A radio power transmission system control method based on hammerstein-imc

Abstract

The present application relates to the wireless power transmission (WPT) technical field, specifically disclose a kind of wireless power transmission system control method based on Hammerstein-IMC, to solve the problems of parameter deviation and communication large time delay and the poor control quality of traditional WPT system control method, using Hammerstein model to describe system, and based on Hammerstein model and internal model control principle (IMC) design closed loop transfer function, further to the defect that closed loop transfer function cannot guarantee the robustness of system, by decomposing M (s), introduce filter to closed loop transfer function is improved, and according to robustness theorem setting closed loop stability condition, to realize the internal model control of WPT system, the output voltage y u Closely track voltage set value u ref , reduce the influence of parameter deviation and communication large time delay. Experimental results show that the IMC control method proposed in the present application can obtain faster tracking performance and higher robustness, and the tracking performance and robustness can be balanced by adjusting a single tuning parameter λ.

Description

Technical Field

[0001] This invention relates to the field of wireless power transfer (WPT) technology, and more particularly to a control method for a wireless power transfer system based on Hammerstein-IMC. Background Technology

[0002] Typically, system output voltage becomes unstable due to variations in system parameters caused by environmental factors. Considering the safety of electrical equipment, a closed-loop control strategy for the output voltage is required. Currently, traditional control methods use linear controllers, which depend on an accurate system model. Therefore, accurately obtaining the system's input and output models is essential. The WPT system is a special type of electroresonance transform system, characterized by high-order nonlinearity, various circuit topologies and corresponding control models, and the randomness of load size and type. Major modeling methods include Generalized State-Space Averaging (GSSA), expanded function description, Discrete Mapped Time, and AC Impedance Analysis. These traditional methods rely on the actual circuit topology, and most have strict requirements on the system's operating state. Even within the same system, the system model can differ significantly under different operating states. Traditional modeling methods often result in more complex models. Furthermore, models obtained through traditional methods suffer from poor versatility. In addition, the WPT system forms a closed loop through a communication link between the primary and secondary sides to control the output voltage, such as... Figure 1 As shown, wireless communication, data sampling, processor computation, and model simplification in the system contribute to time delays. Traditional modeling methods cannot accurately describe systems with time delays.

[0003] The methods described above primarily focus on circuit-level modeling of WPT systems, considering only the steady-state operation. Research on system-level dynamic modeling required for control system design is scarce. While circuit-level modeling methods are effective, they cannot truly reflect shifts in system parameters. The resulting models are of high order, lack versatility, and lack precise time delay parameters, making them inconvenient in practical industrial control processes. Furthermore, time delays can lead to system instability and closed-loop system failures. Therefore, to control systems in a timely and stable manner, it is necessary to employ methods with delay compensation.

[0004] Furthermore, feedback control WPT systems possess complex characteristics such as parameter uncertainty, nonlinearity, and time delay. Traditional PID control struggles to achieve satisfactory control results, and controller parameter tuning often relies on engineering experience, making the process cumbersome. During the time delay, to ensure the stability of the closed-loop system, it is necessary to reduce the integral effect and gain in the PID controller, which slows down the closed-loop response and reduces control quality. Summary of the Invention

[0005] This invention provides a control method for a wireless power transfer system based on Hammerstein-IMC, which solves the technical problem that traditional WPT system control methods suffer from parameter offset and large communication delay, as well as poor control quality.

[0006] To address the above technical problems, this invention provides a control method for a wireless power transfer system based on Hammerstein-IMC, the key of which includes the following steps:

[0007] S1. Construct the Hammerstein model of the WPT system;

[0008] S2. Based on the Hammerstein model and Internal Model Control (IMC) principle, design the closed-loop transfer function, which is constructed as follows:

[0009]

[0010] Where s represents the passed parameter, y u Let represent the output voltage of the WPT system, Q(s) represent the internal model controller, P(s) represent the Hammerstein model, M(s) represent the WPT system model obtained through the data-driven method, D(s) represent the disturbance transfer function, and u ref Indicates the set voltage, u d Indicates a disturbance;

[0011] S3. Decompose M(s) and introduce a filter. Design Q(s) based on the decomposed M(s);

[0012] S4. Set the closed-loop stability conditions according to the robustness theorem;

[0013] S5. Based on the closed-loop transfer function and the closed-loop stability condition, control the WPT system to make the output voltage y u Tracking voltage setpoint u ref .

