Review of the design of power ultrasonic generator for piezoelectric transducer

Highlights

• •The demand design investigates a large number of power ultrasonic applications that seeks out a valuable clue, namely the mechanism consistency of the acting medium and the similarity of ultrasonic signals, it proves the necessity and feasibility of designing a universal modular generator model.
• •Plentiful state-of-the-art power semiconductor devices, digital chips, power conversion circuit modules, impedance matching circuits and control methods are summarized, which lay the foundation of the PUG system. A detailed understanding of the advantages and limitations of each part is essential to help researchers determine the most suitable modular design for the specific application.
• •A new PUG proposed in this paper differing from other traditional ultrasonic generator possesses two feedback channels.

Abstract

The power ultrasonic generator (PUG) is the core device of power ultrasonic technology (PUT), and its performance determines the application of this technology in biomedicine, semiconductor, aerospace, and other fields. With the high demand for sensitive and accurate dynamic response in power ultrasonic applications, the design of PUG has become a hot topic in academic and industry. However, the previous reviews cannot be used as a universal technical manual for industrial applications. There are many technical difficulties in establishing a mature production system, which hinder the large-scale application of PUG for piezoelectric transducers. To enhance the performance of the dynamic matching and power control of PUG, the studies in various PUT applications have been reviewed in this article. Initially, the demand design covering the piezoelectric transducer application and parameter requirements for ultrasonic and electrical signals is overall summarized, and these parameter requirements have been recommended as the technical indicators of developing the new PUG. Then the factors affecting the power conversion circuit design are analyzed systematically to realize the foundational performance improvement of PUG. Furthermore, advantages and limitations of key control technologies have been summarized to provide some different ideas on how to realize automatic resonance tracking and adaptive power adjustment, and to optimize the power control and dynamic matching control. Finally, several research directions of PUG in the future have been prospected.

1. Introduction

The applications of infrasound (f < 20 Hz), audible acoustic wave (20 Hz ≤ f < 20 kHz), and ultrasound (20 kHz ≤ f) are ubiquitous in the human world [1], [2], [3]. Especially, the ultrasound technology used in the range of 20 kHz to 1 GHz [4], [5] has been extensively developed and applied in related fields (e. g. ultrasonic machining, ultrasonic welding, ultrasonic imaging, ultrasonic cleaning, etc.) in the last 70 years, which has been divided into detection ultrasonic technology and power ultrasonic technology (PUT). The PUT involves materials science, acoustics, power electronics, and other disciplines, and mainly studies the generation and control of high-power and high-intensity ultrasonic elastic waves, the interaction law of matters, and its applications. According to the power and intensity of ultrasonic, PUT includes high-power ultrasonic (HPU) technology and micro-power ultrasonic (MPU) technology [6], [7]. As shown in Fig. 1, the low-frequency ultrasound (20 kHz ≤ f < 100 kHz) and medium-frequency ultrasound (100 kHz ≤ f < 1 MHz) have been generally applied in the HPU field [8]. While the high-frequency ultrasound (1 MHz ≤ f < 1 GHz) has been used in MPU applications mainly [9].

Fig. 1.

Schematic diagram of a new power ultrasonic generator system and classification of the acoustic wave.

Although the PUT has been widely utilized in food, medicine, environment, chemical industry, mechanical processing, and other related industries due to the advantages of high controllability, low cost, energy-saving, environmental protection, and no adverse by-products, its further application is severely restricted by the poor performance of the power ultrasonic generator (PUG) [10], [11], [12], [13]. Typically, ultrasonic mechanical vibration is excited and controlled by PUG’s electrical signals. Till date, most PUGs still cannot respond quickly and accurately to the resonance frequency drift caused by the load, temperature, stiffness, processing area, tool wear, and other factors of the ultrasonic vibration system, which leads to the power ultrasonic vibration system operating in the demodulation state at the non-resonant frequency [14], [15]. In this state, the amplitude of the vibration device decreases even to zero [16]. As the ultrasonic vibration gradually disappears, the output of PUG is mainly converted to heat, which cannot ensure the processing quality and protect the ultrasonic vibration system.

Hence, the performance of PUG is closely related to piezoelectric transducer (PT) load. Unlike conventional power adapters which have a relatively stable load, the PUG has a nonlinear high-frequency capacitive PT load which is quite unstable due to the variation of the thermo-mechanical load and self-heating effect of piezoelectric material in ultrasonic vibration system [17], [18], [19]. Generally, ultrasonic load driven by high-frequency mechanical vibration and friction of PT is subject to time-varying load caused by changes in operating conditions, such as driving frequency, power supply voltage, power supply current, load torque, and temperature rise, which results in the control characteristics of ultrasonic load are complex and highly nonlinear [20]. Simultaneously, it is required to work in a pure resistance state wherein the PT load keeps the voltage and current in the same phase and operates at the resonant frequency at all times. The reported PUG has a series of disadvantages, such as slow dynamic response, unstable power control, and poor universality. As shown in Fig. 1, a new PUG proposed in this paper differing from other traditional ultrasonic generators possesses two feedback channels. One is similar to conventional electrical parameter feedback which mainly aims at obtaining the data of amplitude, frequency(f), and phase of electric signals including voltage(u), and current(i). The other is the exclusive feedback channel which directly collects the data of thermo-mechanical loads including force(F) and temperature(T) to enhance the response of dynamic adjustment. Although adding a feedback channel increases the complexity of the power control and frequency control, it is worthwhile because it improves the control accuracy of the whole system, and appends an active prediction module of frequency drift and amplitude mutation. Furthermore, the PUG’s foundational performance is closely related to power semiconductor devices and circuit topologies. In order to achieve the requirements of high efficiency, high power, and high frequency, it is necessary to reduce the switching loss and conduction loss of power semiconductor devices, and harmonic distortions by optimizing soft switching technology, power factor correction (PFC) module, and semiconductor device [21], [22], [23], [24], [25]. Finally, it is of great significance to improve the PUG’s overall performance by implementing comprehensive feedback and robust control, this requires that PUG has a powerful main chip and intelligent algorithm to achieve the sensitive dynamic response of high-speed predicting, tracking, matching, and tuning.

This article is organized as follows. Section II gives the demanding design based on the acting medium which defines the PUG’s key indicators after implementing a comprehensive investigation of power ultrasonic applications in fluid, solid, and microparticle media. Section III reviews the power electronic devices and control chips of PUGs. Section IV reviews PUG's main circuit module design including the switching power supply module, inverter module, and impedance matching module. Section V discusses the PUG’s control technologies for PT load. Finally, Section VI concludes this article.

2. Demand design based on acting medium

HPU devices generally only transmit but do not receive ultrasonic waves. In contrast, MPU technology mainly studies low-intensity ultrasonic technology, and its devices generally include transmitting and receiving ultrasonic equipment simultaneously. Nevertheless, they mainly focus on power output but ignore the effects of ultrasonic frequency, amplitude, and waveform in different acting mediums. Ultrasonic waves can trigger diverse phenomena in different mediums which have been analyzed by corresponding mechanisms. Table 1 shows that these mechanisms can be applied regularly by controlling the ultrasonic frequency, energy density, and acting time. Typically, the PUG plays a decisive role in controlling the parameters of ultrasonic waves. Therefore, it is worth investigating the ultrasonic-acting medium to study the interference factors of ultrasonic signals and provide some key design parameter indicators for the high-performance ultrasonic generator.

Table 1.

Parameter requirements of power ultrasonic generator and mechanism of power ultrasonic technology.

Medium	Mechanism	Application	Ultrasonic and electrical signal parameter
Liquid	Cavitation effect Acoustic streaming Negative pressure effect Surface tension wave theory	Ultrasonic cleaning Ultrasonic levitation Ultrasonic defoaming Ultrasonic atomization	Continuous waves and alternation in multi-bands Frequency range 20 kHz to 100 kHz mainly Automatic resonance frequency tracking Constant power
Gas	Cavitation effect Thermal effect Acoustic streaming	Ultrasonic drying Ultrasonic dust removal	Alternation in multi-bands Continuous high-power ultrasonic wave Frequency range 40 kHz to 200 kHz mainly
Multiphase	Cavitation effect Mechanical effect Thermal effect Acoustic streaming	Ultrasonic extraction Ultrasonic emulsifying Ultrasonic oil production Ultrasonic treatment of waste sludge Ultrasound-assisted transesterification	High power Continuous waves Alternation in multi-bands Frequency range 20 kHz to 60 kHz mainly High frequency, low power, and more energy saving.
Solid	Mechanical effect Thermal effect Static pressure Displacement	Ultrasonic motor Ultrasonic welding Ultrasonic de-icing Ultrasonic machining Ultrasonic consolidation Ultrasonic impact treatment	Constant amplitude control Multi-dimensional superposition Fast frequency automatic tracking Strict anti-interference performance Amplitude range 2 μm to 27 μm mainly Frequency range 20 kHz to 40 kHz mainly
Biological tissue	Mechanical effect Local shear force Thermal effect	Ultrasonic surgery scalpel Ultrasonic vessel sealing and dissecting	Precise constant amplitude control Real-time monitoring of power control Frequency range 20 kHz to 70 kHz mainly
Microparticle	Microstreaming Cavitation effect Acoustic radiation pressure	Acoustic tweezers SAW-based microfluidic Molecular drug targeted delivery	Output power (<2W) mainly Frequency range 1 MHz to 200 MHz mainly Switchability in pulse and continuous signals

