CN110635577A - Nonlinear analysis control method of high-power wireless power transmission system - Google Patents

Nonlinear analysis control method of high-power wireless power transmission system Download PDF

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CN110635577A
CN110635577A CN201910655359.5A CN201910655359A CN110635577A CN 110635577 A CN110635577 A CN 110635577A CN 201910655359 A CN201910655359 A CN 201910655359A CN 110635577 A CN110635577 A CN 110635577A
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power transmission
wireless power
coil
current
transmission system
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CN110635577B (en
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周洪
吴雨
蒋燕
陈诚
邓其军
胡文山
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Wuhan University WHU
Information and Telecommunication Branch of State Grid Hubei Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
    • H02J50/10—Circuit arrangements or systems for wireless supply or distribution of electric power using inductive coupling
    • H02J50/12—Circuit arrangements or systems for wireless supply or distribution of electric power using inductive coupling of the resonant type

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Abstract

The invention discloses a nonlinear analysis control method of a wireless power transmission system, which comprises the following steps: establishing a wireless power transmission system model and a mathematical model of the nonlinear inductor, and substituting the mathematical model established by the nonlinear inductor into a loop equation of the wireless power transmission system model to obtain a state equation of the system; the method comprises the following steps of carrying out nonlinear analysis on a wireless power transmission system, and when judging that the system has a nonlinear phenomenon, adding an adaptive controller in an obtained system state equation, constructing the adaptive controller according to the Lassel invariant set theorem, and maintaining the system to be stable around a balance point by using a negative feedback gain link according to the balance point in a function so as to change the state variable of the system from irregular oscillation into periodic oscillation. The method is adopted to carry out nonlinear analysis and control on the high-power wireless power transmission system with the flat-plate magnetic core coil, so that the state variable of the system is changed from irregular oscillation to periodic oscillation.

Description

Nonlinear analysis control method of high-power wireless power transmission system
Technical Field
The invention belongs to the technical field of wireless power transmission, particularly relates to the technical field of nonlinear analysis control, and particularly relates to a nonlinear control method of a high-power wireless power transmission system with a flat magnetic core coil.
Background
In recent years, wireless power transmission systems have come into the sight of people more, become the hot spot of research of the broad researchers, and can solve the problems of abrasion, safety and the like caused by wires in the traditional circuit system.
However, due to the nonlinearity of the inductor and the capacitor in the wireless power transmission system, and the nonlinearity of the rectifying circuit, the transmitting coil, etc. in the system to different degrees, these nonlinearity conditions will seriously affect the energy transmission, the power, etc. of the wireless power transmission system. Whether the bifurcation phenomenon or the chaotic oscillation causes a plurality of unstable factors for the stable operation of the nonlinear system, and whether the chaotic motion can be effectively controlled into a stable orbit is a long-term concern of people.
Therefore, the research on the nonlinear characteristics of the wireless power transmission system plays an important role in the parameter design of the wireless power transmission system, the research on the energy transmission efficiency of the wireless power transmission system, the system power and other problems. In the aspect of chaotic control, many control methods have appeared, and conventional feedback control has certain robustness, but because the controller parameters are fixed, when the uncertainty is large, the performance of the system is greatly reduced, and even unstable. The control method adopted by the self-adaptive control is still a method based on a mathematical model, the prior knowledge about the model and the disturbance is less, and the information about the model needs to be continuously extracted in the operation process of the system, so that the model is more and more accurate.
Disclosure of Invention
The invention aims to provide a nonlinear analysis control method of a high-power wireless power transmission system aiming at the corresponding defects of the prior art.
The purpose of the invention is realized by adopting the following scheme: the invention discloses a nonlinear analysis control method of a high-power wireless power transmission system, which comprises the following steps:
1) establishing a wireless power transmission system model and a mathematical model of a nonlinear inductor of the wireless power transmission system, and substituting the mathematical model established by the nonlinear inductor into a loop equation of the wireless power transmission system model to obtain a state equation of the system;
2) carrying out nonlinear analysis on the wireless power transmission system, and executing the step 3) when judging that the system has a nonlinear phenomenon;
3) the adaptive controller is built according to the Lassel invariant set theorem, is added in the obtained system state equation, and is used for maintaining the system to be stable around a balance point by using a negative feedback gain link according to the balance point in the function so as to change the state variable of the system from irregular oscillation to periodic oscillation.
