An ultrasonic transducer frequency tracking and dynamic impedance matching system and method

Abstract

The application discloses an ultrasonic transducer frequency tracking and dynamic impedance matching system and method. The application proposes an open magnetic circuit type adjustable inductor, an analytical correction model is established by introducing a leakage magnetic compensation coefficient, an external equivalent air magnetic resistance and a magnetic core effective permeability, and a variable cross-section magnetic core is designed based on the model, so that the inductance value linearly changes with an insertion distance; meanwhile, a collaborative coupling control algorithm based on double sampling point feedback is proposed, a first sampling point is used to drive the inductor to compensate transient phase deviation and record an adjustment direction, the driving frequency is induced to stepwise approach a resonance point according to the adjustment direction, and a second sampling point is used to execute nested loop adjustment, so that dynamic decoupling of frequency tracking and impedance matching is realized. The application significantly improves dynamic stability, convergence speed and energy transmission efficiency of the system under a large power variable load working condition.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic transducer technology, and relates to an ultrasonic transducer frequency tracking and dynamic impedance matching system and method. Background Technology

[0002] Power ultrasound has core application value in high-precision sonochemical processes such as nanomaterial dispersion and industrial-grade biodiesel synthesis. These processes essentially rely on the sonochemical cavitation effect induced by ultrasound in liquid media to achieve particle deagglomeration or accelerate chemical reactions. As a core application scenario in sonochemistry, the nanomaterial dispersion process has almost stringent requirements for the continuity and stability of energy output. In this process, the ultrasonic transducer, as the core component performing energy conversion, is a typical electro-acoustic-mechanical multi-field coupled nonlinear load, and its electrical characteristics are usually characterized in detail using the Butterworth-Van Dyke (BVD) equivalent circuit model.

[0003] In sonochemical cavitation operations (such as processing high-viscosity vegetable oil and methanol mixtures), the transducer is not in a static stable state; its impedance characteristics undergo dramatic evolution driven by multiple physical mechanisms.

[0004] After high-power ultrasound is continuously injected into the reactor, a dense cavitation bubble cloud is formed at the end of the transducer radiator head. The instantaneous generation and collapse of micron-sized bubbles cause a jump-like change in the acoustic radiation impedance of the radiating surface, which is directly reflected in the highly nonlinear fluctuations of the equivalent dynamic resistance and dynamic inductance in the BVD model.

[0005] Internal friction in piezoelectric ceramics generates endogenous heat accumulation, and the temperature rise changes the physical constants of the piezoelectric material, causing the inherent resonant frequency to gradually drift downward.

[0006] In this complex biochemical reaction scenario, the transducer not only faces changes in the external fluid environment but also endures the severe test of high-intensity mechanical vibration losses. Due to the endogenous heat accumulation generated by internal friction of the piezoelectric ceramic, the system will trigger a significant "temperature drift" phenomenon. This temperature rise will change the physical constants of the piezoelectric material, causing its natural resonant frequency to gradually drift downward.

[0007] In a continuous biodiesel production line, if the control system cannot detect and identify the impedance evolution caused by the combined effects of cavitation and heat in real time, the transducer will rapidly deviate from its optimal resonant point. This mismatch not only causes the energy originally intended to drive the chemical reaction to be converted into ineffective heat energy within the transducer, resulting in a severe decrease in electroacoustic conversion efficiency, but also generates a huge reactive power backflow, thus creating severe electrical stress and heat loss on the high-speed switching power devices of the inverter bridge, greatly increasing the risk of damage to the power electronic system.

[0008] To address the aforementioned challenges, frequency tracking and dynamic impedance matching technologies constitute the core control logic of high-performance ultrasonic power supplies. Traditional frequency tracking schemes have evolved from early analog phase-locked loops (PLLs) to feedback algorithms based on direct frequency synthesis (DDS) and fully digital signal processing, aiming to lock the impedance zero-phase point by adjusting the drive frequency in real time. However, a simple frequency modulation strategy can only compensate for the reactive component of the impedance and cannot overcome the impedance magnitude mismatch caused by cavitation load variations. Therefore, a dynamic impedance matching mechanism is introduced, particularly an adjustable reactive element adjusted by a precision stepping mechanism, which can achieve dynamic compensation of the transducer's static capacitance and real-time optimization of the impedance transformation ratio over a wide frequency range.

[0009] The existing solution most similar to the technical path of this invention is a dynamic impedance matching and composite frequency tracking system based on a closed magnetic circuit adjustable inductor, the technical features of which are as follows:

[0010] (1) Hardware structure: The air gap width between the internal magnetic cores is precisely adjusted by relying on the mechanical drive mechanism. The overall equivalent magnetic reluctance is adjusted by changing the longitudinal length of the air gap in the magnetic circuit, so that the inductance decreases accordingly as the air gap expands, thereby achieving smooth switching and continuous compensation of the inductance value over a large range.

[0011] (2) Control logic: The timing strategy of "pre-determining frequency, subsequent matching, and real-time tracking" is adopted.