2.1. Fluid medium

When high-power and high-intensity ultrasonic waves act on the fluid medium (including gas, liquid, and multiphase medium), the ultrasonic cavitation effect, thermal effect, and mechanical effect will be involved in the processing of workpieces. Among them, the ultrasonic cavitation effect can cause a series of secondary effects by collapsing cavitation bubbles, which generally results in the phenomena of micro-eddy current, micro jet, shockwaves, local high temperature and high pressure [10], [26], [27], [28]. So based on these effects, the PUT has been widely utilized in many industrial fields, such as in the ultrasonic cleaning and atomization field which is mainly applied to the cleaning and sterilization of medical equipment [8], [29], anti-scaling and descaling [30], [31], [32], wastewater treatment[33], microbial inactivation[8], agricultural aerosol cultivation[34], atomization drug delivery[35], paint spraying[6], [36], spherical metal powder manufacturing[37], liquid drop levitation[38], and the cleaning of large-scale integrated circuits, optical devices, silicon chips, and other sub-micron particle products [39]. Furthermore, it has been extended to the fields of ultrasonic dust removal by agglomerating smoke particles [40], ultrasonic drying by accelerating the evaporation of water molecules [41], ultrasonic extraction by auxiliary chemical analysis [42], [43], [44], [45], and ultrasonic defoaming of industrial coatings or beverage production [6], [46]. To better serve the above ultrasonic applications based on the fluid medium, the rightmost column of Table 1 shows that the PUG should equip the functions of resonance tracking, constant power control, and multi-channel output, meanwhile the frequency range of ultrasonic signals generated by the inverter unit of PUG generally should meet 20 kHz to 200 kHz.

2.2. Solid medium

As power ultrasonic wave acts on the solid medium (including biological tissue), it causes an intense ultrasonic mechanical effect which makes the solid vibrate in a nonlinear state related to dislocations to crush, cut, bond, consolidate and plasticize the workpiece, and a comprehensive ultrasonic thermal effect which consists of the whole heating by thermal absorption, the local heating by boundary friction, and local high-temperature by cavitation bubbles collapse [47]. According to the above two effects, power ultrasonic applications have been divided into ultrasonic welding, ultrasonic consolidation, ultrasonic impact, ultrasonic-assisted vibration machining, etc. Among them, ultrasonic welding is widely used in the industry of electronic devices, lithium batteries, automotive, aerospace, and nuclear energy [48], as well as the processing of thin-film fabrics, laminated materials, and non-woven protective clothing [49], [50], [51]. Ultrasonic consolidation is a forming technology to directly connect metal materials in a layer-by-layer superimposed manner with the help of the low amplitude, high frequency and mechanical friction of ultrasonic energy. On the strength of possessing characteristics of both ultrasonic welding and laminated additive manufacturing processes, it has been better utilized in material manufacture including metal layered composite structures [52], functionally graded material structures [53], fiber-reinforced metal matrix composite materials [54], smart metal composite materials [55], and sandwich foam honeycomb structures [56], [57], [58], etc. Especially, ultrasonic-assisted machining technology mainly used in drilling [59], turning [60], milling [16], grinding [16], and impact treatment [61], [62], [63], [64] has been studied in recent decades, which can effectively solve the problems of excessive cutting force, high cutting temperature, severe tool wear, and poor surface quality, and process high-performance materials with high hardness, high brittleness, high wear resistance, and high-temperature resistance, such as titanium alloys, carbon fiber-reinforced composite materials, cobalt oxide ceramics, silicon carbide semiconductors. In addition, the PUT has continuously extended its application fields to ultrasonic surgical scalpels [14], ultrasonic vessel sealing [15], ultrasonic deicing [65], ultrasonic-assisted producing 2D nanomaterials [66], non-invasive tissue removal therapy [67], ultrasonic motors [68], [69], and ultrasonic wireless power transmission by crossing metal barriers [70], [71], [72]. Compared with the design requirements in fluid media, the rightmost column of Table 1 clearly shows that the frequency range (20 kHz < f < 70 kHz) is more concentrated. Furthermore, it also indicates that the PUG should be provided with the function of high-speed automatic dynamic tracking, matching, tuning, and keeping constant amplitude.

2.3. Microparticle medium

Surface acoustic wave (SAW) generated by piezoelectric substrate or piezoelectric film, has been utilized to realize the translation, arrangement, separation and merging of cells or particles, to complete fragmentation and mixing of droplets, and to perform synthesis and encapsulation of substances [9], [73]. Although researchers have achieved how to manipulate the microparticle medium with SAW, keeping the accuracy control of SAW still is a technical challenge. In recent years, SAW microfluidic technology has developed quickly to control the acoustic radiation force, acoustic streaming, atomization, suspension, and micro-jetting, which can meet partial requirements in the field of DNA nanoparticles encapsulation [74], acoustic tweezers for particle and fluid micromanipulation [75], preparation of nanoscale contrast agents and lipid nanotubes [76], [77]. Furthermore, sonodynamic therapy, as a new non-invasive treatment method, is widely used to process ultrasonic thrombolysis or deliver drug particles into the cell by releasing nanobubble pressure, which is activated through the effect of cavitation, fluid flow, and acoustic radiation force [78], [79], [80]. Table 1 gives a summary of the applications in the microparticle medium, the results show that the universal PUG should generate simultaneously pulsed and continuous ultrasonic signals of which the frequency range is concentrated from 1 MHz to 200 MHz. In combination with the investigation of new substrate/superstrate materials, alternate acoustic modes, such as transverse SAW or plate waves, may also offer opportunity for new innovations in PUG.

2.4. Discussion

For many biomedical applications, the ultrasonic-driven piezoelectric micro/nano-machine [81], [82] also has great potential in biosensors [83], implantable medical devices [84], and nano-level ultrasonic powered system integration [85], [86]. Although the above biomedical applications do not belong to any medium in Table 1, it is also of great research value in ultrasonic wireless power transmission and self-generating electricity because both require the resonance of transmitting sources and receiving sources to match automatically. Therefore, most of PUT applications in this article require that they work in the best resonant status. Six representative acting mediums are compared in Table 1 and discussed as follows.

• 1)For power ultrasonic applications in machining based on solid medium, the action between the tool head and the processing object is characterized by high-frequency low-amplitude impact (Usually, frequency higher than 20kHz and amplitude less than 27 μm [60]), namely a synthetical characteristic of mechanical effect, thermal effect, displacement and local shearing effect. When the system is working in the non-resonant state, a large amount of electrical energy is lost in capacitive reactive power, which can cause seriously self-heat to PT accompanied by amplitude attenuating. Especially, for power ultrasonic applications in biological tissues, such continuous operation in the non-resonant state is not allowed, it will cause serious medical accidents due to high temperature damage. Therefore, the electrical requirements of PUG in the solid medium are typically higher than in fluid medium and microparticle medium. Simultaneously, most PUT applications based on the solid or fluid medium are concentrated in the low-frequency ultrasound range. While PUT applications based on microparticle medium are mainly high-frequency ultrasound application which has high requirements for operation resolution.
• 2)It is feasible to develop high-performance universal PUGs for processing the medium of fluid, solid, and microparticles. Table 1 has shown that PUG’s electrical requirements are highly similar in the congeneric medium. Although the universal PUG can cater to the needs of most PUT applications, it does not meet the stringent requirements of individual PUT applications for a certain performance such as ultrahigh frequency, ultra-wideband, ultrafast matching. Therefore, the modular design of PUG is necessary. Just replacing the corresponding module, the performance of original modules can be upgraded and the shortage of universal ultrasonic generator will also be compensated. Simultaneously, through the substitution or reconfiguration of modules, both the power output from low power to high power and the frequency output from kHz to GHz can be achieved. The modular design of PUG will be essentially a means to balance the sub-optimal performance of universalization and the high cost of customization, which greatly saves the total cost of products, quickly locks the faulty unit, and is very friendly for later upgrade and maintenance.

3. Core devices in circuit design

The core devices determine the upper limit of PUG, such as power capacity, power loss, and frequency range. It is worth making a comprehensive summary of core devices including power electronic devices and control chips.

3.1. Power electronic device

The power electronic devices of PUG have gone through three stages: electron tube, analog transistor, and switching transistor, among which both the electron tube appeared in 1904 and the analog transistor invented by Bell Labs in 1947 have basically been eliminated due to the poor compatibility with microprocessors. As shown in Fig. 2(a), although six controllable power electronic devices are used for power and frequency conversion in power conversion circuit, the components of transistor, thyristor, GTO, and GTR are limited by switching frequency. While insulated gate bipolar transistor (IGBT) and metal-oxide semiconductor field-effect transistor (MOSFET) have been the mainstream power electronic device used in PUGs owing to their superior performances of switching frequency, power capacity, on-state voltage drop, digital control by microprocessor [88], [89], [90]. Fig. 2(a) also shows that IGBT is mainly suitable for the frequency range 20 kHz to 50 kHz, while MOSFET is better qualified for the frequency range above 20 kHz [40]. However, Fig. 2(b) shows that conventional silicon (Si)-based semiconductor devices can no longer meet the design of high-performance PUG. The performance of high-frequency, high-voltage, and high-temperature of wide band gap (WBG) semiconductors (mainly including SiC and GaN) is superior to traditional Si power devices. Under the same operating voltage, Fig. 3 (a) and (b) show that conventional Si-based semiconductors have larger specific on-resistance (R_on-sp) than SiC-based semiconductors and GaN-based semiconductors. Usually, the R_on-sp under the unipolar action dominates resistive loss in the forward conduction mode. Therefore, with the voltage increasing, Si-based semiconductors have larger on-state power loss than SiC-based semiconductors and GaN-based semiconductors. Fig. 3 (d) indicates that Si-based semiconductors have larger switching loss with increasing frequency than SiC-based semiconductors, which will lead to a decrease in conversion efficiency. Thus, WBG semiconductor devices have emerged in PUG in recent years, which are more suitable for the design of high-performance PUG than conventional Si-based semiconductor devices. In particular, Fig. 2(b) shows that SiC devices are more suitable for high-power applications based on vertical devices (due to their excellent properties of high-voltage and high-temperature), while GaN high electron mobility transistors (HEMTs) are more efficient for high-frequency applications based on lateral transistors. Overall, WBG semiconductor devices are superior to conventional Si counterparts in terms of their higher blocking voltage, higher operating temperature, higher switching frequency, and lower total power loss [91], [92], [93], [94], [95].