[0014] Furthermore, step S3 specifically includes the following steps:

[0015] S31. Decompose M(s) as follows:

[0016] M(s)=M + (s)M - (s),

[0017] Among them, M + (s) represents the non-minimum phase portion containing the time delay and the zeros in the right half-plane, M - (s) represents the minimum phase portion;

[0018] S32. Introduce an nth-order low-pass filter. λ is the time constant of the filter, and Q(s) is designed as

[0019] Furthermore, in step S4, the closed-loop stability condition is designed as follows:

[0020]

[0021]

[0022]

[0023] e≤|1-M + (s)f(s))||rd|=|s||rd|,

[0024] Among them, l m It is the upper limit of the uncertainty between the model and the actual model, ω is the system control frequency, and e m (s) represents the mismatch between the estimated model and the actual model, and e represents the output voltage y. u and set voltage u ref The error between them, where r and d represent the system's reference input and disturbance input, respectively.

[0025] Furthermore, e is calculated by the following formula:

[0026]

[0027] Furthermore, M(s) is expressed as:

[0028]

[0029] Where K represents the open-loop process gain, ω0 represents the natural frequency of the WPT system, ξ represents the damping coefficient, and τ represents the time delay.

[0030] Furthermore, M(s) is decomposed into:

[0031]

[0032] Furthermore, M(s) and Q(s) form a feedback controller C(s), and the output U(s) of C(s) is decomposed as follows:

[0033] U(s) = U1(s) + U2(s),

[0034] Wherein, U2(s) is the U(s) component containing only the time delay, and U1(s) is the remaining component;

[0035] The analytical expressions for U1(s) and U2(s) are:

[0036]

[0037]

[0038] Where E(s) is the error function, and the output is e.

[0039] Furthermore, U1(s) and U2(s) are calculated using the fourth-order Runge-Kutta method.

[0040] Furthermore, λ is determined using the following steps:

[0041] A1. Design maximum sensitivity M s The nonlinear equation between λ and λ;

[0042] A2. Determine the maximum sensitivity M s ;

[0043] A3, Based on a determined M s Solve the nonlinear equation to obtain the initial value of λ;

[0044] A4. Adjust λ until the robustness exponent of the system response is satisfied.

[0045] Further, in step A1, M s The nonlinear equation between λ and λ is expressed as:

[0046]

[0047] Where ω is the control frequency.

[0048] This invention provides a control method for wireless power transfer systems based on Hammerstein-IMC. To address the problems of parameter offset, large communication delays, and poor control quality in traditional WPT system control methods, this invention uses a Hammerstein model to describe the system and designs a closed-loop transfer function based on the Hammerstein model and Internal Model Control (IMC). Furthermore, to address the deficiency that the closed-loop transfer function cannot guarantee system robustness, the method improves the closed-loop transfer function by decomposing M(s) and introducing a filter. Finally, based on the robustness theorem, a closed-loop stability condition is set, thereby achieving internal model control of the WPT system and ensuring the output voltage y... u Closely track the voltage setpoint u ref This reduces the impact of parameter offset and large communication latency.

[0049] The results show that the Hammerstein model is a global model that can more accurately describe the WPT system over a larger operating range. Combined with the proposed IMC control method, faster tracking performance and higher robustness can be achieved, and the tracking performance and robustness can be balanced by adjusting a single tuning parameter λ. Attached Figure Description

[0050] Figure 1 This is a circuit structure diagram of the WPT system provided in an embodiment of the present invention;

[0051] Figure 2 This is a flowchart of a wireless power transfer system control method based on Hammerstein-IMC provided in an embodiment of the present invention;

[0052] Figure 3 This is a schematic diagram of the switching of PS control and inverter output voltage at α provided in an embodiment of the present invention;

[0053] Figure 4 This is a block diagram of the WPT system based on the Hammerstein model provided in an embodiment of the present invention;

[0054] Figure 5 This is a block diagram illustrating the principle of a control method for a wireless power transfer system based on Hammerstein-IMC, provided in an embodiment of the present invention.

