Design method of LC output filter in PWM driven servo motor system

Abstract

The present invention discloses a method for designing an LC output filter in a PWM-driven servo motor system. The method analyzes the EMI of the three-phase servo motor system and establishes an EMI signal transmission model based on the EMI characteristics. The EMI signal transmission model is converted into an RLC model. The RLC model is then used to determine key parameters of the EMI signal transmission model. Finally, the design of the LC output filter is verified based on the key parameters of the EMI signal transmission model. The method derives the key parameters of the EMI signal transmission model by capturing the current oscillation waveform and performing model conversion. Simulation verification is then used to transfer the actual measurement and calculation work of the LC output filter design to a simulation environment, reducing design costs and improving design efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of filters, and in particular to a method for designing an LC output filter in a PWM driven servo motor system. Background Art

[0002] In aerospace environments, servo motors are often placed outside the cabin to serve as actuators for payloads. This requires the servo motor and PWM drive controller to be separated by a certain distance and connected via long cables. In this configuration, the cable's equivalent inductance and the winding's parasitic capacitance form an RLC network. This network generates current oscillations under the switching action of the PWM signal, which in turn can cause radiated or conducted EMI signals. These EMI signals can not only damage the motor itself but also interfere with other electronic equipment in the payload, such as spectral imaging and communication systems.

[0003] The primary means of addressing EMI is to use filters for suppression. Designing an appropriate filter typically involves modeling and measuring multiple motor and drive component parameters, including resistance, inductance, back EMF, fundamental frequency component blocking, inter-turn effects, and parasitic capacitance, using equipment such as a network analyzer. This process is complex, time-consuming, and labor-intensive.

[0004] LC filters primarily consist of passive components such as inductors, capacitors, and resistors, leveraging their properties to suppress conducted EMI in electronic circuits. A simple LC output filter employs an LC network topology, where the inductor allows DC and low-frequency signals to pass while blocking high-frequency noise. Passive filters offer advantages such as simple structure, low cost, high reliability, and low operating expenses. They are not limited by hardware and are currently one of the most widely used methods for harmonic control.

[0005] Designing an LC filter is a complex process that requires reasonable matching and calculation based on the filtering requirements and component characteristics. The general steps include:

[0006] 1) First, measure the system EMI to obtain the required insertion loss of the EMI filter;

[0007] 2) Then select the appropriate LC output filter topology (such as RC, LC, or RLC network);

[0008] 3) Obtain the corner frequency f of the LC output filter c ;

[0009] 4) According to the turning frequency f c You can then select the values of the components in the LC output filter;

[0010] 5) In actual testing, if the designed LC output filter cannot meet the EMI suppression requirements of the system, the component parameters of the EMI filter need to be adjusted to meet the suppression requirements.

[0011] The optimal design of LC filters also needs to consider multiple factors such as harmonics, reactive power compensation, grid frequency fluctuations and economic costs.

[0012] Generally speaking, existing filter design techniques first require measuring and modeling the parameters of multiple components of the motor and its drive using equipment such as a network analyzer. This process requires complex mathematical calculations and extensive measurement, analysis, testing, and modification, presenting a significant challenge for designers.

[0013] Explanation of terms:

[0014] Electromagnetic interference (EMI) refers to any electromagnetic phenomenon that degrades the performance of a device, equipment or system during conduction or in the presence of an electromagnetic field accompanied by voltage or current.

[0015] Pulse Width Modulation (PWM): is a modulation technique that controls the average value of the output voltage or current by changing the width of the pulse. Summary of the Invention

[0016] This paper proposes a design method for an LC output filter in a PWM-driven servo motor system, aiming to effectively suppress the radiated EMI caused by the PWM signal passing through long cables, thereby providing a practical and efficient solution for the electromagnetic compatibility of the motor drive system in aerospace environments.

[0017] To achieve the above object, the present invention adopts the following technical solutions:

[0018] A method for designing an LC output filter in a PWM driven servo motor system, comprising:

[0019] Analyze the EMI of the system and establish an EMI signal transmission model based on the EMI characteristics;

[0020] Convert the EMI signal transmission model into an RLC model;

[0021] Then the RLC model is used to determine the key parameters of the EMI signal transmission model;

[0022] Finally, the design of the LC output filter is verified based on the key parameters of the EMI signal transmission model.

[0023] Furthermore, the RLC model is used to determine the key parameters of the EMI signal transmission model, including:

[0024] In the captured oscillating current waveform, two pulses are selected and the period and pulse current peak are measured. Based on the measurement results, the unknown coefficients in formula (9) are calculated using formulas (10), (13), (14) and (17). Based on the calculated coefficients, the values of R, L and C in the RLC model are obtained in combination with formulas (18), (19) and (20); where R is the equivalent series resistance of the motor drive cable, L is the equivalent inductance of the motor drive cable, and C is the parasitic capacitance of the motor winding.

