A control method for high-efficiency wireless power transmission system

Abstract

The present invention relates to a control method for a high-efficiency wireless power transmission system, which belongs to the field of wireless power transmission technology and solves the problem of poor adaptability of control methods of existing wireless power transmission systems. A control method for a high-efficiency wireless power transmission system includes: determining a value range of the primary and secondary self-inductances of a loosely coupled transformer according to power transmission requirements; selecting a loosely coupled transformer that meets the value range requirements of the primary and secondary self-inductances to construct the high-efficiency wireless power transmission system; determining a transfer function of the high-efficiency wireless power transmission system based on the constructed high-efficiency wireless power transmission system; determining compensator structural parameters based on the transfer function of the high-efficiency wireless power transmission system, and performing closed-loop compensation control on the high-efficiency wireless power transmission system based on the compensator structural parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless power transmission, and in particular to a control method for a high-efficiency wireless power transmission system. Background Art

[0002] The main principles of Wireless Power Transfer (WPT) technology are as follows: Figure 1 As shown in the figure, the left side is the primary side, and the right side is the secondary side. There is no physical connection between the primary and secondary sides. The DC signal input from the front end is converted to an AC signal through the inverter. To regulate the system's output voltage and current and achieve soft switching, a suitable compensation topology is generally incorporated into the primary and secondary sides. Based on the principle of electromagnetic induction, the secondary coil induces an electromotive force. The induced AC voltage is converted to DC through a rectifier and filter circuit to power the electrical equipment. If the primary and secondary sides of the coupling mechanism are misaligned, the system's output voltage will fluctuate significantly. To maintain a constant system output voltage, researchers generally incorporate a closed-loop DC / DC converter before the inverter bridge or after the rectifier bridge. Furthermore, in practical WPT systems, not only energy is transferred between the primary and secondary sides, but also signals are exchanged for real-time voltage and current monitoring and closed-loop control of the primary and secondary sides.

[0003] When the primary and secondary sides of the magnetic coupling mechanism are offset, the input voltage is disturbed, and the load fluctuates, the output characteristics of the WPT system will be affected. In order to reduce the impact of changes in system parameters on the output voltage, the system needs to be stabilized. Common voltage stabilization control methods include the following:

[0004] (1) DC / DC converter control

[0005] To achieve a regulated output voltage in WPT systems, researchers have added DC / DC converters to the front end of the inverter or the back end of the rectifier bridge. By adjusting the DC / DC converter's output, they control the WPT system's final output. Because the DC / DC converter is independent of the WPT system, adjusting it has little impact on the WPT system's performance. Therefore, WPT systems that incorporate a DC / DC converter for voltage regulation have a wider adjustment range. If WPT systems are divided according to the number of AC / DC levels, they can be divided into three stages: DC / AC, AC / AC, and AC / DC. The introduction of an additional DC / DC converter effectively converts the WPT system into a four-stage system, reducing its transmission efficiency. Furthermore, the addition of a DC / DC converter increases the volume and weight of the primary and secondary sides, hindering the miniaturization of WPT systems.

[0006] (2) Inverter control

[0007] Inverter control includes frequency modulation and phase shift control. Frequency modulation control in WPT systems is similar to the control of tightly coupled resonant converters such as LLCs, achieving system voltage regulation through the correspondence between the system output voltage and the inverter frequency f. However, unlike LLC resonant converters, WPT systems experience significant positional offsets between the primary and secondary sides. Frequency modulation further exacerbates the system's non-resonance, significantly increasing the input impedance angle, introducing significant reactive power, and increasing the voltage stress of the compensation components, hindering system efficiency and stable operation. Phase shift control achieves voltage regulation in WPT systems by adjusting the lag angle θ between adjacent inverter bridge arms, thereby adjusting the fundamental RMS value of the inverter output voltage. However, excessively large phase shift angles can result in the loss of the system's soft switching characteristics, and the system's output gain can only be adjusted downward from the full-bridge inverter's reference point. These shortcomings further limit the voltage adjustment range of phase shift control.

[0008] A wireless power transmission system can be composed of an inverter, compensation network, loosely coupled transformer, rectifier bridge, and load circuit. The large number of components involved in resonance in a wireless power transmission system leads to system nonlinearity. The system's dynamic performance and various indicators are closely related to the quality of the controller, and controller design relies on accurate system modeling. Therefore, research on wireless power transmission system modeling is extremely important. Existing modeling methods mainly include the following:

[0009] AC impedance analysis, a frequency-domain analysis method, is used to determine the steady-state solution for the system. While this modeling approach is relatively simple, it only retains the fundamental component during the modeling process, resulting in significant errors compared to the actual operating state of the wireless power transmission system. The discrepancy between theory and practice becomes more pronounced when the system load changes, making it unsuitable for modeling and analyzing complex, high-order systems.

[0010] As research continues to deepen, Seth R. Sanders et al. first proposed the generalized state-space averaging method, which linearizes system variables using Fourier series. During the simplification process, the order of the Fourier series can be arbitrarily selected and includes zero-order components, achieving both simplified system models and relatively accurate models with acceptable errors. Aiguo Patrick Hu of the University of Auckland, New Zealand, first applied the generalized state-space averaging method to modeling wireless power transfer systems, studying the system's steady-state response and dynamic characteristics. Akshya K. Swain et al. used this modeling method to model and analyze a bidirectional wireless power transfer system, designing a compensator and dynamically controlling the system based on the desired compensation characteristics. Hao Hao et al. also used this modeling method to model and analyze a dynamic automotive wireless charging system based on LCL-T compensation. The system utilizes primary-side current control, collecting primary current information and feeding it into the primary-side controller, resulting in excellent dynamic characteristics.

[0011] In the control link, in addition to modeling the wireless power transmission system, the compensator link also needs to be designed. The commonly used compensator is the PID controller. However, the PID controller is only suitable for low-order power supply systems. For high-order energy transmission systems such as wireless power transmission systems, the traditional PID controller is no longer applicable and cannot play an effective control role. Therefore, it is necessary to introduce a higher-order compensator into the wireless power transmission system.