[0012] Initialization phase: Automatic frequency sweep is performed, and the effective value of the transducer terminal current is sampled and compared in real time to lock the frequency point where the maximum current is located in order to initially locate the series resonance region; further, phase difference detection technology is introduced for fine feedback to calibrate the instantaneous series resonance frequency of the transducer.

[0013] Matching stage: The drive motor changes the physical displacement of the inductor, so that the phase difference between the dynamic matching module and the transducer as a whole converges to zero degrees;

[0014] Operation phase: Establish a closed-loop real-time monitoring mechanism to continuously monitor the phase status of the output terminal; once the phase deviation exceeds the preset stable range, periodically trigger the frequency sweep optimization and displacement fine-tuning process to make the output frequency and impedance matching parameters dynamically adjust with the load changes.

[0015] In the current field of power ultrasonic drive, mainstream solutions generally employ closed-circuit adjustable inductors. Their working principle primarily relies on mechanical mechanisms to adjust the air gap width of the internal magnetic core, thereby changing the magnetic reluctance to achieve inductance compensation. However, the strong constraint of the closed magnetic circuit on the magnetic flux causes the inductance to exhibit significant nonlinear characteristics with displacement, greatly increasing the difficulty of modeling and compensating the control system. Furthermore, when handling high-power sonochemical operations such as nanomaterial dispersion or biodiesel synthesis, drastic fluctuations at the load end can easily induce magnetic saturation of the magnetic core, resulting in nonlinear distortion and compromising the system's electrical stability under complex operating conditions.

[0016] A deep analysis of the control logic chain reveals significant technical limitations in the existing "independent adjustment, blind search" strategy when dealing with dynamic operating conditions. The mainstream approach essentially relies on two isolated feedback loops—frequency tracking and impedance matching—lacking effective coordination logic. When the system detects a phase deviation, adjustment commands between different loops often conflict in real time, causing the system to oscillate repeatedly around the equilibrium point and triggering severe transient detuning. This lag in control logic and the "coupling interference" between loops not only cause significant fluctuations in power transmission efficiency but can also damage the drive circuit due to current surges caused by instantaneous detuning, becoming a core bottleneck restricting the system's dynamic response accuracy and operational reliability. Summary of the Invention

[0017] To address the shortcomings of existing technologies, this invention provides an ultrasonic transducer frequency tracking and dynamic impedance matching system and method.

[0018] An ultrasonic transducer frequency tracking and dynamic impedance matching system of the present invention includes:

[0019] The system includes a full-bridge drive module, a DDS signal synthesis module, an impedance matching module, a transducer, a first phase detection module, a second phase detection module, a current RMS detection module, and a control module.

[0020] The DDS signal synthesis module is connected to the full-bridge drive module, the full-bridge drive module is connected to the impedance matching module, and the impedance matching module is connected to the transducer.

[0021] The sampling terminal of the first phase detection module is located on the input side of the impedance matching module, and is used to detect the overall phase difference including the impedance matching module and the transducer; the sampling terminal of the second phase detection module is located on the input side of the transducer, and is used to detect the phase difference of the transducer itself; the sampling terminal of the current RMS detection module is located at the same point as the sampling terminal of the second phase detection module, and is used to detect the RMS value of the current flowing through the transducer.

[0022] The control module is connected to the DDS signal synthesis module, the impedance matching module, the first phase detection module, the second phase detection module, and the current RMS detection module, respectively.

[0023] The impedance matching module includes an adjustable inductor, and the control module is configured to:

[0024] When the absolute value of the phase difference detected by the first phase detection module exceeds a preset threshold, the adjustable inductor is first driven to adjust its inductance value to compensate for the transient phase deviation and the inductor adjustment direction is recorded until the phase difference of the first phase detection module converges to within the preset threshold; then, the DDS signal synthesis module is induced to adjust its driving frequency according to the recorded inductor adjustment direction and the frequency adjustment direction is recorded; if the phase difference of the second phase detection module still exceeds the preset threshold, a nested loop is executed:

[0025] Fine-tune the adjustable inductor in a direction opposite to the initial adjustment direction of the inductor so that the phase difference of the first phase detection module returns to within the preset threshold. At the same time, continue to step-adjust the driving frequency in the recorded frequency adjustment direction until the phase difference of the second phase detection module converges to within the preset threshold.

[0026] In one embodiment of the present invention, the adjustable inductor is an open magnetic circuit adjustable inductor, including a double-layer frame, a motor, a lead screw, a nut, a coil, and a magnetic core. The motor is fixed to the upper layer of the double-layer frame, and the magnetic core is fixed to the lower layer of the double-layer frame. The motor drives the nut and the coil to move axially relative to the magnetic core through the lead screw, so as to change the length of the magnetic core inserted into the coil.

[0027] In one embodiment of the present invention, the magnetic core is a composite profile magnetic core, with its front end being a cylinder of uniform cross-section and its rear end being a gradually decreasing cross-sectional area along the axial direction.

[0028] In one embodiment of the invention, the axial distribution of the cross-sectional area of ​​the gradient is configured such that the inductance value of the adjustable inductor increases linearly with the increase of the length of the magnetic core inserted into the coil.

[0029] In one embodiment of the present invention, the inductance value of the adjustable inductor is determined based on a magnetic circuit analytical model, which introduces leakage magnetic flux compensation coefficient, external equivalent air magnetic reluctance and effective magnetic permeability of the magnetic core as compensation correction parameters.

