CN111614343A - 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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CN111614343A
CN111614343A CN202010517369.5A CN202010517369A CN111614343A CN 111614343 A CN111614343 A CN 111614343A CN 202010517369 A CN202010517369 A CN 202010517369A CN 111614343 A CN111614343 A CN 111614343A
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CN111614343B (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
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
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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 charging systems of devices such as electric automobiles, smart homes, organ transplantation and the like.
Considering that the ICPT system is a high frequency resonance system, although harmonic components of alternating voltage and current generated during the operation of the system are negligible, fundamental components of the two are difficult to obtain accurate measurement results 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;
carrying out quantization processing on 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 BDA0002530641750000021
wherein, x (t) ∈ R10Is a vector of the states of the system,
Figure BDA0002530641750000031
is the derivative of the system state vector x (t), y (t) ∈ R2Measuring an output vector for a system, said system measured output vector comprising measurements of system load voltage and load current, z (t) ∈ R10As the system output vector, ω (t) ∈ R1And v (t) ∈ R1Respectively process noise and measurement noise of the system, SA、SB、SC、SDAnd SLIs a matrix of known coefficients with suitable dimensions, wherein S isACan be obtained by the generalized state space-average equation;
the filter model may be:
Figure BDA0002530641750000032
wherein the gain H of the filterA、HBAnd HLFor a matrix of coefficients to be determined of suitable dimensions, xh(t)∈R10In order to be a vector of the filter states,
Figure BDA0002530641750000033
for the filter state vector xhDerivative of (t), zh(t)∈R10Is a filter output vector comprising an estimate of the system output vector z (t),
Figure BDA0002530641750000034
for a filter input vector, the filter input vector and the system measurement output vector y (t) can be expressed as:
Figure BDA0002530641750000035
where Ψ is a sensor failure random matrix, which can be expressed as:
Figure BDA0002530641750000036
wherein the random variable is
Figure BDA0002530641750000037
For describing the fault condition of the jth sensor: when the random variable is changed
Figure BDA0002530641750000038
When the sensor j is in a complete fault state, the jth system measures an output vector yj(t) is 0, when
Figure BDA0002530641750000039
When the sensor j is in a partial fault state, the jth system measures an output vector yj(t) the result is not exactly the same as the actual value of the system when
Figure BDA00025306417500000310
When the sensor j is in a normal working state, the jth system measures an output vector yj(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 BDA00025306417500000311
wherein, (t) ∈ R20For the augmented system state vector, the augmented system state vector is composed of the system state vector x (t) and the filter state vector xh(t) the compound is formed by increasing,
Figure BDA00025306417500000312
is the derivative of the augmented system state vector (t), θ (t) ∈ R2(ii) is a noise vector of the augmented system, the noise vector augmented by the process noise ω (t) and the measurement noise v (t), (t) ∈ R10For amplifying system outputVectors representing the system output vector z (t) and the filter output vector zhThe error between (t), i.e. (t) ═ z (t) -zh(t)，Am、BmAndLa coefficient matrix with suitable dimensions, which is in the following specific form:
Figure BDA0002530641750000041
wherein the content of the first and second substances,L Tis a coefficient matrixLTranspose of (2), coefficient matrixAmAndBmcontains the random matrix Ψ, so both can also be expressed as
Figure BDA0002530641750000042
Here, the first and second liquid crystal display panels are,
Figure BDA0002530641750000043
Figure BDA0002530641750000044
here, the first and second liquid crystal display panels are,
Figure BDA0002530641750000045
is the expectation of the random matrix Ψ.
