Method and system for controlling parameter-uncertain relay WPT system with time delay

Abstract

The invention relates to the technical field of wireless power transmission (WPT), and particularly discloses a control method and system for a relay WPT system with uncertain parameters and time delay, and the method comprises the steps: firstly, building a state space model of the relay WPT system with uncertain system parameters such as mutual inductance and output load and interval time-varying time delay; then, a passive dynamic output feedback controller is connected with an uncertain relay WPT system model with time-varying delay, and controller design is converted into a stability analysis problem; and then, stability analysis is carried out by using an LMI method, and parameters of the controller are determined. Finally, the effectiveness of the designed controller is verified through simulation. A simulation result shows that the relay WPT system considering the time-varying time delay and the parameter uncertainty is kept stable under the control of the controller and has good convergence performance.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless power transfer (WPT), and in particular to a control method and system for a WPT system with uncertain parameters and a time delay. Background Art

[0002] In recent years, wireless power transfer (WPT) technology has been widely used in the industrial field. It transmits power wirelessly by constructing a high-frequency magnetic field, thus avoiding the possibility of cable corrosion and making the transmission process flexible. It is widely used in electric vehicle charging, high-speed trains, medical implants, household appliances, mobile phones and other fields. However, there are still many problems that have not been well solved in WPT technology. For WPT systems, the transmission distance is very limited, ranging from a few millimeters to tens of centimeters.

[0003] In order to extend the transmission distance, some researchers have proposed a power relay WPT system (Power-relay WPT, PR-WPT), or simply referred to as a relay WPT system, which extends the transmission distance by introducing an additional transmission coil and its resonant capacitor between the transmitting unit and the receiving unit as a relay unit. Its topology is as follows: Figure 1 However, the introduction of the relay coil has brought new problems to the WPT system. First, due to the introduction of the relay coil, the coupling relationship between the coils has changed from one to two, that is, the coupling mutual inductance M1 between the transmitting coil and the relay coil and the coupling mutual inductance M2 between the relay coil and the receiving coil as shown in Figure 2 As shown in Figure 2, the load may vary within a certain range, which increases the parameter uncertainty of the WPT system. Secondly, the extended transmission distance will make the delay in the system state more obvious, and the delay varies within a range. This parameter uncertainty and delay will cause system instability and affect the transmission performance of the system. Summary of the invention

[0004] The present invention provides a control method and system for a relay WPT system with uncertain parameters and time delay, and solves the technical problem that parameter uncertainty and time delay of the relay WPT system lead to unstable system transmission.

[0005] In order to solve the above technical problems, the present invention provides a control method for a parameter uncertain relay WPT system with time delay, comprising the steps of:

[0006] S1. System modeling of the relay WPT system with uncertain parameters and time delay is performed to obtain a state space model;

[0007] S2. Based on the state space model, construct a full-order passive dynamic output feedback controller with a coefficient matrix to be determined;

[0008] S3, solving the full-order passive dynamic output feedback controller to obtain a coefficient matrix, and then obtaining a full-order passive dynamic output feedback controller determined by the coefficient matrix;

[0009] S4. A full-order passive dynamic output feedback controller determined by a coefficient matrix is ​​used to perform closed-loop control on the relay WPT system in operation.

[0010] Furthermore, the state vector x(t) of the state space model is related to at least one of the current of the transmitting coil, the relay coil, the receiving coil and the voltage of the resonant capacitor of the three; the state vector input control vector u(t)=s(t)E of the state space model dc , E dc represents the system input DC voltage, s(t) is a square wave function related to time t, inverter operating frequency T, operating cycle number n, and initial phase θ.

[0011] Furthermore, the square wave function s(t) is constructed as: s(t) is equal to a; when s(t) is equal to -a, a is a natural number not equal to 0, and N is a set of integers.