Fig. 2.

(a) Different types of controllable power electronic devices. (b) Graphical comparison of relevant physical and electronic properties of Si, SiC and GaN and their benefits in devices applications [87].

Fig. 3.

(a) Specific on-resistance (R_on-sp) versus breakdown voltage (V_b) for SiC MOSFETs (blue symbols) and GaN HEMTs (red symbols) [96]. (b) Comparison of the unipolar limit of R_on-sp versus blocking voltage for some device types in Si and SiC [97]. (c) Comparison of full SiC and mixed Si/SiC inverter efficiency as a function of output load at a representative heatsink temperature of 65℃ and the value of the switching frequency 32 kHz [98]. (d) Efficiency of SiC and Si wind turbine converters at full power rating and different switching frequencies [99].

Recent researches show that SiC MOSFET is a candidate for substituting Si IGBT devices [100]. Fig. 3(c) shows that SiC MOSFET’s efficiency is higher than Si IGBT under the condition of output power lower than 3000 W. Fig. 3 (a) and (b) show that when the breakdown voltage below 1000 V, GaN MOSFETs will be more competitive over their SiC devices, while when the breakdown voltage higher than 1000 V, SiC devices are recognized as the best choice. Therefore, GaN MOSFETs can provide a high breakdown voltage and simultaneously possess a lower specific on-resistance and a higher switching frequency with respect to both Si and SiC counterparts. Generally, they can be better to be used for on-board converters and ultrasonic generators [101].

Although WBG devices have many advantages over Si devices, the drift region of the WBG power device is usually narrower than that of the corresponding Si device with the same rated power, which allows WBG devices to possess smaller junction capacitance, gate resistance, and switching time constant [102]. However, during switching transients under high dv/dt, high di/dt, and high operating frequency conditions, the parasitic inductance of WBG devices tends to trigger voltage and current overshoots, high-frequency ringing noise, and electromagnetic interference (EMI) problems, which have a significant impact on reliably generating high-precision and high-resolution high-frequency ultrasonic signals [103]. The technologies solving the above problems mainly include active gate drive technology, modulation technology, damping technology, passive technology [91], [104], etc. The solution paths usually start with hardware design (including circuit topology, ground connection, PCB board layout, and component characteristics) or control techniques such as slowing down switch speed and optimizing switching processes.

For WBG devices performance, the main interest focuses on how to improve packaging technology. Due to their high sensitivity to parasitic inductance, even low inductance is easy to lead to high voltage overshoot, ringing noise, and EMI, causing dynamic characteristic deviation. Therefore, the parasitic inductance in the current commutation loop (CCL) should be minimized. Fig. 4 (a) shows the internal distribution and equivalent diagram of the parasitic inductance of the SiC MOSFET package. Fig. 4 (b) shows the high-frequency CCL at the switching transient of the SiC device in the double pulse test circuit. The CCL’s total inductance value of practical circuits should be as small as possible. Fig. 4 (c) indicates that the additional parasitic inductance of SiC MOSFET can change the switching waveforms (represented by the green line), which is one of the main reasons affecting the switching accuracy and resolution. Therefore, reducing parasitic inductance has been a significant subject in device and power module packaging in recent years. Several packaging technologies (such as 2.5D or 3D packaging) have been employed in practical production to decrease the parasitic inductance of WBG devices [104].

Fig. 4.

(a) Packaging parasitic inductances about the internal distribution of SiC MOSFET and equivalent diagram. (b) High-frequency CCL of SiC device in double pulse test circuit (indicated by the red line). (c) Switching waveforms of switching transients of SiC MOSFET considering parasitic parameter [103].

3.2. Control chip

As shown in Fig. 5, the control chip will perform numerical and logical operations on the feedback signals including u, i, f, F, and T, and monitor the running status of the PT load in real-time. If the chip’s calculation results show that the PT’s output power fluctuates, the switching power supply module will be adjusted through PWM1. Simultaneously, if the calculation results show that the PT’s resonant frequency drifts, the inverter module will be regulated through PWM2 to track the new resonant point, and the impedance values of matching modules will be changed for impedance matching correspondingly. Therefore, the performance of digital processing and calculating of control chips plays a decisive role in PUG’s overall dynamic response. Early analog chips are no longer suitable for PUG. While digital chips have significantly strengthened the stability and reliability of PUG with the advantages of fewer components, simplified hardware circuit structure, and powerful data-handling capacity. Moreover, multiple control strategies and software programs make them easy to simultaneously achieve real-time online collection, storage, analysis, and automatic diagnosis of operating data. Generally, the microcontroller unit (MCU), digital signal processor (DSP), or field programmable gate array (FPGA) is used to realize powerful pulse width modulation (PWM) generation and perform the power and frequency control algorithm. Table 2 shows the above three mainstream digital chips used in PUG, which are as follows.

• 1)Although the 8-bit or 16-bit MCU chips have been applied for ultrasonic power supplies for many years, they do not have the computing performance required for automatic frequency tracking such as lower working frequency and processing speed, so they have been gradually replaced by 32-bit MCU chips. As the representative of 32-bit MCU chips, the STM32 series is created by STMicroelectronics which is widely applied in PUG due to supporting various mainstream operating systems, low power consumption, and good control capability.
• 2)Compared with MCU chips, DSP chips such as the TMS320 series produced by Texas Instruments have a higher CPU operating speed and excellent algorithm processing [20], [105]. Table 2 illustrates that powerful PWM algorithms can be built into DSP chips to implement power and frequency regulation. But DSP chips also have some disadvantages such as high-frequency clocks interference and sampling delay.
• 3)FPGA chip belongs to a highly flexible reconfigurable semi-custom circuit which contains programmable modules such as logic block, I/O module and interconnection module, so its internal logic function can be arbitrarily set based on demands [15]. Simultaneously, the FPGA chip is a type of Ai chips due to its fine compatibility with artificial intelligence, which experts in parallel processing and peripheral control circuits processing. Based on the above advantages of FPGA, it has been widely used as the main chip of dc-ac converters in recent years. Compared with MCU and DSP integrated circuits, FPGA has the advantage of flexibility when changes occur, and the capacities of its integrating digital hardware with high-speed and parallel processing functions make it can shorten the execution time of inverter control algorithm. Therefore, the applications of FPGA control chips are becoming increasingly widespread.

Fig. 5.

Feedback input and PWM control output of chips.

Table 2.

Mainstream digital chips for ultrasonic generator.

Type	Representative	Characteristics
MCU	STM32 series	High integration, lower cost; Fast processing speed; Supporting operating systems.
DSP	TMS320series	Built-in strong PWM algorithm; High stability, high cost and high-precision; Focus on core algorithm processing; Especially suitable for arithmetic-intensive.
FPGA	Virtex series	Semi-custom circuit; High efficiency high cost and high flexibility; Peripheral control circuits processing; Ai chip and expert in parallel processing; Especially suitable for control-intensive and communication-intensive tasks.

Based on the above three control chips, various ultrasonic generators are developed by corresponding companies. The PUG based on DSP chips has a strong advantage in data processing of feedback signals and high-precision control algorithm processing. But in terms of the control speed of peripheral circuits, it is inferior to FPGA chips. Furthermore, it is worth investigating how to combine the direct digital synthesizer (DDS) chip with the above three main control chips for better realizing the high-precision phase-controlled output of sine wave or square wave, and overcoming the shortcomings of single control chip. Therefore, J.-D. Wang et al. [106], [107] adopted the strategy of joining the MCU chip and DDS chip in the ultrasonic drive and control system to achieve higher tracking accuracy and faster tracking speed than traditional methods. J. Zheng et al. [108] proposed a circuit board design scheme based on the MCU and DDS chip to generate multi-channel high-precision phase-shifted sine waves and planned to replace the master MCU with an FPGA chip to achieve improvement in future work.

3.3. Discussion

Fig. 6 (a) shows that the GaN IGBT can be selected in circuit design of huge power with frequency lower than 100 kHz, which will avoid the insufficient switching frequency of Si or SiC IGBT and make full use of the advantage of IGBT’s large power capacity simultaneously. In addition, Fig. 6 (a) also indicates that SiC MOSFET prefers to be applied in the medium and low power or frequency field, while GaN MOSFET is more suitable for high frequency and low power field. It is well known that PUG’s speed of voltage adjustment, current regulation, and frequency conversion is not only restricted by power semiconductor devices but also controlled by main control chips. Fig. 6 (b) shows that FPGA and DSP have their own advantages in terms of control precision and control speed, but the high cost limits their large-scale application. While MCU chip has great advantages in cost and basically meets most HPU applications, but the mediocre performance also hinders its further expansion. Therefore, in order to give full play to the superiority of each chip and avoid its shortages, the study of joint chip schemes has been gradually emerging.

Fig. 6.

Selection recommendation of core devices in PUG’s circuit design.