[0025] According to Kirchhoff's voltage law, the loop of the RLC circuit is expressed by equation (1):

[0026]

[0027] Where i(t) or i(x) is a function of current, Vin is the input value, switching between 0V and Vin;

[0028] Differentiating both sides of the equation and dividing them by L forms a standard second-order differential equation:

[0029]

[0030] Its characteristic equation is s 2 +(R / L)*s+1 / LC=0, the two solutions of the characteristic equation are calculated using the quadratic formula:

[0031]

[0032] where α is the Neper frequency in rad / s, which describes the damping rate and is expressed as

[0033]

[0034] ω0 is the resonant radian frequency in rad / s, expressed as:

[0035]

[0036] The step response is underdamped, which means that α 2 Less than ω0 2 , whose radian frequency ω d Expressed as:

[0037]

[0038] The solution to equation (3) has the following form:

[0039] i(t)=B1·e -αt ·Cos(ω d t)+B2·e -αt ·Sin(ω d t) (7)

[0040] A step function is applied by turning the switch from 0V to Vin, satisfying two initial conditions:

[0041] (1) When t = 0, the current i(t) is zero;

[0042] (2) When t = 0, the voltage on L is Vin, which can be expressed as L·(di(t)) / dt;

[0043] Under these two conditions, find the coefficients B1 and B2:

[0044]

[0045] The current oscillation is expressed as:

[0046] i(t)=B2·e -αt ·Sin(ω d t) (9)

[0047] The vertical axis of the coordinate is the current amplitude, and the horizontal axis is time; T d is the period of oscillation, for T d , coefficient ω d It is derived from the following formula:

[0048]

[0049] The time point at which the nth pulse has a positive peak is defined as t n The time point when the nth pulse has a negative peak value is defined as t' n ;t' n t n Add T d Half of t' n =t n +π / ω d ;

[0050] The peak-to-peak value of the nth pulse is defined as i p-pn

[0051]

[0052] Select the nth pulse and the mth pulse to be measured, "m" is the sequence number later than "n";

[0053] i p-pn and i p-pm The ratio is expressed as:

[0054]

[0055] α is solved for:

[0056]

[0057] According to equation (11), B2 is expressed as t n function;

[0058]

[0059] Calculate t n The measured value of the oscillating current is expressed by equation (9). All peak points have extreme values. Therefore, when t=t n When , the derivative of equation (9) should be zero and can be expressed as:

[0060]

[0061] therefore

[0062]

[0063] Thus, t n According to formula (17), we can get:

[0064]

[0065] Once you get t n , B2 can be calculated by equation (14);

[0066] Therefore, ω d , B2 and t n By T d 、i p-pn and i p-pm Solve the measurement results of ;

[0067] Once you know d , α and B2, the values of R, L and C can be determined (where R, L and C are the equivalent series resistance of the motor drive cable, the equivalent inductance of the motor drive cable and the parasitic capacitance of the motor winding under the RLC model respectively);

[0068] According to equation (8), the calculation formula of L is

[0069]

[0070] Where V in is the PWM swing voltage;

[0071] According to equation (4), R is calculated by the following formula

[0072] R=2·L·α (19)

[0073] According to equations (5) and (6), the calculation formula for C is

[0074]

[0075] In the captured oscillating current waveform, T d It is measured using the vertical cursors in the oscilloscope.

[0076] Furthermore, the design verification of the LC output filter based on the key parameters of the EMI signal transmission model specifically includes:

[0077] Based on the values of R, L, and C determined by the RLC model, a simulation circuit for the EMI signal transmission model is constructed. In the EMI signal transmission model, the sum of the winding equivalent series resistance Resr and the drive cable resistance Rc is 1 / 1.5 of R. Rc can be measured directly on the drive cable. The drive cable equivalent inductance Lc is 1 / 1.5 of L, and the winding parasitic capacitance Cw is 1.5 times C. Therefore, the values of Resr, Lc, and Cw in the EMI signal transmission model can be determined;

[0078] Then add 1 LC filter on each phase and use the equivalent series resistance (equivalent resistance of the inductor in the filter).

[0079] The natural oscillation frequency f0 in the LC filter circuit is also the cutoff frequency f of the LPF (low-pass filter). C Generally speaking, it should be designed to be much lower than the PWM frequency, and a frequency difference of 3 times is safe. On the other hand, the response frequency of the motor must also be considered, and it can be about 10 times the motor response frequency. Combining these two factors, the cutoff frequency f of the system can be determined. C .f C and the inductor L in the LC filter f The value of capacitance C f The relationship between the values of is determined by the following formula:

[0080]

[0081] Build a simulation circuit and try different L f and C f value, evaluate the filtering performance, output voltage and charging current, and determine the optimal L value of the LC filter f and C f Theoretically, given the cutoff frequency, find L f and C f There are countless possible combinations of these values. However, in reality, there are some engineering considerations, such as the size of the inductor and capacitor, the cost of aerospace components, and the rated current and voltage. After comprehensive consideration, the number of possible combinations is very limited.

[0082] As can be seen from the above technical solution, the present invention's method for designing an LC output filter in a PWM-driven servo motor system determines the motor system network parameters by acquiring the current oscillation waveform in the servo motor drive cable, and then uses simulation tools to complete the passive filter design. This method minimizes the measurement and modification of actual circuits, allowing most design work to be completed in a simulated environment.