[0012] Furthermore, the relay WPT system includes a transmitting unit, a relay unit and a receiving unit; the transmitting unit includes a transmitting coil L p And the transmitting compensation capacitor C connected in series with it p The receiving unit includes a receiving coil L s And the receiving compensation capacitor C connected in parallel with it s The relay unit includes a first relay coil L1 and a relay compensation capacitor C connected in parallel therewith. r and the second relay coil L2, wherein the first relay coil L1 and the transmitting coil L p In contrast, the second relay coil L2 and the receiving coil L s relatively;

[0013] The uncertain parameters of the relay WPT system include the mutual inductance M1 between the transmitting coil and the first relay coil, the mutual inductance M2 between the receiving coil and the second relay coil, and the equivalent load resistance R o , modeled as:

[0014] M1=M 10 +ΔM1,M2=M 20 +ΔM2,R o =R o0 +ΔR o , M 10 、M 20 , R o0Respectively represent M1, M2,

[0015] R o Nominal values, △M1, △M2, △R o Respectively represent M1, M2, R o The disturbance amount is the change amount;

[0016] The delay of the relay WPT system is modeled as τ(t), and satisfies 0<τ d ≤τ(t)≤τ D , where τ d and τ D Both are known constants, representing the lower and upper bounds of the delay respectively.

[0017] Furthermore, the state space model is modeled as:

[0018]

[0019] in, That is, dx(t) represents the derivative of x(t), A0 represents the state coefficient matrix of the state vector related to the circuit parameters of the relay WPT system, and A u represents the control coefficient matrix of the input control vector related to the circuit parameters of the relay WPT system, x(t-τ(t)) represents the state vector with time-varying delay variable τ(t), △A0, △A u Represents matrices A0 and A respectively u The disturbance of A1 is represented by the coefficient matrix of the delay term, △A1 is represented by the disturbance of A1, τ is represented by the delay, C is represented by the output selection matrix, y(t) is represented by the output voltage of the relay WPT system, and κ(t) is represented by the initial state of x(t).

[0020] Furthermore, the step S2 specifically includes the steps of:

[0021] S21. Construct the basic model of full-order passive dynamic output feedback controller;

[0022] S22, integrating the basic model with the state space model of the relay WPT system to obtain a first controller;

[0023] S23, converting the first controller into an exponentially stable second controller.

[0024] Further, in step S21, the basic model of the full-order passive dynamic output feedback controller is expressed as:

[0025]

[0026] Among them, x c (t) represents the state matrix of the controller, Ac , B c 、E c represents the coefficient matrix of the controller to be determined, Represents x c The derivative of (t);

[0027] In step S22, let:

[0028]

[0029] The superscript T on the right indicates the matrix transpose;

[0030] The first controller is represented as:

[0031]

[0032] in, represents the augmented state vector with time-varying delay variable τ(t);

[0033] In the step S23, the second controller is represented as:

[0034]

[0035] represents the replaced integration variable, Represents the augmented state vector pair Derivatives of, custom parameters

[0036] Furthermore, the step S3 comprises the steps of:

[0037] S31. Based on the second controller, construct an inequality:

[0038]

[0039] Where * refers to the symmetric term, and each element in the matrix Ψ is defined as:

[0040]

[0041] sym() means to perform symmetric transformation on the matrix, with custom parameters H, J, R, Z represent different positive definite matrices, and the relaxation matrix

[0042] S32. Solve the constructed inequality to obtain the controller coefficient matrix: A c , B c 、E c .

[0043] The present invention also provides a control system for a parameter-uncertain relay WPT system with time delay, characterized in that it is provided with a modeling module, a controller building module, a controller solving module, and a controller application module, which are respectively used to execute steps S1 to S4 in the control method.

[0044] The control method and system of the parameter uncertain relay WPT system with time delay provided by the present invention firstly establish the state space model of the relay WPT system with uncertain system parameters such as mutual inductance and output load and interval time-varying delay; then, the passive dynamic output feedback controller is connected with the uncertain relay WPT system model with time-varying delay, and the controller design is transformed into a stability analysis problem; then, the LMI method is used to perform stability analysis and determine the parameters of the controller. Finally, the effectiveness of the designed controller is verified by simulation. The simulation results show that the relay WPT system considering time-varying delay and parameter uncertainty remains stable under the control of the controller and has good convergence performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a circuit topology diagram of a parameter uncertain relay WPT system with time delay provided by an embodiment of the present invention;

[0046] Figure 2 is a schematic diagram of multiple mutual inductance changes caused by relay coil offset provided by an embodiment of the present invention;

[0047] Figure 3 It is a state trajectory diagram of a PR-WPT system provided by an embodiment of the present invention in the presence of state delay and parameter uncertainty;

[0048] Figure 4 It is a phase trajectory diagram of a PR-WPT system without closed-loop control provided by an embodiment of the present invention;

[0049] Figure 5 It is a phase trajectory diagram of a PR-WPT system with closed-loop control provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The following specifically illustrates the implementation mode of the present invention in conjunction with the accompanying drawings. The embodiments are provided for illustrative purposes only and cannot be understood as limiting the present invention. The accompanying drawings are provided for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0051] In order to solve the problem of system instability caused by time delay and parameter uncertainty, an embodiment of the present invention proposes a control method for a parameter uncertain relay WPT system with time delay, which constructs a passive dynamic output feedback controller to achieve the purpose of suppressing the mutual inductance changes and interval time-varying delays in the WPT system and keeping the PR-WPT system stable.

