDA0004092008350000042
    The matrix N ∫ The concrete form of (A) is as follows:
    Figure FDA0004092008350000043
    wherein the content of the first and second substances,
    Figure FDA0004092008350000044
    for said positive definite symmetric matrix Q s3 The inverse matrix of (d);
    multiplying both sides of the sufficient condition by the diagonal matrices J and J at the same time T The resulting linear matrix inequality is of the form:
    Figure FDA0004092008350000045
    wherein, the first and the second end of the pipe are connected with each other,
    Figure FDA0004092008350000046
    Figure FDA0004092008350000047
    and &>
    Figure FDA0004092008350000048
    Are respectively a matrix S A 、S B 、S C 、S D 、H Am And H Bm Transpose of (3), matrix Y, H Am 、H Bm And H Lm Can be defined as:
    Figure FDA0004092008350000049
    here, the first and second liquid crystal display panels are,
    Figure FDA00040920083500000410
    for said positive definite symmetric matrix Q s3 Is inverted matrix of->
    Figure FDA00040920083500000411
    For said symmetric matrix Q s2 Transposed matrix of (H) A 、H B And H C Is the filter gain; />
    The filter gain is:
    Figure FDA00040920083500000412
    and tracking all state variable change conditions of the SP type ICPT system in real time by obtaining the filter gain.
  6. 6. A method for filter design according to any of claims 1-5 wherein the filter is an H-infinity filter.
  7. 7. An SP-type ICPT system for implementing the SP-type ICPT system filter design method of claim 1 wherein the system includes: the device comprises a direct current chopping module, an electric energy transmitting device module, an electric energy receiving device module, a voltage and current detection module, a wireless communication module and an H infinite filtering module; the output end of the direct current chopping module is connected to the electric energy transmitting device module, an air gap is formed between the electric energy transmitting device module and the electric energy receiving device module, the electric energy transmitting device module and the electric energy receiving device module are connected through mutual inductance, the output end of the electric energy receiving device module is connected to the input end of the voltage and current detection module, the output end of the voltage and current detection module is connected to the input end of the wireless communication module, and the output end of the wireless communication module is connected to the H infinite filtering module.
  8. 8. The SP-type ICPT system of claim 7 wherein the power transmitting means module includes: the direct current power supply module, the high-frequency inverter, the primary side resonance compensation network, the direct current power supply module, the high-frequency inverter and the primary side resonance compensation network are electrically connected in sequence; the power receiving device includes: the secondary side resonance compensation network, the rectifier and the load are electrically connected in sequence; the voltage current detection module includes: a voltage sensor and a current sensor.
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