Piezoelectric actuator driving circuit and modeling method thereof

Abstract

The invention belongs to the related technical field of switching power supplies and piezoelectric ceramics, and discloses a piezoelectric actuator driving circuit and a modeling method thereof, the circuit comprises a flyback converter, a PWM wave generator, a feedback compensation circuit, an unloading module and a control signal conditioning module, and an output line of the flyback converter is also provided with a feedback network; the control signal conditioning module receives a control signal VDA and modulates and amplifies the VDA to generate Vcon, the Vcon and a feedback signal Vfb output by the feedback network are added to obtain a loop error signal VE, the feedback compensation circuit receives the VE and modulates the VE to obtain VEA, the PWM wave generator is controlled by the VEA to change the duty ratio D of generated PWM waves, and the flyback converter controls the change of output voltage Vout through the change of the D; the unloading module is controlled by the VEA at the same time, and unloading is selectively carried out after internal logic judgment. The method is relatively simple, lower in energy consumption, higher in bandwidth and smaller in ripple.

Description

Technical Field

[0001] The present invention belongs to the technical field related to switching power supplies and piezoelectric ceramics, and more specifically, relates to a piezoelectric actuator drive circuit and a modeling method thereof. Background Art

[0002] The feature size of microfabrication technology has become smaller and smaller, gradually entering the sub-nanometer level from the nanometer level. The requirements for the motion accuracy, speed, acceleration, and motion degrees of freedom of the drive system of manufacturing equipment are also increasing day by day. Ultra-precision positioning platforms are required in more and more occasions. Such ultra-precision positioning platforms provide a load platform that can achieve ultra-precision positioning and precise motion for fields such as lithography technology, numerical control machining, biotechnology, and nano-surface topography measurement. Currently, the typical representative that embodies the highest achievements of nano-level ultra-precision positioning platforms is the lithography machine. Piezoelectric actuators are mainly used for precision and ultra-precision micro-vibration suppression, such as being applied to high-end lithography machines and scanning transmission electron microscopes to achieve vibration suppression and nano-level precision composite positioning. At the same time, they are widely used in the field of precision machining (such as precision lathes), the medical field (such as magnetic resonance imagers), etc. Compared with traditional transmission methods, they simplify the system structure, have the advantages of fast response, micro-nano level volume, and at the same time, their frequency range also has ultra-wide frequency band adaptability.

[0003] The actuator piezoelectric ceramics in the piezoelectric active vibration damping platform is an actuating component driven by the inverse piezoelectric effect, which has the characteristics of high-speed response, high positioning accuracy, and high bandwidth. When the piezoelectric active vibration damping platform is working, the piezoelectric actuator composed of piezoelectric ceramics not only provides the inertial force and damping force required for vibration damping, but also provides the positioning force to support the load. For a single piezoelectric actuator, a sufficiently high voltage needs to be input to it to provide enough voltage to drive the piezoelectric actuator to generate sufficient deformation. It is impossible to achieve such a high voltage output only by the DA output of the controller, and a corresponding drive circuit must be used to generate it. At the same time, the drive circuit should also meet the requirements of input-output relationship, output voltage sensitivity, amplitude-frequency characteristics, and voltage output ripple noise for the working conditions of the precision active vibration damping system.

[0004] The drive circuit of the piezoelectric actuator can be divided into linear drive and switching drive according to its specific circuit implementation principle. Although the linear drive has a smaller voltage output ripple, its energy consumption is too high. Such a high energy consumption will not only affect the service life of the piezoelectric ceramics but also lead to an increase in its non-linearity, which is an unacceptable consequence. Due to its special working principle, the switching drive has greatly reduced energy consumption, but the output ripple is slightly larger. Summary of the Invention

[0005] In view of the above defects or improvement requirements of the prior art, the present invention provides a piezoelectric actuator drive circuit and a modeling method thereof, which are used to solve the problem that the output ripple of the existing switching drive circuit of the piezoelectric actuator is relatively large.

[0006] To achieve the above object, according to one aspect of the present invention, there is provided a piezoelectric actuator drive circuit, including a flyback converter, a PWM wave generator, a feedback compensation circuit, a unloading module, and a control signal conditioning module. A feedback network is further provided on the output line of the flyback converter; the control signal conditioning module receives a control signal V DA and conditions and amplifies the control signal V DA to generate V con , V con is added to the feedback signal V fb output by the feedback network to obtain a loop error signal V E . The feedback compensation circuit receives V E and modulates it to obtain a feedback compensation signal V EA . The PWM wave generator controls and changes the duty cycle D of the generated PWM wave by the feedback compensation signal V EA . The flyback converter controls the change of the output voltage V out by the change of the duty cycle D; the unloading module is also controlled by the feedback compensation signal V EA , and after internal logic judgment, it selectively unloads.

[0007] According to the piezoelectric actuator drive circuit provided by the present invention, it further includes a rectification and filtering module and an output rectification module. The rectification and filtering module receives the primary side voltage, rectifies and filters it, and then inputs it into the flyback converter. The output voltage of the flyback converter is output after passing through the output rectification module. The feedback network is connected to the output side of the output rectification module, and the output end of the unloading module is connected to the output rectification module.