[0052] Specifically, the control method of the parameter uncertain relay WPT system with time delay provided by the embodiment of the present invention specifically includes the steps of:

[0053] S1. System modeling of the relay WPT system with uncertain parameters and time delay is performed to obtain a state space model;

[0054] S2. Based on the state space model, construct a full-order passive dynamic output feedback controller with a coefficient matrix to be determined;

[0055] S3, solving the full-order passive dynamic output feedback controller to obtain a coefficient matrix, and then obtaining a full-order passive dynamic output feedback controller determined by the coefficient matrix;

[0056] S4. A full-order passive dynamic output feedback controller determined by a coefficient matrix is ​​used to perform closed-loop control on the relay WPT system in operation.

[0057] The following is a more detailed description of steps S1 to S3.

[0058] (1) Step S1: WPT system modeling

[0059] In this example, Figure 1 Taking the parameter uncertain relay WPT system with delay as an example, the specific process of modeling is explained. Figure 1 As shown, the inverter consists of four switching tubes S p1 -S p4 The rectifier consists of four diodes D1-D4, and the inverter converts the system's DC input voltage E dc Convert to s(t)E dc , s(t) is a square wave function, which can be written as:

[0060]

[0061] Where t represents the time, T is the inverter operating frequency, n is the number of operating cycles, N is an integer set, and θ is the initial phase. When s(t) changes from 1 to -1 or from -1 to 1, the input voltage direction is reversed. The value of s(t) 1 or -1 here is only an example, and s(t) can be a or -a (a is a natural number not equal to 0).

[0062] The transmitting unit includes a transmitting coil L p And the transmitting compensation capacitor C connected in series with itp , transmitting coil L p The internal resistance is R p The receiving unit includes a receiving coil L s And the receiving compensation capacitor C connected in parallel with it s , receiving coil L s The internal resistance is R s The relay unit includes a first relay coil L1 and a relay compensation capacitor C connected in parallel therewith. r and the second relay coil L2, wherein the first relay coil L1 and the transmitting coil L p In contrast, the second relay coil L2 and the receiving coil L s In contrast, the internal resistances of the first relay coil L1 and the second relay coil L2 are represented by R1 and R2, respectively. f Represents the filter capacitor, R L Indicates the load resistance. In addition, the equivalent input resistance before the rectifier bridge can be taken as R o =π 2 R L / 8.

[0063] based on Figure 1 The circuit structure of the relay WPT system can be expressed as:

[0064]

[0065] Among them, i p / i p (t), i1 / i1(t), i2 / i2(t), i s / i s (t) represents the current of the transmitting coil, the first relay coil, the second relay coil, and the receiving coil, respectively, u p / u p (t),u r / u r (t),u s / u s (t) represent the transmitting compensation capacitor voltage, the relay compensation capacitor voltage and the receiving compensation capacitor voltage, respectively, and are all variables that change with time t. represents the transmitting coil current i p The derivative with respect to time t, It represents the derivative of the current i1 on the relay coil inductance L1 with respect to time t, represents the derivative of the current i2 on the relay coil inductance L2 with respect to time t, Represents the receiving coil current i s The derivative with respect to time t, Indicates the transmitting compensation capacitor voltage u p The derivative with respect to time t, Represents the relay compensation capacitor voltage u r The derivative with respect to time t, Indicates the receiving compensation capacitor voltage u s The derivative with respect to time t.