4. Main circuit module design

The main circuit modules of PUG convert low-frequency ac sinusoidal signals into ultrasonic frequency ac signals by combining power electronic technology with modern intelligent control technology, then the matching circuit module filters the ultrasonic signals into proximate ideal sinusoidal signals which excite PTs to output the ultrasonic frequency vibrations and work in near pure resistance state [109], [110].

Based on the integration level of power electronic devices, three levels of PUG’s main circuit design mode have been presented in Fig. 7, which are discrete device level, power module level, and device system level, corresponding to Fig. 7 (a), Fig. 7 (b), and Fig. 7 (c), respectively. PUG based on the discrete device in Fig. 7 (a) generally has ten common topological connection modes, which possess the advantages of stronger integrity, more compactness, lower cost, and high conversion efficiency. While its shortcomings usually include a long development cycle, strong specificity, poor scalability, and difficulty in hardware upgrade and fault maintenance in the later stage. For PUG based on the device system, the signal generator, power amplifier, and filter are generally jointed to generate the required power ultrasonic signal. The advantages of PUG in Fig. 7 (c) mainly include the shortest development cycle and plentiful waveform types, which brings great superiority to set the ultrasonic waveform for customers, especially scientific researchers. But its limitations (such as bulky body, high costs, and poor electrical efficiency) indicate that it is not suitable for large-scale industrial applications [67], [111], [112]. As shown in Fig. 7 (b), PUG based on the power module is essentially a semi-custom development mode, which allows developers to devote more energy to control systems. The main advantages of this design include short development time, strong reconfigurability and scalability, and being very friendly to later upgrades and maintenance.

Fig. 7.

Three levels of PUG’s main circuit design based on the integration level of power electronic devices. (a) Discrete device level. (b) Power module level. (c) Device system level.

In summary, the main circuit design based on power module (mainly including the switching power supply module, inverter module, and impedance matching module) has multiple advantages compared with the design modes of traditional discrete device level and device system level. Therefore, section IV will expand based on the power module.

4.1. Switching power supply module

The switching power supply module focuses on the ac-dc converter and dc-dc converter, which can achieve power factor correction and power adjustment. There are six typical topologies in switching power supply module which include the buck topology, boost topology, flyback topology, push–pull topology, half-bridge topology, and full-bridge topology. Among them, the buck or boost converter does not include the high-frequency transformer, which is superior to the transformer-based structures in terms of efficiency, small size and power density, but additional care must be taken for the leakage current issue [113], [114]. In contrast, the latter four are isolated converters with transformer-based structures, which make them convenient to achieve the transformation of step-up, step-down, and polarity. However, these topologies do not have the PFC module and soft switching topologies, which cause poor power factor and low efficiency. Therefore, soft-switching topologies and PFC topologies emerged and have been widely applied in switching power supply modules, which can significantly improve the switching loss, achieve high-frequency operation, and decrease the total harmonic distortion (THD) [115]. Especially, soft-switching mechanisms of the topologies, including zero voltage switching (ZVS) and zero current switching (ZCS), are identified as one of the performance benchmarks. The ZVS turn-on and ZCS turn-off are true soft-switching commutations, which can fully eliminate the switching loss. ZVS is more applicable with MOSFET and ZCS is desirable with minority-carrier devices for high-power applications [116]. There are mainly four soft-switching technologies based on the resonant circuit, active buffer, and switching control strategy, including zero voltage transition (ZVT), zero current transition (ZCT), triangular current mode (TCM), and critical conduction mode (CRM), which have been applied in switching power supply modules.

4.1.1. dc-dc converter

As shown in Fig. 8, two practical micro-power ultrasonic power driving systems for handheld acoustic devices were developed, one board (a) is designed to drive a 1–25 MHz thickness mode (TM) transducer in a handheld, battery-powered nebulizer, another board (b) for enhancing the capacity of a rechargeable lithium metal battery which is designed to drive a 30–100 MHz SAW transducer. Their power management unit uses the boost converter to step-up voltages from input to output, while the buck converter to step-down voltages [5]. Therefore, the dc-dc converter of switching power supply module includes boost converter and buck converter.

Fig. 8.

Diagrams of the driving circuits. (a) TM board. (b) SAW board [5].

4.1.1.1. Boost converter

The drawbacks of the conventional boost converter are high switching loss and electromagnetic interference issues during the reverse recovery process of the boost diode. ZCT, TCM, CRM, and ZVT have been applied to improve the above issues in boost converters. ZCT boost converters are more suitable for minority-carrier semiconductor devices, especially IGBTs in high-power applications [117]. Although TCM and CRM possess the natural ZVS by modulating the current of their boost inductor, they have the shortcoming of high current ripple that will increase the conduction loss [118], [119]. Thus, the first three soft-switching technologies are less preferable for low-power battery-powered modules, whereas the ZVT boost converter has the advantages of wide voltage input and excellent high-frequency switching. As shown in Fig. 9, although the auxiliary circuit loss of the boost converter with active clamping is normally higher than the ZVT boost converter, they have higher efficiency, higher PF and higher switching frequency in a wide power range and are better suitable to the medium and low-power of battery-powered module [120], [121], [122].

Fig. 9.

Circuit scheme of a ZVT boost converter with active clamping [123].

4.1.1.2. Buck converter

Compared with the classic buck converter (Fig. 10a), the synchronous buck converter (Fig. 10b) uses a controllable power semiconductor switch S₂ (mainly MOSFET) instead of freewheeling diode VD₁ to avoid the diode reverse recovery power loss, so synchronous buck converter is fully superior of the classic buck converter in terms of voltage ratio and conversion efficiency. Generally, the voltage ratio of buck converters has a great restriction on the sensitivity of voltage regulation. Fig. 11 shows that the modified interleaved buck converter with an extended duty cycle is particularly suitable for high conversion ratio while gaining interleaving advantage (e. g. output current ripple, efficiency, reliability).

Fig. 10.

Topologies of buck converter. (a) Classic buck converter. (b) Synchronous buck converter.

Fig. 11.

Comparison of the voltage ratio [124].

4.1.2. ac-dc converter

The classic ac-dc converters are divided into the flyback ac-dc converter, push–pull ac-dc converter, half-bridge ac-dc converter, and full-bridge ac-dc converter. Practically, these typical single-stage isolated ac-dc converters are rarely used in practical circuits due to lack of PFC function. Therefore, it is necessary to add the stage of PFC module in typical ac-dc converters to obtain high-power factor. Fig. 12(a) shows a single-stage PFC structure that only uses one conversion unit to realize PFC and dc output regulation, so this structure is mainstream in single-stage PFC ac-dc converters due to its high-power factor, high efficiency, simple structure, and lowest cost. Another single-stage PFC converter is the quasi single- stage PFC converter, its controller shares common switches between the PFC module and dc-dc converter, which can simplify the control complexity, save the number of switching elements, and maintain similar characteristics with two-stage converter, but for most single-stage PFC converters, their maximum output power is less than 1000 W. Fig. 12(b) shows a traditional two-stage ac-dc converter with a PFC module, although it has high-power factor, high power capacity, and low supply current harmonics, its power efficiency is lower than single-stage PFC structure due to the two-stage power processing design, so two-stage ac-dc converter mainly applied in high power applications. Overall, compared with traditional two-stage power supplies, the single-stage configuration reduces the cost and size, simplifies the design, and improves the efficiency through the integration of PWM controller and switching semiconductor, it is suitable for LED lamp drivers, piezoelectric element drivers, and other adapters. In addition, the rectifier bridge has a certain influence on power efficiency for each ac-dc converter, especially in micro-power applications. Therefore, the detailed topologies of rectifier bridges and four ac-dc converters are as follows.

Fig. 12.

Structure diagram of ac-dc converter. (a) Single-stage. (b) Two-stage.

4.1.2.1. Rectifier bridge

Fig. 13 illustrates six passive rectifiers and two active rectifiers. Among them, the rectifier based on the junction diode in Fig. 13(a) is the most commonly used in PUG field, but it is not a feasible scheme in low-voltage and low-power biomedical applications, such as implantable medical devices (power range mainly: few microwatts - tens of watts) charged with ultrasonic energy transfer (UET) or inductive power transfer (IPT). Therefore, five modified passive rectifiers based on MOSFETs in Fig. 13(b)-(f) emerged for optimizing the conversion efficiency of the diode rectifier bridge. Although the power efficiency is improved by controllable MOSFETs in modified passive rectifiers, their efficiencies are more sensitive to the MOSFET threshold voltage (V_th). Furthermore, these configurations have one potential drawback which can result in a large leakage current when the effective V_th of the MOSFET becomes very small or even negative due to the excessive dc bias voltage. Compared with passive rectifiers, active rectifiers can further decrease the conduction losses of the pass transistors operating as switches in the deep triode region. Fig. 13(g) shows a typical active rectifier with cross-coupled PMOS switches, its overall power consumption is very low and independent of the MOSFET drain current, which results in its excellent power efficiency at high output power. However, new challenges appeared when implantable medical devices powered by IPT or UET at a high operating frequency. Synchronous rectifiers based on self-driven eGaN MOSFETs shown in Fig. 13(h) will be an optimal scheme for these applications due to their high switching speeds, low on-state resistance, and specifically low total gate charge. Typically, most ac-dc converters still adopt the rectifier based on the junction diode when switching power supply module powered by municipal power supply.

Fig. 13.

Rectifier topologies of ac-dc converter [125]. (a) Junction diode-based passive rectifier. (b) Diode-connected MOS passive rectifier. (c) Gate-cross coupled passive rectifier. (d) Differential fully gate-cross coupled passive rectifier. (e) External-V_th cancelation passive rectifier. (f) Self-V_th cancelation passive rectifier. (g) Active rectifier with cross-coupled PMOS switches. (h) Synchronous rectifier using self-driven eGaN MOSFETs.