The system state equation obtained in the step 1) is
Figure RE-GDA0002277495610000021
n is the number of state variables, and the self-adaptive feedback control law u is added in the obtained system state equation in the step 3)jI.e. adding a control law u to the right of at least one equation of state of the systemjThe system state equation is changed to:n is the number of state variables, j is 1,2, and m is the number of added control items, and an adaptive controller designed for a nonlinear system is as follows:
Figure RE-GDA0002277495610000023
wherein: u. ofjIs an adaptive control law, gammajIs the law of self-adaptation,
Figure RE-GDA0002277495610000031
εjis a variable feedback control intensity, pjDenotes xiThe corresponding stable point. x is the number ofiRepresents the control law ujAdded to the i-th control variable, pjDenotes xiA corresponding stable point, for example j 1, i 2, indicates the first control item u1Added to the second state variable.
Constructing a formula for realizing the functions of automatic prediction and stable fixed point:
Figure RE-GDA0002277495610000032
wherein: rhoj∈Rn，
Figure RE-GDA0002277495610000033
xiIs the state variable of the system, pjIs a stable point, lambda, constructed to meet the stability of LyapunovjIs a parameter (constant) when xiInfinitely close to steady-state value x0Time, rhojAlso close to this value.
Modeling by adopting a state space method according to a loop equation of a wireless power transmission system model and the relation between the voltage and the current at two ends of a resonant capacitor in a transmitting end circuit and a receiving end circuit of the wireless power transmission system, and taking UCs∈R、UCd∈R、is∈R、idE, taking four state variables as the state variables, and obtaining the state equation of the system as follows:
order to
Figure RE-GDA0002277495610000035
Wherein R iss＝Rp+R0，Rd＝Rq+Rw，UsIs the supply voltage isIs the current of the transmitting-end circuit, idIs the current of the receiving-side circuit, UCsIs the voltage across the resonant capacitor, U, in the transmitting-end circuitCdIs the voltage of a resonant capacitor in the receiving end circuit, LsIs the current at the receiving end is isInductance of time-receiving coil, LdIs the current at the receiving end is idInductance of time-receiving coil, mutual inductance of transmitter coil and receiver coil
Figure RE-GDA0002277495610000036
CSIs a resonant capacitor connected in series to the coil, CdIs a resonant capacitor connected in series with the receiving coil, xiIs the state variable of the system.
Selecting voltage U at two ends of capacitor at receiving endCdAnd transmitting coil terminal current isAs a control state variable, the obtained controlled system expression is:
Figure RE-GDA0002277495610000041
wherein, it is madeWherein R iss＝Rp+R0，Rd＝Rq+Rw，UsIs the supply voltage isIs the current of the transmitting-end circuit, idIs the current of the receiving-side circuit, UCsIs the voltage across the resonant capacitor, U, in the transmitting-end circuitCdIs the voltage of a resonant capacitor in the receiving end circuit, LsIs the current at the receiving end is isInductance of time-receiving coil, LdIs the current at the receiving end is idInductance of time-receiving coil, mutual inductance of transmitter coil and receiver coil CSIs a resonant capacitor connected in series to the coil, CdIs a resonant capacitor, gamma, connected in series with the receiving coiljIs adaptiveThe law,
Figure RE-GDA0002277495610000044
εjis a variable feedback control strength, xiIs the state variable of the system, pjDenotes xiCorresponding stable point, λjIs a parameter that is a function of,
Figure RE-GDA0002277495610000045
step 1) establishing a mathematical model of the nonlinear inductor by using a piecewise function method.