[0066] According to the above differential equations, the state space model of the relay WPT system can be expressed as:

[0067] dx(t)=A0x(t)dt+A u u(t)dt (3)

[0068] Where x(t) represents the state vector related to the current of the transmitting coil, the relay coil, the receiving coil and the resonant capacitor voltage, which can be expressed as x(t)=[i p i1 i2 i s u p u r u s ] T (superscript T represents matrix transposition) (specifically, one or more of the seven states can be selected as feedback state variables, and the remaining unselected states are taken as 0), u(t) represents the input control vector of the relay WPT system and u(t) = s(t)E dc , A0 represents the state coefficient matrix of the state vector related to the circuit parameters of the relay WPT system, A u The control coefficient matrix of the input control vector related to the circuit parameters of the relay WPT system is represented by the differential equation shown in formula (2) which is arranged in the form of a state space matrix to obtain A0 and A u .

[0069] based on Figure 1 The relay WPT system shown, A0, A u The details are as follows:

[0070]

[0071] As discussed above, during operation, the mutual inductance and load may vary within a certain range, which can be described as the uncertain parameters of the relay WPT system, namely, M1, M2 and load R o :

[0072]

[0073] Among them, M 10 、M 20 , R o0 Respectively represent M1, M2, R o Nominal value of △M1, △M2, △R o Respectively represent M1, M2, R o The disturbance amount is the change amount.

[0074] Assuming that there is a delay, the model of the relay WPT system considering parameter uncertainty and delay is expressed as:

[0075] dx(t)= (A0+ΔA0)x(t)dt+(A1+ΔA1)x(t-τ(t))dt+(A u +ΔA u )u(t)dt (7)

[0076] Where τ(t) represents the time-varying state delay and satisfies 0<τ d ≤τ(t)≤τ D , where τ d and τ D are all known constants, representing the lower and upper bounds of the delay. x(t-τ(t)) represents the state vector with the time-varying delay variable τ(t), △A0, △A u Represents matrices A0 and A respectively u A1 represents the coefficient matrix of the delay term, and △A1 represents the disturbance of A1.

[0077] Combining the initial state κ(t) of x(t) and the system output y(t), the complete description of the relay WPT system is as follows:

[0078]

[0079] That is, dx(t), τ represents the delay, C represents the output selection matrix, C = [0 0 0 0 0 0 1].

[0080] In other embodiments, the transmitting coil, the relay coil, the receiving coil and the resonant capacitor (i.e., the resonant network) are designed differently from the present application, and the modeling process is the same for different resonant networks, except that the parameters related to the resonant network, such as A0, A u The specific content is different.

[0081] (2) Step S2: Design controller

[0082] Step S2 specifically includes the following steps:

[0083] S21. Construct the basic model of full-order passive dynamic output feedback controller;

[0084] S22, integrating the basic model with the state space model of the relay WPT system to obtain a first controller;

[0085] S23, converting the first controller into an exponentially stable second controller.

[0086] Taking the system model shown in equation (8) as an example, the controller design process is explained.

[0087] In step S21, based on the system model shown in equation (8), a full-order passive dynamic output feedback controller is designed, and its basic model is expressed as follows:

[0088]

[0089] Among them, x c (t) represents the state matrix of the controller, Represents x c The derivative of (t), A c , B c 、E c represents the coefficient matrix of the controller to be determined.

[0090] In step S22, let:

[0091]

[0092] Then the closed-loop controller can be written as:

[0093]

[0094] in, represents the augmented state vector with time-varying delay variable τ(t).

[0095] In step S23, it is known that Definition 1:

[0096] If you have:

[0097]

[0098] Then the controller (11) is called exponentially stable. e is the natural base, ‖‖ represents the vector norm, express The derivative of Indicates taking The maximum value on [-τ,0].

[0099] Obviously there are:

[0100]

[0101] Among them, the customized parameters Indicates the replaced integral variable (to avoid confusion with the previous x(t), the integral variable is changed to ), Represents the augmented state vector pair The derivative of .

[0102] Then the controller shown in equation (11) can be rewritten as:

[0103]

[0104] (3) Step S3: Solve the coefficient matrix A of the controller c , B c 、E c

[0105] Known Theorem 1:

[0106] For a given τ d , τ D and a preset positive real number α, the closed-loop system is exponentially stable if there exist positive definite matrices H, J, R, Z, and the matrix A c , B c 、E c , and the relaxation matrix This makes the inequality feasible:

[0107]

[0108] Among them, * represents the symmetric term, the matrix Ψ is a symmetric matrix, and the elements in the symmetric matrix are:

[0109]

[0110] Among them, sym() means to perform symmetric transformation on the matrix, and the customized parameters

[0111] Using the MATLAB LMI toolbox to solve Theorem 1, we get the controller coefficient matrix that satisfies the conditions: A c , B c 、E c , the design of the controller is completed.