4.1.2.2. Flyback ac-dc converter

Single-stage PFC flyback topology is widely used in small power PUG due to its simple structure and high-power factor. Generally, the PFC boost stage and the dc-dc flyback stage are integrated for single-stage converters. The PFC boost stage operates in discontinuous conduction mode (DCM), while the dc-dc flyback stage operates in the boundary of DCM/continuous conduction mode (CCM), this can improve efficiency by using the leakage energy of high-frequency transformer or using soft-switching technology [126]. It is worth noting that compared with the flyback converter operated at a fixed frequency, the quasi-resonant single-stage PFC flyback operated at a variable frequency has an enhanced transient response in DCM operation which possesses smaller EMI filters and lower switch loss. However, the leakage inductance in the flyback converter will cause high voltage spikes in the power switch as power loss. Therefore, the resistance capacitor diode (RCD) buffer circuit and active clamp circuit can be used to suppress these voltage spikes, but they will reduce efficiency. Fig. 14 shows a quasi-resonant flyback converter that uses a split resonant capacitor to solve this problem [127].

Fig. 14.

Structure diagram of a quasi-resonant flyback [128].

4.1.2.3. Push–pull ac-dc converter

Push-pull converter is mainly used for high-power dc-dc converters with the low input voltage, such as high-power PUG, photovoltaic, and battery-powered systems. Its current-fed push–pull (CPP) topologies can provide high voltage conversion ratios, due to the effects of the active boost and passive voltage gain of high-frequency isolation transformers in low-voltage and high-current applications. Therefore, CPP converter has better transformer utilization than single-ended topologies (such as the flyback or forward converter), and fewer power switches than full-bridge converter. Typically, CPP topologies are mainly divided into single inductor and dual inductor, the dual inductor CPP is obtained by applying the duality principle to the voltage-fed half-bridge converter [129]. Compared with the switches in single inductor CPP, the switches of S₁ and S₂ (in Fig. 15) used in dual inductor CPP only need to withstand half voltage of the single inductor CPP. Because this switch can reduce the voltage and the isolation required by the transformer is smaller, its complexity is further reduced. A new topology of bi-directional CPP converter working in CCM was proposed in [130], [131], which realized full soft switching operation at a fixed switching frequency through control algorithms. It also explained the soft switching operation of single inductor and dual inductor push–pull converters.

Fig. 15.

Schematic of the dual inductor CPP topology [129].

4.1.2.4. Half-bridge ac-dc converter

The advantages of the half-bridge topology are well known, including high power factor due to low distortion in the source current and isolation between input and output, As shown in Fig. 16(a), a single-stage PFC module with half-bridge topology was proposed, in which the inductor work in DCM, this topology has high power factor and its output power higher than 1000 W [132]. Compared with the single-stage PFC module, the soft-switching characteristics of quasi single-stage PFC converter based on LLC resonant topology in Fig. 16(b) are not affected by the boost stage. Moreover, it can achieve high power factor, low THD, and high efficiency in the whole input voltage range. Therefore, half-bridge topology has incomparable advantages in switching power supplies when the output power is between 300 W and 1000 W.

Fig. 16.

(a) Single-stage PFC module with half-bridge topology [132]. (b) Quasi single-stage ac-dc converter with half-bridge LLC resonant converter [133].

4.1.2.5. Full-bridge ac-dc converter

As shown in Fig. 17, the improved single-stage PFC converter based on full bridge phase shift controller is applied in a wide range of voltage output without low-frequency voltage ripple, it has good power factor, conversion characteristics, and efficiency, so this topology can be used as a potential of high-power single-stage converter. Typically, the high-power PUG will integrate ac-dc boost input converters with dc-dc full-bridge converters. The modified single-stage full-bridge converter with two controllers is a better choice to achieve the best features of the two-stage and single-stage converter [134]. Namely, its performance is close to the two-stage converter, while its cost is close to the single-stage converter. But adding an additional controller will increase the cost, and complexity to some extent.

Fig. 17.

Single stage converter with full bridge ac-dc converter [135].

4.2. Inverter module

The inverter module of PUG acts as a dc-ac converter to modulate the input direct current into ultrasonic frequency (f ≥ 20 kHz) ac signals, which drive PT to generate ultrasonic vibration [136]. It is well known that the smooth dc link input voltage of inverter module is generally obtained through a diode bridge rectifier with large capacity capacitors. However, the inverting process will cause inevitably generate the narrow pulse input current in the front stage rectifier circuit powered by ac line voltage sources, which can result in serious THD and low power factor. Therefore, it is desirable to add PFC modules such as boost converter, buck-boost converter, and flyback converter working in DCM mode to improve the power factor. In addition, the problem of reduced efficiency and reliability due to increased PFC module can be solved by integrating the PFC stage into the resonant inverter stage [137].

4.2.1. Power amplifier

As shown in Fig. 18, the integration of the flyback converter and Class E resonant inverter is a better scheme that has high efficiency and high-power factor, because the dc link voltage in this single switch high power factor resonant inverter can be effectively reduced by selecting the appropriate transformer turns ratio. Moreover, Fig. 18 (b) shows a single switch resonant inverter which has higher efficiency than two-stage resonant inverter shown in Fig. 18 (a). In addition, the topology of Class D power amplifier, which has gradually occupied the low-frequency field due to its high efficiency, is also widely used in small power ultrasonic signal generators. However, the maximum signal swing amplitude in the above two is not higher than the power supply voltage, so it cannot effectively drive the PT under limited battery voltage [138].

Fig. 18.

(a) Two-stage resonant inverter for driving PCT. (b) Proposed single switch resonant inverter [139].

4.2.2. Multilevel inverter

As one of the most attractive solutions for implementing medium voltage/high voltage high-power converters, the multilevel inverter (MLI) [67] is configured by a unique arrangement of single/multiple dc power supply panels and semiconductor devices to generate low distortion near sinusoidal voltage, high-quality waveforms with low harmonic content and low dv/dt stress, which significantly reduces THD, and the voltage stress on the switch is far lower than the output voltage. There are two types of cascaded-transformer multilevel inverter (CTMLI) including conventional CTMLI (Fig. 19a) and low component merged cells CTMLI (Fig. 19b) can eliminate the needs for numerous numbers of dc sources and floating capacitors while suffering the cost of required transformers. The topology in Fig. 19(b) has more advantage than conventional CTMLI due to merging two cells to save almost half of switch count. Moreover, some MLIs also have further strategic advantages, namely transformer-free operation, capacitor-free, modularity, voltage and current scalability, high redundancy of switching states, and fault-tolerant operation, but these advantages are accompanied by the cost of a large number of passive and active components, such as the dc power supply, flying capacitor, inductor, diode, and switch. Therefore, the volume, cost, and complexity of multilevel inverter increase [140].

Fig. 19.

Cascaded-transformer multilevel inverter (CTMLI) [141]. (a) The conventional CTMLI. (b) Low component merged cells CTMLI.

4.2.3. Bridge inverter

Fig. 20 illustrates a topology of current-fed full-bridge inverter for driving high-power PT loads. Generally, the high-power and high-frequency switching inverter only operate reliably under the condition of meeting the ZVS requirements which will be beneficial to reduce the serious problem of inverter fault caused by ringing. Therefore, various PWM technologies emerged to realize the ZVS function. Among them, sine pulse width modulation (SPWM) technology has obvious advantages which can adjust the output voltage amplitude and frequency of the dc-ac inverter to obtain the desired value. In this case, the power converter switch is set to the on or off state according to the comparison results between the high-frequency constant amplitude triangle wave (carrier wave) and two low-frequency reference sine waves with adjustable amplitude and/or frequency. Another advantage of SPWM is that increasing the switching frequency of triangular wave will reduce the size and cost of the inverter output filter, so this technology is suitable to support the high switching frequency requirements of modern single-phase dc-ac power converters [142]. To increase the output power of PUG, the full-bridge inverter consisting of SiC MOSFETs and grid drive circuits with negative turn-off voltage is designed for ZVS operation when the load impedance is highly variable [143].

Fig. 20.

Topology of current-fed full-bridge inverter with the PT [146].

For pulsed PUGs, it is a better scheme to generate the wide pulse and narrow pulse in one generator. Simultaneously, to ensure high power factor and high efficiency, the phase-shifting full-bridge converter with LC resonant network and transformer emerged which possesses a simple circuit structure and high conversion efficiency, but its control is a bit complex [144]. Compared with the active PFC, passive solutions also have attractive advantages, including reliability, low cost, robust performance, and relatively less EMI generation. Examples of these solutions such as LC filters, and valley-filling circuits. [145] used inductors and parallel resonant cells as single-stage PFC which allows the efficiency to be significantly improved. It can be applied in a variety of applications, such as plasma power generation and any other capacitive load.

4.3. Impedance matching module

Impedance matching module is indispensable in PUG no matter whether the PT load is stable or time-varying, which can compensate for the parameters of PT’s equivalent circuit model. Under optimal operating state, this module allows PTs to work in a pure resistance state in which sinusoidal ultrasonic waves will be generated. Therefore, this section explores the load characteristic of piezoelectric transducers, impedance matching mechanism, and matching circuit topology for obtaining the optimal operating states.

