An underwater wireless charging system mutual inductance identification method based on Kalman filter

Abstract

The application discloses a method for mutual inductance identification of underwater wireless charging based on a Kalman filter. The method comprises the following steps: preliminarily identifying the primary mutual inductance according to the charging state of the underwater wireless charging system; establishing the state equation and the observation equation of the underwater wireless charging system by using the primary mutual inductance, and discretizing the state equation and the observation equation to obtain the recursive form of the state equation and the observation equation; performing recursive filtering by using the Kalman filter to obtain the filtered primary coil current and the secondary coil current, and performing secondary identification of the mutual inductance according to the filtered primary coil current and the secondary coil current and the input voltage of the primary compensation network and the secondary compensation network to obtain the secondary mutual inductance; performing deviation comparison to obtain the final mutual inductance, and realizing the mutual inductance identification of the underwater wireless charging. The method can effectively suppress the measurement noise and the input noise in the identification process, can accurately identify the mutual inductance of the underwater wireless charging system without increasing an auxiliary circuit and without knowing the load, and can reduce the error of the mutual inductance identification.

Description

TECHNICAL FIELD

[0001] The present application relates to a mutual inductance identification method, in particular to a mutual inductance identification method for an underwater wireless charging system based on a Kalman filter. BACKGROUND

[0002] With the progress and development of science and technology, ocean resources have been developed and explored. As an important equipment for underwater resource exploration and military patrol, autonomous underwater vehicle (AUV) has become a research hotspot in the field of ocean engineering, and has wide economic, scientific and military value. The power supply of AUV usually adopts the mode of replacing lithium ion battery or wired charging with wet plug-in connector, however, the former needs manual operation, has low degree of automation, insufficient concealment and other shortcomings, and even long time work will affect the sealing performance of AUV; the latter needs to use high-precision underwater wet plug-in connector as the docking power supply, which has high equipment cost, poor safety, short service life, complex maintenance and high maintenance cost. In order to solve the problem of energy supply of AUV, underwater wireless charging (UWPT) is becoming a new type of underwater energy transmission method. However, in actual application, there are irregular sea current disturbances in seawater environment, and AUV and charging equipment are difficult to realize accurate docking, which will cause misalignment between primary coil and secondary coil and directly affect the mutual inductance between coils, and further affect the output performance of the system. Therefore, the mutual inductance parameters between coils need to be identified in order to monitor and control the state of the system.

[0003] The existing mutual inductance identification method of underwater wireless charging system usually needs to know the load or introduce additional circuit, but in actual situation, the load is often unknown and variable, and the introduction of additional circuit will make the implementation process more complex. In addition, some methods are only suitable for a certain specific topology structure and cannot be extended to other topology structures. And compared with the wireless charging system on the shore, the signal collection of underwater wireless charging system is more easily disturbed. SUMMARY

[0004] In order to solve the problems in the background art, the present application provides a mutual inductance identification method for underwater wireless charging based on Kalman filter. First, according to the type of system compensation network and the characteristics of Kalman filter, a suitable state space model is established for the compensation network; then the established state space model is converted into a state observation equation suitable for Kalman filter; finally, the mutual inductance of the system is identified according to the working state of the system by using the filtered state variable.

[0005] The technical scheme adopted by the present application is:

[0006] The mutual inductance identification method for underwater wireless charging based on Kalman filter of the present application comprises the following steps:

[0007] Step 1: Based on the charging status of the underwater wireless charging system, the primary inductance of the underwater wireless charging system is initially identified; the underwater wireless charging system includes an inverter circuit, a compensation network, a rectifier circuit, and a filter circuit. The compensation network includes a primary-side compensation network, a secondary-side compensation network, a secondary-side coil, and a primary-side coil.

[0008] Step 2: Based on the preliminary identification of the first mutual inductance, establish the state equation and observation equation of the underwater wireless charging system, and discretize the state equation and observation equation to obtain the recursive state equation and observation equation.