[0030] In one embodiment of the present invention, the impedance matching module further includes a fixed inductor, a first matching capacitor and a second matching capacitor. The adjustable inductor, the fixed inductor and the first matching capacitor are connected in series between the full-bridge drive module and the transducer. The second matching capacitor is connected in parallel to the input terminal of the transducer.

[0031] The ultrasonic transducer frequency tracking and dynamic impedance matching method of the present invention includes the following steps:

[0032] S1: The system is initialized and frequency sweep is performed to determine the initial value of the transducer series resonant frequency and the corresponding peak value of the effective current.

[0033] S2: Real-time acquisition of the phase difference between the first sampling point and the second sampling point. The first sampling point is set at the input end of the impedance matching network to characterize the overall phase deviation of the driving signal after passing through the impedance matching network and the transducer. The second sampling point is set at the input end of the transducer to characterize the phase deviation of the transducer itself.

[0034] S3: When the absolute value of the phase difference at the first sampling point exceeds a preset threshold, the coordinated coupling adjustment of impedance matching and frequency tracking is initiated.

[0035] S3a: Based on the lead-lag relationship between voltage and current at the first sampling point, drive the adjustable inductor to adjust its inductance value to compensate for transient phase deviation, and record the inductor adjustment direction until the phase difference at the first sampling point converges to within the preset threshold.

[0036] S3b: Based on the recorded inductor adjustment direction, synchronously induce the driving frequency to approach the current resonant point of the transducer in steps, and record the frequency adjustment direction;

[0037] S3c: Detect the phase difference of the second sampling point. If it still exceeds the preset threshold, perform nested loop adjustment: finely adjust the inductance value of the adjustable inductor in the direction opposite to the initial adjustment direction of the inductor so that the phase difference of the first sampling point returns to within the preset threshold. At the same time, continue to step-adjust the driving frequency in the recorded frequency adjustment direction until the phase difference of the second sampling point converges to within the preset threshold.

[0038] S3d: Perform end fine-tuning, finely adjust the inductance value of the adjustable inductor in the direction opposite to the initial adjustment direction of the inductor, and ensure that the final phase difference of the first sampling point is stable within the preset threshold.

[0039] In one embodiment of the present invention, the frequency sweep in S1 includes: traversing the driving frequency range with a preset large step size, detecting the effective value of the current flowing through the transducer at each frequency point, determining the frequency corresponding to the point with the maximum effective value of the current as the initial value of the series resonant frequency, and recording the maximum effective value of the current as the peak value of the effective value of the current.

[0040] In one embodiment of the present invention, after S1, a composite frequency tracking step is further included: comparing the effective value of the current at the current driving frequency with the peak value of the effective value of the current; if the current effective value of the current is within a preset proportion range of the peak value, then the lead-lag relationship between voltage and current is determined based on the phase difference of the second sampling point and the driving frequency is adjusted step by step; if the current effective value of the current is lower than the lower limit of the preset proportion range of the peak value, then the current extreme value is searched with a preset small step size and the peak value of the effective value of the current is updated.

[0041] In one embodiment of the present invention, an independent impedance matching step is included before S3: the phase difference of the first sampling point is detected, and if its absolute value is greater than the preset threshold, the adjustable inductor is driven to increase or decrease its inductance value according to the lead-lag relationship between voltage and current, and the detection and adjustment are repeated until the phase difference of the first sampling point converges to within the preset threshold.

[0042] This invention employs an open magnetic circuit design instead of the traditional closed magnetic circuit, fundamentally avoiding the risk of core saturation under high-power conditions and ensuring the stability of electrical performance. Furthermore, by deriving a formula specifically for the relationship between the inductance value and insertion distance of this inductor, and innovatively introducing three compensation coefficients to compensate for subtle deviations between the theoretical model and the actual device, the system achieves a highly accurate digital mapping foundation. This precise fitting ensures that every mechanical displacement is converted into the expected inductance compensation, thereby eliminating the blind adjustment caused by inaccurate models in traditional solutions.

[0043] Further reasoning reveals that, thanks to the accurate analytical model, this invention can transform the originally complex nonlinear physical process into a linear relationship at the hardware level by changing the geometric cross-sectional area of ​​the magnetic core. This improvement represents a qualitative leap for the control system: it not only greatly simplifies the computational burden of the control algorithm but also makes impedance adjustment intuitive and predictable. This linearization characteristic enables deep coupling of subsequent algorithms, eliminating the need for the system to rely on complex table lookups or high-frequency feedback iterations to find the equilibrium point, as is common in traditional solutions.

[0044] Ultimately, based on the aforementioned highly linear hardware platform and accurate mathematical model, the frequency tracking and dynamic impedance matching collaborative algorithm implemented in this invention optimizes the tuning process from "compensation after detuning" to "quasi-resonant synchronous optimization".