And 2) carrying out nonlinear analysis on the established wireless power transmission system model by using a numerical analysis method, wherein the nonlinear analysis comprises solving the wireless power transmission system model by using the numerical analysis method to obtain solutions of the transmitting coil and the receiving coil under different input voltages, and if voltage and current waveforms of the transmitting end and the receiving end are forked, namely when the waveforms are non-sinusoidal waves, the nonlinear phenomenon of the system is indicated. The current waveform will change for different input voltages. The non-linearity is proved to exist, voltage and current waveforms of a transmitting end and a receiving end are forked, namely, the waveforms are non-sine waves, and if the non-linearity phenomenon does not occur, the waveforms are sine waves.
The invention has the advantages that: according to the invention, the nonlinear characteristic analysis is carried out on the high-power wireless electric energy transmission system, and the self-adaptive controller is designed to control the nonlinear wireless electric energy transmission system. From the simulation experiment result, the state variable of the system shows irregular oscillation before the controller is added, and the state variable of the system quickly converges to a periodic oscillation state after the controller is added and is stably maintained, so that the chaos and the fluctuation of the system are finally stabilized, and the system is restored to a normal operation state, which shows that the controller of the invention has a good chaos oscillation suppression effect.
Drawings
Fig. 1 is an equivalent circuit diagram illustrating an exemplary wireless power transmission system according to an embodiment of the present invention;
FIG. 2 is a graph of inductance-current relationship obtained by maxwell simulation in the example;
FIG. 3 is a simplified circuit diagram of a wireless power transmission system at different input voltages U according to an embodiment of the present inventionSCurrent i of lower transmitting end coilsTime response graph of (a); wherein FIG. 3(a) input voltage UsWhen the voltage is 300V, transmitting a coil current response graph; FIG. 3(b) input Voltage UsWhen the voltage is 850V, a current response graph of the transmitting coil is obtained; FIG. 3(c) input Voltage UsWhen the voltage is 1500V, transmitting a coil current response graph;
fig. 4 is a phase diagram of the current-voltage relationship of the input/output coil side of the wireless power transmission system under different input voltages in the embodiment of the present invention; wherein FIG. 4(a) input voltage UsWhen the voltage is 300V, a voltage-current phase diagram of a transmitting end and a receiving end is obtained; FIG. 4(b) input Voltage UsWhen the voltage is 850V, the voltage and the current phase diagrams of the transmitting end and the receiving end are obtained; FIG. 4(c) input Voltage UsWhen the voltage is 1500V, the voltage and current phase diagrams of the transmitting end and the receiving end are obtained;
FIG. 5 is a control schematic block diagram of a controller in an embodiment of the present invention;
fig. 6 is a time response graph of an input-side current after a fixed parameter of a wireless power transmission system is applied to a controller according to an embodiment of the present invention; wherein, after applying the controller, U in FIG. 6(a)sThe current of the emitting end is in a stable state when the voltage is 850V; FIG. 6(b) after applying the controller, UsAnd the current of the emitting end is in a stable state when the voltage is 1500V.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Referring to fig. 1, the embodiment discloses a nonlinear analysis control method for a wireless power transmission system, which performs nonlinear characteristic analysis on a high-power wireless power transmission system, and designs an adaptive controller to control the nonlinear wireless power transmission system, and includes the following steps:
1) and establishing a model for the nonlinear flat magnetic core coil, and substituting the model into a loop model of the wireless power transmission system to obtain a state equation of the system.
2) And carrying out nonlinear analysis on the established model by using a numerical analysis method, establishing a simulink block diagram according to a loop equation of the MATLAB pair system, and carrying out nonlinear characteristic analysis on the system.
3) The adaptive controller is built according to the Lassel invariant set theorem, is added in the obtained system state equation, and is used for maintaining the system to be stable around a balance point by using a negative feedback gain link according to the balance point in the function so as to change the state variable of the system from irregular oscillation to periodic oscillation.
The invention takes a typical two-coil magnetic coupling wireless power transmission system as an example.