[0012] In summary, the modeling and control of wireless power transmission systems are key and challenging aspects of the technology's practical application. Existing literature is limited, and further in-depth research is needed. Research on the modeling and control of wireless power transmission systems can further advance the practical application of wireless power transmission technology, improving the system's dynamic characteristics and closed-loop control effectiveness, and is of far-reaching significance. Summary of the Invention

[0013] In view of the above analysis, the embodiments of the present invention aim to provide a control method for an efficient wireless power transmission system, so as to solve the problem of poor adaptability of the control method of the existing wireless power transmission system.

[0014] The present invention discloses a control method for a high-efficiency wireless power transmission system, comprising:

[0015] Determine the value range of the primary and secondary self-inductance of the loosely coupled transformer according to the power transmission requirements;

[0016] Selecting a loosely coupled transformer that meets the value range requirements of the primary and secondary side self-inductances to build the high-efficiency wireless power transmission system;

[0017] Based on the constructed high-efficiency wireless power transmission system, determining a transfer function of the high-efficiency wireless power transmission system;

[0018] Compensator structural parameters are determined according to a transfer function of the high-efficiency wireless power transmission system, and closed-loop compensation control is performed on the high-efficiency wireless power transmission system based on the compensator structural parameters.

[0019] On the basis of the above solution, the present invention also makes the following improvements:

[0020] Furthermore, the high-efficiency wireless power transmission system includes:

[0021] The primary and secondary side compensation capacitors are used to compensate for the primary side self-inductance and secondary side self-inductance of the loosely coupled transformer respectively;

[0022] The interleaved parallel Boost circuit is used to boost the DC input voltage and control the interleaved parallel Boost circuit to output a boosted AC voltage according to a control signal from a feedback control circuit;

[0023] A loosely coupled transformer is used to transform the AC voltage output by the interleaved parallel Boost circuit;

[0024] The rectifier and filter circuit is used to rectify and filter the AC voltage after the loosely coupled transformer is transformed, and output a filtered DC voltage;

[0025] The feedback control circuit is used to sample the filtered DC voltage and compensate the sampled DC voltage according to the compensator structural parameters to generate the control signal.

[0026] Furthermore, the staggered parallel Boost circuit includes an inductor L1, an inductor L2, switch tubes Q1-Q4 and a voltage stabilizing capacitor C in ; Among them, the switch tubes Q1 and Q3 are the upper and lower bridge arms in the first bridge arm respectively; the switch tubes Q2 and Q4 are the upper and lower bridge arms in the second bridge arm respectively;

[0027] The positive electrode of the DC input voltage is connected to one end of the inductor L1 and one end of the inductor L2 at the same time, the negative electrode of the DC input voltage is connected to one end of the steady-state capacitor and the common node of the two lower bridge arms at the same time, the other end of the voltage-stabilizing capacitor is connected to the common node of the two upper bridge arms, the other end of the inductor L1 is connected to the midpoint of the upper and lower bridge arms in the first bridge arm, and the other end of the inductor L2 is connected to the midpoint of the upper and lower bridge arms in the second bridge arm. The voltage between the two midpoints is the boosted AC voltage output by the interleaved parallel Boost circuit.

[0028] Furthermore, the power transmission requirements include a maximum current flowing through the primary side of the loosely coupled transformer, a maximum voltage across the primary side compensation capacitor of the loosely coupled transformer, and a maximum voltage across the secondary side compensation capacitor of the loosely coupled transformer.

[0029] Furthermore, the range of the self-inductance of the primary and secondary sides of the loosely coupled transformer is determined based on formulas (1)-(4):

[0030]

[0031]

[0032]

[0033]

[0034] Among them, I LP Indicates the current flowing through the primary side of the loosely coupled transformer, I LP_max Indicates the maximum current flowing through the primary side of the loosely coupled transformer; U C1 Indicates the voltage across the primary compensation capacitor of the loosely coupled transformer, U C1_max Indicates the maximum voltage across the primary compensation capacitor of the loosely coupled transformer; U C2 Represents the voltage across the secondary compensation capacitor of the loosely coupled transformer, U C2_max Indicates the maximum voltage across the secondary compensation capacitor of the loosely coupled transformer; I LS Indicates the current value flowing through the secondary side of the loosely coupled transformer, U O Indicates the DC voltage after filtering, L P , L S They represent the primary and secondary self-inductances of the loosely coupled transformer, ω represents the switching angular frequency of the interleaved parallel Boost circuit, and k represents the coupling coefficient of the loosely coupled transformer.

[0035] Furthermore, the value range of the primary and secondary self-inductances of the loosely coupled transformer is determined based on formulas (5)-(6):

[0036]

[0037] G 0_min ≤G0≤G 0_max (6)

[0038] R represents the load resistance at rated power, U in Indicates the DC input voltage, G0 indicates the relative voltage gain, G 0_min , G 0_max Represent the minimum and maximum relative voltage gain respectively.

[0039] Furthermore, the transfer function G of the high-efficiency wireless power transmission system is p (s) is:

[0040] G p (s) = C(sI-A)-1 N (7)

[0041] in,

[0042]

[0043] in,

[0044] Z 3×3 represents the zero matrix of order 3,

[0045]

[0046]

[0047]

[0048] in,

[0049] C=[0 … 0 1] 1×18 ,

[0050]

[0051]

[0052]

[0053] Where D represents the duty cycle of the interleaved parallel boost circuit, C1 and C2 represent the primary and secondary compensation capacitors of the loosely coupled transformer, respectively, and M is the mutual inductance between the primary and secondary coupling mechanisms. Δ = M 2 -L p L s , C F is the filter capacitor in the rectification and filtering circuit; X 1,ss 、X 2,ss 、......、X 18,ss Form the steady-state solution matrix X ss , determine X by formula (8) ss :

[0054] X ss =-A -1 BU ss (8)

[0055] in,

[0056]

[0057] U ss Indicates the static operating point of the DC input voltage.

[0058] Furthermore, the feedback control circuit includes: a voltage sampling circuit, a compensation control circuit, and a PWM modulator; wherein,

[0059] The voltage sampling circuit is used to sample the filtered DC voltage;

[0060] The compensation control circuit is used to calculate the deviation between the sampled DC voltage and the voltage set value; and is also used to obtain the control signal based on the deviation and the compensator structural parameters;

[0061] The PWM modulator is used to control the conduction state of each switch tube in the staggered parallel Boost circuit based on the control signal, so as to achieve closed-loop compensation control of the high-efficiency wireless power transmission system.