[0055] Figure 6 This is provided by the embodiments of the present invention. Figure 5 The equivalent circuit diagram;

[0056] Figure 7 These are experimental results of IMC with different λ values ​​provided in the embodiments of the present invention, where (a) and (d) correspond to λ = 6.6 × 10⁻⁶. -4 λ = 4 × 10 -3 The output voltage of the closed-loop system and the output current of the inverter are shown in (b) and (e), respectively, which correspond to the dynamic response of the reference change in (a) and (d), respectively. (c) and (f) correspond to the dynamic response of the load change in (a) and (d), respectively.

[0057] Figure 8 The diagram shows the experimental results of PID control provided in this embodiment of the invention, where (a) corresponds to the output voltage of the closed-loop system and the output current of the inverter, (b) shows the dynamic response to the reference change, and (c) shows the dynamic response to the load change. Detailed Implementation

[0058] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are 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.

[0059] The Hammerstein model consists of nonlinear static characteristics and a linear time-invariant autoregressive model (ARX model) with exogenous inputs. Data-driven modeling has been widely used in industry. The model's structure and parameters can be obtained simply by identifying sampled input and output data, independent of specific circuit topologies and parameters. The input and output sampled data required for model identification are readily available. Furthermore, the system model can be optimized using relevant performance indicators. This method outperforms traditional modeling methods in various aspects and has attracted increasing attention in the field of power electronics. Data-driven WPT system modeling can accurately estimate model parameters after system offset and communication delays. An internal model control (IMC) method was designed based on model algorithmic control (MAC), dynamic matrix control (DMC), and Smith predictors. The IMC method is simple to design and can improve the system's robustness and anti-interference capabilities, especially in systems with large time delays. Using the IMC method in WPT systems can better address the problems of system parameter offset and large communication delays. Based on these theoretical foundations, this invention provides a control method for a wireless power transfer system based on Hammerstein-IMC, which solves the problems of parameter offset, large communication delay, and poor control quality in traditional WPT system control methods.

[0060] like Figure 2 As shown, this embodiment of the invention provides a control method for a wireless power transfer system based on Hammerstein-IMC, including the following steps:

[0061] S1. Construct the Hammerstein model of the WPT system;

[0062] S2. Based on the Hammerstein model and internal model control principle, design the closed-loop transfer function. The closed-loop transfer function is constructed as follows:

[0063]

[0064] Where s represents the passed parameter, y u Let represent the output voltage of the WPT system, Q(s) represent the internal model controller, P(s) represent the Hammerstein model, M(s) represent the WPT system model obtained through a data-driven method, D(s) represent the disturbance transfer function, and u refIndicates the set voltage, u d Indicates a disturbance;

[0065] S3. Decompose M(s) and introduce a filter. Design Q(s) based on the decomposed M(s);

[0066] S4. Set the closed-loop stability conditions according to the robustness theorem;

[0067] S5. Controlling the WPT system based on the closed-loop transfer function and closed-loop stability condition to make the output voltage y u Tracking voltage setpoint u ref .

[0068] As an example, Figure 1 This illustrates a typical closed-loop WPT system, consisting of a primary side and a secondary side. The primary side comprises a DC power supply, an inverter, an LCC compensation network, and a transmitting coil L, connected in sequence. p The secondary side includes sequentially connected receiving coils L s Series compensation capacitor C s 1. Rectifier circuit, 2. Filter capacitor C d Load resistance R L The LCC compensation network includes a series compensation inductor L f Series compensation capacitor C p and parallel compensation capacitor C f U dc u represents the DC input voltage of the WPT system. ab i represents the first effective value of the inverter output voltage. f u cf L respectively f The current and voltage, i p u cp L respectively p The current and voltage, u cf Indicate C f The voltage, M represents L p and L s Mutual intuition between them, i s u cs L s The current and voltage, i r u r U represents the current and voltage of the rectifier circuit, respectively. o R represents L The voltage is the system output voltage, and R1, R2, and R3 represent L respectively. f L p and L s The equivalent series resistance.