[0009] Step 3: Based on the recursive state equation and observation equation, use a Kalman filter to perform recursive filtering to obtain the primary and secondary coil currents of the underwater wireless charging system after filtering. Based on the filtered primary and secondary coil currents of the underwater wireless charging system, as well as the input voltages of the primary and secondary compensation networks, perform secondary identification of the mutual inductance of the underwater wireless charging system to obtain the secondary mutual inductance of the underwater wireless charging system.

[0010] Step 4: Compare the deviations between the primary and secondary mutual inductances of the underwater wireless charging system to obtain the final mutual inductance of the underwater wireless charging system, thus realizing mutual inductance identification for underwater wireless charging.

[0011] In step one, the primary mutual inductance of the underwater wireless charging system is initially identified based on its charging state. To find the relationship between the system's mutual inductance and measurable parameters, a sinusoidal steady-state analysis of the system is required. Based on Kirchhoff's voltage law and the characteristics of the SS-type compensation network, the specific steps are as follows:

[0012] a) The underwater wireless charging system is in a non-charging state:

[0013] When the underwater wireless charging system is not charging, the system's output power is low, and the system does not charge the underwater vehicle's battery pack.

[0014]

[0015] Where M represents the initial mutual inductance of the underwater wireless charging system; U s The input voltage u of the secondary-side compensation network p The effective value of f; f is the operating frequency of the underwater wireless charging system; I p Let i be the current flowing through the primary coil. p Valid value.

[0016] b) The underwater wireless charging system is charging:

[0017] When the underwater wireless charging system is in charging mode, the system's output power is high enough to charge the underwater vehicle's battery pack.

[0018]

[0019] Among them, U p The input voltage u of the primary-side compensation network s The effective value of R; p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; I s Let i be the current flowing through the secondary coil. s Valid value.

[0020] In step two, the state equation and observation equation of the underwater wireless charging system are established based on the preliminary identification of the mutual inductance, as follows:

[0021]

[0022]

[0023] u = [u p ,u s ] T

[0024] y = [i p i s ] T

[0025] Where, x(t) and Let A be the state variables and their derivatives of the underwater wireless charging system at time t; B be the system matrix; u(t) be the input control variable of the underwater wireless charging system at time t; w(t) be the input noise at time t; C be the observation matrix; v(t) be the observation noise at time t; and y(t) be the system observations of the underwater wireless charging system at time t. p and i s These are the currents of the primary and secondary circuits of the underwater wireless charging system, respectively. and These are the primary-side compensation capacitor and its voltage across it, and the secondary-side compensation capacitor and its voltage across it, respectively, for the underwater wireless charging system; u p and u s These are the input voltages of the primary-side compensation network and the secondary-side compensation network of the underwater wireless charging system, respectively.

[0026] The input voltage u of the primary-side compensation network of the underwater wireless charging system p The input voltage u of the secondary-side compensation network s The current i in the primary loop p and the current i in the secondary circuit s Specifically as follows:

[0027]

[0028] Among them, L p and L s These are the self-inductances of the primary and secondary coils, respectively; M is the initial mutual inductance of the underwater wireless charging system; R p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; C p and C s These are the resonant capacitances of the primary-side compensation network and the secondary-side compensation network, respectively.

[0029] The system matrix A, control matrix B, and observation matrix C are as follows:

[0030]

[0031]

[0032]

[0033] Among them, L s and L p These are the self-inductances of the secondary coil and the primary coil, respectively; R p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; M is the initial mutual inductance of the underwater wireless charging system; C p and C s These are the resonant capacitances of the primary-side compensation network and the secondary-side compensation network, respectively.

[0034] In step two, the recursive state equation and observation equation can be derived as follows:

[0035]

[0036] Where X(k+1) and X(k) are the states of the underwater wireless charging system at time k+1 and time k, respectively; Φ is the discretized system matrix; G is the discretized control matrix; U(k) is the input control quantity of the underwater wireless charging system at time k; Γ is the noise driving matrix; W(k) and V(k) are the input noise and observation noise of the underwater wireless charging system at time k, respectively, where W(k) and V(k) are uncorrelated white noise with zero mean and variance matrices of Q and R, respectively. Y(k) is the observation signal of the underwater wireless charging system at time k; H is the discretized observation matrix.