[0112] Corresponding to the above control method, an embodiment of the present invention also provides a control system for a parameter uncertain relay WPT system with time delay, which is provided with a modeling module, a controller construction module, a controller solving module, and a controller application module, which are respectively used to execute steps S1 to S4 in the above control method.

[0113] The control method and system of the parameter uncertain relay WPT system with time delay provided by the embodiment of the present invention have the beneficial effects of:

[0114] 1) A passive dynamic output feedback controller is proposed to suppress the impact of changes in sensitive parameters of the PR-WPT system. The advantages of the passive dynamic output feedback controller are twofold. First, the controller does not need to know the complete state information to perform control, nor does it need to establish an observer in advance. Second, the controller contains adjustable parameters, by adjusting these parameters, better control performance may be obtained;

[0115] 2) Since the influence of interval time-varying delay increases with the increase of power transmission distance, this example considers the system stability analysis under the influence of interval time-varying delay. In addition, the controller design does not require the derivative of the time-varying delay. Instead, only the upper and lower bounds of the time-varying delay need to be known;

[0116] 3) The feedback state variables can be freely and flexibly combined under the proposed control framework. Single variable feedback or multivariable feedback can be used as needed, so the proposed controller can be widely used in engineering practice.

[0117] In order to verify the effectiveness of the designed controller, some simulations are carried out in this example. The system parameters are shown in Table 1.

[0118] Table 1 System parameters

[0119]

[0120] Considering that not all system states can be observed in engineering practice, this example adopts single state variable control, that is, the matrix is ​​selected as [0 0 0 0 0 0 1] T Therefore, the feedback information is from the only output voltage u s Extracted from.

[0121] Assume that the parameters {M1,M2,R L The uncertainty on the upper part is ±20%, and the delay interval is [0.0001s, 0.0002s]. The closed-loop PR-WPT system has multiple mutual inductance uncertainties and state delays. The state simulation curve of the system is as follows: Figure 3 As shown. Figure 3 As shown, the delay occurs in the state and the parameters {M1,M2,R L}In the event of disturbance, the state of the PR-WPT system is convergent under the action of the designed passive dynamic output feedback controller.

[0122] Figure 4 is the phase trajectory of the PR-WPT system without closed-loop control, Figure 5 is the phase trajectory of the PR-WPT system after the loop is closed. Figure 4 and Figure 5It can be seen that for the uncontrolled PR-WPT system, there is uncertainty in its phase trajectory. By adding a passive dynamic feedback controller, the uncertainty of the system phase trajectory is eliminated, thereby improving the robust performance of the PR-WPT system during the convergence process.

[0123] It can be seen from the experimental results that the control method and system proposed in the embodiments of the present invention effectively solve the multiple mutual inductance uncertainty problems and state delay problems caused by the introduction of relay coils in the WPT system, so that the PR-WPT system remains stable during system operation and further improves the robust performance of the system during the convergence process.

[0124] In summary, the control method and system of a relay WPT system with uncertain parameters and time delay provided by the embodiment of the present invention firstly establishes a state space model of the relay WPT system with uncertain system parameters such as mutual inductance and output load and interval time-varying delay; then, the passive dynamic output feedback controller is connected to the uncertain relay WPT system model with time-varying delay, and the controller design is transformed into a stability analysis problem; then, the LMI method is used to perform stability analysis and determine the parameters of the controller. Finally, the effectiveness of the designed controller is verified by simulation. The simulation results show that the relay WPT system considering time-varying delay and parameter uncertainty remains stable under the control of the controller and has good convergence performance.

[0125] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A control method for a WPT system with uncertain parameters and time delay, characterized in that: Includes steps: S1. System modeling of the relay WPT system with uncertain parameters and time delay is performed to obtain a state space model; S2. Based on the state space model, construct a full-order passive dynamic output feedback controller with a coefficient matrix to be determined; S3, solving the full-order passive dynamic output feedback controller to obtain a coefficient matrix, and then obtaining a full-order passive dynamic output feedback controller determined by the coefficient matrix; S4. A full-order passive dynamic output feedback controller determined by a coefficient matrix is ​​used to perform closed-loop control on the relay WPT system in operation.