Preferably, the sufficient condition for robust mean square progressive stabilization of the filtering error augmentation system may be:
Figure BDA0002530641750000046
wherein the content of the first and second substances,
Figure BDA0002530641750000047
and
Figure BDA0002530641750000048
respectively being said matrix
Figure BDA0002530641750000049
And
Figure BDA00025306417500000410
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);
two sides of the robust mean square progressive sufficient condition of the filtering error augmentation system are respectively multiplied by the diagonal matrix J to be a diag { N }∫I, I } and
Figure BDA00025306417500000411
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 BDA00025306417500000412
wherein Q iss1＞0，Qs3Greater than 0 is positive definite symmetric matrix, Qs2In the form of a symmetrical matrix, the matrix is,
Figure BDA0002530641750000051
is the symmetric matrix Qs2And satisfies the transposed matrix of
Figure BDA0002530641750000052
The matrix N∫The specific form of (b) may be:
Figure BDA0002530641750000053
wherein the content of the first and second substances,
Figure BDA0002530641750000054
for said positive definite symmetric matrix Qs3The inverse matrix of (d);
multiplying both sides of the sufficient condition by the diagonal matrices J and J at the same timeTThe resulting linear matrix inequality is of the form:
Figure BDA0002530641750000055
wherein the content of the first and second substances,
Figure BDA0002530641750000056
Figure BDA0002530641750000057
and
Figure BDA0002530641750000058
are respectively a matrix SA、SB、SC、SD、HAmAnd HBmTranspose of (2), matrix Y, HAm、HBmAnd HLmCan be defined as:
Figure BDA0002530641750000059
here, the first and second liquid crystal display panels are,
Figure BDA00025306417500000510
for said positive definite symmetric matrix Qs3The inverse of the matrix of (a) is,
Figure BDA00025306417500000511
is the symmetric matrix Qs2Transposed matrix of (H)A、HBAnd HCIs the filter gain;
the filter gain may be:
Figure BDA00025306417500000512
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 design method and the system of the H infinite filter, which are provided by the invention, take the external disturbance and random sensor fault factors into consideration, remarkably improve the fault tolerance and robustness of the SP type ICPT system, simultaneously can estimate the state variables which are difficult to measure according to the 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 conditions 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 diagram illustrating simulation results of actual and estimated values of output current under external disturbance and random sensor failure in an embodiment of the method and system for designing a SP-type ICPT system filter 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 and be integral therewith, 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 BDA0002530641750000081
wherein u isac(t) output of high frequency inverterA voltage; cpAnd CsRespectively representing primary and secondary resonance compensation capacitance values, LpAnd LsRespectively representing the inductance of the primary side coupling coil and the secondary side coupling coil; rpAnd RsRespectively representing the internal resistances 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 isd、CdAnd RdRespectively representing a filter inductor, a filter capacitor and a load resistor; u. ofcp(t) and ip(t) representing the voltage across the load resistor and the current through the load resistor, respectively; logic function si(t) and sr(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 uac(t) and ucs(t) direction determination.
Carrying out quantization processing on variables in the state space model through Fourier transform;
Figure BDA0002530641750000091
wherein<·>1Representing the first harmonic component of the alternating state variable, Re<·>1And Im<·>1Respectively representing the real and imaginary parts of the first harmonic component,<·>0representing the fundamental component of the dc state variable.
Establishing the generalized state space average equation of the SP type ICPT system:
Figure BDA0002530641750000092
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 BDA0002530641750000101
wherein x (t) ∈ R10Is a state space vector whose corresponding expression is:
Figure BDA0002530641750000102
here, xi(t) (i ═ 1, …,10) represents the ith state variable of the system.
y(t)∈R2For measuring the output vector, its corresponding expression is
y(t)＝[y1(t) y2(t)]T(6)
Here, yj(t) (j ═ 1,2) represents the measured value of sensor j, where y represents the measured value of sensor j1(t) represents the system load voltage ud(t) measurement, y, by a voltage sensor 402 as shown in FIG. 22(t) represents the system load current id(t) measurement values obtained by the current sensor 401 shown in fig. 2.