[0062] Furthermore, the control signal is a duty cycle; and the voltage setting value is a sampling result of the rated output voltage by the voltage sampling circuit.

[0063] Furthermore, determining the compensator structural parameters according to the transfer function of the high-efficiency wireless power transmission system includes:

[0064] Get the original gain function G0(s) of the uncompensated system:

[0065] G0(s)=G M (s)G p (s)H(s) (6)

[0066] Among them, G M (s) is the transfer function of the PWM modulator, and H(s) is the transfer function of the voltage sampling circuit;

[0067] Draw the Bode plot of the original gain function G0(s) of the uncompensated system, ignore the zeros and poles at high frequencies, and only retain the zeros and poles at low frequencies to obtain the simplified gain function G0′(s);

[0068] Based on the simplified gain function G0′(s), the zero poles and low-frequency gain of the compensator in the compensation control circuit are designed according to the desired shear frequency and phase margin, and then the compensator structure parameters are determined.

[0069] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0070] This invention discloses a control method for a high-efficiency wireless power transmission system. It quantitatively analyzes the system's efficiency improvement and studies the system's key electrical parameters based on voltage and current stresses and the difficulty of implementing closed-loop control. It also provides a specific method for determining the range of values for the primary and secondary self-inductances of a loosely coupled transformer based on power transmission requirements.

[0071] In addition, the present invention also provides a specific process for determining the compensator structural parameters based on the transfer function of the high-efficiency wireless power transmission system. When the primary and secondary sides of the coupling mechanism are offset, the system output voltage is maintained constant by adjusting the duty cycle of the preceding interleaved parallel Boost. This present invention is the first to perform small-signal modeling of the proposed WPT system. By rationally designing the compensator, the stability of the system is theoretically verified, and guidance is provided for the writing of the control program in the experiment.

[0072] In the present invention, the above-mentioned technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of the present invention will be described in the following description, and some advantages will become apparent from the description or be learned through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0074] Figure 1 It is a structural diagram of a high-efficiency wireless power transmission system;

[0075] Figure 2 is a flow chart of a control method for a high-efficiency wireless power transmission system in an embodiment of the present invention;

[0076] Figure 3 It is the schematic diagram of the interleaved parallel Boost circuit;

[0077] Figure 4 The waveforms of the Q1-Q4 driving circuit and UAB at different duty cycles are shown below;

[0078] Figure 5 is the function image of G0 and GBR changing with duty cycle;

[0079] Figure 6 The relationship between loss reduction and primary and secondary side losses under different relative voltage gains;

[0080] Figure 7 The change of the primary current ILP with the primary and secondary self-inductance before and after the offset;

[0081] Figure 8 The voltage UC1 across the primary compensation capacitor changes with the self-inductance of the primary and secondary sides before and after the offset;

[0082] Figure 9 The voltage UC2 across the secondary compensation capacitor changes with the self-inductance of the primary and secondary sides;

[0083] Figure 10The change of the relative voltage gain G0 before and after the offset with the self-inductance of the primary and secondary sides;

[0084] Figure 11 This is the equivalent circuit diagram of the high-efficiency wireless power transmission system;

[0085] Figure 12 This is a closed-loop control block diagram for a high-efficiency wireless power transmission system;

[0086] Figure 13 is the original gain function of the uncompensated system and its reduced-order image;

[0087] Figure 14 is the original gain function image of the system after compensation. DETAILED DESCRIPTION

[0088] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, and are not used to limit the scope of the present invention.

[0089] First, the high-efficiency wireless power transmission system in this embodiment is introduced as follows:

[0090] like Figure 1 As shown, the high-efficiency wireless power transmission system includes an interleaved parallel Boost circuit (with both inversion and boost functions), a compensation network and coupling mechanism (including primary and secondary side compensation capacitors, and a loosely coupled transformer), a rectifier and filter circuit, and a feedback control circuit; wherein the primary and secondary side compensation capacitors are used to compensate for the primary side self-inductance and secondary side self-inductance of the loosely coupled transformer, respectively; the interleaved parallel Boost circuit is used to boost the DC input voltage and also to control the output of the boosted AC voltage of the interleaved parallel Boost circuit according to the control signal of the feedback control circuit; the loosely coupled transformer is used to transform the AC voltage output by the interleaved parallel Boost circuit, thereby realizing energy transmission between the primary and secondary sides; the rectifier and filter circuit is used to rectify and filter the AC voltage transformed by the loosely coupled transformer and output a filtered DC voltage; wherein D1-D4 are four rectifier diodes; the feedback control circuit is used to sample the filtered DC voltage and compensate the sampled DC voltage according to the compensator structure parameters to generate the control signal.

[0091] Specifically, the staggered parallel Boost circuit includes an inductor L1, an inductor L2, switch tubes Q1-Q4 and a voltage stabilizing capacitor C in; Among them, the switching tubes Q1 and Q3 are the upper and lower bridge arms in the first bridge arm respectively; the switching tubes Q2 and Q4 are the upper and lower bridge arms in the second bridge arm respectively; the positive pole of the DC input voltage is connected to one end of the inductor L1 and one end of the inductor L2 at the same time, the negative pole of the DC input voltage is connected to one end of the steady-state capacitor and the common node of the two lower bridge arms at the same time, the other end of the voltage-stabilizing capacitor is connected to the common node of the two upper bridge arms, the other end of the inductor L1 is connected to the midpoint of the upper and lower bridge arms in the first bridge arm, and the other end of the inductor L2 is connected to the midpoint of the upper and lower bridge arms in the second bridge arm. The voltage between the two midpoints is the boosted AC voltage output by the staggered parallel Boost circuit.

[0092] Specifically, the feedback control circuit includes: a voltage sampling circuit, a compensation control circuit, and a PWM modulator; wherein the voltage sampling circuit is used to sample the filtered DC voltage; the compensation control circuit is used to calculate the deviation between the sampled DC voltage and the voltage set value; and is also used to obtain the control signal based on the deviation and the compensator structure parameters; the control signal is a duty cycle; the voltage set value is the sampling result of the voltage sampling circuit on the rated output voltage; the PWM modulator is used to control the conduction state of each switch tube in the interleaved parallel Boost circuit based on the control signal to achieve closed-loop compensation control of the high-efficiency wireless power transmission system.