[0008] According to another aspect of the present invention, there is provided a modeling method for a piezoelectric actuator drive circuit. Based on the above piezoelectric actuator drive circuit, the modeling method includes:

[0009] Performing an equivalent topology transformation on the structure topology diagram of the flyback converter so that the primary side inductor and the secondary side inductor of the flyback converter are integrated into one body;

[0010] Obtaining the small signal model of the flyback converter after the equivalent topology transformation;

[0011] According to the waveform diagrams of each parameter within one switching period in the small signal model, obtaining the average value of each parameter, and further obtaining the average equivalent topology structure of the flyback converter within the switching period;

[0012] According to the DC operating point in the small signal model, converting the average equivalent topology structure of the flyback converter within the switching period into an equivalent DC topology structure;

[0013] Based on the Taylor expansion of the DC static operating point in the equivalent DC topology, obtain the equivalent AC topology of the flyback converter;

[0014] According to the equivalent AC topology of the flyback converter, obtain the transfer function between the duty cycle and the output voltage of the flyback converter;

[0015] Based on the transfer function between the duty cycle and the output voltage of the flyback converter, perform the modeling of the piezoelectric actuator drive circuit.

[0016] According to the modeling method of the piezoelectric actuator drive circuit provided by the present invention, perform an equivalent topology transformation on the structure topology diagram of the flyback converter, so that the primary inductor and the secondary inductor of the flyback converter are integrated into one, specifically including:

[0017] Perform a horizontal mirror flip on the secondary topology of the flyback converter;

[0018] Based on the topology structure after the horizontal mirror flip, perform an equivalent topology transformation on the secondary inductor and the primary input voltage.

[0019] According to the modeling method of the piezoelectric actuator drive circuit provided by the present invention, when performing the equivalent topology transformation of the secondary inductor and the primary input voltage, the voltage of the primary side is equivalent to the voltage of the secondary side, specifically as follows:

[0020]

[0021] Among them, V S is the secondary side voltage before the equivalent topology transformation; V P is the primary side voltage before the equivalent topology transformation; N P , N S are the number of turns of the primary side coil and the number of turns of the secondary side coil respectively; n is the ratio of the number of turns of the secondary side coil to the number of turns of the primary side coil; V in is the primary side voltage input in the initial topology of the flyback converter; the integrated inductor L S after the equivalent topology transformation is:

[0022] Among them, the primary side inductor L P is denoted as L m after integration, I P,peak is the peak value of the primary side current, and I S,peak is the peak value of the secondary side current.

[0023] According to the modeling method of the piezoelectric actuator drive circuit provided by the present invention, the small-signal model includes a power supply, a switching tube, an integrated inductor, a diode, an output capacitor, and an output load; the parameters of each component of the small-signal model include the voltage v1(t) across the switching tube; the voltage v g(t); voltage v across the inductor L (t); voltage v2(t) across the diode; voltage v o (t) across the output load; current i1(t) flowing through the switching transistor; current i2(t) flowing through the diode; current i(t) flowing through the inductor.

[0024] According to the modeling method of the piezoelectric actuator driving circuit provided by the present invention, in one switching period T of the small-signal model s the average values of the various parameters are as follows:

[0025]

[0026] where d1 is the ratio of the conduction time of the switching transistor to the period; d2 is the ratio of the discharge time of the secondary-side inductor to the period; the integrated inductor L after equivalent topological transformation = L m / n 2 , L m is the integrated primary-side inductor, and n is the ratio of the number of turns of the secondary-side coil to the number of turns of the primary-side coil; R e (d1) represents a variable resistor whose magnitude is controlled by the duty ratio d1.

[0027] According to the modeling method of the piezoelectric actuator driving circuit provided by the present invention, the transfer function between the duty ratio of the flyback converter and the output voltage is shown by the following formula:

[0028]

[0029] where represents the AC quantity under the DC operating point bias of V o ; represents the AC quantity under the DC operating point bias of D; V g is the DC component of the power supply voltage; s represents the complex variable in the Laplace transform; R L represents the load resistance; C out is the output capacitor; L P is the primary-side inductor.

[0030] According to the modeling method of the piezoelectric actuator driving circuit provided by the present invention, the modeling of the piezoelectric actuator driving circuit further includes:

[0031] Obtaining the transfer function between the feedback signal V fb and the output voltage V O according to the circuit structure of the feedback network;

[0032] Obtaining the loop error signal V E and V con and V fbThe transfer function between them, and then obtain V E and V fb The transfer function between them;

[0033] According to the circuit structure of the feedback compensation circuit, obtain the feedback compensation signal V EA and the loop error signal V E The transfer function between them;

[0034] According to the transfer functions of the components on the drive circuit, obtain the open-loop transfer function of the loop of the drive circuit;

[0035] Model the piezoelectric actuator drive circuit according to the open-loop transfer function of the loop.