[0069] In practical applications of WPT systems, the secondary side or load may be removed, leading to system safety and stability issues. The selected LCC-S topology features a constant current characteristic on the primary side. When the receiver or load is removed, the current in the primary coil remains approximately constant, reducing the complexity of system control and the current stress on the inverter circuit. The WPT system employs a primary-side LCC composite compensation method and a secondary-side LC series compensation method. The system's operating frequency is denoted by f0.

[0070] Typically, to meet the system output voltage stability requirements, the collected data is fed back to the primary side via wireless communication. On the primary side, the output voltage is adjusted by phase shift (PS). The principle of phase shift control and the inverter's output voltage are as follows: Figure 3 As shown. d represents the duty cycle of the inverter phase shift angle. α represents the angle of duration for which switches S1 and S4 (or S2 and S3) are simultaneously open. The duty cycle d is calculated using the error between the output voltage and the set voltage. Previous studies have shown that... Figure 1 The system shown is nonlinear.

[0071] In this embodiment, the control-oriented modeling of the WPT system is performed using the Hammerstein method, which enables the model to accurately describe both steady-state and transient behavior. The Hammerstein model consists of nonlinear and linear components, accurately characterizing the behavior of nonlinear systems and addressing the dynamic response characteristics at large operating points, a problem that small-signal models cannot solve. The Hammerstein model of the WPT system is as follows: Figure 4 As shown. Where f(d) is the nonlinear static characteristic of the WPT system, d is the duty cycle (control variable), and G... p (s) is a linear time-invariant model. Voltage output u o The relationship between d and d can be simplified as follows:

[0072] u o =f(d)G p (s) (1)

[0073] The static nonlinearity of the Hammerstein model is described by f(d) = sin(πd / 2). Furthermore, this nonlinear function can also be identified from the static input-output data (measured after all transients have disappeared). The dynamic linear model can be identified from the dynamic input and output data, which relates to the transient response generated by an appropriate excitation signal (e.g., a pseudo-random binary sequence (PRBS)).

[0074] The principle of the IMC control method based on the Hammerstein model is as follows: Figure 5 As shown. When the nonlinear component f(·) of the WPT system is fully compensated, Figure 5 Equivalent to Figure 6 (Standard internal model control structure). Where Q(s) represents the internal model controller. P(s) represents the Hammerstein model of the WPT system. M(s) represents the mathematical model of the actual system object obtained through a data-driven method. e represents the output voltage y. u and set voltage u ref The error between them. C(s) represents the feedback controller, U(s) represents the output of the feedback controller, and D(s) represents the disturbance transfer function. The control objective of this invention is to force the output voltage y u Tracking set value u ref , Figure 6 The corresponding closed-loop transfer function is expressed as:

[0075]

[0076] The steady-state error of the system can be expressed as:

[0077]

[0078] Note 1: If the controlled object P(s) is stable and P(s) = M(s), then Q(s) = M can be calculated. -1 (s). Disturbance u d ≠0 and step input u ref ≠0. According to equation (2), when y u =u ref When the system output remains equal to the set value, ideal control performance can be obtained.

[0079] Note 2: The closed-loop system is stable. Q(0)M(0)=1, where Q(0) represents the steady-state gain of the controller, and M(0) represents the estimated model gain. Disturbance u d ≠0 and step input u ref ≠0. According to equation (3), even if P(s) ≠ M(s), y u =u ref .

[0080] Unlike the ideal situation described above, practical applications also need to consider the following issues:

[0081] 1) Communication delays are unavoidable, and they will occur in M. -1 If a pure delay is introduced in (s), then M -1 (s) is physically difficult to achieve;

[0082] 2) If the actual system model contains RHP (right half-plane) zeros, then the controller Q(s) will have RHP poles, and the controller itself will be unstable, which will lead to instability of the closed-loop system.

[0083] 3) The model M(s) is strictly rational, but the ideal controller is irrational, that is, an nth-order differentiator will appear in the controller;

[0084] 4) If the closed-loop system is composed of an ideal controller, the output of the closed-loop system is sensitive to model error, i.e., P(s)≠M(s), and the robustness of the closed-loop system may not be guaranteed.