[0093] Preferably, the feedback control circuit may further include a Bluetooth module, a secondary-side DSP controller, and a primary-side DSP controller including a compensation control circuit; the communication between the primary and secondary sides adopts an HC-05 Bluetooth module, and the value after output voltage conversion is sampled into the secondary-side DSP controller and sent to the primary side through the Bluetooth module. After receiving the sampled value, the primary-side DSP controller compares it with the voltage set value to obtain a deviation, and then obtains the control signal based on the deviation and the compensator structure parameters, thereby controlling the duty cycle of Q1-Q4, and keeping the output voltage constant when the primary and secondary sides offset and the input voltage fluctuates.

[0094] A specific embodiment of the present invention discloses a control method for a high-efficiency wireless power transmission system, the flow chart of which is as follows: Figure 2 Shown, including:

[0095] Step S1: determining the value range of the primary and secondary self-inductances of the loosely coupled transformer according to the power transmission requirements;

[0096] Step S2: Selecting a loosely coupled transformer that meets the value range requirements of the primary and secondary side self-inductances to build the high-efficiency wireless power transmission system;

[0097] Step S3: Based on the constructed high-efficiency wireless power transmission system, determining a transfer function of the high-efficiency wireless power transmission system;

[0098] Step S4: determining compensator structural parameters according to the transfer function of the high-efficiency wireless power transmission system, and performing closed-loop compensation control on the high-efficiency wireless power transmission system based on the compensator structural parameters.

[0099] Preferably, the power transmission requirements include the maximum current flowing through the primary side of the loosely coupled transformer, the maximum voltage across the primary side compensation capacitor of the loosely coupled transformer, and the maximum voltage across the secondary side compensation capacitor of the loosely coupled transformer. The process of determining the value range of the primary and secondary side self-inductances of the loosely coupled transformer in step S1 is analyzed as follows:

[0100] Figure 3 This is the schematic diagram of the staggered parallel Boost. L1, Q1 and Q3 form the first Boost converter, L2, Q2 and Q4 form the second Boost converter, C in is the voltage stabilizing capacitor, and Z is the equivalent impedance of the subsequent circuit.

[0101] Drawing on the definition of the Boost circuit duty cycle, the ratio of the on-time of Q3 and Q4 to the entire cycle is defined as the duty cycle D. Q1 and Q3, Q2 and Q4 are complementary turned on, and Q4 is turned on half a cycle later than Q3. Figure 4 The driving signal of the switch tubes Q1-Q4 and the output voltage U of the staggered parallel Boost AB The waveforms at different duty cycles define θ dead For U AB The angle corresponding to the dead time. θ dead It can be expressed as follows:

[0102]

[0103] According to Fourier transform, the fundamental effective value U of the interleaved parallel Boost output voltage UAB AB1 It can be expressed as:

[0104]

[0105] The output gain of the interleaved parallel Boost is:

[0106]

[0107] The voltage gain of a traditional full-bridge inverter can be expressed as:

[0108]

[0109] Since the staggered parallel Boost proposed in the present invention is an improvement on the traditional full-bridge inverter, the present invention defines the ratio of the gain of the staggered parallel Boost to the gain of the full-bridge inverter as the relative voltage gain G0:

[0110]

[0111] For the convenience of discussion, in this embodiment, the ratio of the DC bus voltage U Cin and the input voltage U in is defined as the boost ratio:

[0112]

[0113] Figure 5 is the function image of G0 and G BR changing with the duty cycle. When the duty cycle D is less than 0.27, the dead time of U AB is too large, resulting in the relative voltage gain G0 being lower than 1, and the front-stage system cannot play a boosting role. When the duty cycle D is greater than 0.67, the boost ratio G BR is higher than 3, and the DC bus voltage U Cin is too large. At this time, the voltages borne by the four switching tubes and the bus capacitor (i.e., the voltage stabilizing capacitor) are too large. Selecting switching tubes and bus capacitors with higher withstand voltages not only increases the cost of the system but also is not conducive to the stable operation of the system and affects the reliability of the system. Therefore, the optimal value range of the duty cycle D is 0.27 < D < 0.67, that is, the interleaved parallel Boost operates in the Figure 5 shaded area.

[0114] According to the coupled inductor principle and the controlled source equivalent model of the loosely coupled transformer, when the compensation capacitors on the primary and secondary sides resonate with the self-inductances on the primary and secondary sides respectively, the relationship between the system output voltage U O and the input voltage U in , the duty cycle D, and the parameters of the coupling mechanism are as follows. In Equation (7), R is the load resistance under the rated power condition.

[0115]

[0116] In this embodiment, the loss of the system is reduced by boosting the voltage on the primary DC bus and reducing the primary current. In this embodiment, the efficiency of the system is quantitatively analyzed to further explain the reason for the improvement of the system efficiency and to guide the parameter design in the following text. In the WPT system, the losses of the inverter circuit, rectifier circuit, and DC / DC converter are basically fixed and account for a relatively small proportion. The losses of the system are mainly concentrated on the coupling mechanism. Therefore, in this embodiment, the losses on the loosely coupled transformer are mainly analyzed. Let the parasitic resistances on the primary and secondary sides of the coupling mechanism be R LP and R LS , respectively. Then the copper loss of the loosely coupled transformer can be expressed as:

[0117] P loss = I LP 2 R LP + I LS2 R LS (8)

[0118] When the primary side adopts staggered parallel Boost for boost conversion, the fundamental effective value of the primary DC bus voltage is increased by G0 times compared with the traditional full-bridge inverter. When the system transmission power remains unchanged, the primary side current becomes:

[0119]

[0120] According to formula (7), in order to ensure that the output voltage remains unchanged, when the coupling coefficient is constant, the relationship between the self-inductance of the primary and secondary sides of the loosely coupled transformer before and after the change is:

[0121]

[0122] Assuming that the self-inductance value of the primary side becomes a times of the original value, and the self-inductance value of the secondary side becomes b times of the original value, the relationship between the two can be expressed as:

[0123]

[0124] According to the principle of coupled inductance, the square of the number of turns on the primary and secondary sides is proportional to the self-inductance value. On a single side of the loosely coupled transformer, the parasitic resistance on the coil is proportional to the number of turns. At this time, the resistance on the primary and secondary coils is:

[0125]