4.3.1. PT’s equivalent circuit

In power ultrasonic applications, the inverse piezoelectric effect of PT generally is employed to convert the high-frequency electrical signal provided by PUG into high-frequency mechanical vibration. But PT has obvious nonlinear effects, such as frequency drift, hysteresis, and modal interaction, while its modal interaction may appear as one or more modal responses at frequencies other than the operating frequency. These nonlinear effects mostly cause losses within the piezoelectric material, namely, dielectric loss, elastic loss, and piezoelectric loss [26], [147]. To explore the mechanism of the above nonlinear effects， there are three PT’s equivalent circuits including the Mason model, KLM model, and BVD model, which can be selected depending on the practical situation [148], [149], [150], [151], [152]. Compared with the KLM model and Mason model, the BVD model has a significant advantage that does not require physical parameters, making it easy to implement centralized components after obtaining impedance and admittance. Fig. 21 illustrates an MHz-level plate PT and a kHz-level bolt-clamped Langevin transducer (BLT), respectively. MHz-level plate PTs generally are used to generate low-intensity ultrasonic with the frequency higher than 1 MHz, while BLT designed by Langevin in 1920 is typically utilized to generate high-intensity ultrasonic vibration of 20 to 100 kHz. Although differing in structure and function, they have the same vibration mode, namely thickness mode. Therefore, the PT’s impedance analysis only needs to be based on one equivalent model, typically based on the BVD equivalent model due to its stronger adaptability. Fig. 22 (b) illustrates a PT’s BVD model which possesses an electric branch composed of C₀ and R₀, and a mechanical branch composed of R₁, L₁, and C₁. The parameter value of an electric branch usually is constant once the PT is manufactured, while the electrical parameters of the mechanical branch change usually with the fluctuation of PT’s vibration state [153], [154]. Fig. 22 (c) and (d) show the BVD equivalent circuit of a single-resonance, and multi-resonance respectively [155], [156].

Fig. 21.

The schematic diagram of PT. (a)MHz-level plate PT. (b) kHz-level BLT [157].

Fig. 22.

(a) Electrical symbols of PT. (b) BVD model of PT. (c) the simplified equivalent circuit of a single-resonance BVD. (d) the simplified equivalent circuit of a multi-resonance.

4.3.2. Impedance matching mechanism

The analysis based on the simplified Butterworth-Van Dyke (SBVD) equivalent circuit model is the most common in power ultrasonic transducers [158]. The mechanical branch is a typical RLC series resonance circuit, and its expression formulas of admittance and impedance have been shown in Table 3. According to the impedance expression, two resonant frequencies have been identified in PT’s BVD equivalent circuit. One is mechanical series resonance frequency f_s which can be obtained when series resonance occurs in the mechanical branch, the other is mechanical parallel resonance frequency f_p which is the natural resonance frequency determined by the interaction of the mechanical branch and the electric branch [159]. The most important fact is that the value of C₁ is generally much smaller than C₀, so it is unambiguous that f_p is slightly larger than f_s from the expression formulas in Table 3. Typically, PT is suitable for operating at the mechanical series resonance point due to there being maximum admittance. Meanwhile, the expression formula of the quality factor Q_m of the mechanical branch is shown in Table 3 [160]. Generally, the value of Q_m attenuates as the R₁ increases with the load, and it is easy to cause resonance frequency drift and affect the stability of output power.

Table 3.

Expression formula of PT’s equivalent circuit.

Items	Expression formula
Admittance of the SBVD model	$Y_T=G+jB={j\omega C}_0+\frac{1}{{R_1+j\omega L}_1+\frac{1}{{j\omega C}_1}}$
Impedance of the SBVD model	$Z_T=\frac{1}{\omega C_0}\left(\frac{\left({\omega }_s^2-{\omega }^2\right)+j\omega \frac{R_1}{L_1}}{-\omega \frac{R_1}{L_1}+j\left({\omega }_p^2-{\omega }^2\right)}\right)$
Quality factor of the mechanical branch	$Q_m=\frac{\sqrt{L_1/C_1}}{R_1}$
Admittance circle of BVD model	${\left(G-\frac{1}{2R_1}-\frac{1}{R_0}\right)}^2+{\left(B-\omega C_0\right)}^2={\left(\frac{1}{2R_1}\right)}^2$
Admittance circle of SBVD model	${\left(G-\frac{1}{2R_1}\right)}^2+{\left(B-\omega C_0\right)}^2={\left(\frac{1}{2R_1}\right)}^2$
Notes	${\omega }_s=\frac{1}{\sqrt{L_1{C}_1}}$, ${\omega }_p=\frac{1}{\sqrt{L_1{C}_p}}$,$C_p=\frac{C_0{C}_1}{C_1+C_0}$, $f_p=\frac{1}{2\pi \sqrt{L_1{C}_p}}$

When series resonance occurs in the mechanical branch, as shown in Fig. 23 (a) and (d), a resonance circuit and an admittance circle O will be obtained in which six characteristic frequencies can be extracted including f_n corresponding to the maximum impedance frequency, f_p corresponding to the parallel resonance frequency, f_a corresponding to the system anti-resonance frequency, f_m corresponding to the maximum admittance, f_s corresponding to the series resonance frequency, f_r corresponding to the resonance frequency of the entire system. The optimal operating state of PUG system can be achieved once the frequency keeping $f_m=f_s=f_r$ or $f_n={f_p=f}_a$ [161]. Since the resistance R₀ is too large to consider its influence, the SBVD model at the frequency f_s and its corresponding admittance circle O₁ have shown in Fig. 23 (b) and (e), respectively. It can be found immediately that the impedance value of the whole system is not the minimum. To reach the optimal state, a pure resistance equivalent circuit obtained by impedance matching has been shown in Fig. 23 (c), and its corresponding admittance circle O₂ is shown in Fig. 23 (e), which is equivalent to the downward translation $\omega C_0$ of the admittance circle O₁. Then the condition of $f_{m2}=f_{s2}=f_{r2}$ will be achieved where the voltage and current also remain in the same phase.

Fig. 23.

(a) BVD model at frequency f_s. (b) SBVD model at frequency f_s. (c) Impedance matched BVD model at frequency f_s. (d) Admittance circle of BVD model at frequency f_s. (e) Admittance circle of BVD model at frequency f_s after simplified and matched.

4.3.3. Matching circuit topology

The matching circuit of PUG determines whether the PT operates normally and efficiently based on its essential functions of tuning, changing resistance, and filtering. The tuning function compensates the PT’s equivalent impedance for making it appear a pure resistance and improving the output efficiency of the inverter by eliminating reactive power loss. And the changing resistance function mainly transforms the PT’s equivalent resistance to the inverter side by a high-frequency transformer for increasing the output power so that the designed power can be output under a certain bus voltage. Furthermore, the high-order harmonics generated by the inverter are eliminated through the coupling resonance of matching circuit which ensures that the electrical signal acted on PT keeps a fine sinusoidal waveform, and ultimately obtains a pure PT’s vibration mode.

As shown in Fig. 24, four common matching topologies for PT are generally suitable for the situation of fixed-out frequency [162], [163], [164]. Among them, the superiority of series L-type matching topology (Fig. 24a) is convenient for calculating the required impedance matching value, but this topology has its inherent disadvantage in that it is typically only used on the occasion where PT’s working frequency is stable. Fig. 24 (b) and (c) illustrate the LC-type matching which is more suitable for PT with the large impedance as it further decreases the impedance of the system. Especially, the required value of the series matching inductance under the condition of the same coupling resonance frequency will be decreased. The network T-type matching topology (Fig. 24d) possesses the function of changing resistance and tuning simultaneously, which can easier achieve resonance by adjusting three matching parameters L_t1, L_t2, and C_t. On most occasions, especially under no-load or constant load conditions, these models obtain a better impedance matching between the output end of the inverter and the input end of the transducer. However, although the above static matching networks with fixed impedance values can improve the PT’s working state for pursuing the ideal sinusoidal vibration stage, they do not consider the influence of the fluctuation of ultrasonic vibration loads in the design stage which results in them unable to handle resonant drift. Therefore, the dynamic matching circuit adopting adjustable precision inductance or capacitance was proposed to adapt the situation of variable PT’s parameters by adjusting the inductance or capacitance parameters automatically or manually.

Fig. 24.

Topology of matching circuits. (a) Series L-type matching. (b) Series-parallel LC-type matching. (c) Parallel LC-type matching. (d) Network T-type matching.

4.4. Discussion

The mainstream modular PUG for high-power applications is mainly composed of the full-bridge switch power supply module, full-bridge inverter module, and T-type impedance matching network. Generally, almost all ultrasonic generators require high conversion efficiency and high-power factor, so it is necessary to utilize soft-switching topologies and PFC topologies in PUG’s modular design [165]. Fig. 25 (a) preliminarily demonstrates the power flow direction of modules, the power distribution of sub-modules, and the applicable power level distribution. Fig. 25 (b) further shows the integration relationship between modules based on the principle of power level matching principle. Fig. 25 (c) shows a practical PUG designed for an ultrasonic vessel sealing and dissecting system which is composed of the Buck converter, H-bridge inverter, and FPGA chip. According to the power level distribution in Fig. 25, further discussion is as follows.