[0037] The discretized system matrix Φ, the discretized control matrix G, and the discretized observation matrix H are as follows:

[0038]

[0039]

[0040] H = C

[0041] Where A is the system matrix; T s B is the sampling period of the underwater wireless charging system; C is the control matrix; and D is the observation matrix.

[0042] Perform Kalman filtering on the system. The Kalman filter recursive process is as follows to obtain the linear minimum variance estimate of state X(j) based on the observed signals {Y(1),Y(2),...,Y(k)}:

[0043] State prediction:

[0044]

[0045] Status Update:

[0046]

[0047] Filter gain matrix:

[0048] K(k+1)=P(k+1|k)H T [HP(k+1|k)H T +R] -1

[0049] Covariance matrix prediction:

[0050] P(k+1|k)=ΦP(k|k)Φ T +ΓQΓ T

[0051] Covariance matrix update:

[0052] P(k+1|k+1)=[IK(k+1)H]P(k+1|k)

[0053] The selection of initial values ​​for state variables requires extra attention. Since all state variables are zero before the system is powered on, the state variables at t=0 are generally selected as zero. In addition, the selection of parameters P(00), Q, and R is generally done by trial and error. During the experiment, the values ​​of the three parameters are continuously changed until the estimated value converges to the best value, which is the optimal value.

[0054] In step four, the final mutual inductance of the underwater wireless charging system is obtained by comparing the deviations between the primary mutual inductance M and the secondary mutual inductance M′, as detailed below:

[0055] When the deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is less than or equal to the preset error empirical value ε, the secondary mutual inductance M′ is used as the final mutual inductance of the underwater wireless charging system; when the deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is greater than the preset error empirical value ε, the primary mutual inductance M is used as the final mutual inductance of the underwater wireless charging system, and in this case, the state observation equation needs to be updated using M.

[0056] The preset error empirical value ε is set based on the results of simulation and physical tests. The primary mutual inductance M of the underwater wireless charging system is determined according to the charging state of the underwater wireless charging system. The secondary mutual inductance M′ of the underwater wireless charging system is based on the filtered primary coil current i′ of the underwater wireless charging system. p and secondary coil current i s ′ and the input voltage u of the primary-side compensation network p and the input voltage u of the secondary compensation network s The mutual inductance of the underwater wireless charging system is obtained through secondary identification. Further identification of the system's mutual inductance using a Kalman filter can improve the accuracy of mutual inductance parameter identification.

[0057] The specific deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is as follows:

[0058]

[0059] The beneficial effects of this invention are:

[0060] The method of the present invention can effectively suppress measurement noise and input noise during the identification process, and can accurately identify the mutual inductance of the underwater wireless charging system without adding auxiliary circuits or knowing the load, thereby reducing the error of mutual inductance identification. Attached Figure Description

[0061] Figure 1 Diagram showing the components of an underwater wireless charging system;

[0062] Figure 2 This is a schematic diagram of an underwater wireless charging system using an SS-type compensation network.

[0063] Figure 3 A schematic diagram of a non-charging state where the system is not charging the battery pack;

[0064] Figure 4 A schematic diagram illustrating the charging status of the system charging the battery pack;

[0065] Figure 5 This is the equivalent circuit diagram of an SS-type compensation network. Detailed Implementation

[0066] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] The underwater wireless charging mutual inductance identification method based on Kalman filter of the present invention includes the following steps:

[0068] Step 1: Based on the charging status of the underwater wireless charging system, the primary inductance of the underwater wireless charging system is initially identified; the underwater wireless charging system includes an inverter circuit, a compensation network, a rectifier circuit, and a filter circuit. The compensation network includes a primary-side compensation network, a secondary-side compensation network, a secondary-side coil, and a primary-side coil.