[0045] The core advantage of this algorithm lies in its deeply collaborative dynamic hedging mechanism: as the driving frequency approaches the target resonant point, the algorithm does not adjust in isolation, but guides the adjustable inductor to perform synchronous compensation through real-time logic feedback. This collaborative stepping strategy ensures that the system can offset the inductive reactance disturbance caused by frequency changes to the matching network in real time throughout the entire optimization cycle, keeping the system dynamically in a purely resistive state with an overall phase difference close to zero. This "accompanied" matching optimization fundamentally eliminates the severe detuning phenomenon that is prone to occur in traditional schemes under parameter adjustment transients, not only maximally suppressing reactive power loss, but also ensuring the continuity and stability of ultrasonic energy output. Even under complex load conditions with drastic fluctuations such as sonochemical cavitation, the system can still achieve extremely high electrical safety and control robustness by virtue of this ability to synchronously approach the resonant point. Attached Figure Description

[0046] Figure 1 This is a system structure diagram of an embodiment of this application;

[0047] Figure 2 This is the impedance matching and transducer equivalent circuit diagram.

[0048] Figure 3 This is a schematic diagram of the adjustable inductor structure according to an embodiment of this application;

[0049] Figure 4 This is a flowchart illustrating the method of an embodiment of this application;

[0050] Figure 5 Here is a flowchart of the composite frequency tracking process;

[0051] Figure 6 Here is the flowchart for the impedance matching procedure;

[0052] Figure 7 Flowchart of the matching and frequency-following coupling algorithm. Detailed Implementation

[0053] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0055] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.

[0056] The primary objective of this application is to achieve high linearity control and rapid convergence of the system through deep synergy between physical structure optimization and algorithmic approaches. First, this application proposes an open magnetic circuit adjustable inductor, utilizing its inherent large air gap characteristic to fundamentally avoid the risk of magnetic saturation, and establishes a precise analytical function model between the core insertion length and the inductance. To further simplify control complexity, this application compensates for the deviation between the theoretical model and actual measurements through geometric optimization of the cylindrical core shape, thereby achieving linearization of the inductance adjustment and providing a robust hardware foundation for precise quantitative digital compensation.

[0057] Building upon this foundation, a further objective of this application is to eliminate system oscillations by establishing a cooperative logic between frequency and impedance. This application proposes a frequency tracking and dynamic impedance matching coupling algorithm based on dual-sampling-point feedback. This algorithm establishes a nested cooperative adjustment mechanism: it prioritizes using an adjustable inductor to compensate for the phase deviation at the input of the matching network to ensure drive safety; subsequently, it actively induces the drive frequency to approach the true resonant point of the load based on the inductor adjustment trend, and uses multiple iterative cycles to offset the inductive reactance fluctuations caused by frequency drift in real time. This coupling strategy of "inductor locking, frequency tracking, and dynamic compensation" achieves deep decoupling of frequency and impedance interference at the physical level. By eliminating blind searches and logical conflicts between control loops, this application significantly improves the dynamic stability and convergence speed of the system, achieving a leapfrog improvement in system service reliability.

[0058] Figure 1 The figure shown is a framework diagram of the frequency tracking and dynamic impedance matching system proposed in an embodiment of this application. Figure 1 The hardware system includes a full-bridge driver module, an impedance matching module, a transducer, a DDS signal synthesis module, two phase detection modules, a current RMS detection module, and an STM32 control module.

[0059] In the hardware system, the output of the STM32 control module is connected to the input of the DDS signal synthesis module and the motor drive input of the impedance matching module to receive control signals from the STM32 control module. The output of the DDS signal synthesis module is connected to the signal input of the full-bridge drive module, providing it with operating control signals. The output of the full-bridge drive module is connected to the power input of the impedance matching module, transmitting power drive signals to the operating circuit. The output of the impedance matching module is connected to the transducer input, matching the transducer's static capacitance and filtering the square wave from the full-bridge drive module into a sine wave.

[0060] In this embodiment, one of the two phase detection modules has its input terminal connected to the output terminal of the full-bridge driver or the input terminal of the impedance matching module, denoted as sampling point 1, used to acquire the phase difference including the impedance matching and the overall transducer. The other phase detection module has its input terminal connected to the output terminal of the impedance matching module or the input terminal of the transducer, denoted as sampling point 0, used to acquire the phase difference between the two ends of the transducer. The input terminal of the current detection module is connected to sampling point 0, used to acquire the effective value of the current passing through the transducer. The output terminals of the two phase detection modules and the current effective value detection module are connected to different input terminals of the STM32 control module, used to receive the sampled signals and feed back to adjust the output of the DDS signal synthesis module, and to control the adjustment of the adjustable inductor in the impedance matching module.

[0061] Figure 2 The diagram shown is the equivalent circuit diagram of the transducer, which includes adjustable inductor L3, fixed inductor L2, capacitor C3, capacitor C2, static capacitor C0, dynamic resistor R1, dynamic capacitor C1, and dynamic inductor L1.

[0062] One end of the adjustable inductor L3 is one input terminal of the impedance matching module, and the other end is connected to the fixed inductor L2. The other end of the fixed inductor L2 is connected to capacitor C3. The other end of capacitor C3 is connected to capacitor C2 and the transducer. The other end of capacitor C2 and the transducer is connected to the other input terminal of the impedance matching module. The adjustable inductor L3 provides an adjustable inductance value, and the fixed inductor L2 provides a fixed inductance value. Together, they allow control over both the upper and lower limits of the adjustable range of the series inductor. Capacitor C3 increases the required inductance value of the series inductor and expands its adjustment range. C2, together with the series inductor, forms an LC impedance matching network.