[0036] According to the modeling method of the piezoelectric actuator drive circuit provided by the present invention, the open-loop transfer function T0 of the loop of the drive circuit is as follows:

[0037]

[0038] Wherein, Is the relationship between the duty cycle and the output amplitude and the transfer function of the duty cycle and the input signal; Is the transfer function from the duty cycle of the flyback converter to the output voltage.

[0039] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the piezoelectric actuator drive circuit and its modeling method provided by the present invention:

[0040] 1. The drive circuit is provided with a feedback network and a feedback compensation circuit. The feedback compensation circuit modulates the loop error signal formed by adding the feedback signal and the conditioned and amplified control signal to obtain a feedback compensation signal. The duty cycle D of the generated PWM wave is controlled and changed through the feedback compensation signal, and then the output voltage of the flyback converter is controlled and changed. There is also a unloading module controlled by the feedback compensation signal, which can quickly unload when unloading is required, and can better control the stability of the output voltage and reduce the ripple; this configuration is relatively simple, has less energy consumption, higher bandwidth, and smaller ripple;

[0041] 2. When modeling the flyback converter, through equivalent topological transformation, the research circuit is greatly simplified without changing the output electrical characteristics; the small-signal model analysis method is adopted to convert non-linear devices into linear devices. Specifically, the switching tube is converted into an equivalent resistor, and the diode is converted into a power output device, so as to obtain the transfer function for linear devices, and the bandwidth can be optimized through the transfer function;

[0042] 3. A complete modeling method for the drive circuit is provided, enabling the optimization of bandwidth through the transfer function and solving the problem of bandwidth parametric adjustment for the drive control of piezoelectric actuators. The provided modeling method can provide effective circuit transfer function modeling in actual design, better guiding the selection of electrical parameters. Description of the Drawings

[0043] Figure 1 is a schematic diagram of the piezoelectric brake drive circuit provided by an embodiment of the present invention;

[0044] Figure 2 is a functional block diagram of the drive circuit provided by an embodiment of the present invention;

[0045] Figure 3 is a timing diagram of the PWM generator provided by an embodiment of the present invention;

[0046] Figure 4 is a schematic diagram of the flyback converter provided by an embodiment of the present invention; where (a) is the structural schematic diagram and (b) is the circuit timing diagram;

[0047] Figure 5 is a schematic diagram of the horizontal mirror flip of the secondary side in the topological transformation I provided by an embodiment of the present invention;

[0048] Figure 6 is a schematic diagram of the equivalent topological changes of the secondary side inductor and the primary side input voltage in the topological transformation II provided by an embodiment of the present invention;

[0049] Figure 7 is a schematic diagram of rewriting signal variables in the topological transformation III provided by an embodiment of the present invention;

[0050] Figure 8 is a waveform diagram of each electrical parameter within the switching period of the flyback converter provided by an embodiment of the present invention;

[0051] Figure 9 is the average equivalent topological structure within the switching period of the flyback converter provided by an embodiment of the present invention;

[0052] Figure 10 is the equivalent DC topological structure of the flyback converter provided by an embodiment of the present invention;

[0053] Figure 11 is the equivalent AC equivalent topological structure of the flyback converter provided by an embodiment of the present invention;

[0054] Figure 12 is a schematic diagram of the feedback network provided by an embodiment of the present invention;

[0055] Figure 13 is a schematic diagram of the feedback summing circuit provided by an embodiment of the present invention;

[0056] Figure 14It is a schematic diagram of a feedback compensation circuit using type II compensation provided by an embodiment of the present invention;

[0057] Figure 15 It is a schematic diagram of the open-loop transfer function before loop compensation provided by an embodiment of the present invention;

[0058] Figure 16 It is a schematic diagram of the open-loop transfer function after loop compensation provided by an embodiment of the present invention;

[0059] Figure 17 It is the schematic diagram of the overall circuit provided by an embodiment of the present invention. Detailed implementation manners

[0060] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0061] Please refer to Figure 1 and Figure 2 , this embodiment provides a piezoelectric actuator driving circuit, which includes a flyback converter, a PWM wave generator, a feedback compensation circuit, a unloading module and a control signal conditioning module. A feedback network is also provided on the output line of the flyback converter; the control signal conditioning module receives the control signal V DA and after conditioning and amplifying the control signal V DA , generates V con . V con and the feedback signal V fb output by the feedback network are added to obtain the loop error signal V E . The feedback compensation circuit receives V E and modulates it to obtain the feedback compensation signal V EA . The PWM wave generator controls the change of the duty cycle D of the generated PWM wave by the feedback compensation signal V EA . The flyback converter controls the change of the output voltage V out by the change of the duty cycle D; the unloading module is also controlled by the feedback compensation signal V EA . After internal logic judgment, it selectively unloads and quickly unloads when unloading is required. The control signal can be output by the control board. V con and the feedback signal V fb output by the feedback network can be added through the feedback summing network.