[0069] In step one, the primary mutual inductance of the underwater wireless charging system is initially identified based on its charging state. To find the relationship between the system's mutual inductance and measurable parameters, a sinusoidal steady-state analysis of the system is required. Based on Kirchhoff's voltage law and the characteristics of the SS-type compensation network, the specific steps are as follows:

[0070] a) The underwater wireless charging system is in a non-charging state:

[0071] When the underwater wireless charging system is not charging, the system's output power is low, and the system does not charge the underwater vehicle's battery pack.

[0072]

[0073] Where M represents the initial mutual inductance of the underwater wireless charging system; U s The input voltage u of the secondary-side compensation network p The effective value of f; f is the operating frequency of the underwater wireless charging system; I p Let i be the current flowing through the primary coil. p Valid value.

[0074] b) The underwater wireless charging system is charging:

[0075] When the underwater wireless charging system is in charging mode, the system's output power is high enough to charge the underwater vehicle's battery pack.

[0076]

[0077] Among them, U p The input voltage u of the primary-side compensation network s The effective value of R; p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; I s Let i be the current flowing through the secondary coil. s Valid value.

[0078] Step 2: Based on the preliminary identification of the first mutual inductance, establish the state equation and observation equation of the underwater wireless charging system, and discretize the state equation and observation equation to obtain the recursive state equation and observation equation.

[0079] In step two, the state equations and observation equations of the underwater wireless charging system are established based on the preliminary identification of the mutual inductance, as follows:

[0080]

[0081]

[0082] u = [u p ,u s ] T

[0083] y = [i p i s ] T

[0084] Where, x(t) and Let A be the state variables and their derivatives of the underwater wireless charging system at time t; B be the system matrix; u(t) be the input control variable of the underwater wireless charging system at time t; w(t) be the input noise at time t; C be the observation matrix; v(t) be the observation noise at time t; and y(t) be the system observations of the underwater wireless charging system at time t. p and i s These are the currents of the primary and secondary circuits of the underwater wireless charging system, respectively. and These are the primary-side compensation capacitor and its voltage across it, and the secondary-side compensation capacitor and its voltage across it, respectively, for the underwater wireless charging system; u p and u s These are the input voltages of the primary-side compensation network and the secondary-side compensation network of the underwater wireless charging system, respectively.

[0085] The input voltage u of the primary-side compensation network of the underwater wireless charging system p The input voltage u of the secondary-side compensation network s The current i in the primary loop p and the current i in the secondary circuit s Specifically as follows:

[0086]

[0087] Among them, L p and L s These are the self-inductances of the primary and secondary coils, respectively; M is the initial mutual inductance of the underwater wireless charging system; R p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; C p and C s These are the resonant capacitances of the primary-side compensation network and the secondary-side compensation network, respectively.

[0088] The system matrix A, control matrix B, and observation matrix C are as follows:

[0089]

[0090]

[0091]

[0092] Among them, L s and L p These are the self-inductances of the secondary coil and the primary coil, respectively; R p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; M is the initial mutual inductance of the underwater wireless charging system; C p and C s These are the resonant capacitances of the primary-side compensation network and the secondary-side compensation network, respectively.

[0093] In step two, the recursive state equation and observation equation can be derived as follows:

[0094]

[0095] Where X(k+1) and X(k) are the states of the underwater wireless charging system at time k+1 and time k, respectively; Φ is the discretized system matrix; G is the discretized control matrix; U(k) is the input control quantity of the underwater wireless charging system at time k; Γ is the noise driving matrix; W(k) and V(k) are the input noise and observation noise of the underwater wireless charging system at time k, respectively, where W(k) and V(k) are uncorrelated white noise with zero mean and variance matrices of Q and R, respectively. Y(k) is the observation signal of the underwater wireless charging system at time k; H is the discretized observation matrix.

[0096] The discretized system matrix Φ, the discretized control matrix G, and the discretized observation matrix H are as follows:

[0097]

[0098]

[0099] H = C

[0100] Where A is the system matrix; T s B is the sampling period of the underwater wireless charging system; C is the control matrix; and D is the observation matrix.