[0085] Therefore, the process model needs to be decomposed: the controller should be designed using only the part containing the stable zeros and stable poles.

[0086] Specifically, step S3 includes the following steps:

[0087] S31. Decompose M(s) as follows:

[0088] M(s)=M + (s)M - (s) (4)

[0089] Among them, M + (s) represents the non-minimum phase portion containing the time delay and the zeros in the right half-plane, M - (s) represents the minimum phase portion;

[0090] S32. Introduce an nth-order low-pass filter f(s), and define Q(s) based on f(s):

[0091]

[0092] f(s) is then expressed as:

[0093]

[0094] Where λ is the time constant of the filter, which can balance the tracking performance and robustness of the controller and requires special design.

[0095] Since the WPT system can be described using a second-order time delay, n can be set to 2. The feedback controller C(s) can be obtained as follows:

[0096]

[0097] The output of controller C(s) is:

[0098]

[0099] E(s) is the error function, and the output is e.

[0100] Note 3: M(s) and P(s) are usually mismatched. According to the robustness theorem, the closed-loop stability condition of IMC is:

[0101]

[0102]

[0103]

[0104] e≤|1-M + (s)f(s))||rd|=|s||rd| (12)

[0105] l m It is the upper limit of the uncertainty between the estimated model and the actual model, ω is the system control frequency, and e m (s) represents the mismatch between the estimated model and the actual model, and e represents the output voltage y. u and set voltage u ref The error between them, where r and d represent the system's reference input and disturbance input, respectively.

[0106] When the low frequency ω≤1 / λ, M can be obtained. + f(s)≈1 and e=0. When ω≥1 / λ, then |f(s)| is very small, and |M + (s)f(s)e m (s)|≈0. This means that equations (11) and (12) can be the same. For high-frequency and low-frequency dynamics, λ should be large enough to ensure that the closed-loop response is close enough to the nominal M. + The response of f(s).

[0107] Assume the model of the WPT system has been simplified to the following model:

[0108]

[0109] Where K represents the open-loop process gain, ω0 represents the natural frequency of the WPT system, ξ represents the damping coefficient, and τ represents the time delay. M(s) can be decomposed into:

[0110]

[0111] Due to the significant time delay in the closed-loop system, the controller output is decomposed as follows:

[0112]

[0113] Please note that only U2(s) includes a time delay. The analytical expressions for U1(s) and U2(s) are:

[0114]

[0115]

[0116] The decomposed U1(s) and U2(s) can be calculated separately. For digital simulation, they can be represented in state-space form:

[0117]

[0118] and

[0119]

[0120] In this context, (18) represents the state and output of the non-delayed part of the controller, (19) represents the state and output of the delayed part of the controller, A1, B1, and C1 represent the state, input, and output coefficient matrices of the non-delayed part of the controller, and A2, B2, and C2 represent the state, input, and output coefficient matrices of the delayed part of the controller.

[0121] The control output is the sum of the outputs of the above models:

[0122] y(t)=y1(t)+y2(t) (20)

[0123] The state equations in equations (18)-(20) should be discretized when implemented in a digital controller. For equation (20) with pure time delay, traditional methods typically use Pad'e to approximate the pure time delay, modeling and controlling the WPT system based on input nonlinearity and communication delay approximation or Taylor series expansion. However, if the time delay is large, the accuracy of the approximation cannot be guaranteed. Furthermore, for large time delays, the order of the cascade expansion will be very high, which is unpredictable in control system implementation. To avoid this problem, this example uses the fourth-order Runge-Kutta (RK4) method, which can solve the fractional time delay problem in digital simulation in a computationally efficient manner.

[0124] The general form of the state differential equation is:

[0125]

[0126] Where A and B represent the state and input coefficient matrices of the discrete system model, respectively.

[0127] If the initial state is x(t0) = x0, then x(t) k+1 It can be calculated using the RK4 algorithm as shown in equation (22), where k = 1, 2, ...

[0128]

[0129] Where K n Here, n = 1, ..., 4 represents the average slope, and h is the simulation interval. In the case of fractional delay, the value of h can be dynamically changed to ensure that the fractional delay is handled correctly.