(1) Wireless power transmission system model
FIG. 1 is a simplified diagram of a wireless power transfer system, wherein RS＝Rp+R0,Rd＝Rq+RwAnd obtaining a loop equation of the system simplified model according to the kirchhoff voltage law and a circuit theory:
Figure RE-GDA0002277495610000061
Figure RE-GDA0002277495610000062
wherein, USIs the voltage of a voltage source, R0Is the internal resistance of the voltage source. RpIs the loss internal resistance of the transmitting coil, LSIs the inductance of the transmitter coil, and M is the mutual inductance between the coils. CSIs a resonance capacitor connected in series with the coil, and the parasitic capacitance of the transmitting coil is very small relative to the resonance capacitor CSIt can be ignored and therefore the effect of parasitic capacitance. A resistor R for loadwIs represented by RqIs the loss resistance, L, of the receiving coildIs the inductance of the receiving coil. CdThe parasitic capacitance of the receiving coil is very small and can be ignored relative to the resonant capacitance of the receiving coil, so that the parasitic capacitance is ignored. Current of circuit in which the transmitting coil is located isIndicating the circuit in which the receiving coil is locatedBy idAnd (4) showing.
The inductance of a flat core coil is related to the structure of the coil itself, the core, and the current flowing through the coil. Under normal working conditions, the working frequency of the ferrite core is below 300kHz, the working loss of the ferrite core is extremely small under the frequency, and because the difference between the inductance of the flat core coil in high-frequency work and the direct current inductance is not large, a direct current inductance is adopted to replace an alternating current inductance to establish a model, inductance simulation is carried out on the flat core coil by using MAXWELL, and only the influence of the magnetic permeability of the core and the thickness of the core on a system is considered.
Conducting current solving is carried out on the coil simulation model, excitation is added, a solving domain is set, a subdivision domain and a solving method are set, and an inductance-current relation curve of the model under the parameters of the table 1 is obtained through simulation and is shown in the figure 2.
According to the inductance-current relation graph obtained by simulation, the inductance is gradually reduced along with the increase of the current after the flat magnetic core is added into the coil.
And (3) establishing a mathematical model of the nonlinear inductor by using a piecewise function method to obtain a formula (2).
TABLE 1
Figure RE-GDA0002277495610000071
Figure RE-GDA0002277495610000081
Wherein L (i) is the value of the coil inductance when the current is i, L0Is the initial inductance value of the coil, LS0Is the saturation value of the coil inductance, I, with sufficiently large current0Is the current value of the inductor just after it changes, ISIs the current value at which the inductance just reaches saturation.
It is known that the output of a nonlinear system is not proportional to the input.
From the above equation, we can obtain that the current in the transmitting terminal circuit is isInductance of time:
Figure RE-GDA0002277495610000083
current of i in receiving terminal circuitdInductance of time:
Figure RE-GDA0002277495610000084
in order to analyze the influence of the nonlinear inductance on the whole wireless power transmission system, we further analyzed the simplified system model of fig. 1, wherein the model of the inductance is expressed by the nonlinear inductance as shown in formula (4), and the value of the coupling coefficient k between the transmitting coil and the receiving coil is assumed to have a relation only with the relative distance value of the two coils, that is, the coupling coefficient k is assumed to be a determined value.
And (3) modeling by adopting a state space method according to a loop equation formula (1) and the relation between the voltage and the current at two ends of the resonant capacitor in the circuits of the transmitting end and the receiving end.
Get UCs∈R、UCd∈R、is∈R、idE.r four are state variables, respectively denoted as vector x (t) ═ x1(t) x2(t)x3(t)x4(t)}T，UsFor input, y is the output of the system. The state equation of the system is obtained as follows:
Figure RE-GDA0002277495610000091
the output equation is:
y＝Ax
A＝[0 0 1 0]
order toWherein R iss＝Rp+R0，Rd＝Rq+Rw，UsIs the supply voltage isIs the current of the transmitting-end circuit, idIs the current of the receiving-side circuit, UCsIs the voltage across the resonant capacitor, U, in the transmitting-end circuitCdIs the voltage of a resonant capacitor in the receiving end circuit, LsIs the current at the receiving end is isInductance of time-receiving coil, LdIs the current at the receiving end is idInductance of time-receiving coil, mutual inductance of transmitter coil and receiver coil
Figure RE-GDA0002277495610000093
xiIs the state variable of the system.
From the state loop equations we can see that the system is a non-autonomous system with a single input and a single output, with four state variables, and the state equation is a fourth order differential equation.