[0063] Figure 3 The diagram shows the structure of the adjustable inductor L3 in the impedance matching module. The device adopts a double-layer frame design, which organically combines the drive system and electromagnetic components. It mainly consists of motor 1, lead screw 2, coil 3, magnetic core 4, and support frame.

[0064] In terms of mechanical structure, the frame is divided into upper and lower layers: the motor and lead screw are fixed to the upper frame base. To accurately convert the rotational motion of the motor (controlled by the STM32 control module) into linear reciprocating motion, baffles are installed between the fixing parts at both ends of the lead screw, and a fixing rod passing through the hole at the top of the nut restricts the rotation of the nut, allowing it to move only axially. The hook at the bottom of the nut hangs into the lower space through a slot in the upper base, used to suspend and drive the coil to move synchronously.

[0065] In terms of working principle, the base extension of the lower frame is equipped with a support structure that holds the magnetic core in place, and the magnetic core is fixed by the support structure. When the motor drives the lead screw to rotate, the coil moves synchronously with the nut, thereby changing its relative position with the magnetic core—the deeper the magnetic core is inserted into the coil, the higher the inductance value. In this way, precise control of the motor's rotation angle can achieve precise adjustment of the L3 inductance value.

[0066] The derivation of the relationship between the length x of the cylindrical magnetic core inserted into the coil and the inductance value L of the adjustable inductor is as follows:

[0067] Ohm's law for magnetic circuits is as follows:

[0068]

[0069] in F is the magnetic flux, R is the magnetomotive force, and F = NI, where N is the number of turns and I is the current.

[0070] The formula for calculating magnetic reluctance is as follows:

[0071]

[0072] in Where A is the magnetic circuit length and A is the magnetic circuit cross-sectional area. It is the absolute permeability, which can be expanded into the product of the free permeability and the relative permeability. ), where the vacuum permeability is .

[0073] Inductance L is defined as magnetic flux linkage The ratio to the current I:

[0074]

[0075] Magnetic Link It is the total magnetic flux multiplied by the number of turns:

[0076]

[0077] Substituting Ohm's law formula (1) into formula (4), we get:

[0078]

[0079] Substituting formula (5) into formula (3) yields the inductance calculation formula:

[0080]

[0081] The formula for calculating the inductance of a magnetic core with an air gap is as follows:

[0082]

[0083] The reluctance consists of three parts: a magnetic core, a radial air gap, and an axial air gap. It is a magnetic core reluctance ( ) and radial air gap magnetoresistance ( Parallel reluctance, It is the magnetic reluctance of the air gap.

[0084] The axial air gap magnetic reluctance is as follows:

[0085]

[0086] It is the coil length. It is the cross-sectional area of ​​the coil. This is the length of the magnetic core inserted into the coil.

[0087]

[0088] in It is the relative permeability of the magnetic core. It is the cross-sectional area of ​​the magnetic core.

[0089]

[0090] Parallel reluctance as follows:

[0091]

[0092] Total magnetic reluctance as follows:

[0093]

[0094] Substituting the total magnetic reluctance into formula (7) yields the inductance calculation formula:

[0095]

[0096] Due to the demagnetizing effect and lateral magnetic leakage, the following modifications are made to formula (13): increase the global magnetic leakage compensation coefficient K, and increase the external equivalent air magnetic resistance. and the effective permeability of the magnetic core .

[0097] Effective permeability of magnetic core This refers to the actual permeability of a magnetic core under its real, non-closed geometry. A magnetized core will generate N and S poles at its two ends. These two poles will produce a magnetic field inside the core that is opposite in direction to the original magnetic field, known as a "demagnetizing field." This causes a sharp drop in the actual magnetic permeability of the core.

[0098] Assume the external excitation magnetic field is Due to the demagnetizing effect inside the magnetic core, the actual internal magnetic field... It will be very small:

[0099]

[0100] The demagnetizing field is proportional to the magnetization M of the magnetic core, and the proportionality constant is called the demagnetizing factor. The demagnetization factor is determined solely by the geometry of the object.

[0101]

[0102] According to electromagnetic constitutive relations Substituting formula (15) into formula (14) yields:

[0103]

[0104] Based on the inherent properties of the material, the actual internal magnetic flux density B is determined by the actual internal magnetic field. Determined by multiplying by the absolute permeability of the material:

[0105]

[0106] The effective permeability of the magnetic core is defined. :

[0107]

[0108] Combining formulas (17) and (18), we can obtain:

[0109]

[0110] Combining formulas (16) and (19), we can obtain:

[0111]

[0112] After sorting, we can obtain:

[0113]

[0114] Air magnetic resistance It is the total magnetic reluctance encountered by the magnetic field lines as they travel through the entire three-dimensional open space (air) back to the other end of the coil after exiting both ends. To derive it precisely, a volume integral of the magnetic field distribution throughout the entire three-dimensional space outside the coil is required:

[0115]

[0116] Cross-sectional area As the magnetic field lines diverge in the air, the integral changes constantly and has no analytical solution; it can only be solved by finite element simulation.