[0126] Before and after the interleaved parallel Boost circuit is used, the secondary current remains unchanged. The copper loss of the loosely coupled transformer is expressed as:

[0127]

[0128] The reduction in copper loss of the loosely coupled transformer before and after adding the staggered parallel Boost for boosting can be summarized as follows:

[0129]

[0130] Among them, P loss-primary and P loss-secondary Represent the losses of the primary and secondary sides respectively. Figure 6 The relationship between the loss reduction and the primary and secondary losses under different relative voltage gains. In the WPT system, the input and output voltage levels are generally the same. When the S / S compensation topology is used, the currents on the primary and secondary coils are generally the same. Since the self-inductance and parasitic resistance of the primary side of the loosely coupled transformer are generally greater than those on the secondary side, when the staggered parallel Boost is not used for boost conversion, the primary side loss is generally greater than the secondary side loss, that is, Figure 6 In order to keep the output voltage unchanged, when the primary self-inductance value increases by more than 2 times, that is, a≥2, the vertical coordinate △Ploss / P loss-secondary The value of is greater than 0, which proves that increasing the primary DC bus voltage can reduce coil losses and improve efficiency. The larger the ratio of primary loss to secondary loss, the more obvious the efficiency improvement effect.

[0131] Depend on Figure 6 It can be seen that when the relative voltage gain G0 is different, the slope and direction of the curve are also different. In order to ensure that the vertical coordinate of the curve in the shaded area is greater than 0 when a ≥ 2, that is, the system efficiency is improved, the value of G0 is generally around 2, that is, the primary DC bus voltage is increased by about 2 times.

[0132] The stress of passive components includes voltage stress and current stress. The passive components in the WPT system proposed in the present invention include: the primary compensation capacitor C1 of the loosely coupled transformer, the secondary compensation capacitor C2, the primary self-inductance L P , secondary side self-inductance L S The increased voltage stress across the compensation capacitor complicates component selection and increases system costs. Furthermore, high-voltage compensation capacitors typically have large parasitic resistance, which not only reduces system efficiency but also easily causes temperature drift, reducing the stability of the WPT system. The high current flowing through the loosely coupled transformer causes severe coil heating, and the system losses scale with the square of the current, significantly reducing system efficiency.

[0133] In this embodiment, the primary current I LP The relationship between the parameters in the primary and secondary side self-inductance circuits is:

[0134]

[0135] I LP Indicates the current flowing through the primary side of the loosely coupled transformer, I LP_max Indicates the maximum current flowing through the primary side of the loosely coupled transformer; U O Indicates the DC voltage after filtering, L P , L S where ω represents the primary and secondary self-inductances of the loosely coupled transformer, ω represents the switching angular frequency of the interleaved parallel boost circuit, and k represents the coupling coefficient of the loosely coupled transformer. For example, when the coupling mechanism is offset from the horizontal alignment to the maximum distance, the coupling coefficient varies from 0.112 to 0.082.

[0136] According to the previous analysis, the core and winding space of the secondary side of the loosely coupled transformer is smaller than that of the primary side, so the secondary side self-inductance is smaller. Therefore, in this analysis, the range of the primary side self-inductance is: 500-1500μH, and the range of the secondary side self-inductance is: 100-500μH. According to formula (15), the primary side current I when the primary and secondary sides are facing each other and when the primary and secondary sides are offset to the farthest distance can be obtained. LPAs the self-inductance of the primary and secondary sides changes, the data on the right represents the effective value of the primary current.

[0137] Depend on Figure 7 It can be seen that when the primary and secondary sides are offset and the coupling coefficient decreases, the primary current increases significantly. In order to reduce the loss on the primary coil, the effective value of the primary current is generally lower than 5A before and after the offset. The dotted line represents the contour line of the primary current value of 5A, and the arrow represents the area where the primary current is less than 5A is located on the upper right side of the curve. When the primary and secondary sides are offset, the 5A contour line moves to the upper right direction. In order to keep the primary current I LP The value is less than 5A, and the value range of the primary and secondary self-inductance should be Figure 7 The intersection of (a) and (b) is the area to the upper right of the 5A contour line in Figure (b). When the output current of the system remains unchanged, the secondary current I LS It has nothing to do with the self-inductance of the primary and secondary sides. The calculated effective value of the secondary current I LS It is 5.55A. Since the volume and number of turns of the secondary side of the loosely coupled transformer are small, the parasitic resistance is small, and the loss on the secondary coil is small, the design value of the secondary current in this system is within a reasonable value range.

[0138] Next, the present invention focuses on analyzing the voltage stress of the primary and secondary compensation capacitors. Based on the circuit principle and the resonant characteristics of the primary compensation capacitor and the primary self-inductance, the relationship between the peak voltage across the compensation capacitor C1 and the primary and secondary self-inductance is:

[0139]

[0140] U C1_max Indicates the maximum value of the voltage across the primary compensation capacitor of the loosely coupled transformer.

[0141] According to formula (16), we can draw the U before and after the offset C1 As the primary and secondary self-inductances change, such as Figure 8 The peak voltage across the compensation capacitor is generally lower than 4kV, so the present invention retains the original secondary side offset.

[0142] Similarly, the peak value of the voltage across the compensation capacitor C2 is shown in the following formula: C2 The limit is 1.5kV. The arrow in the figure represents U C2 The region less than 1.5 kV is located on the lower side of the curve.

[0143]

[0144] Among them, I LS Indicates the current value flowing through the secondary side of the loosely coupled transformer; U C2_maxIndicates the maximum value of the voltage across the secondary compensation capacitor of the loosely coupled transformer. C2 As the primary and secondary self-inductance changes, Figure 9 shown.

[0145] After the above analysis, the stress of the passive components has been limited to a reasonable range. Since the WPT system proposed in the present invention is a closed-loop control system, in the process of parameter design, in addition to considering the stress of the passive components, the possibility of realizing the closed-loop system must also be considered. According to the above analysis, the duty cycle of the front-stage staggered parallel Boost is more suitable to work between 0.27-0.67, and the closer the duty cycle is to 0.5, the better the overall performance of the system. The relationship between the output voltage and the duty cycle D can be known from formula (7), but formula (7) is a transcendental equation, and the analytical solution of D cannot be obtained. Therefore, the present invention analyzes and designs parameters based on the relative voltage gain G0 mentioned above. According to formulas (5) and (7), the relative voltage gain G0 can also be expressed as:

[0146]

[0147] Where R represents the load resistance at rated power, which is 20Ω for example, and U in Indicates the DC input voltage, G0 indicates the relative voltage gain, G 0_min , G 0_max Respectively represent the minimum and maximum relative voltage gain. G 0_max =2.6, G 0_min =1; and the values of the primary and secondary self-inductances are such that the relative voltage gain G0 is as close to G0 as possible before and after the primary and secondary sides are offset. * =0.5.