[0101] Perform Kalman filtering on the system. The Kalman filter recursive process is as follows to obtain the linear minimum variance estimate of state X(j) based on the observed signals {Y(1),Y(2),...,Y(k)}:

[0102] State prediction:

[0103]

[0104] Status Update:

[0105]

[0106] Filter gain matrix:

[0107] K(k+1)=P(k+1|k)H T [HP(k+1|k)H T +R] -1

[0108] Covariance matrix prediction:

[0109] P(k+1|k)=ΦP(k|k)Φ T +ΓQΓ T

[0110] Covariance matrix update:

[0111] P(k+1|k+1)=[IK(k+1)H]P(k+1|k)

[0112] The selection of initial values ​​for state variables requires extra attention. Since all state variables are zero before the system is powered on, the state variables at t=0 are generally chosen to be zero. In addition, the selection of parameters P(0|0), Q, and R is generally done by trial and error. During the experiment, the values ​​of the three parameters are continuously changed until the estimated value converges to the best value, which is the optimal value.

[0113] Step 3: Based on the recursive state equation and observation equation, use a Kalman filter to perform recursive filtering to obtain the primary and secondary coil currents of the underwater wireless charging system after filtering. Based on the filtered primary and secondary coil currents of the underwater wireless charging system, as well as the input voltages of the primary and secondary compensation networks, perform secondary identification of the mutual inductance of the underwater wireless charging system to obtain the secondary mutual inductance of the underwater wireless charging system.

[0114] Step 4: Compare the deviations between the primary and secondary mutual inductances of the underwater wireless charging system to obtain the final mutual inductance of the underwater wireless charging system, thus realizing mutual inductance identification for underwater wireless charging.

[0115] In step four, the final mutual inductance of the underwater wireless charging system is obtained by comparing the deviations between the primary mutual inductance M and the secondary mutual inductance M′, as detailed below:

[0116] When the deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is less than or equal to the preset error empirical value ε, the secondary mutual inductance M′ is used as the final mutual inductance of the underwater wireless charging system; when the deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is greater than the preset error empirical value ε, the primary mutual inductance M is used as the final mutual inductance of the underwater wireless charging system, and in this case, the state observation equation needs to be updated using M.

[0117] The preset error empirical value ε is set based on the results of simulation and physical tests. The primary mutual inductance M of the underwater wireless charging system is determined according to the charging state of the underwater wireless charging system. The secondary mutual inductance M′ of the underwater wireless charging system is based on the filtered primary coil current i′ of the underwater wireless charging system. p and secondary coil current i s ′ and the input voltage u of the primary-side compensation network p and the input voltage u of the secondary compensation network s The mutual inductance of the underwater wireless charging system is obtained through secondary identification. Further identification of the system's mutual inductance using a Kalman filter can improve the accuracy of mutual inductance parameter identification.

[0118] The deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is as follows:

[0119]

[0120] like Figure 1 The diagram shows the components of an underwater wireless charging system. The system includes an inverter circuit, a primary-side compensation network, a secondary-side compensation network, a rectifier circuit, a filter circuit, and a magnetic coupler coil. The coil, primary-side compensation network, and secondary-side compensation network are collectively referred to as the compensation network or resonant network. dc The input voltage of the inverter circuit is usually constant, while u bat This represents the voltage across the battery pack. During operation, the underwater wireless charging system may be in two different states.

[0121] like Figure 2 As shown, this is an underwater wireless charging system using an SS-type compensation network. To illustrate the method of this invention, [the following is a description of the system]. Figure 2 The specific circuit shown is not limited to the method of the present invention. Figure 2 The circuit shown. Figure 2 Winning the bid and Figure 1The specific modules are: inverter circuit 101, primary-side compensation network 102, coil 103, secondary-side compensation network 104, rectifier circuit 105, filter circuit 106, and compensation network 107. Q1, Q2, Q3, and Q4 are the four power switches of inverter circuit 101, and D1, D2, D3, and D4 are the four diodes of rectifier circuit 105. o C is the filter inductor of filter circuit 106. o This is the filter capacitor for filter circuit 106. dc u is the input voltage of the inverter circuit. bat R represents the voltage across the AUV battery pack. L To compensate for the equivalent load of the network, R p C is the parasitic resistance of the primary coil 103. p L is the compensation capacitor for the primary-side compensation network 102. p The self-inductance of the primary coil 103; and R s C is the parasitic resistance of the secondary coil 103. s L is the compensation capacitor for the secondary side compensation network 102. s This is the self-inductance of the secondary coil 103. p i is the output voltage of inverter circuit 101. p U is the current in the primary loop. s The input voltage for rectifier circuit 105, i s This represents the current in the primary loop.