z(t)∈R10For 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)∈R1And v (t) ∈ R1Respectively process noise and measurement noise of the system, SA、SB、SC、SDAnd SLIs a known matrix of suitable dimensions, in which SACan 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 BDA0002530641750000103
wherein the filter gain HA、HBAnd HLA matrix to be determined of suitable dimensions; x is the number ofh(t)∈R10Is the state space vector of the filter; z is a radical ofh(t)∈R10Is the output vector of the filter, which represents the estimation result of z (t);
Figure BDA0002530641750000104
is the input vector to the filter, which represents the actual case of y (t) being transmitted to the filter, and the corresponding form can be described as:
Figure BDA0002530641750000105
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 ∞ filter under random sensor failure
Figure BDA0002530641750000111
Can be defined as:
Figure BDA0002530641750000112
wherein the random matrix Ψ ∈ R2×2For describing the degree of failure of the sensor, and an expanded form of the matrix may be defined as:
Figure BDA0002530641750000113
random variable here
Figure BDA0002530641750000114
For describing the jth sensorBarrier condition, the essential features of this variable are as follows:
Figure BDA0002530641750000115
wherein the random variable is
Figure BDA0002530641750000116
Is noted as iota and variance, respectivelyjAnd
Figure BDA0002530641750000117
both are used to characterize the failure level of sensor j.
According to given desired iotajSum variance
Figure BDA0002530641750000118
The expectation and variance of the obtainable random matrix Ψ are:
Figure BDA0002530641750000119
Figure BDA00025306417500001110
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 BDA00025306417500001111
wherein the augmented state vector (t) and the augmented noise vector θ (t) are respectively expressed as:
Figure BDA00025306417500001112
(t) error of the system (14)A difference vector representing the deviation between the actual value and the estimated value of the system output, i.e. (t) ═ z (t) -zh(t)。Am、BmAndLa coefficient matrix with suitable dimensions, which is in the following specific form:
Figure BDA0002530641750000121
wherein the content of the first and second substances,L Tis a coefficient matrixLTranspose of (2), coefficient matrixAmAndBmcontains the random matrix Ψ, so both can also be expressed as
Figure BDA0002530641750000122
Here, the first and second liquid crystal display panels are,
Figure BDA0002530641750000123
Figure BDA0002530641750000124
here, the first and second liquid crystal display panels are,
Figure BDA0002530641750000125
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 BDA0002530641750000126
wherein the content of the first and second substances,
Figure BDA0002530641750000127
and
Figure BDA0002530641750000128
respectively being said matrix
Figure BDA0002530641750000129
And
Figure BDA00025306417500001210
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((t))＝T(t)Q∫(t) (20)
introducing a basic definition of an infinite operator, and solving the expectation of the Lyapunov function F (t) infinite operator;
the infinitesimal operator of an arbitrary function f (t) can be defined as:
Figure BDA00025306417500001211
considering that the system (14) has a random matrix Ψ for describing the sensor failure, the expectation of an infinitesimal operator corresponding to the lei apunov function f (t) can be solved by the formula (21).
Ε{LF((t))}＝Ε{Σ1(t)-T(t)(t)+γ2θT(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 BDA0002530641750000131
wherein, sigma1It can also be described as:
Figure BDA0002530641750000132
obtaining a sufficient condition of gradual stable mean square of the system (14) according to the schur complement theory;
in view of
Figure BDA0002530641750000133
It is therefore easy to deduce the matrix
Figure BDA0002530641750000134
And
Figure BDA0002530641750000135
the expected values of (a) are:
Figure BDA0002530641750000136
therefore ∑1The expectation is that:
Figure BDA0002530641750000137
according to the Shu's complementary theory, sigma1The expectation of (c) is converted into the following form:
Figure BDA0002530641750000138
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 mean square gradual stabilization of the system, namely:
if the mean square of the system is gradually stable, the system satisfies the following conditions:
Figure BDA0002530641750000139
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 both sides of the formula (22) simultaneously to obtain
Figure BDA00025306417500001310
Substituting equation (19) into equation (27) yields:
Figure BDA0002530641750000141
considering the requirement for system mean square asymptotic stabilization as e { F ((+ ∞)) } < e { F ((0)) }, we can deduce from equation (28):
Figure BDA0002530641750000142
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 optional example, the specific step of solving the gain of the filter according to the sufficient condition is:
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 BDA0002530641750000143
wherein Q iss1＞0，Qs3Greater than 0 is positive definite symmetric matrix, Qs2In the form of a symmetrical matrix, the matrix is,