[0062] Further, the piezoelectric actuator driving circuit further includes a rectifying and filtering module and an output rectifying module. The rectifying and filtering module receives the primary side voltage, rectifies and filters it, and then inputs it into the flyback converter. The output voltage of the flyback converter is output after passing through the output rectifying module. The feedback network is connected to the output side of the output rectifying module, and the output end of the unloading module is connected to the output rectifying module.

[0063] Reference Figure 1 , where V in is the voltage input to the primary side of the flyback converter, which is used to supply energy to the entire driving circuit; V out is the output voltage after being amplified and modulated by the driving circuit, which is used to drive the load. In this patent, it specifically refers to the piezoelectric actuator; V fb is the feedback voltage obtained by sampling V out through the feedback network, which is used to feedback the output voltage signal in real time to improve the circuit tracking performance and accuracy; V DA is the analog control signal instruction issued by the upper computer of the controller after digital-to-analog conversion, which controls the output of the driving circuit; V con is obtained by signal conditioning of V DA . Because the control voltage output by the controller after digital-to-analog conversion is generally weak and has no driving ability, it needs to be modulated and amplified to obtain the control voltage V con ; V E is the error voltage obtained by adding V fb and V con ; The feedback compensation circuit modulates the error signal to obtain the feedback compensation signal V EA . D is the duty cycle of the PWM wave output by the PWM wave generator, which is directly controlled by the compensation voltage V EA .

[0064] This embodiment provides a piezoelectric actuator driving circuit based on a flyback switching power supply and its modeling. The purpose is to provide a high-bandwidth and low-ripple piezoelectric actuator driving circuit board and its modeling, thereby solving the problems of large ripple and insufficient bandwidth during the operation of the piezoelectric actuator driving circuit board.

[0065] This embodiment selects a switching driving circuit and reduces its ripple and noise through design. According to the application of the transformer in the topology structure of the isolated switching power supply, it naturally has the effect of electrical isolation between the input and output, effectively avoiding current circulation, and thus has a higher safety level. Further, the two most widely used topology structures in the isolated switching power supply are the flyback converter and the forward converter, both of which have the advantages of flexible transformer inductance value, wide voltage-current ratio, and multi-channel output. Among them, the flyback converter has an additional advantage: it does not require an additional magnetic core reset circuit. Therefore, the flyback converter has additional applications compared to the forward topology.

[0066] According to whether the transformer inductor current in the flyback transformer is continuous or discontinuous in each cycle, the operating state of the flyback transformer is divided into the continuous current mode (CCM), the discontinuous current mode (DCM), and the boundary current mode (BCM). Among them, in the DCM and BCM states of the flyback converter, the secondary side inductor current of the transformer drops to zero in each switching cycle, that is, the energy on the primary side is completely transferred to the secondary side. Compared with the system in the CCM state, the utilization rate of the transformer is higher and the system volume is smaller.

[0067] As Figure 2 shown, the piezoelectric actuator drive circuit can realize the function of amplifying the weak signal output by the main control board into the drive signal required by the piezoelectric actuator, and under the action of sampling negative feedback, realize the fast and accurate tracking of the input and output voltages to the control signal, and improve the system robustness. To further reduce the system error and improve the stability, a reasonable loop compensation circuit is designed, and the following analyzes each link of the circuit.

[0068] Furthermore, this embodiment also provides a modeling method for a piezoelectric actuator drive circuit. The modeling method is based on the above piezoelectric actuator drive circuit and is used to optimize the setting parameters of the drive circuit. The modeling method includes:

[0069] Perform an equivalent topology transformation on the structure topology diagram of the flyback converter so that the primary side inductor and the secondary side inductor of the flyback converter are integrated into one body;

[0070] Obtain the small-signal model of the flyback converter after the equivalent topology transformation;

[0071] According to the waveform diagrams of various parameters in one switching cycle in the small-signal model, obtain the average values of the various parameters, and then obtain the average equivalent topology structure of the flyback converter within the switching cycle;

[0072] According to the DC operating point in the small-signal model, convert the average equivalent topology structure of the flyback converter within the switching cycle into an equivalent DC topology structure;

[0073] Based on the Taylor expansion of the DC static operating point in the equivalent DC topology structure, obtain the equivalent AC topology structure of the flyback converter;

[0074] According to the equivalent AC topology structure of the flyback converter, obtain the transfer function between the duty ratio and the output voltage of the flyback converter;

[0075] Based on the transfer function between the duty cycle of the flyback converter and the output voltage, the piezoelectric actuator drive circuit is modeled.