[0148] When the primary and secondary sides are offset, the required relative voltage gain G0 value changes. By adjusting the value of the front-stage staggered parallel Boost duty cycle D in real time, the required relative voltage gain G0 is achieved to maintain the constant voltage characteristic of the output. Figure 4 The relative voltage gain G0 is between 1 and 2.6, and the closer it is to 2, the better the overall performance of the system. According to formula (18), the change of the relative voltage gain G0 before and after the offset with the primary and secondary self-inductance can be obtained as follows: Figure 10 This embodiment aims to obtain a more appropriate value of the primary and secondary self-inductance based on the restricted area obtained above. Figure 10 , it can be found that when the value range of the primary and secondary self-inductance is Figure 10When the value of the relative voltage gain G0 before and after the offset is within the circle, the value satisfies the conditions mentioned above. When other conditions are the same, the farther the value point of the primary and secondary self-inductance is from the three contour lines, the smaller the voltage and current stress. Combined with the simulation of the magnetic coupling mechanism, the self-inductance values of the primary and secondary sides are 1177μH and 282μH respectively, that is, Figure 10 Point P in .

[0149] Based on the above introduction, the range of values for the primary and secondary self-inductances of the loosely coupled transformer can be determined. On this basis, the construction of the high-efficiency wireless power transmission system in step S2 can be performed. Here, the process of determining the transfer function of the high-efficiency wireless power transmission system in step S3 is explained as follows:

[0150] In order to deeply analyze the control method of the system, the present invention performs small signal modeling on the proposed system. Figure 11 is the equivalent circuit diagram of the WPT system proposed in this invention, g Q1 and g Q2 is the switching function of the switches Q1 and Q2, g D is the switching function of the rectifier bridge. Figure 11 From the equivalent circuit diagram of , the differential equation of the WPT system proposed in this invention can be obtained as shown in formula (19).

[0151]

[0152] The following three formulas are respectively g Q1 、g Q2 and g D The expression of g. Q1 (t) = 1 means the switch tube Q1 is turned on and Q3 is turned off, g Q1 (t)=0 means the switch tube Q1 is turned off and Q3 is turned on, g Q2 The same is true for (t). D When (t)=1, the rectifier bridge works in the positive half cycle. D When (t)=-1, the rectifier bridge operates in the negative half cycle.

[0153]

[0154]

[0155]

[0156] Will <g Q1 (t)> k 、 <g Q2 (t)> k and <g D (t)> k Performing Fourier expansion at k=0 and ±1, we can obtain:

[0157]

[0158]

[0159]

[0160] Similarly, the variables in formula (19) can also be approximated by Fourier series, as shown below:

[0161]

[0162] in I L1 , I L2 and U Cin In , there are AC and DC components, so the 0th and ±1st order Fourier series are retained; U C1 、U C1 , I LP and I LS The waveform is a sine function, so only ±1-order Fourier series are retained, U CF The fluctuation is small and the waveform is close to DC, so only the 0th order Fourier series is retained. The ±1st order Fourier series are conjugate symmetric, so only the real and imaginary parts of the +1st order Fourier series need to be solved to obtain the real and imaginary parts of the -1st order Fourier series. For ease of analysis, let:

[0163]

[0164] Then the generalized state variable can be expressed as:

[0165] x(t)=[x1,x2,…,x 18 ] T (28)

[0166] Then, the present invention analyzes the product of the switching function and the state variable in formula (19). Based on the convolution characteristics of the periodic signal, the product of the switching function and the state variable is Fourier expanded to obtain the form of multiplication or addition of the 0th and ±1st order Fourier series of each variable, as shown in the following formula:

[0167]

[0168] Substitute the above equation and the differential expression of the state variables in equation (27) into the differential equation of equation (19). After substituting the Fourier decomposition form of each variable, the differential equation of equation (19) can be equivalent to:

[0169]

[0170] In the above formula, u(t)=[U in ] is the DC input voltage, y(t)=[U O ]=[U CF ] is the output voltage. A, B, C, and D are represented as follows.

[0171] For ease of explanation, the matrix A is decomposed into multiple 3×3 matrices for representation.

[0172]

[0173]

[0174] C=[0 … 0 1] 1×18 (33)

[0175] D=[0] (34)

[0176] Among them, Z 3×3 Represents a zero matrix of order 3. A 11 、A 22 、A 33 and A 55 The expression is:

[0177]

[0178] The expressions of other matrices in A are:

[0179]

[0180]

[0181] Where D represents the duty cycle of the interleaved parallel boost circuit, C1 and C2 represent the primary and secondary compensation capacitors of the loosely coupled transformer, respectively, and M is the mutual inductance between the primary and secondary coupling mechanisms. Δ = M 2 -L p L s , C F is the filter capacitor in the rectifier and filter circuit. 1,ss 、X 2,ss 、......、X 18,ss Form the steady-state solution matrix X ss , determine X by formula (36) ss :

[0182] in,

[0183]

[0184] U ss Indicates the static operating point of the DC input voltage.

[0185] In steady state, the state variables in Equation (30) do not change with time, so their derivatives are 0, that is, the left side of the equation is 0. Based on this, the steady-state solution of the system can be obtained as follows:

[0186]

[0187] Add the disturbance to the state variable, that is:

[0188]

[0189] Substituting equation (37) into equation (30), ignoring the steady-state variables and the second-order AC small signal variables, the small signal model of the WPT system proposed in this invention can be obtained as follows:

[0190]

[0191] Where N is given by equation (41), in order to calculate D and output voltage U O The transfer function of the present invention assumes that the input voltage U in No fluctuation, that is:

[0192]

[0193] According to formula (38), the duty cycle D and output voltage U O The small signal transfer function can be derived as follows:

[0194]

[0195] For ease of explanation, N is decomposed into multiple small matrices for representation:

[0196]

[0197] in:

[0198]

[0199] Figure 12 This is the closed-loop control block diagram of the WPT system proposed in the present invention. C (s) is the transfer function of the compensator, G M (s) is the transfer function of the PWM modulator, G P (s) is the transfer function of the WPT system proposed in this paper, and H(s) is the transfer function of the voltage sampling circuit.