(2) Analysis of non-linear characteristics
MATLAB is used for researching the nonlinear phenomenon existing in the nonlinear system by adopting a numerical method, and a Longge Kutta method is selected as a solving method. The system model is solved by a numerical method, and the solution of the transmitting coil under different input voltages can be obtained.
According to the actual wireless power transmission system, the parameter adopted in the solution is Rs＝Rp+R0＝0.1Ω， Rq＝0Ω，Rd＝Rq+Rw＝1.3Ω，Cs＝Cd106.14nF, 0.5 coupling coefficient k, I0＝30A，Is＝120A， L0＝49.5uH，Ls028.5 uH. Varying the amplitude U of the input voltagesWhen the input voltage amplitudes are respectively 300V, 850V and 1500V, the current i flowing through the transmitting coil is obtainedsThe time response curve of (a) is shown in fig. 3.
The amplitude of the input voltage is continuously changed, and the current waveform of the transmitting coil is gradually changed along with the increase of the amplitude of the input voltage. When the amplitude of the input voltage is small, the whole circuit oscillates normally; when the amplitude of the input voltage is increased by the amplitude of the input voltage until the amplitude of the input voltage is about 850V, the circuit is in abnormal oscillation; continuing to increase the input voltage magnitude, the entire circuit is still in abnormal oscillation.
In order to more conveniently see whether the system has the chaos phenomenon, the chaos attractor phase diagram of the transmitting coil and the receiving coil under different input voltages is obtained through simulation by adopting the parameters, as shown in fig. 4. We can see that when the voltage amplitude is small, the orbit of the system is a circle period orbit; when the voltage amplitude is gradually increased to 850V, the track of the system suddenly generates a chaos phenomenon; the voltage is continuously increased, the system track is larger, and the chaos phenomenon is still obvious.
The nonlinear characteristic analysis is performed on the system, the numerical method is used for solving the wireless power transmission system model in the embodiment to obtain the solutions of the transmitting coil and the receiving coil under different input voltages, and if the voltage and current waveforms of the transmitting end and the receiving end are forked, namely the waveforms are non-sine waves, the nonlinear phenomenon of the system is indicated. The non-linearity is proved to exist, voltage and current waveforms of the transmitting end and the receiving end can be forked, namely, the waveforms are non-sine waves, and if the non-linearity phenomenon does not occur, the waveforms are sine waves. When the system has nonlinear phenomenon, the following controller is added for control, and the nonlinear phenomenon of the system is overcome. In practical application, the practical signal can be directly taken to see whether the system has nonlinearity or not.
(3) Adaptive control
According to the analysis, when the input voltage reaches above 850V, the system generates a nonlinear phenomenon, the invention aims to design an adaptive controller by adopting a Lyapunov method, and the adaptive control method is introduced from the aspect of stability analysis. Consider a nonlinear system:
Figure RE-GDA0002277495610000111
wherein x ∈ Rn,t∈[0,∞],f(x)∈RnIs a smooth vector field, and meets the consistency condition of Lipschitz, namely:
||fi(x)||＝||fi(x)-fi(x0)||≤k||xi-xi0||≤k||x-x0||∞ (7)
in the formula, | | x-x0||∞Is x-x0Infinity norm, | | x-x0||∞＝maxj||xj-x0f||(j＝1,2,......,n)， x0＝(x01,x02,...,x0n)TIs a balance point of equation (6).
Adding a control law u to the right of the equation of state of the systemjThen the system equation is:
Figure RE-GDA0002277495610000112
where n is the number of state variables, i 1,2, 3.. n, j 1, 2.. n, m is the number of control terms added, and the adaptive control law u is the number of state variablesjThe design of (2) is required to ensure that the output has no stable error. When the position of a stable point of a system cannot be known, a function of automatically predicting and stabilizing the fixed point can be realized by constructing a feedback-free disturbance, and the function design mode is as follows:
Figure RE-GDA0002277495610000113
wherein: rhoj∈Rn，xiIs the state variable of the system, pjIs a stable point, lambda, constructed to meet the stability of LyapunovjIs a parameter (constant) which is a simple low pass filter when x isiInfinitely close to steady-state value x0Time, rhojAlso close to this value.