[0117] The global leakage flux compensation coefficient K is a reduction factor because many magnetic field lines leak out from the middle side without passing through the complete N turns, so a factor needs to be multiplied.

[0118] This application's embodiments achieve high-precision fitting of inductance parameters by introducing three compensation coefficients to analytically compensate for the gap between the theoretical physical model and the actual measured values. This precise digital characterization method provides a robust control basis for dealing with drastic impedance fluctuations in sonochemical operations. The final compensated formula is:

[0119]

[0120] As can be seen from formula (23), the relationship between the inductance value and the insertion distance x is nonlinear, which is not conducive to subsequent feedback control. Therefore, this embodiment of the application constructs nonlinear spatial reluctance compensation by introducing a non-linearly shaped magnetic core with a gradually varying cross-sectional area. By designing a magnetic core with a variable cross-sectional area, the inductance value changes linearly with the insertion distance. This embodiment derives a specific magnetic core geometric profile design formula to forcibly correct the originally complex nonlinear inductance value mapping into a feature where the inductance value changes linearly with the insertion distance. This improvement greatly reduces the logic operation overhead of the control system, makes the impedance regulation process highly predictable, and further improves the control convenience of the regulating mechanism.

[0121] The total magnetic reluctance after compensation is:

[0122]

[0123] The rate of change of magnetic reluctance can be obtained by differentiating the total magnetic reluctance with respect to the insertion distance x:

[0124]

[0125] Differentiating formula (23) with respect to x yields the rate of change of inductance:

[0126]

[0127] The target inductance is now set to a constant rate of change. Then the target inductance function is:

[0128]

[0129] The above formula If the inductance is the value of an empty coil, then the corresponding target total magnetic reluctance must satisfy:

[0130]

[0131] The target magnetoresistance derivative is:

[0132]

[0133] Let the cross-sectional area function of the variable cross-section magnetic core at a distance l from the tip be: When the length of the magnetic core inserted into the coil is x, the actual total magnetic reluctance is:

[0134]

[0135] Differentiating equation (30) yields the actual rate of change of magnetic reluctance:

[0136]

[0137] Combining formulas (29) and (31), we get:

[0138]

[0139] propose And by organizing, we can obtain:

[0140]

[0141] This is the axial distribution function of the magnetic core cross-sectional area.

[0142] like Figure 3 The diagram shows an adjustable inductor made with a variable cross-sectional area magnetic core. Due to the small initial inductance of the air-core coil, there is a bottleneck caused by a sudden change in initial magnetic reluctance. This application proposes a composite profile magnetic core: its front end is a cylinder with a constant cross-section, used to quickly cross the nonlinear low-inductance region within a very short stroke. The diameter of this cylinder is smaller than that of the air-core coil, allowing the cylinder to smoothly enter the interior of the air-core coil; its rear end is a gradually shrinking cross-sectional area, used to provide strict linear inductance compensation after entering the impedance matching operating region.

[0143] Figure 4The method described in this application involves first initializing the STM32 control system, followed by an initialization frequency sweep. Because the transducer impedance is minimum at the series resonant frequency, the effective current value is maximum. The initialization frequency sweep program rapidly detects the effective current value with large step sizes to locate the approximate position of the series resonant frequency and records the current effective value at this time. Subsequently, a composite frequency tracking program is run to find the series resonant frequency, and then an impedance matching program is run to achieve appropriate impedance matching. Then, the phase difference is judged at sampling point 1. If a phase difference greater than 5° is detected, it indicates that frequency drift has occurred, and a matching + frequency-following coupling algorithm is run until normal operation is restored.

[0144] The composite frequency tracking program in the embodiments of this application is as follows: Figure 5 As shown, the current effective current value I is first obtained and compared with the maximum effective current value recorded during the previous frequency sweep. If the current effective current value is between 0.9 and 1 times the maximum current value, the phase difference at sampling point 0 is checked. If the phase difference is less than 5°, it indicates that this is the series resonant point, and the composite frequency tracking program exits. Otherwise, it checks whether the voltage leads the current. If so, the driving frequency is decreased; otherwise, the driving frequency is increased. The phase difference is checked again, and the process is repeated until the phase difference condition is met, at which point the composite frequency tracking program exits. If the obtained current effective value I is less than 0.9 times the maximum current value, it indicates that the deviation from the series resonant point is too far. A small step size is used to search for the current extremum. If the obtained current effective value is greater than the maximum current value, the record of the maximum current value should be updated. Then, the impedance matching program is run.

[0145] The impedance matching procedure in the embodiments of this application is as follows: Figure 6 As shown, the phase difference at sampling point 1 is first detected. If the phase difference is less than 5°, it indicates impedance matching, and the impedance matching program exits. If the phase difference is greater than 5°, it is determined whether the voltage leads the current. If so, the adjustable inductance value is decreased; otherwise, the adjustable inductance value is increased. The phase difference is then checked again, and the process repeats until the phase difference condition is met, at which point the impedance matching program exits.