[0200] The transfer function of the PWM modulator is shown below, where V m The value is 3.3V.

[0201]

[0202] The given value of the system output voltage U Oref The output voltage is 100V. After the voltage divider circuit, amplifier circuit and differential circuit, it is converted into a 2V voltage signal and sent to the ADC sampling port of the DSP. Therefore, the voltage sampling transfer function H(s) can be expressed as:

[0203]

[0204] In step S4, the compensator structural parameters are determined according to the transfer function of the high-efficiency wireless power transmission system, including:

[0205] Step S41: obtaining the original gain function G0(s) of the uncompensated system;

[0206] Step S42: Draw a Bode plot of the original gain function G0(s) of the uncompensated system, ignore the zeros and poles at high frequencies, and retain only the zeros and poles at low frequencies (for example, high-frequency zeros and poles far from the desired shear frequency after compensation can be ignored), to obtain a simplified gain function G0′(s);

[0207] Step S43: Based on the simplified gain function G0′(s), the zero-pole and low-frequency gain of the compensator in the compensation control circuit are designed according to the desired shear frequency and phase margin, and the compensator structural parameters are determined. This improves the system's low-frequency gain, increases the system's mid-frequency bandwidth, and suppresses high-frequency ripple.

[0208] To help those skilled in the art better understand the process of determining compensator structural parameters, the following example is given:

[0209] Equation (44) is the original gain function of the uncompensated system. When the primary and secondary sides are facing each other, the original gain function of the uncompensated system is as follows: Figure 13 As shown in the curve.

[0210] G0(s)=G M (s)G p (s)H(s) (44)

[0211] The Bode plot of the original gain function G0(s) of the uncompensated system has 17 poles and 15 zeros, making the system too complex to analyze. Most of the zeros and poles have little effect on closed-loop control. Therefore, the present invention simplifies the original gain function G0(s), ignoring the zeros and poles at high frequencies and retaining only the main zeros and poles to obtain a simplified gain function G0′(s), as shown in Figure 2. Figure 13 As shown in the curve. The original gain function after reduction has a zero point Z0, corresponding to the angular frequency ω Z0 , a pole P0, corresponding to the angular frequency ω P0 , and a pair of conjugate poles P1,2 =a±bi, the corresponding angular frequency is The unit of angular frequency is rad / s. Therefore, G0′(s) can be expressed as follows, where K is the low-frequency gain.

[0212]

[0213] When the primary and secondary sides of the loosely coupled transformer shift position, the coupling coefficient k changes, causing a slight shift in the system's static operating point. Table 1 shows the changes in the low-frequency gain, poles, and zeros of the original gain function G0′(s) as the coupling coefficient decreases from 0.112 to 0.082.

[0214] Table 1 Numerical values of parameters of the original gain function under different coupling coefficients

[0215]

[0216] According to the system parameters under different coupling coefficients in the table above, combined with Figure 13 The Bode plot after mid-order reduction shows that the system's low-frequency gain is low before the compensator is added. In the mid-frequency range, the amplitude-frequency characteristic curve crosses the 0dB line at a rate of -40dB / dec, and the phase margin is low. When the coupling coefficient varies between 0.112 and 0.082, the system's amplitude-frequency and phase-frequency characteristics are similar, and both exhibit the aforementioned problems. Therefore, compensation is necessary. Wireless power transmission systems are high-order power transmission systems, and traditional PI controllers may no longer be applicable. Therefore, this article uses a high-order 3P3Z compensator to compensate the system:

[0217]

[0218] Since the present invention uses a wireless communication module to send the sampled values of the secondary side to the primary side, there is a certain communication delay between the primary and secondary sides. In order to ensure that the system has sufficient phase margin, the shear frequency should be appropriately reduced. When the primary and secondary sides are offset from being aligned, the target shear frequency of the present invention is 1.5kHz-2kHz. At the same time, in order to ensure that the system has sufficient stability, the phase margin of the system after compensation should be greater than 30 degrees. In order to suppress the high-frequency spikes of the system output voltage near the switching frequency, the present invention will p3 It is configured at 1 / 2 of the angular frequency corresponding to the switching frequency of the staggered parallel Boost converter. Based on the above-mentioned target expectations, the present invention studies the 3P3Z compensator and obtains the following expression (i.e., compensator structural parameters):

[0219]

[0220] Then the original gain function of the system after adding the compensator is:

[0221] G0(s)=G C (s)G M (s)G p (s)H(s) (48)

[0222] Figure 14 Taking the case of a positively aligned primary and secondary sides as an example, the original gain function of the compensated system is plotted. The compensated system has a clipping frequency of 1.5kHz and a phase margin of 66.9 degrees. This phase margin is greater than 45 degrees, improving system stability. The compensated system exhibits high low-frequency gain and crosses the 0dB line at a rate of -20dB / dec in the mid-frequency range. In the high-frequency range, the amplitude-frequency characteristic curve decreases at a rate of -40dB / dec, effectively suppressing high-frequency ripple near the switching frequency.

[0223] When the primary and secondary sides offset and the coupling coefficient changes, the system's shear frequency and phase margin change slightly, as shown in Table 2. The shear frequency varies from 1.5 kHz to 1.93 kHz, both within the given range, and the phase margin varies from 66.9 degrees to 74 degrees, both greater than 45 degrees. The system maintains good stability under full-range offset conditions.

[0224] Table 2 Shear frequency and phase margin of the compensated system under different coupling coefficients

[0225]

[0226] During closed-loop compensation control of the high-efficiency wireless power transmission system based on the compensator structural parameters, a bilinear transformation method can be used to discretize the obtained compensator structural parameters to obtain digital compensator structural parameters. The output voltage is collected in real time by a secondary-side voltage sampling circuit and transmitted to a primary-side DSP controller. In the primary-side DSP control program, the collected output voltage value is compared with a given value and fed into a digital compensator to obtain a corresponding duty cycle value. This is used to control the individual switches of the preceding interleaved parallel Boost converter, maintaining a constant output voltage when the primary and secondary sides shift position.