Figure BDA0002530641750000144
is the symmetric matrix Qs2And satisfies the transposed matrix of
Figure BDA0002530641750000145
The matrix N∫The specific form of (b) may be:
Figure BDA0002530641750000146
wherein the content of the first and second substances,
Figure BDA0002530641750000147
for said positive definite symmetric matrix Qs3The inverse matrix of (d);
multiplying both sides of the sufficient condition by the diagonal matrices J and J at the same timeTThe resulting linear matrix inequality is of the form:
Figure BDA0002530641750000148
wherein the content of the first and second substances,
Figure BDA0002530641750000149
Figure BDA00025306417500001410
and
Figure BDA00025306417500001411
are respectively a matrix SA、SB、SC、SD、HAmAnd HBmTranspose of (2), matrix Y, HAm、HBmAnd HLmCan be defined as:
Figure BDA0002530641750000151
here, the first and second liquid crystal display panels are,
Figure BDA0002530641750000152
for said positive definite symmetric matrix Qs3The inverse of the matrix of (a) is,
Figure BDA0002530641750000153
is the symmetric matrix Qs2Transposed matrix of (H)A、HBAnd HCIs the filter gain;
the filter gain may be:
Figure BDA0002530641750000154
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 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 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 S1、S2、S3And S4Wherein, 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/S4,S2/S3) Method for obtaining output voltage u of high-frequency inverter 202 in operating modeac(t)。
In an alternative example, in the above SP type ICPT system, the primary resonant compensation network 203 further includes: with internal resistance RpPrimary side coupling coil LpAnd primary side compensation capacitor CpWherein the primary side of the compensating capacitor CpAnd primary side coupling coil LpConnected in series and having a primary compensation capacitor CpTwo endsVoltage and current flowing through the primary side coupling coil LpRespectively is denoted as ucp(t) and ip(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 RsSecondary side coupling coil L ofsAnd secondary side compensation capacitor CsWherein the secondary side compensates the capacitor CsCoil L coupled with secondary sidesConnected in parallel and the secondary side compensates the capacitance CsVoltage at two ends and secondary side compensation inductor L flowing throughsRespectively is denoted as ucs(t) and is(t)。
In one example, in the above-mentioned SP type ICPT system, the primary side coupling coil LpCoil L coupled with secondary sidesThe 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 D1、D2、D3And D4Wherein the bridge rectifier circuit composed of the four diodes realizes the conversion of alternating current to direct current and obtains a load voltage ud(t) and load current id(t)。
In an optional example, in the above SP type ICPT system, the load 303 further includes: filter inductance LdFilter capacitor CdAnd a load resistance RdWherein the filter inductance LdAnd a filter capacitor CdCommon for removing load voltage ud(t) and load current id(t) unwanted ripple.
In one example, in the above-described SP-type ICPT system, the voltage current detection module 400 further includes: current sensor 401, voltageA sensor 402, wherein the current sensor 401 and the voltage sensor 402 are respectively used for measuring the load voltage ud(t) and load current id(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 1 μ s, and the electrical parameters of the SP type ICPT system are as follows:
electrical parameter summarization for SP-type ICPT systems
Parameter name Parameter value Parameter name Parameter value
Primary side coupling coil inductance Lp(μH) 126 Secondary side coupling inductance Ls(μH) 126
Internal resistance R of primary side coupling coilp(Ω) 0.0017 Secondary side coupling coil resistor Rp(Ω) 0.0017
Primary side resonance compensation capacitor Cp(μF) 2.4 Secondary side resonance compensating capacitor Cs(μF) 2
Load inductance Ld(mH) 3 Load capacitance Cd(μF) 220
Load resistance Rd(Ω) 15 Mutual inductance M (mu H) 44.1
Resonant frequency fo(kHZ) 10 Switching angular frequency omega0(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 BDA0002530641750000171
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 BDA0002530641750000172
FIG. 3 shows the random variation of the system sensor fault, in which the sensor 1 is used to measure the load voltage ud(t) a voltage sensor, the sensor 2 being for measuring a load current id(t) current sensors, and the random fault conditions of both passing through random variables
Figure BDA0002530641750000181
And
Figure BDA0002530641750000182
a description will be given. Random variable
Figure BDA0002530641750000183
And
Figure BDA0002530641750000184
the expectation and variance of (c) are:
Figure BDA0002530641750000185
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 ud(t) and load current id(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 simulation result verifies that the designed H-infinity filter not only can inhibit the influence of external disturbance on the system, but also can accurately estimate the actual change situation of the measurement output.