The adaptive feedback controller designed for the nonlinear system is as follows:
Figure RE-GDA0002277495610000121
wherein: u. ofjIs the control law. Law of adaptation
Figure RE-GDA0002277495610000122
εjIs a variable feedback control intensity, an initial control intensity epsilonj(0) Is 0, then εjIs a monotonically increasing function that reaches a maximum value by the time the system reaches a stable point. At the same time, because of the control law uj～(xi-ρj) And the feedback disturbance can not change the stable point of the system, so that the output of the system is ensured to have no steady-state error.
FIG. 5 is a schematic block diagram of the application of adaptive control, LPT representing a low pass filter, controller ujDependent on the difference between the output of the actual signal and the LPT filtering, and on the variable control strength epsilonjIt is related.
We use an adaptive feedback control method to control the system state equation with a flat core coil. In order to measure the control state variable conveniently, the voltage U at two ends of a capacitor at a receiving end is selectedCdAnd transmitting coil terminal current isThese two easily measurable quantities are used as control state variables, and control terms are applied to the second and third equations, and the final controlled system expression is equation (11):
Figure RE-GDA0002277495610000123
the output equation is:
y＝Ax
A＝[0 0 1 0]
numerical simulation analysis was performed according to Matlab, at which time we used the same simulation parameters, Rs＝Rp+R0＝0.1Ω，Rq＝0Ω，Rd＝Rq+Rw1.3 Ω, coupling coefficient k 0.5, I0＝30A，Is＝120A， L0＝49.5uH，Ls0＝28.5uH，Cs＝Cd＝106.14nF。
When the input voltage amplitude is set to 850V, the initial value of the controller is set to be lambda1＝0，λ2＝0，γ1＝0，γ2And (0), the original system state equation can know that the system is in a chaotic state at the moment. Using the same simulation parameters, changing the parameters of the controller to lambda1＝1，γ1＝2，λ2＝0.05，γ2Setting the simulation step size to 0.00001s, after applying the controller, we can clearly see that the voltage and current of the transmitting end and the receiving end are gradually stabilized, we amplify the current of the transmitting end, and the stabilized state is as shown in fig. 6 (a).
When the input voltage amplitude is adjusted to 1500V, the controller parameter lambda is adjusted1＝2，γ1＝3，λ2＝0.05，γ2After the controller is applied, we can clearly see that the voltage and current of the transmitting terminal and the receiving terminal are gradually stabilized, and we amplify the current of the transmitting terminal, and the stabilized state is shown in fig. 6 (b).
These four parameters γ of the controller of the present embodiment1、γ2、λ1、λ2The method is selected on the basis that the constructed control law can keep the system output to have no steady-state error, and can be correspondingly adjusted according to actual conditions. According to the constructed function, the stability of the whole system can be satisfied when lambda is larger than or equal to 0 and gamma is larger than or equal to 0.
From the simulation experiment result, before the controller is added, the system state variable is represented as irregular oscillation, and after the controller is added, the system state variable is rapidly converged to a periodic oscillation state and is stably maintained, the chaos and the fluctuation of the system are finally stabilized, and the system is restored to a normal operation state, which shows that the designed controller has a good chaotic oscillation suppression effect.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and it is apparent that those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (8)

1. A nonlinear analysis control method of a high-power wireless power transmission system is characterized by comprising the following steps:
1) establishing a wireless power transmission system model and a mathematical model of a nonlinear inductor of the wireless power transmission system, and substituting the mathematical model established by the nonlinear inductor into a loop equation of the wireless power transmission system model to obtain a state equation of the system;
2) carrying out nonlinear analysis on the wireless power transmission system, and executing the step 3) when judging that the system has a nonlinear phenomenon;
3) and constructing an adaptive controller, adding the adaptive controller in the obtained system state equation, and using a negative feedback gain link to maintain the system to be stable around a balance point according to the balance point in the function so as to change the system state variable from irregular oscillation into periodic oscillation.