[0146] The impedance matching and frequency tracking coupling algorithm proposed in this application is as follows: Figure 7 As shown. When the system experiences frequency drift, causing the absolute value of the phase difference at sampling point 1 to exceed 5 degrees, the algorithm immediately activates the adjustment mechanism.

[0147] First, the system determines the lead-lag relationship between voltage and current by detecting the positive or negative characteristic of the phase difference at that point: if the voltage leads the current, the value of the adjustable inductor is decreased; otherwise, the inductor value is increased. During the adjustment process, the system records the direction of inductor adjustment and repeatedly detects and fine-tunes until the phase difference at sampling point 1 is reduced to within 5 degrees.

[0148] After initial phase compensation, the system immediately intervenes in frequency adjustment based on the recorded inductor adjustment direction. If the initial inductor adjustment direction was increasing, the system increases the driving frequency accordingly; conversely, it decreases the driving frequency and simultaneously records the adjustment direction of that frequency. Subsequently, the system detects the phase difference at sampling point 0: if this value is still greater than 5 degrees, it enters the coordinated loop adjustment stage. In this loop, the system first fine-tunes the adjustable inductor in the direction opposite to the initial recording, forcing the phase difference at sampling point 1 to return to within 5 degrees; then, it continues to step-adjust the driving frequency along the recorded frequency direction. This coupling process of "frequency stepping and inductor compensation" will continuously loop until the phase difference at sampling point 0 drops to within 5 degrees and the loop exits. Finally, the system performs final fine-tuning, fine-tuning the inductor in the direction opposite to the recording to ensure that the final phase difference at sampling point 1 is stable at or below 5 degrees. At this point, the system has fully realized the coordinated control of frequency tracking and dynamic impedance matching, and the program execution is complete.

[0149] In summary, this application aims to address core technical challenges in dynamic impedance matching systems based on stepper motor-driven lead screw adjustment under high-power conditions, including hardware signal distortion, poor linearity of adjustment, and system control oscillations caused by strong frequency-impedance coupling. Traditional closed-circuit inductors are prone to magnetic saturation under high power, leading to nonlinear signal distortion, and their inductance changes with displacement exhibits high nonlinearity, significantly increasing control complexity. Furthermore, existing algorithms often treat frequency tracking and impedance matching as independent adjustment processes. When severe frequency drift occurs, the lack of effective coordination logic easily leads to compensation conflicts between the two control loops, causing the system to oscillate repeatedly around the equilibrium point, and even triggering power protection due to instantaneous detuning, severely restricting the system's dynamic stability and tracking accuracy.

[0150] To overcome the aforementioned shortcomings, this application first designs an open magnetic circuit adjustable inductor, utilizing its inherent large air gap characteristic to fundamentally avoid magnetic saturation and ensure signal purity under high-power output. By thoroughly deriving the analytical relationship between the cylindrical magnetic core insertion distance and the inductance, and introducing a compensation correction formula for the gap between the theoretical model and reality, this application achieves accurate characterization of impedance matching parameters. Furthermore, to further improve the ease of adjustment, this application optimizes the complex nonlinear mapping into a linear relationship between the insertion distance and the inductance by improving the geometry of the magnetic core, laying the hardware foundation for precise digital control.

[0151] Based on the linearization characteristics of the aforementioned hardware, this application further proposes a cooperative coupling control algorithm for frequency tracking and dynamic impedance matching. This algorithm abandons the traditional approach of independent and unrelated frequency and impedance adjustment, achieving deep decoupling of phase compensation and frequency optimization by establishing a logical mapping relationship between the two. When the system experiences resonance shift, the algorithm employs a coupling strategy of "real-time inductor phase-locking and active frequency induction," prioritizing the use of adjustable inductors to compensate for transient phase deviations, ensuring the power transistor always operates within a safe range, and then dynamically approaching the new resonance point based on the inductor adjustment trend. This cooperative mechanism effectively eliminates self-excited oscillations and adjustment conflicts between different control loops, significantly shortens the system's steady-state convergence time, and ensures that energy transfer efficiency remains optimal under high-power variable load conditions.