FIG. 6 shows the real-time error estimation results of all state variables of the system, where di(t) (i ═ 1, …,10) respectively represent the estimation error of the i-th state variable, and di(t)＝zi(t)-zhi(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 10-3And the estimation error of each state variable shows the trend of continuously attenuating along with time, which shows that the H-infinity filtering designed by the inventionThe device can not only accurately estimate the actual change condition of the measurement output, but also 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 ud(t) and load current id(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 obtained estimation result is basically consistent with the change trend of the actual measurement output.
FIG. 9 shows the real-time error estimation results for all state variables of the system, where di(t) (i ═ 1, …,10) respectively represent the estimation error of the i-th state variable, and di(t)＝zi(t)-zhi(t) of (d). As can be seen from the figure, the estimation errors of all state variables of the system are increased immediately in the switching transient state of the sensor fault condition and are recovered to the allowable error range in a short time, which shows that the H ∞ 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 and modifications to these embodiments may be made by those skilled in the art without departing from the spirit and scope of the invention, and these changes and modifications are within the scope of the invention.

Claims (10)

  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;
    and solving the gain of the filter according to the sufficient condition.
  2. 2. The method of filter design for an SP-type ICPT system as described in claim 1 wherein said establishing a generalized state space average equation for said SP-type ICPT system comprises:
    establishing a state space model of the SP type ICPT system according to kirchhoff's law;
    carrying out quantization processing on variables in the state space model through Fourier transform;
    establishing the generalized state space average equation of the SP type ICPT system.
  3. 3. The method of designing a filter for an SP type ICPT system as described in claim 1 wherein said modeling a filter error augmentation system for said SP type ICPT system under external disturbances and stochastic sensor faults comprises:
    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.
  4. 4. A method for filter design in a SP-type ICPT system as claimed in claim 3 wherein the external perturbation generalized state space model is:
    Figure FDA0002530641740000011
    wherein, x (t) ∈ R10Is a vector of the states of the system,
    Figure FDA0002530641740000012
    is the derivative of the system state vector x (t), y (t) ∈ R2Measuring an output vector for a system, said system measured output vector comprising measurements of system load voltage and load current, z (t) ∈ R10As the system output vector, ω (t) ∈ R1And v (t) ∈ R1Respectively process noise and measurement noise of the system, SA、SB、SC、SDAnd SLIs a matrix of known coefficients with suitable dimensions, wherein S isACan be obtained by the generalized state space-average equation;
    the filter model may be:
    Figure FDA0002530641740000021
    wherein the gain H of the filterA、HBAnd HLFor a matrix of coefficients to be determined of suitable dimensions, xh(t)∈R10In order to be a vector of the filter states,
    Figure FDA0002530641740000022
    for the filter state vector xhDerivative of (t), zh(t)∈R10Is a filter output vector comprising an estimate of the system output vector z (t),
    Figure FDA0002530641740000023
    for a filter input vector, the filter input vector and the system measurement output vector y (t) can be expressed as:
    Figure FDA0002530641740000024
    where Ψ is a sensor failure random matrix, which can be expressed as:
    Figure FDA0002530641740000025
    wherein the random variable is
    Figure FDA0002530641740000026
    For describing the fault condition of the jth sensor: when the random variable is changed
    Figure FDA0002530641740000027
    When the sensor j is in a complete fault state, the jth system measures an output vector yj(t) is 0, when
    Figure FDA0002530641740000028
    When the sensor j is in a partial fault state, the jth system measures an output vector yj(t) the result is not exactly the same as the actual value of the system when
    Figure FDA0002530641740000029