• 1)Micropower – such applications are mainly powered by batteries, such as biomedical implantable devices, intelligent wearable devices, handheld acoustofluidics, and acoustic tweeters, which require the highest conversion efficiency and device miniaturization. Their input voltage is mainly between 1.5 V and 12 V, and the output power is typically less than 10 W. Therefore, the switching power supply module generally uses a boost converter, while the inverter module uses the topologies such as Class D, Class E, and half-bridge. For devices powered by high voltage and large capacity batteries, the switching power supply module can choose the buck converter due to its advantages of the wide voltage input range and high efficiency.
• 2)Low power –such applications are mostly household or small medical equipment, such as ultrasonic atomizing humidifiers, ultrasonic cleaning machines, ultrasonic aerosol drug delivery, ultrasonic sterilization equipment, ultrasonic motor, ultrasonic assisted micro hole drilling, etc. Generally, they are powered by the municipal single-phase power supply, and their output power is usually less than 300 W. For low power PUG, the switching power supply module generally chooses the quasi single-stage PFC flyback converter or half-bridge converter, while the inverter module uses the Class E topology or half-bridge converter.
• 3)Medium power – most of these applications belong to large-scale application scenarios, such as agricultural aerosol cultivation, industrial parts cleaning, ultrasonic assisted grinding, ultrasonic plastic welding, ultrasonic impact strengthening, and ultrasonic deicing. They are also basically powered by the municipal single-phase power supply, and their output power is usually less than 1000 W. The switching power supply module should select the quasi single-stage PFC bridge converter or dual inductor CPP converter, while the inverter module can choose the current-fed full-bridge inverter [166]. Furthermore, for outdoor portable applications or uninterruptible emergency power supplies typically powered by batteries, the boost converter or buck converter should be preferred as the switching power supply module, which can obtain dc links at more efficient power transmission before entering the inverter module.
• 4)High power – such applications are typically specific applications, such as ultrasonic metal welding, ultrasonic consolidation, ultrasonic oil field emulsification, ultrasonic sludge treatment, etc. Their output power is greater than 1000 W. Therefore, the switching power supply module generally selects the dual inductor CPP converter or single-stage PFC full-bridge converter, while the inverter module uses a phase-shifting full-bridge inverter or multilevel inverter.

Fig. 25.

(a) The chart of the power distribution of sub-modules and its applicable power level distribution. (b) The integration relationship between modules based on the principle of power level matching principle. (c) A practical PUG composed of the Buck converter, H-bridge inverter, and FPGA chip [15].

Generally, the PUG combined by the above modules meets most power ultrasonic application scenarios, while the matching modules should be selected according to the specific application, but most ultrasonic power supplies utilize series L-type or series–parallel LC-type. For large-scale industrial or commercial applications, low-cost combinations will be preferred on the premise that the performance meets the requirements.

5. Key control technologies

The stress concentration area inside the PT inevitably produces a serious self-heating effect, which causes a series of adverse effects, such as dramatical resonance frequency drift and amplitude attenuation. Unfortunately, PT’s operating state will deteriorate further following serious resonance drift due to its high-quality factor. Supposing the PUG does not perform dynamic matching to handle the PT’s resonance drift, a series of adverse effects occur, such as the self-heating effect enhancing, electro-acoustic conversion efficiency decreasing, the aging process accelerating, and damaged by withstanding high current and voltage stress. To keep PT away from operating under the non-resonant state, the PUG must track resonance frequency in time. Even working at a new resonance frequency, keeping a consistent output power state is still difficult due to load changes. Therefore, it is necessary to realize the functions of dynamic frequency tracking control and adaptive power control in PUG.

5.1. Dynamic frequency tracking control

The essence of dynamic frequency tracking control is to keep the PT located at resonant frequency throughout the whole processing quickly and accurately. Electrical impedance is an important parameter of PT that dominates optimal energy transmission and equipment safety. Prevalent impedance matching methods rely on expensive off-line instruments and trials to build optimized static matching circuits, each designed only for one specific transducer at the neighborhood of a certain frequency. At present, dynamic tracking mainly includes hardware tracking and frequency modulation tracking.

5.1.1. Hardware tracking

Generally, hardware tracking realizes online resonant frequency tracking by utilizing dynamic matching components such as the adjustable precision inductor or capacitor. Even though the parameters of PT’s equivalent circuit change, hardware tracking can still keep phase angle to be equality to zero between the current and voltage on the PUG’s output by adjusting the value of the precision inductor or capacitor without changing the inverter output frequency [167]. Fig. 26 shows an experimental schematic based on an adjustable inductor that matches the inherent capacitance of ultrasonic vibration cutting transducer, but the resonant parameters were obtained by the impedance analyzer offline [168]. Therefore, to achieve effective matching for online-working transducers, it is required to conduct real-time impedance measurements and provide instantaneous feedback to the matching network. Fig. 27 shows a schematic of a dynamic impedance matching network, in which the inductor and capacitor groups constitute a variable matching network controlled by an MCU. Based on the improved L-type variable matching network circuit, Z. Jin et al. [169] developed an online PT impedance analysis and matching system, which can adjust its parameters following fluctuating working conditions. Experimental results indicated that hardware tracking could realize resonant tracking and reduce the reflected power. It is undoubtedly the most effective to realize the PT working in the pure resistance state by directly matching the PT’s dynamic parameters, which greatly simplifies the frequency conversion control of the power supply. But this increases the hardware investment, and the matching value of the matching network needs to be adjusted frequently during the work process which will decline its reliability.

Fig. 26.

Experiment schematic [168].

Fig. 27.

Schematic of the dynamic impedance matching network [169].

5.1.2. Frequency modulation tracking

Frequency modulation tracking, as another dynamic matching control technology, can make the output frequency of PUG’s inverter automatically switch to a new resonant state of the transducer under the condition of not changing the component parameters of the matching circuit, and it is designed mainly based on the series resonance frequency of the PT’s mechanical branch. Three traditional methods of frequency tracking are as follows.

5.1.2.1. Maximum current method

To achieve automatic resonance tracking, the maximum current method is employed based on the principle of minimum impedance. This method is easy to find the best resonant point by detecting whether the output current value is the maximum. But it is seriously limited by the shortcomings of weak sensitivity, low accuracy, and slow dynamic response.

5.1.2.2. Phase control method

The phase control method based on the phase-locked loop (PLL) principle is introduced in frequency automatic tracking, which realizes fast resonance tracking by detecting and judging whether the phase difference between the input voltage and current of the matching network is zero [170]. The traditional PLL circuit with flexible adaptability and quick response can eliminate the deficiencies of the maximum current method. However, it needs a fine feedback signal, otherwise it is easily affected by external interferences, especially in the case of fluctuating loads dramatically, which causes the failure of automatic tracking because of losing the lock. Furthermore, when there are multiple resonance points in the vibration system, it cannot identify the optimum resonant point.

5.1.2.3. Maximum output power method

The optimal resonant point can be calculated by sampling PT’s voltage and current based on the principle of maximum output power obtained at the resonance frequency. S. Ben-Yaakov et al. [171] proposed a tracking method that offers the maximum output power for any load, and the experiment results verified that when the phase shift of the diode’s input current and voltage is zero, the system’s voltage gain and power are at their maximum by calculating the amplitude of sampled current and voltage. By applying the proposed approach, the system’s operation can be made independent of input voltage, load variations, temperature (within the permitted range), and the spread and nonlinearity of the PT parameters, as well their drift with time, but it more suitable for various applications that need to generate the high output voltage. This method can effectively avoid the interference of multiple resonance points and has high tracking accuracy, but its dynamic response is slow and its sensitivity is insufficient [172].

In order to better implement frequency modulation tracking, it is necessary to improve the above three traditional methods. An available method adds a nonlinear gain in the PLL which can reduce the phase-locking time to achieve fast initial locking and maintain closed-loop stability of resonance tracking [173]. Fig. 28 shows a schematic of the static capacitance broadband compensation based PLL automatic resonance frequency tracing, in which the reasons for losing lock, interference of anti-resonance frequency and large tracking errors are analyzed theoretically and this method has advantages over the conventional PLL method in terms of enhanced tracing accuracy, and immunity to antiresonance frequency tracing and losing lock. X. Liu et al. [160] developed a PLL with logic release and intervention to ensure that the PT always runs at around 55.5 kHz, and employed a sliding-mode controller with reduced-order sensing and auxiliary PLL frequency discriminator to handle extreme load changes. Although the above improvement schemes make up for the deficiencies of PLL, no method can perfectly realize fast, accurate and reliable resonance tracking.

Fig. 28.

Schematics of the static capacitance broadband compensation based PLL automatic resonance frequency tracing [174].

5.1.2.4. Other new methods

With the development of digital control chips, intelligent sensors, power-integrated circuit technology, and intelligent control algorithm. High-performance chips with powerful computing power and low cost began to be used in PUG, so some new methods emerged. To realize the micro-stepping motion of microfluidic sampling and automatic tracking of the PT’s resonance frequency, an integrated MCU with PLL integrated circuit was proposed to adjust the PT driving circuit [175]. To overcome the shortcomings of conventional PID controllers, such as tedious parameter tuning and uncertain optimal parameters, a particle swarm optimization (PSO) PID simulation model was proposed in [176], which can determine the optimal control parameters by the PSO search. Fig. 29 shows a system’s schematic diagram of the ultrasonic driving and control system, in which a high-performance FPGA chip calculates the collected data to solve the mechanical resonance frequency instead of a searching algorithm. This strategy based on the characteristics of the admittance circle of PT effectively avoids the influence of the system variation and brings better accuracy and faster tracking speed than traditional PLL-based methods, especially under low power consumption conditions. Furthermore, H. Zhang et al. [177] proposed an artificial neural network method to characterize the response performance based on the radial basis function, which extracts the peak overshoot percentage and settling time from the harmonic excitation response signal of the transducer. This method can predict the new resonance frequency and provide support for the control system. As an enough practical auxiliary tool, it probably produces a good effect with in-depth research and improves the efficiency of traditional resonance frequency tracking technology.

Fig. 29.

The system’s schematic diagram of the ultrasonic driving and control system [106].