2. The control method of the WPT system with uncertain parameters and delay according to claim 1, characterized in that: The state vector x(t) of the state space model is related to at least one of the current of the transmitting coil, the relay coil, the receiving coil and the voltage of the resonant capacitor of the three; the state vector input control vector u(t)=s(t)E of the state space model dc , E dc represents the system input DC voltage, s(t) is a square wave function related to time t, inverter operating frequency T, operating cycle number n, and initial phase θ.

3. The control method of the WPT system with uncertain parameters and delay according to claim 2, characterized in that: The square wave function s(t) is constructed as follows: s(t) is equal to a; when s(t) is equal to -a, a is a natural number not equal to 0, and N is a set of integers.

4. The control method of the WPT system with uncertain parameters and delay according to claim 3, characterized in that: The relay WPT system includes a transmitting unit, a relay unit and a receiving unit; the transmitting unit includes a transmitting coil L p And the transmitting compensation capacitor C connected in series with it p The receiving unit includes a receiving coil L s And the receiving compensation capacitor C connected in parallel with it s The relay unit includes a first relay coil L1 and a relay compensation capacitor C connected in parallel therewith. r and the second relay coil L2, wherein the first relay coil L1 and the transmitting coil L p In contrast, the second relay coil L2 and the receiving coil L s relatively; The uncertain parameters of the relay WPT system include the mutual inductance M1 between the transmitting coil and the first relay coil, the mutual inductance M2 between the receiving coil and the second relay coil, and the equivalent load resistance R o , modeled as: M1=M 10 +ΔM1,M2=M 20 +ΔM2,R o =R o0 +ΔR o , M 10 、M 20 , R o0 Respectively represent M1, M2, R o Nominal values, △M1, △M2, △R o Respectively represent M1, M2, R o The disturbance amount is the change amount; The delay of the relay WPT system is modeled as a variable τ(t), and satisfies 0<τ d ≤τ(t)≤τ D , where τ d and τ D Both are known constants, representing the lower and upper bounds of the delay respectively.

5. The control method of the WPT system with uncertain parameters and delay according to claim 4, characterized in that: The state space model is modeled as: in, That is, dx(t) represents the derivative of x(t), A0 represents the state coefficient matrix of the state vector related to the circuit parameters of the relay WPT system, and A u represents the control coefficient matrix of the input control vector related to the circuit parameters of the relay WPT system, x(t-τ(t)) represents the state vector with time-varying delay variable τ(t), △A0, △A u Represents matrices A0 and A respectively u The disturbance amount of A1 is represented by the coefficient matrix of the delay term, △A1 is represented by the disturbance amount of A1, τ is represented by the delay, C is represented by the output selection matrix, y(t) is represented by the output voltage of the relay WPT system, and κ(t) is represented by the initial state of x(t).

6. The control method of the WPT system with uncertain parameters and delay according to claim 5, characterized in that: The step S2 specifically includes the following steps: S21. Construct the basic model of full-order passive dynamic output feedback controller; S22, integrating the basic model with the state space model of the relay WPT system to obtain a first controller; S23, converting the first controller into an exponentially stable second controller.

7. The control method of the WPT system with uncertain parameters and delay according to claim 6, characterized in that: In step S21, the basic model of the full-order passive dynamic output feedback controller is expressed as: Among them, x c (t) represents the state matrix of the controller, A c , B c 、E c represents the coefficient matrix of the controller to be determined, Represents x c The derivative of (t); In step S22, let: The superscript T on the right indicates the matrix transpose; The first controller is represented as: in, represents the augmented state vector with time-varying delay variable τ(t); In the step S23, the second controller is represented as: represents the replaced integration variable, Represents the augmented state vector pair Derivatives of, custom parameters 8. The control method of the WPT system with uncertain parameters and time delay according to claim 7, characterized in that: The step S3 comprises the steps of: S31. Based on the second controller, construct an inequality: Where * refers to the symmetric term, and each element in the matrix Ψ is defined as: sym() means to perform symmetric transformation on the matrix, with custom parameters H, J, R, Z represent different positive definite matrices, and the relaxation matrix S32. Solve the constructed inequality to obtain the controller coefficient matrix: A c , B c 、E c .

9. A control system for a WPT system with a time-delayed parameter uncertainty relay, characterized in that: It is provided with a modeling module, a controller building module, a controller solving module, and a controller application module, which are respectively used to execute steps S1 to S4 in the control method according to any one of claims 1 to 8.

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