    When the sensor j is in a normal working state, the jth system measures an output vector yj(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 FDA00025306417400000210
    wherein, (t) ∈ R20For the augmented system state vector, the augmented system state vector is composed of the system state vector x (t) and the filter state vector xh(t) the compound is formed by increasing,
    Figure FDA00025306417400000211
    is the derivative of the augmented system state vector (t), θ (t) ∈ R2(ii) is a noise vector of the augmented system, the noise vector augmented by the process noise ω (t) and the measurement noise v (t), (t) ∈ R10To augment a system output vector, the vector representing the system output vector z (t) and the filter output vector zhThe error between (t), i.e. (t) ═ z (t) -zh(t)，Am、BmAndLa coefficient matrix with suitable dimensions, which is in the following specific form:
    Figure FDA0002530641740000031
    wherein the content of the first and second substances,L Tis a coefficient matrixLTranspose of (2), coefficient matrixAmAndBmcontains the random matrix Ψ, so both can also be expressed as
    Figure FDA0002530641740000032
    Here, the first and second liquid crystal display panels are,
    Figure FDA0002530641740000033
    Figure FDA0002530641740000034
    here, the first and second liquid crystal display panels are,
    Figure FDA0002530641740000035
    is the expectation of the random matrix Ψ.
  5. 5. The design method of the filter of the SP type ICPT system according to claim 1, wherein the sufficient condition for the robust mean square progressive stabilization of the filtering error augmentation system is:
    Figure FDA0002530641740000036
    wherein the content of the first and second substances,
    Figure FDA0002530641740000037
    and
    Figure FDA0002530641740000038
    respectively being said matrix
    Figure FDA0002530641740000039
    And
    Figure FDA00025306417400000310
    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.
  6. 6. 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:
    for the positive definite matrix Q∫Decompose and define a matrix N∫The specific form of (a);
    two sides of the robust mean square progressive sufficient condition of the filtering error augmentation system are respectively multiplied by the diagonal matrix J to be a diag { N }∫I, I } and
    Figure FDA00025306417400000311
    and solving the filter gain.
  7. 7. The method of claim 6,wherein said positive definite matrix Q∫The decomposition is carried out, and the specific form can be as follows:
    Figure FDA0002530641740000041
    wherein Q iss1＞0，Qs3Greater than 0 is positive definite symmetric matrix, Qs2In the form of a symmetrical matrix, the matrix is,
    Figure FDA0002530641740000042
    is the symmetric matrix Qs2And satisfies the transposed matrix of
    Figure FDA0002530641740000043
    The matrix N∫The specific form of (b) may be:
    Figure FDA0002530641740000044
    wherein the content of the first and second substances,
    Figure FDA0002530641740000045
    for said positive definite symmetric matrix Qs3The inverse matrix of (d);
    multiplying both sides of the sufficient condition by the diagonal matrices J and J at the same timeTThe resulting linear matrix inequality is of the form:
    Figure FDA0002530641740000046
    wherein the content of the first and second substances,
    Figure FDA0002530641740000047
    Figure FDA0002530641740000048
    and
    Figure FDA0002530641740000049
    are respectively a matrix SA、SB、SC、SD、HAmAnd HBmTranspose of (2), matrix Y, HAm、HBmAnd HLmCan be defined as:
    Figure FDA00025306417400000410
    here, the first and second liquid crystal display panels are,
    Figure FDA00025306417400000411
    for said positive definite symmetric matrix Qs3The inverse of the matrix of (a) is,
    Figure FDA00025306417400000412
    is the symmetric matrix Qs2Transposed matrix of (H)A、HBAnd HCIs the filter gain;
    the filter gain may be:
    Figure FDA0002530641740000051
    and tracking all state variable change conditions of the SP type ICPT system in real time by obtaining the filter gain.
  8. 8. A method for filter design according to any of claims 1-7 wherein the filter is an H-infinity filter.
  9. 9. An SP-type ICPT system 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.
  10. 10. The SP type ICPT system of claim 9 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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