[0227] Those skilled in the art will appreciate that all or part of the process steps of the above-described embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, such as a magnetic disk, an optical disk, a read-only memory, or a random access memory.

[0228] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A control method for a high-efficiency wireless power transmission system, characterized in that: include: Determine the value range of the primary and secondary self-inductance of the loosely coupled transformer according to the power transmission requirements; Selecting a loosely coupled transformer that meets the value range requirements of the primary and secondary side self-inductances to build the high-efficiency wireless power transmission system; Based on the constructed high-efficiency wireless power transmission system, determining a transfer function of the high-efficiency wireless power transmission system; Determining compensator structural parameters according to a transfer function of the high-efficiency wireless power transmission system, and performing closed-loop compensation control on the high-efficiency wireless power transmission system based on the compensator structural parameters; The high-efficiency wireless power transmission system comprises: The primary and secondary side compensation capacitors are used to compensate for the primary side self-inductance and secondary side self-inductance of the loosely coupled transformer respectively; The interleaved parallel Boost circuit is used to boost the DC input voltage and control the interleaved parallel Boost circuit to output a boosted AC voltage according to a control signal from a feedback control circuit; A loosely coupled transformer is used to transform the AC voltage output by the interleaved parallel Boost circuit; The rectifier and filter circuit is used to rectify and filter the AC voltage after the loosely coupled transformer is transformed, and output a filtered DC voltage; a feedback control circuit, configured to sample the filtered DC voltage and compensate the sampled DC voltage according to the compensator structural parameters to generate the control signal; The interleaved parallel Boost circuit includes an inductor ,inductance , switch tubes Q1-Q4 and voltage stabilizing capacitors ; Among them, the switch tubes Q1 and Q3 are the upper and lower bridge arms in the first bridge arm respectively; the switch tubes Q2 and Q4 are the upper and lower bridge arms in the second bridge arm respectively; The positive terminal of the DC input voltage is connected to the inductor One end and the inductor One end of the DC input voltage is connected to the negative pole of the DC input voltage and the common node of the two lower bridge arms. The other end of the stabilizing capacitor is connected to the common node of the two upper bridge arms. The other end of the inductor is connected to the midpoint of the upper and lower bridge arms in the first bridge arm. The other end is connected to the midpoint of the upper and lower bridge arms in the second bridge arm, and the voltage between the two midpoints is the boosted AC voltage output by the staggered parallel Boost circuit.

2. The control method for a high-efficiency wireless power transmission system according to claim 1, characterized in that: The power transmission requirements include the maximum current flowing through the primary side of the loosely coupled transformer, the maximum voltage across the primary side compensation capacitor of the loosely coupled transformer, and the maximum voltage across the secondary side compensation capacitor of the loosely coupled transformer.

3. The control method for a high-efficiency wireless power transmission system according to claim 2, characterized in that: Based on formulas (1)-(4), the value range of the primary and secondary self-inductance of the loosely coupled transformer is determined as follows: （1） （2） （3） （4） in, Indicates the current value flowing through the primary side of the loosely coupled transformer, Indicates the maximum current flowing through the primary side of the loosely coupled transformer; It represents the voltage across the primary compensation capacitor of the loosely coupled transformer. Indicates the maximum value of the voltage across the primary compensation capacitor of the loosely coupled transformer; It represents the voltage across the secondary compensation capacitor of the loosely coupled transformer, Indicates the maximum value of the voltage across the secondary compensation capacitor of the loosely coupled transformer; Indicates the current value flowing through the secondary side of the loosely coupled transformer, represents the DC voltage after filtering, 、 They represent the primary and secondary self-inductances of the loosely coupled transformer, Represents the switching angular frequency of the interleaved parallel Boost circuit, Represents the coupling coefficient of the loosely coupled transformer.

4. The control method for a high-efficiency wireless power transmission system according to claim 3, characterized in that: The value range of the primary and secondary self-inductance of the loosely coupled transformer is also determined based on formulas (5)-(6): （5） （6） Indicates the load resistance at rated power. Indicates the DC input voltage, represents the relative voltage gain, 、 Represent the minimum and maximum relative voltage gain respectively.

5. The control method for a high-efficiency wireless power transmission system according to claim 4, characterized in that: The transfer function of the high-efficiency wireless power transmission system for: （7） in, ， in, represents the zero matrix of order 3, ， ； in, ， ， ； ； Where D represents the duty cycle of the interleaved parallel Boost circuit. and They represent the primary and secondary compensation capacitors of the loosely coupled transformer, M is the mutual inductance between the primary and secondary coupling mechanisms, , is the filter capacitor in the rectification and filtering circuit; 、 、......、 Forming the steady-state solution matrix , determined by formula (8) : （8） in, , ， Indicates the static operating point of the DC input voltage.

6. The control method for a high-efficiency wireless power transmission system according to claim 5, characterized in that: The feedback control circuit includes: a voltage sampling circuit, a compensation control circuit, and a PWM modulator; wherein, The voltage sampling circuit is used to sample the filtered DC voltage; The compensation control circuit is used to calculate the deviation between the sampled DC voltage and the voltage set value; and is also used to obtain the control signal based on the deviation and the compensator structural parameters; The PWM modulator is used to control the conduction state of each switch tube in the staggered parallel Boost circuit based on the control signal, so as to achieve closed-loop compensation control of the high-efficiency wireless power transmission system.

7. The control method for a high-efficiency wireless power transmission system according to claim 6, characterized in that: The control signal is a duty cycle; the voltage set value is a sampling result of the voltage sampling circuit on the rated output voltage.

8. The control method for a high-efficiency wireless power transmission system according to claim 6 or 7, characterized in that: The determining of compensator structural parameters according to the transfer function of the high-efficiency wireless power transmission system includes: Get the raw gain function of the uncompensated system : （6） in, is the transfer function of the PWM modulator, is the transfer function of the voltage sampling circuit; Plotting the raw gain function of the uncompensated system The Bode plot of the simplified gain function is obtained by ignoring the zero poles at high frequencies and retaining only the zero poles at low frequencies. ; Based on the simplified gain function , according to the desired shear frequency and phase margin, the zero poles and low-frequency gain of the compensator in the compensation control circuit are designed, and then the compensator structure parameters are determined.

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