[0152] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. An ultrasonic transducer frequency tracking and dynamic impedance matching system, characterized in that, include: The system includes a full-bridge drive module, a DDS signal synthesis module, an impedance matching module, a transducer, a first phase detection module, a second phase detection module, a current RMS detection module, and a control module. The DDS signal synthesis module is connected to the full-bridge drive module, the full-bridge drive module is connected to the impedance matching module, and the impedance matching module is connected to the transducer. The sampling terminal of the first phase detection module is located on the input side of the impedance matching module, and is used to detect the overall phase difference including the impedance matching module and the transducer; the sampling terminal of the second phase detection module is located on the input side of the transducer, and is used to detect the phase difference of the transducer itself. The sampling terminal of the current RMS detection module is located at the same point as the sampling terminal of the second phase detection module, and is used to detect the RMS value of the current flowing through the transducer. The control module is connected to the DDS signal synthesis module, the impedance matching module, the first phase detection module, the second phase detection module, and the current RMS detection module, respectively. The impedance matching module includes an adjustable inductor, and the control module is configured to: When the absolute value of the phase difference detected by the first phase detection module exceeds a preset threshold, the adjustable inductor is first driven to adjust its inductance value to compensate for the transient phase deviation and the inductor adjustment direction is recorded until the phase difference of the first phase detection module converges to within the preset threshold; then, the DDS signal synthesis module is induced to adjust its driving frequency according to the recorded inductor adjustment direction and the frequency adjustment direction is recorded; if the phase difference of the second phase detection module still exceeds the preset threshold, a nested loop is executed: Fine-tune the adjustable inductor in the direction opposite to the initial adjustment direction of the inductor so that the phase difference of the first phase detection module returns to within the preset threshold. At the same time, continue to step-adjust the driving frequency in the recorded frequency adjustment direction until the phase difference of the second phase detection module converges to within the preset threshold. The adjustable inductor is an open magnetic circuit type adjustable inductor, including a double-layer frame, a motor, a lead screw, a nut, a coil, and a magnetic core. The motor is fixed to the upper layer of the double-layer frame, and the magnetic core is fixed to the lower layer of the double-layer frame. The motor drives the nut and the coil to move axially relative to the magnetic core through the lead screw, so as to change the length of the magnetic core inserted into the coil. The magnetic core is a composite profile magnetic core, with its front end being a cylinder with a uniform cross-section and its rear end being a gradually shrinking cross-sectional area along the axial direction. The axial distribution of the cross-sectional area of ​​the gradient is configured such that the inductance value of the adjustable inductor increases linearly with the increase of the length of the magnetic core inserted into the coil.

2. The system according to claim 1, characterized in that, The inductance value of the adjustable inductor is determined based on a magnetic circuit analytical model, which incorporates leakage flux compensation coefficient, external equivalent air magnetic reluctance, and effective permeability of the magnetic core as compensation and correction parameters.

3. The system according to claim 1, characterized in that, The impedance matching module further includes a fixed inductor, a first matching capacitor, and a second matching capacitor. The adjustable inductor, the fixed inductor, and the first matching capacitor are connected in series between the full-bridge drive module and the transducer. The second matching capacitor is connected in parallel to the input terminal of the transducer.

4. A method for frequency tracking and dynamic impedance matching of an ultrasonic transducer, employing the system described in any one of claims 1-3, characterized in that... The method includes the following steps: S1: The system is initialized and frequency sweep is performed to determine the initial value of the transducer series resonant frequency and the corresponding peak value of the effective current. S2: Real-time acquisition of the phase difference between the first sampling point and the second sampling point. The first sampling point is set at the input end of the impedance matching network to characterize the overall phase deviation of the driving signal after passing through the impedance matching network and the transducer. The second sampling point is set at the input end of the transducer to characterize the phase deviation of the transducer itself. S3: When the absolute value of the phase difference at the first sampling point exceeds a preset threshold, the coordinated coupling adjustment of impedance matching and frequency tracking is initiated. S3a: Based on the lead-lag relationship between voltage and current at the first sampling point, drive the adjustable inductor to adjust its inductance value to compensate for transient phase deviation, and record the inductor adjustment direction until the phase difference at the first sampling point converges to within the preset threshold. S3b: Based on the recorded inductor adjustment direction, synchronously induce the driving frequency to approach the current resonant point of the transducer in steps, and record the frequency adjustment direction; S3c: Detect the phase difference of the second sampling point. If it still exceeds the preset threshold, perform nested loop adjustment: finely adjust the inductance value of the adjustable inductor in the direction opposite to the initial adjustment direction of the inductor so that the phase difference of the first sampling point returns to within the preset threshold. At the same time, continue to step-adjust the driving frequency in the recorded frequency adjustment direction until the phase difference of the second sampling point converges to within the preset threshold. S3d: Perform end fine-tuning, finely adjust the inductance value of the adjustable inductor in the direction opposite to the initial adjustment direction of the inductor, and ensure that the final phase difference of the first sampling point is stable within the preset threshold.

5. The method according to claim 4, characterized in that, The frequency sweep in S1 includes: traversing the driving frequency range with a preset large step size, detecting the effective value of the current flowing through the transducer at each frequency point, determining the frequency corresponding to the point with the maximum effective value of the current as the initial value of the series resonant frequency, and recording the maximum effective value of the current as the peak value of the effective value of the current.

6. The method according to claim 5, characterized in that, Following S1, a composite frequency tracking step is also included: comparing the current effective value at the current driving frequency with the peak value of the current effective value; if the current effective value of the current is within a preset proportion range of the peak value, then the lead-lag relationship between voltage and current is determined based on the phase difference of the second sampling point and the driving frequency is adjusted step by step; if the current effective value of the current is lower than the lower limit of the preset proportion range of the peak value, then the current extreme value is searched with a preset small step size and the peak value of the current effective value is updated.

7. The method according to any one of claims 4-6, characterized in that, Before S3, an independent impedance matching step is also included: detecting the phase difference of the first sampling point; if its absolute value is greater than the preset threshold, the adjustable inductor is driven to increase or decrease its inductance value according to the lead-lag relationship between voltage and current, and the detection and adjustment are repeated until the phase difference of the first sampling point converges to within the preset threshold.

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