[0130] Sensitivity quantitatively represents the sensitivity of the closed-loop transfer function to changes in process parameters. The smaller the sensitivity, the stronger the robustness of the control system to model mismatch. Maximum sensitivity is denoted by M. s λ represents the robustness performance index of a closed-loop system. λ can be obtained by solving for M. s The nonlinear equation between M and the open-loop transfer function containing the controller is obtained. s Defined as:

[0131]

[0132] By combining equations (6) and (8), we obtain C(s) as follows:

[0133]

[0134] If the time delay in the above equation is relatively small, then e -τs ≈1-τs, then M s It becomes:

[0135]

[0136] Note that λ is the only adjustable parameter in IMC, and it plays a role in balancing tracking speed and robustness. s As a performance metric, λ can help us find the optimal value to achieve the desired control performance, and its empirical value satisfies M. s ≤2. Typically, by M s The λ generated by optimization can only be used as an initial value, and from this point, λ is subsequently adjusted until the robustness exponent of the system response is satisfied.

[0137] Theoretically, the Hammerstein-IMC-based wireless power transfer system control method provided by this invention addresses the problems of parameter offset, large communication delay, and poor control quality in traditional WPT system control methods. It uses a Hammerstein model to describe the system and designs a closed-loop transfer function based on the Hammerstein model and internal model control principles. Furthermore, to address the deficiency that the closed-loop transfer function cannot guarantee system robustness, it improves the closed-loop transfer function by decomposing M(s) and introducing a filter. Finally, it sets closed-loop stability conditions according to the robustness theorem, thereby achieving internal model control of the WPT system and ensuring the output voltage y... u Closely track the voltage setpoint u ref This reduces the impact of parameter offset and large communication latency.

[0138] The following experiment will verify this.

[0139] This embodiment provides experimental results to verify the effectiveness of the proposed modeling and control method. On the primary side, an STM32H7 control board is used to implement IMC control, signal processing, and communication functions. On the secondary side, an STM32F042 is used to implement sampling and communication functions. The main parameters of the system are shown in Table 1. The experimental results of model parameter estimation and IMC control are shown below.

[0140] Table 1 Main parameters of the experiment

[0141]

[0142] Reasonable parameter estimates for the Hammerstein model were generated at the steady-state operating point of D = 0.8. The estimated model parameters are shown in Table 2, where the second-order model achieves a higher fitness ratio than the first-order model. This indicates that the second-order model is more accurate than the first-order model for the considered WPT system.

[0143] Table 2 Estimated parameters for steady-state operating point

[0144]

[0145] To verify the good performance of the proposed Hammerstein-IMC-based wireless power transfer system control method, transient response tests and load variation tests were conducted in this example. All tests exhibited the same trajectory: they consisted of two setpoint variations, i.e., u ref =161→181V and u ref =181→201V, and a single load change, i.e., R L =64→32Ω. The control period is 1ms. After the system output reaches a steady state, the setpoint and load change. The performance of the IMC control based on the Hammerstein model is as follows: Figure 7 As shown, two values ​​of λ were tried, namely λ = 6.6·10. -4 and λ = 4·10 -3 Note that, based on the above method, when the sensitivity M... s When λ = 2, λ is calculated to be 6.77·10. -4 After adjustment, λ is set to 6.6·10. -4 Similarly, when M s When λ = 1, λ = 4·10 -3 For comparison, results for PID control (considering time delay) are also given; see [link to relevant documentation]. Figure 8 In both experiments, CH3 on the oscilloscope recorded the waveform of the output voltage, while CH4 recorded the waveform of the inverter current.