[0076] Reference Figure 3 , the principle of the PWM wave generator is as follows: The input signal V EA is compared with the ramp reference voltage V RAMP inside the generator. When V EA > V RAMP , the generator outputs a high voltage; when V EA < V RAMP , the generator outputs a low voltage. The duration of the high voltage in one cycle is T on , the duration of the low voltage is T off , and the time of one cycle is T s . The duty cycle is D, and the output amplitude is V M = V RAMP,max - V RAMP,min . d represents the actual amount of the duty cycle. According to the triangle similarity theorem, the relationship between the duty cycle and the output amplitude and the transfer function between the duty cycle and the input signal can be obtained:

[0077]

[0078] Since there are too many non-linear elements in the drive circuit, such as switching transistors and diodes, which is not conducive to studying the response of the drive circuit system, the small-signal analysis method is used to transform the non-linear components into dynamic resistances, and then the system response analysis of the flyback converter is carried out. The specific modeling and analysis process of the flyback converter is as follows:

[0079] a) Equivalent topology transformation:

[0080] The initial topology structure of the flyback converter before equivalent topology transformation is as Figure 4 shown. Figure 4 In it, T represents the transformer, which is the general representation of the flyback converter; I s is the secondary side current before equivalent topology transformation; I p is the primary side current before equivalent topology transformation; V pwm is the voltage given by the PWM wave generator to the base of the switching transistor Q in the flyback converter before equivalent topology transformation; R L represents the load resistance; D out is the diode; C out is the output capacitor.

[0081] First, in order to facilitate the analysis of the influence of the independent variables on the primary side on the output terminal of the secondary side, the electrical properties of the primary side are subjected to an equivalent topological transformation and added to the secondary side to ensure that the electrical properties of the secondary side remain unchanged. An equivalent topological transformation is performed on the structural topology diagram of the flyback converter, so that the primary inductor and the secondary inductor of the flyback converter are integrated into one, specifically including:

[0082] Perform a horizontal mirror flip on the secondary side topology of the flyback converter; that is, in the first step of the topological transformation, perform a horizontal mirror flip on the secondary side topology to align the inductance homonymous ends of the primary side and the secondary side. The flipped topology diagram is as Figure 5 shown.

[0083] Then, based on the topological structure after the horizontal mirror flip, perform an equivalent topological transformation on the secondary inductor and the primary input voltage.

[0084] Refer to Figure 6 , since it is necessary to maintain the electrical characteristics unchanged before and after the equivalent topological transformation, the voltage of the primary side is equivalent to the voltage of the secondary side. The specific method of equivalent topological transformation of the secondary inductor and the primary input voltage by equivalent the voltage of the primary side to the voltage of the secondary side is as follows:

[0085]

[0086] Among them, V S is the secondary side voltage before the equivalent topological transformation; V P is the primary side voltage before the equivalent topological transformation; N P , N S are the number of turns of the primary side coil and the number of turns of the secondary side coil respectively; n is the ratio of the number of turns of the secondary side coil to the number of turns of the primary side coil; V in is the primary side voltage input in the initial topological structure of the flyback converter;

[0087] Furthermore, due to the energy conservation and magnetic potential conservation of the primary and secondary transformers, there is:

[0088]

[0089] N P I P,peak = N S I S,peak (3)

[0090] Combining (2) and (3), the integrated inductor L S after the equivalent topological transformation can be obtained as::

[0091]

[0092] Among them, the primary inductor L P is denoted as L m after integration, EP is the energy of the primary-side transformer, E S is the energy of the secondary-side transformer, I P,peak is the peak value of the primary-side current, I S,peak is the peak value of the secondary-side current. That is, when (1) and (4) are established, the topological transformation can be carried out as shown in the figure without changing the output electrical characteristics.

[0093] Then, while maintaining the electrical characteristics, rewrite the signal variables:

[0094] The last step is to divide each electrical quantity (the voltage and current of each component) in the equivalent topology into a time-varying DC component and a time-varying AC component. Since in practice, the output of the flyback converter contains both DC components and system response components (referred to as low-frequency disturbances and high-order harmonic components) caused by the change of the duty cycle, as well as high-frequency disturbance components caused by the switching frequency and switching frequency harmonics, in engineering, the response of the system we will analyze to the low-frequency disturbance component is called the small-signal model of the system. Next, the small-signal model of the flyback converter is studied by using the switching network averaging method.

[0095] Specifically, referring to Figure 7 , the small-signal model includes a power supply, a switching transistor, a combined inductor, a diode, an output capacitor, and an output load; the parameters of each component of the small-signal model include the voltage v1(t) across the switching transistor, with the positive end closer to the power supply; the voltage v g (t) of the power supply, with the positive end closer to the switching transistor; the voltage v L (t) across the inductor; the voltage v2(t) across the diode; the voltage v o (t) across the output load; the current i1(t) flowing through the switching transistor; the current i2(t) flowing through the diode; and the current i(t) flowing through the inductor.

[0096] The study of the small-signal model is as follows:

[0097] As Figure 3 shown in the switching transistor state in (b), a switching period T s can be divided into three parts, and the times of the three parts are: d1T S , d2T S , (1 - d1 - d2)·T S , where d1 is the ratio of the conduction time of the switching transistor to the period; d2 is the ratio of the discharge time of the secondary-side inductor to the period; for the convenience of calculation, the following idealized assumptions are made:

[0098] Within d1T S , the switching transistor is conducting, and the switching transistor is regarded as an ideal wire, without considering its internal voltage drop.