2. The method of claim 1, wherein: an adaptive controller is constructed according to the Lassel invariant set theorem.
3. The method according to claim 1 or 2, characterized in that: the system state equation obtained in the step 1) isN, n is the number of state variables, and an adaptive feedback control law u) is added into the obtained system state equation in the step 3)jI.e. adding a control law u to the right of at least one equation of state of the systemjThe system state equation is changed to:n, n is the number of state variables, j is 1,2,3, m, m is the number of control items added, and the adaptive controller designed for the nonlinear system is as follows:
Figure FDA0002136707590000013
wherein: u. ofjIs an adaptive control law, gammajIs the law of self-adaptation,
Figure FDA0002136707590000021
εjis a variable feedback control intensity, pjDenotes xiThe corresponding stable point.
4. The method of claim 3, wherein: constructing a formula for realizing the functions of automatic prediction and stable fixed point:
Figure FDA0002136707590000022
wherein: rhoj∈Rn，
Figure FDA0002136707590000023
xiIs the state variable of the system, pjIs a stable point, lambda, constructed to meet the stability of LyapunovjIs a parameter (constant) when xiInfinitely close to steady-state value x0Time, rhojAlso close to this value.
5. A method according to claim 1 or 3, characterized in that: modeling by adopting a state space method according to a loop equation of a wireless power transmission system model and the relation between the voltage and the current at two ends of a resonant capacitor in a transmitting end circuit and a receiving end circuit of the wireless power transmission system, and taking UCs∈R、UCd∈R、is∈R、idE, taking four state variables as the state variables, and obtaining the state equation of the system as follows:
Figure FDA0002136707590000024
order to
Figure FDA0002136707590000025
Wherein R iss＝Rp+R0，Rd＝Rq+Rw，UsIs the supply voltage isIs the current of the transmitting-end circuit, idIs the current of the receiving-side circuit, UCsIs the voltage across the resonant capacitor, U, in the transmitting-end circuitCdIs the voltage of a resonant capacitor in the receiving end circuit, LsIs the current at the receiving end is isInductance of time-receiving coil, LdIs the current at the receiving end is idInductance of time-receiving coil, mutual inductance of transmitter coil and receiver coil
Figure FDA0002136707590000026
CSIs a resonant capacitor connected in series to the coil, CdIs a resonant capacitor connected in series with the receiving coil, xiIs the state variable of the system.
6. The method of claim 5, wherein: selecting voltage U at two ends of capacitor at receiving endCdAnd transmitting coil terminal current isAs a control state variable, the obtained controlled system expression is:
Figure FDA0002136707590000031
wherein, it is made
Figure FDA0002136707590000032
Wherein R iss＝Rp+R0，Rd＝Rq+Rw，UsIs the supply voltage isIs the current of the transmitting-end circuit, idIs the current of the receiving-side circuit, UCsIs the voltage across the resonant capacitor, U, in the transmitting-end circuitCdIs the voltage of a resonant capacitor in the receiving end circuit, LsIs the current at the receiving end is isInductance of time-receiving coil, LdIs the current at the receiving end is idInductance of time-receiving coil, mutual inductance of transmitter coil and receiver coil
Figure FDA0002136707590000033
CSIs a resonant capacitor connected in series to the coil, CdIs a resonant capacitor, gamma, connected in series with the receiving coiljIs the law of self-adaptation,
Figure FDA0002136707590000034
εjis a variable feedback control strength, xiIs the state variable of the system, pjDenotes xiCorresponding stable point, λjIs a parameter that is a function of,
Figure FDA0002136707590000035
7. the method of claim 1, wherein: step 1) establishing a mathematical model of the nonlinear inductor by using a piecewise function method.
8. The method of claim 1, wherein: and 2) carrying out nonlinear analysis on the established wireless power transmission system model by using a numerical analysis method, wherein the nonlinear analysis comprises solving the wireless power transmission system model by using the numerical analysis method to obtain solutions of the transmitting coil and the receiving coil under different input voltages, and if voltage and current waveforms of the transmitting end and the receiving end are forked, namely when the waveforms are non-sinusoidal waves, the nonlinear phenomenon of the system is indicated.
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