[0146] Figure 7 (b) Figure 7 (e) and Figure 8 (b) are respectively Figure 7 (a) Figure 7 (d) and Figure 8 (a) shows the scaled portion of the transient output response. These waveforms demonstrate that the control system can track these points well at different steady-state operating points. λ = 6.6·10 -4 The IMC scheme achieves optimal performance, namely, it exhibits rapid dynamic response characteristics at different operating points, with a settling time of only 3ms, while when using λ = 4.10 -4 At this point, the value increases to 16 ms. This demonstrates the effectiveness of λ in balancing transient performance and robustness. In contrast, the settling time of the PID controller is approximately 15 ms, which is significantly slower than the IMC controller because the IMC controller is designed based on the identified model, which incorporates sufficient knowledge of the system dynamics, and the communication delay is properly compensated for. On the other hand, Figure 7 (a) Figure 7 (d) and Figure 8 The inverter current waveform in (a) shows that a fast transient response can cause inverter current overshoot. Therefore, λ should be carefully selected to avoid inverter damage.

[0147] Figure 7 (c) Figure 7 (f) and Figure 8 (c) shows the output response after the load switched from 64Ω to 32Ω. In all tests, the output voltage dropped by approximately 6V, while the recovery times for the three control tests were 6.5ms, 13ms, and 13ms, respectively. This indicates that the IMC control method can quickly recover to the steady state under external stability testing by optimizing λ, thus improving the system's robustness.

[0148] Experimental results show that the Hammerstein model is a global model that can more accurately describe the WPT system over a larger operating range. Combined with the proposed IMC control method, faster tracking performance and higher robustness can be achieved, and the tracking performance and robustness can be balanced by adjusting a single tuning parameter λ.

[0149] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A control method for a wireless power transfer system based on Hammerstein-IMC, characterized in that, Including the following steps: S1. Construct the Hammerstein model of the WPT system; S2. Based on the Hammerstein model and internal model control principle, design the closed-loop transfer function, which is constructed as follows: ， in, Indicates passing parameters. This represents the output voltage of the WPT system. Indicates the internal model controller. This represents the Hammerstein model. This represents the WPT system model obtained through a data-driven approach. This represents the disturbance transfer function. Indicates the set voltage. Indicates a disturbance; S3. Decomposition And introduce filters based on decomposition design Step S3 specifically includes the following steps: S31, will The breakdown is as follows: ， in, The non-minimum phase portion includes the time delay and the zeros in the right half-plane. This is the minimum phase portion; S32. Introduce an nth-order low-pass filter. λ is the time constant of the filter. Designed for ; S4. Set the closed-loop stability condition according to the robustness theorem; the closed-loop stability condition is designed as follows: ， ， ， ， in, It is the upper limit of the uncertainty between the estimated model and the actual model. It is the system control frequency. It estimates the degree of mismatch between the model and the actual model. Indicates output voltage and set voltage The error between them , These represent the system's reference input and disturbance input, respectively. S5. Based on the closed-loop transfer function and the closed-loop stability condition, control the WPT system to make the output voltage... Tracking voltage setpoint .

2. The control method for a wireless power transfer system based on Hammerstein-IMC according to claim 1, characterized in that, Calculated by the following formula: 。 3. The control method for a wireless power transfer system based on Hammerstein-IMC according to claim 2, characterized in that, Represented as: ， in, Indicates the open-loop process gain. This represents the natural frequency of the WPT system. Indicates the damping coefficient. Indicates a time delay.

4. The control method for a wireless power transfer system based on Hammerstein-IMC according to claim 3, characterized in that, Decomposed into: 。 5. The control method for a wireless power transfer system based on Hammerstein-IMC according to claim 4, characterized in that, and Composition of feedback controller , Output The breakdown is as follows: ， in, For those containing only time delay Quantity, The remaining component; and The parsing expression is: ， ， in It is represented as an error function.

6. The control method for a wireless power transfer system based on Hammerstein-IMC according to claim 5, characterized in that: The fourth-order Runge-Kutta method was used to calculate the results respectively. and .

7. The control method for a wireless power transfer system based on Hammerstein-IMC according to any one of claims 2 to 6, characterized in that, The following steps are used to determine λ: A1. Design maximum sensitivity The nonlinear equation between λ and λ; A2. Determine the maximum sensitivity ; A3, based on certainty Solve the nonlinear equation to obtain the initial value of λ; A4. Adjust λ until the robustness exponent of the system response is satisfied.

8. The control method for a wireless power transfer system based on Hammerstein-IMC according to claim 7, characterized in that: In step A1, The nonlinear equation between λ and λ is expressed as: 。

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