[0099] Within d2T SInside, the switching transistor is turned off, and the secondary inductor supplies current to the load. The diode is regarded as an ideal wire, and the internal voltage drop is not considered.

[0100] Within (1 - d1 - d2)·T S inside, the primary inductor current returns to zero. According to the relationship between voltage and current: V = L(di / dt), it can be known that the voltage across the inductor is zero. Therefore, the negative terminal of the switching transistor is equivalently grounded. That is, within (1 - d1 - d2)·T S there is:

[0101]

[0102] In fact, the essence of both the switching transistor and the diode is a switch. For the non-linear system composed of switches, it is necessary to average the electrical parameters within one switching period to eliminate the high-order disturbances of the switching frequency and high-frequency harmonics to the system.

[0103] According to Figure 7 the waveforms of various parameters within one switching period of the flyback converter are obtained as shown in Figure 8 the figure.

[0104] According to the above waveform relationship, the average value can be obtained as follows:

[0105]

[0106] Among them, <v1(t)> is the average value of the voltage across the switching transistor within one switching period; <v g (t)> is the average value of the voltage across the power supply within one switching period; <v o (t)> is the average voltage across the output load within one switching period; <v2(t)> is the average value of the voltage across the diode within one switching period. <v2(t)> is the average value of the inductor voltage within one switching period; <i1(t)> is the average value of the current flowing through the switching transistor within one switching period; <i2(t)> is the average value of the current flowing through the diode within one switching period. i pk represents the peak value of the current on the inductor converted by the transformer;

[0107] Furthermore, according to the inductor volt-second principle, we can get:

[0108] [<v g (t)> - 0]×d1T S =[-<v o (t)> - 0]×d2T S (11)

[0109] At the same time, there is also:

[0110]

[0111] Where L = L m / n 2 Combining (6)(7)(8)(9) and substituting (11)(12) into them, we can obtain:

[0112] In the small signal model, a switching cycle T s The average values ​​of the internal parameters are:

[0113]

[0114]

[0115] Where d1 is the ratio of the switch conduction time to the cycle; d2 is the ratio of the secondary inductor discharge time to the cycle; the fused inductor after the equivalent topology transformation is L = L m / n 2 , L m is the primary inductance after fusion, n is the ratio of the number of turns of the secondary coil to the number of turns of the primary coil; R e (d1) represents a variable resistor whose size is controlled by the duty cycle d1.

[0116] In formula (15),<p(t)> =<i2(t)><v2(t)> , which means that the input switch is equivalent to a variable resistor R e (d1), the size is controlled by the duty cycle, and the output end completes the power transfer of the input end without additional energy loss. Based on the above electrical characteristics, the topology can be further simplified as follows Figure 9 As a supplement, Figure 9 The premise is that the flyback converter has completed a switching cycle and takes its average, so it no longer contains high-order interference from switching frequency and high-order harmonics, and only retains low-order disturbances caused by DC components and duty cycle. Figure 9 In the figure, diode is replaced by P to represent a power output device; p(t) represents the specific value of P.

[0117] Next, determine the DC operating point of the small signal model and its equivalent DC circuit. In the DC state, the inductor L is regarded as an ideal conductor and the capacitor C out Assuming it is an open circuit, we can get Figure 10 Equivalent DC topology. Figure 10 The medium parameter is Figure 9 The DC component of the corresponding parameter in .

[0118] Taylor expansion based on the DC static operating point in the equivalent DC topology structure specifically includes:

[0119] A disturbance is introduced near the DC static operating point for small signal analysis, and simplified symbols of the parameters are introduced. The duty cycle d1 is replaced by d.<v1(t)> ,<v2(t)> Use v1, v2 instead,<i1(t)> , <i2(t)用i1、i2代替;则有:

[0120]

[0121] By Taylor expanding the dependent variables i1 and i2 at the DC static operating point and separating the DC static operating point to find the first-order partial differential term, we can obtain:

[0122]

[0123] in, generation

[0124] Table of AC quantities under I1 DC operating point bias; represents the AC quantity under the I2 DC operating point bias; represents the AC quantity under the bias of V1 DC operating point; represents the AC quantity under the V2 DC operating point bias; represents the AC quantity under the DC operating point bias of D; j1 represents the primary virtual current source; j2 represents the secondary virtual current source; g2 represents the secondary virtual voltage source. D is the DC component of the duty cycle. In formula (17), taking i1 as an example, I1 is the DC component of i1, that is, corresponding to Figure 10 The amount in.

[0125] From formula (10), we can see that in one switching cycle, the average voltage across the inductor is 0, just like the DC equivalent circuit. According to the electrical characteristics of formula (18), the equivalent AC topology of the flyback converter can be obtained. The equivalent AC topology of the flyback converter is as follows: Figure 11 shown.