5.2. Adaptive power control

Typically, adaptive power control can keep constant PT’s load output even with the vibration system operating at a new resonance frequency point. In the application fields of ultrasonic cleaning, ultrasonic atomization, etc., the PUG’s constant power output can avoid an unstable operating state caused by frequency drifting or load changes. For some special applications, more precise and strict control performance needs to be implemented to ensure that the PT’s output amplitude is constant, especially in the processing of ultrasonic grinding, ultrasonic polishing, and ultrasonic atomization powder manufacturing. Therefore, it is necessary to employ the constant amplitude control method by keeping the PT’s working current constantly, which can avoid PUG from being damaged by the periodically or irregularly sharp jump load in the actual process [170], [178]. This method allows the voltage to change in proportion to the load, and the voltage amplitude adjustment is mainly controlled by adjusting the output voltage switching power supply module.

The essence of constant amplitude control is to control the vibration of piezoelectric materials [180]. Most critical indirect control method for PT’s vibration amplitude is timely feedback of voltage amplitude and current amplitude due to the vibration mechanism based on inverse piezoelectric effect. However, many traditional resonant frequency tracking based on electrical feedback exist some drawbacks, such as low amplitude adjustment speed caused by frequent frequency sweeping and low amplitude accuracy caused by electrical parameter feedback. Although by PLL method the stability, accuracy, and sensitivity of the ultrasonic amplitude control is optimized, problems such as losing lock and anti-resonance frequency tracking still cannot be solved reliably. Fig. 30 shows a block diagram of the fuzzy proportional-integral-derivative (PID) control system for constant frequency ultrasonic amplitude control, which applied direct amplitude feedback by laser displacement sensor. It is obvious that direct feedback can avoid many external interferences to achieves high-precision and rapid adjustment of ultrasonic amplitude at a constant frequency. Eventually, this method is illustrated by amplitude control of the ultrasonic welding process, while it can be extendable to other ultrasonic machining fields that need high precision and dynamic performance. But direct amplitude feedback by laser displacement sensor has expensive cost, and is limited by the operating space, acting medium, and surrounding environment. Fig. 31 shows a dual loop automatic resonance tracking scheme with a band-pass filter oscillator and power regulation, which can exploit the PT’s intrinsic resonance point through a sensing bridge. It guarantees automatic resonance tracking and maximum electrical power converted into mechanical motion, regardless of process variations and environmental interferences. Simultaneously, an amplitude control for a switching power stage can provide different power levels for regulating the output mechanical motion. However, each control loop of this scheme is independently controlled, so it needs to be further improved into linkage type. Fig. 32 shows an ultrasonic driving and control system with LC matching network and class D power amplifier, which can indeed increase the system’s tolerance of load fluctuation dramatically. Unlike the traditional methods, this control system used two current sensors to collect two groups of current signals rather than collecting the voltage and current signals. Owing to its simple structure and high performance, the proposed matching method can be widely applied in most ultrasonic systems, especially the power ultrasonic systems. But the principle of this method is still based on the traditional phase control method, so it is still limited for ultrasonic applications with multiple resonance points or a highly fluctuating environment. Furthermore, S. Ghenna et al. [181] employed the vector control method technology based on a PT’s model in the rotating reference frame, then performed the real-time resonance frequency tracking and amplitude control. And results also show that this method also was utilized in multiple piezoelectric transducers to realize their simultaneous operation because of its versatility. But this method has not been verified in other applications.

Fig. 30.

Block diagram of the fuzzy proportional-integral-derivative control system for constant frequency ultrasonic amplitude control [179].

Fig. 31.

Dual loop automatic resonance tracking scheme with a BPF oscillator and power regulation [15].

Fig. 32.

Ultrasonic driving and control system [107].

5.3. Discussion

Several key control methods have been introduced with respective advantages and disadvantages. Overall, they all can realize automatic resonance tracking. Usually, the pure PLL phase control tracking method is only used to track the local resonant frequency, but not suitable for large frequency range sweep tracking [15], [174], [179]. Other methods (including the maximum current method [182], maximum power method [183], self-sensing model method [184], composite tracking method [106], etc.) can usually perform both global sweep frequency tracking and local resonance frequency tracking. The traditional resonance tracking control methods are discussed as follows.

• 1)In terms of feedback requirements, the maximum current method only needs to collect PT’s current amplitude, while the maximum power method needs to collect PT’s voltage and current amplitude at the same time and perform the product operation. Therefore, the latter has better control accuracy and stability than the former, but has higher requirements for acquisition sensors. Although, they have the common disadvantages such as insufficient sensitivity and slow dynamic response, fortunately both can identify multi resonance point interference. The PLL phase control method needs to collect PT’s phase data of voltage and current and perform difference calculation. Its biggest advantage is its sensitive and fast dynamic response capability, which is not available in other methods. But it is vulnerable to external interference, especially when there are multiple resonance points.
• 2)In terms of function expansion, the maximum current method can not only set PT’s overcurrent protection, but also achieve constant amplitude control. Furthermore, the maximum power method has more expandable functions, such as achieving PT’s overvoltage protection, PT’s overcurrent protection setting, constant amplitude control, and constant power control. However, the PLL phase control method does not have the above expansion functions.

Therefore, the combination of PLL phase method and maximum power method can not only achieve excellent fast dynamic response, precision, accuracy, and anti-interference capability, but also perform PT’s constant amplitude control and constant power control. In fact, some new control methods are emerging which mainly rely on control algorithms and chip computing power to optimize, but their control principle has not changed. Furthermore, the adjustable dynamic impedance matching network is superior to static matching networks, which can better filter the harmonic signal to ensure PT operating on near pure resistance state [185]. It is worth trying to combine hardware tracking with frequency modulation tracking to achieve complete closed-loop control of electrical signals.

However, essentially most of existing control methods are passive control schemes. By analyzing PT’s historical operating data, and then adjusting its operating state. This hysteretic control scheme is difficult to predict PT’s future operating state, so that the control system must monitor PT at the highest operating speed throughout the whole process to maintain excellent rapid dynamic response, accuracy and accuracy. The expectation in the future is to obtain the functional relationship between the five parameters of force, temperature, resistance, inductance and capacitance, then establish the PT’s force thermoelectric coupling model. By putting this model into PUG’s control system as a prediction module, which can monitor or import external force-thermal data, the new PUG will sense the amplitude and speed of PT resonance frequency drift and amplitude fluctuation in advance, so as to achieve the combination of active prediction and passive monitoring, and close the hysteresis to zero, At the same time, the control system does not have to run at the highest speed in the whole process.

6. Conclusion

This paper investigates a large number of power ultrasonic applications that seeks out a valuable clue, namely the mechanism consistency of the acting medium and the similarity of ultrasonic signals, it proves the necessity and feasibility of designing a universal modular generator model. At the same time, the plentiful state-of-the-art power semiconductor devices, digital chips, power conversion circuit modules, and control methods are summarized, which lay the foundation of the PUG system. A detailed understanding of the advantages and limitations of each part is essential to help researchers determine the most suitable modular design for the specific application. Following are the brief summary and perspective to the PUG’s future development based on the authors’ knowledge.

• 1)High degree customization of ultrasonic generator is not conducive to large-scale, intensive production, and increases research and development consumption of the PUG system. While based on similar parameter requirements in the same type of medium, such as fluid, solid, and microparticle, developing the universal ultrasonic generator is feasible. However, the universal PUG does perform inferior to the customized one in specific applications. Therefore, the modular design of PUG is a better scheme to balance the sub-optimal performance of universalization and the high cost of customization.
• 2)It is the most economical scheme to select the appropriate topology module according to the power level. For micro-power applications powered by batteries, the PUG is required to be high efficiency and miniaturization. It is advisable to select transformerless modules, such as ZVS boost modules and power amplifier modules, which are easy for power integration. For other applications powered by power grids, the single-stage PFC module should be given priority, which is superior to the two-stage module in power loss, device amount, and volume size. Based on the module design, the low-cost strategy is still to use Si-devices, but WBG devices are preferred for high-performance PUG. Furthermore, due to the high-frequency and high-power of PUT’s application trend, GaN or SiC MOSFET is more suitable in PUG design. With the development of power-integrated circuits, high-performance modules of PUG with little size while large power capacity should be designed and manufactured in the future.
• 3)With the development of high-performance digital chips, advanced sensors, and intelligent control algorithms, high-speed and high-resolution acquisition has been achieved by collection sensors, and simultaneously numerous data obtained by feedback also can be calculated and analyzed by control chips in time, so some new situations emerge. Firstly, the upgrading of traditional tracking methods has achieved a fine effect that remedies the drawbacks of single tracking to a certain extent. Secondly, the combination of two methods can be implemented well without causing system crash, typically the combination of PLL phase method and maximum power method is optimum. Finally, powerful data operation and algorithm execution of main chips (such as FPGA and DSP) allow PUG quickly constructs an admittance circle in which acquire resonance information. However, the above new situations all belong to passive control which has the inherent defect of hysteretic adjustment. The expectation in the future is to achieve the combination of active prediction and passive control, and close the hysteresis to zero, which can be realized by employing the more perfect artificial intelligence algorithm, high-speed automatic adjustment matching circuit, or the new enhanced non-electrical parameters (such as force, temperature, and displacement) feedback channel for sensing more external interference factors.

CRediT authorship contribution statement

Kuan Zhang: Methodology, Investigation, Formal analysis, Writing – review & editing. Guofu Gao: Project administration, Formal analysis, Writing – review & editing. Chongyang Zhao: Data curation, Investigation. Yi Wang: Data curation, Investigation. Yan Wang: Writing – review & editing. Jianfeng Li: Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.