[0122] like Figure 3 The diagram shows a system unable to charge the battery pack. The dashed lines indicate that no current flows through the wires. In this case, the system's output power is too low to provide constant current or constant voltage charging for the AUV battery pack. Based on the relationships between the variables in the circuit, the mutual inductance M and i can be deduced. p u s The relationship, and thus based on i p u s A preliminary identification of the mutual inductance M is performed.

[0123] like Figure 4 The diagram shows the system charging the battery pack. At this point, the system output power is high enough to provide constant current or constant voltage charging for the AUV battery pack. Based on the relationships between the variables in the circuit, the mutual inductances M and u are derived. p i p u s i s R p R s The relationship, and thus based on u p i p u s is A preliminary identification of the mutual inductance M is performed.

[0124] like Figure 5 The diagram shown is the equivalent circuit diagram of an SS-type compensation network. To utilize a Kalman filter, it is necessary to... Figure 2 The system shown is simplified to Figure 3 The analysis circuit is shown. In Figure 3 in, u p To compensate for the input voltage on the primary side of the network, u s To compensate for the input voltage on the secondary side of the network. C p L is the value of the primary-side compensation capacitor. p C is the self-inductance value of the primary coil. s L is the value of the primary-side compensation capacitor. s R is the self-inductance value of the primary coil. p R is the parasitic resistance value of the primary coil. s This represents the parasitic resistance value of the secondary coil. This is the voltage across the primary-side compensation capacitor. i is the voltage across the primary-side compensation capacitor. p i is the current flowing through the primary coil. s This is the current flowing through the secondary coil.

[0125] Using the initially obtained mutual inductance M as a known parameter, the system is modeled. Based on Kirchhoff's voltage and current laws, a system of differential equations is established, thus deriving the system's state-space model. The state and observation equations are then discretized and transformed into a form suitable for Kalman filtering. Recursive filtering is then applied to the system, utilizing the filtered primary and secondary coil currents i′. p 、i′ s and u p u s The mutual inductance of the system is identified and determined as M′. Based on actual requirements, a tolerable error of ε is set, and the result of the mutual inductance identification is finally obtained based on the deviation between M and M′.

Claims

1. A method for identifying mutual inductance in underwater wireless charging based on a Kalman filter, characterized in that: The method includes the following steps: Step 1: Based on the charging status of the underwater wireless charging system, the primary inductance of the underwater wireless charging system is initially identified; the underwater wireless charging system includes an inverter circuit, a compensation network, a rectifier circuit, and a filter circuit. The compensation network includes a primary-side compensation network, a secondary-side compensation network, a secondary-side coil, and a primary-side coil. Step 2: Based on the preliminary identification of the first mutual inductance, establish the state equation and observation equation of the underwater wireless charging system, and discretize the state equation and observation equation to obtain the recursive state equation and observation equation. Step 3: Based on the recursive state equation and the observation equation, use a Kalman filter to perform recursive filtering to obtain the primary coil current and secondary coil current of the underwater wireless charging system after filtering. Based on the filtered primary coil current and secondary coil current of the underwater wireless charging system, as well as the input voltage of the primary compensation network and the input voltage of the secondary compensation network, perform secondary identification of the mutual inductance of the underwater wireless charging system to obtain the secondary mutual inductance of the underwater wireless charging system. Step 4: Compare the deviations between the primary and secondary mutual inductances of the underwater wireless charging system to obtain the final mutual inductance of the underwater wireless charging system, thus realizing mutual inductance identification for underwater wireless charging.

2. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 1, characterized in that: In step one, the primary mutual inductance of the underwater wireless charging system is initially identified based on its charging status, as detailed below: a) The underwater wireless charging system is in a non-charging state: Where M represents the initial mutual inductance of the underwater wireless charging system; U s The input voltage u of the secondary-side compensation network p The effective value of f; f is the operating frequency of the underwater wireless charging system; I p Let i be the current flowing through the primary coil. p The effective value; b) The underwater wireless charging system is charging: Among them, U p The input voltage u of the primary-side compensation network s The effective value of R; p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; I s Let i be the current flowing through the secondary coil. s Valid value.

3. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 1, characterized in that: In step two, the state equation and observation equation of the underwater wireless charging system are established based on the preliminary identification of the mutual inductance, as follows: in=[in p ,in s ] T y=[i p ,i s ] T Where x(t) and x(t) are the state variables and their derivatives of the underwater wireless charging system at time t, respectively; A is the system matrix; B is the control matrix; u(t) is the input control variable of the underwater wireless charging system at time t; w(t) is the input noise at time t; C is the observation matrix; v(t) is the observation noise at time t; y(t) is the system observation of the underwater wireless charging system at time t; i p and i s These are the currents of the primary and secondary circuits of the underwater wireless charging system, respectively. and These are the primary-side compensation capacitor and its voltage across it, and the secondary-side compensation capacitor and its voltage across it, respectively, for the underwater wireless charging system; u p and u s These are the input voltages of the primary-side compensation network and the secondary-side compensation network of the underwater wireless charging system, respectively.

4. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 3, characterized in that: The input voltage u of the primary-side compensation network of the underwater wireless charging system p The input voltage u of the secondary-side compensation network s The current i in the primary loop p and the current i in the secondary circuit s Specifically as follows: Among them, L p and L s These are the self-inductances of the primary and secondary coils, respectively; M is the initial mutual inductance of the underwater wireless charging system; R p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; C p and C s These are the resonant capacitances of the primary-side compensation network and the secondary-side compensation network, respectively.

5. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 3, characterized in that: The system matrix A, control matrix B, and observation matrix C are as follows: Among them, L s and L p These are the self-inductances of the secondary coil and the primary coil, respectively; R p and R s These are the parasitic resistance values ​​of the primary and secondary coils, respectively; M is the initial mutual inductance of the underwater wireless charging system; C p and C s These are the resonant capacitances of the primary-side compensation network and the secondary-side compensation network, respectively.

6. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 1, characterized in that: In step two, the recursive state equation and observation equation can be derived as follows: Where X(k+1) and X(k) are the states of the underwater wireless charging system at time k+1 and time k, respectively; Φ is the discretized system matrix; G is the discretized control matrix; U(k) is the input control quantity of the underwater wireless charging system at time k; Γ is the noise driving matrix; W(k) and V(k) are the input noise and observation noise of the underwater wireless charging system at time k; Y(k) is the observation signal of the underwater wireless charging system at time k; and H is the discretized observation matrix.

7. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 6, characterized in that: The discretized system matrix Φ, the discretized control matrix G, and the discretized observation matrix H are as follows: H = C Where A is the system matrix; T s B is the sampling period of the underwater wireless charging system; C is the control matrix; and D is the observation matrix.

8. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 1, characterized in that: In step four, the final mutual inductance of the underwater wireless charging system is obtained by comparing the deviations between the primary mutual inductance M and the secondary mutual inductance M′, as detailed below: When the deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is less than or equal to the preset error empirical value ε, the secondary mutual inductance M′ is used as the final mutual inductance of the underwater wireless charging system; when the deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is greater than the preset error empirical value ε, the primary mutual inductance M is used as the final mutual inductance of the underwater wireless charging system.

9. The underwater wireless charging mutual inductance identification method based on a Kalman filter according to claim 8, characterized in that: The specific deviation ε′ between the primary mutual inductance M and the secondary mutual inductance M′ is as follows:

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