[0126] According to circuit theory, we can get:

[0127]

[0128] in Represents V o The AC quantity under the DC operating point bias. s represents the complex variable in the Laplace transform; Represents V g AC quantity under DC operating point bias;

[0129] Combination Figure 11 By converting the secondary inductance into equation (18), the transfer function between the duty cycle and the output voltage of the flyback converter can be obtained as shown in the following equation:

[0130]

[0131] Furthermore, the modeling of the piezoelectric actuator drive circuit also includes:

[0132] Obtaining the feedback signal V fb and the transfer function between the output voltage V O ;

[0133] Obtaining the loop error signal V E and the transfer function between V con and V fb , and then obtaining the transfer function between V E and V fb ;

[0134] Obtaining the feedback compensation signal V EA and the transfer function between the loop error signal V E ;

[0135] Obtaining the loop open-loop transfer function of the drive circuit according to the transfer functions of each component on the drive circuit;

[0136] Modeling the piezoelectric actuator drive circuit according to the loop open-loop transfer function.

[0137] The modeling of the flyback converter loop compensation circuit is as follows:

[0138] If the system does not perform loop compensation, the output voltage of the converter is directly divided by a resistor, and the resistor voltage division amount is used as the output feedback signal, which is added to the input control signal and then sent to the PWM wave generator, thus closing the loop. If loop compensation is performed, the flyback converter samples the output voltage through the output rectification and resistor voltage division circuit, takes the sampled information as a signal, adds it to the input control signal, and sends it to the error amplifier.

[0139] The feedback network converts the output voltage V O of the flyback transformer into the feedback signal V fb through voltage division modulation. Referring to the structure shown in Figure 12 , R D , R U represent the resistors in the feedback network circuit, and C F represents the capacitor in the feedback network; its transfer function can be obtained through circuit knowledge:

[0140]

[0141] As shown in Figure 13 the feedback summing circuit, the control signal V conWith the feedback signal V fb The sum is performed through this circuit to obtain the error voltage V E . For Figure 13 the circuit shown, the node voltage method is used. V cc represents the supply voltage of the drive circuit; R1, R2, R3, and R4 represent the resistors in the feedback summing circuit; it can be obtained that:

[0142]

[0143] After simplification, it can be obtained that:

[0144]

[0145] In the steady state, V E is 0. From this, the relationship between V fb and V con can be determined, that is, the gain and bias of the loop are obtained. Further, the transfer function between the feedback signal and the error signal can be obtained:

[0146]

[0147] The research uses a feedback compensation circuit as Figure 14 shown. R5, R6, and R7 represent the resistors in the feedback compensation circuit; C1 and C2 represent the capacitors in the feedback network; from the virtual short and virtual open of the ideal amplifier, there are:

[0148]

[0149] After simplification, it is obtained that:

[0150]

[0151] Therefore, the zeros and poles of the feedback compensation circuit are:

[0152]

[0153] z represents the zero of the feedback compensation circuit; p1 and p2 represent the two poles of the feedback compensation circuit; in order to achieve a better response of the control signal, the bandwidth optimization of the drive board is very important.

[0154] The open-loop transfer function T0 of the loop of the drive circuit is as follows:

[0155]

[0156] The specific parameter settings in the drive circuit can be optimized according to the open-loop transfer function of the loop; specifically, the resistance and capacitance values in the feedback compensation circuit are optimized. The overall circuit schematic diagram of the drive circuit is as Figure 17 shown.

[0157] Substitute specific parameters

[0158] The open-loop margin of the loop can be improved by changing the resistance and capacitance values of the feedback compensation circuit to enhance the system stability, expand the bandwidth, and improve the system response. For example Figure 16 The bandwidth reaches 3000 Hz, which is 50 times higher than that without adding a feedback compensation circuit such as Figure 15 .

[0159] It is easy for those skilled in the art to understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A piezoelectric actuator driving circuit, characterized in that, It includes a flyback converter, a PWM wave generator, a feedback compensation circuit, a load unloading module, and a control signal conditioning module. A feedback network is also provided on the output line of the flyback converter; the control signal conditioning module receives the control signal V DA and conditions and amplifies the control signal V DA to generate V con , V con is added to the feedback signal V fb output by the feedback network to obtain the loop error signal V E . The feedback compensation circuit receives V E and modulates it to obtain the feedback compensation signal V EA . The PWM wave generator controls and changes the duty cycle D of the generated PWM wave by the feedback compensation signal V EA . The flyback converter controls the change of the output voltage V out by the change of the duty cycle D; the load unloading module is also controlled by the feedback compensation signal V EA and selectively unloads after internal logic judgment.

2. The piezoelectric actuator driving circuit according to claim 1, wherein It further includes a rectifying and filtering module and an output rectifying module. The rectifying and filtering module receives the primary side voltage, rectifies and filters it, and then inputs it into the flyback converter. The output voltage of the flyback converter is output after passing through the output rectifying module. The feedback network is connected to the output side of the output rectifying module, and the output end of the unloading module is connected to the output rectifying module.

3. A modeling method for a piezoelectric actuator driving circuit, characterized in that, Based on the piezoelectric actuator driving circuit according to claim 1 or 2 above, the modeling method includes: Performing an equivalent topological transformation on the structural topology diagram of the flyback converter so that the primary side inductor and the secondary side inductor of the flyback converter are integrated into one; Obtaining the small-signal model of the flyback converter after the equivalent topological transformation; According to the waveform diagrams of various parameters within one switching period in the small-signal model, obtaining the average values of the various parameters, and further obtaining the average equivalent topological structure within the switching period of the flyback converter; According to the DC operating point in the small-signal model, converting the average equivalent topological structure within the switching period of the flyback converter into an equivalent DC topological structure; Based on the Taylor expansion of the DC static operating point in the equivalent DC topological structure, obtaining the equivalent AC topological structure of the flyback converter; According to the equivalent AC topological structure of the flyback converter, obtaining the transfer function between the duty cycle and the output voltage of the flyback converter; Based on the transfer function between the duty cycle and the output voltage of the flyback converter, performing the modeling of the piezoelectric actuator driving circuit.

4. The modeling method of the piezoelectric actuator driving circuit according to claim 3, characterized in that Performing an equivalent topological transformation on the structural topology diagram of the flyback converter so that the primary side inductor and the secondary side inductor of the flyback converter are integrated into one, specifically including: Performing a horizontal mirror flip on the secondary side topology of the flyback converter; Based on the topological structure after the horizontal mirror flip, performing an equivalent topological transformation on the secondary side inductor and the primary side input voltage.

5. The modeling method of the piezoelectric actuator driving circuit according to claim 4, characterized in that When performing the equivalent topological transformation on the secondary side inductor and the primary side input voltage, the voltage on the primary side is equivalently transformed into the voltage on the secondary side, specifically as follows: Among them, V S is the secondary side voltage before the equivalent topological transformation; V P is the primary side voltage before the equivalent topological transformation; N P , N S are the number of turns of the primary side coil and the number of turns of the secondary side coil respectively; n is the ratio of the number of turns of the secondary side coil to the number of turns of the primary side coil; V in is the primary side voltage input in the initial topological structure of the flyback converter; The integrated inductor L S after the equivalent topological transformation is: Among them, the original side inductor is L P After fusion, it is denoted as L m , I P,peak is the peak value of the original side current, and I S,peak is the peak value of the secondary side current.

6. The modeling method of the piezoelectric actuator driving circuit according to claim 3, characterized in that, The small-signal model includes a power supply, a switching transistor, a combined inductor, a diode, an output capacitor, and an output load; the parameters of each component of the small-signal model include the voltage v1(t) across the switching transistor; the voltage v g (t) of the power supply; the voltage v L (t) across the inductor; the voltage v2(t) across the diode; the voltage v o (t) across the output load; the current i1(t) flowing through the switching transistor; the current i2(t) flowing through the diode; the current i(t) flowing through the inductor.

7. The modeling method of the piezoelectric actuator driving circuit according to claim 6, characterized in that, The average value of each parameter within one switching period T in the small-signal model is as follows: s ​ Among them, d1 is the ratio of the conduction time of the switching tube to the period; d2 is the ratio of the discharge time of the secondary inductor to the period; the integrated inductor L after the equivalent topology transformation is L m / n 2 ,L m is the integrated primary inductor, n is the ratio of the number of turns of the secondary coil to the number of turns of the primary coil; R e (d1) represents a variable resistor whose value is controlled by the duty cycle d1.

8. The modeling method of the piezoelectric actuator driving circuit according to claim 6, characterized in that The transfer function between the duty cycle and the output voltage of the flyback converter is shown in the following formula: Among them, represents the alternating quantity under the DC operating point bias of V o ; represents the alternating quantity under the DC operating point bias of D; V g is the DC component of the power supply voltage; s represents the complex variable in the Laplace transform; R L represents the load resistance; C out is the output capacitance; L P is the primary inductance.

9. The modeling method of the piezoelectric actuator driving circuit according to claim 3, characterized in that Performing the modeling of the piezoelectric actuator driving circuit further includes: Obtain the feedback signal V according to the circuit structure of the feedback network fb and the transfer function between the output voltage V O ; Obtain the loop error signal V according to the circuit structure of feedback summation E and V con and V fb to obtain the transfer function between them, and further obtain the transfer function between V E and V fb ; Obtain the feedback compensation signal V according to the circuit structure of the feedback compensation circuit EA and the loop error signal V E to obtain the transfer function therebetween; According to the transfer functions of each component on the driving circuit, obtaining the loop open-loop transfer function of the driving circuit; Performing the modeling of the piezoelectric actuator driving circuit according to the loop open-loop transfer function.

10. The modeling method of the piezoelectric actuator driving circuit according to claim 9, characterized in that, The loop open-loop transfer function T0 of the driving circuit is as follows: Among them, is the relationship between the duty cycle and the output amplitude and the transfer function of the duty cycle and the input signal; is the transfer function from the duty cycle of the flyback converter to the output voltage.

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