[0083] Specifically, the present invention analyzes the EMI of a three-phase servo motor system and establishes an EMI signal transmission model based on the EMI characteristics. This model is then converted into an RLC model. The RLC model is then used to determine the key parameters of the EMI signal transmission model. Finally, the design of the LC output filter is verified based on these key parameters. By capturing the current oscillation waveform and performing model conversion, the present invention derives the key parameters of the EMI signal transmission model.

[0084] The proposed LC output filter design method effectively suppresses EMI radiated from long cables in motor drive systems. By moving the design process into a simulation environment, it significantly reduces the need for actual circuit measurements and modifications, improving design efficiency. The method has been demonstrated to be effective in practical systems, particularly in the design of customized small motors or compact instruments, providing a flexible and practical EMI suppression solution.

[0085] This invention is applicable to servo motor systems in aerospace environments, as well as some small terrestrial servo motor systems. It should be emphasized that in terrestrial environments, the motor and controller are typically integrated, the housing shields EMI, and long cables are not typically used to connect the motor and driver, thus preventing severe current oscillations.

[0086] The key innovations of the method of the present invention include:

[0087] By capturing the current oscillation waveform and model conversion, the key parameters of the EMI signal transmission model are derived;

[0088] By using simulation verification, the actual measurement and calculation work of LC output filter design is transferred to the simulation environment, which reduces the design cost and improves the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 The control voltage and drive current detection waveforms of the embodiment of the present invention;

[0090] Figure 2 is the damped oscillation of the current on the phase A conductor of the embodiment of the present invention;

[0091] Figure 3 is a terminal-related equivalent circuit of a three-phase motor winding according to an embodiment of the present invention;

[0092] Figure 4 is an equivalent circuit diagram of a cable and a motor according to an embodiment of the present invention;

[0093] Figure 5 is an equivalent circuit diagram (EMI signal transmission model) of the cable and winding according to an embodiment of the present invention;

[0094] Figure 6 is an AC equivalent circuit diagram of an embodiment of the present invention;

[0095] Figure 7 : is an RLC equivalent circuit diagram of an embodiment of the present invention;

[0096] Figure 8 This is a typical underdamped current oscillation in the RLC circuit of the embodiment of the present invention;

[0097] Figure 9 It is the measurement of the current oscillation period of the embodiment of the present invention;

[0098] Figure 10 is a comparison of the step responses of the RLC model and the EMI signal transmission model according to an embodiment of the present invention;

[0099] Figure 11 This is a simulation circuit and EMI signal transmission model of the LC filter according to an embodiment of the present invention;

[0100] Figure 12 is the square wave response of the LC filter system according to an embodiment of the present invention;

[0101] Figure 13 This is the waveform of the phase A current after the filter is installed in the embodiment of the present invention;

[0102] Figure 14 This is the amplified waveform of the A-phase current after the filter is installed in the embodiment of the present invention;

[0103] Figure 15 It is a flow chart of a method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0104] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0105] The LC output filter design method for suppressing electromagnetic interference described in this embodiment starts with a real case, analyzes the EMI of a three-phase servo motor system, and models it based on the EMI characteristics. Then, the RLC model is used to determine the key parameters of the EMI signal transmission model. Finally, the design of the LC output filter is verified.

[0106] The following are specific instructions:

[0107] Electromagnetic Interference Analysis and System Modeling

[0108] The switching action of PWM causes current oscillations, which generate EMI radiation through the long cables of the motor drive system. Therefore, an AC signal must be transmitted along the cable. Use an oscilloscope and current probe to capture the current signal passing through phase a in the cable. Figure 1 The measurement results are shown.

[0109] In this test, the input of Channel 1 (C1) is a current probe on the phase a conductor of the cable. C2 is a voltage probe that tests the logic input of phase a in the driver IC, C3 tests the logic control voltage of phase B, and C4 tests the logic control voltage of phase C. Channel 1 is set to AC input, while the other channels are set to DC. It can be seen that each switching action generates current ripple. Expanding the waveform, as shown Figure 2 As shown, the ripple is found to be a damped oscillation with a maximum peak-to-peak amplitude of 350mA, a period of 150ns, and a duration of about 1.5μS.

[0110] exist Figure 2 In Figure 1, since the driver IC has a dead time of 2.5 μs, the oscillation begins 2.5 μs after the TTL signal on Phase A (C2) rises. It can be concluded that the current oscillation is a response to the PWM switching action.

[0111] In addition, as an AC signal, the response to a rising edge or a falling edge is the same in amplitude and frequency. To simplify the analysis, the present invention only considers the rising edge of phase A.

[0112] In various studies of industrial motors, many different circuit models are used to describe the winding behavior of a passive 2-port network consisting of a resistor (R), an inductor (L), and a capacitor (C). The ideal circuit form of the required model should represent the main physical phenomena present in the motor winding. Since the focus of this study is on the current oscillations in the cable, the resonance within the winding does not need to be considered. Therefore, if Figure 3 As shown, the windings are modeled using lumped terminal-related equivalent circuits.

[0113] exist Figure 3 Where Rw is the winding resistance, Lw is the winding inductance, Ci is the interwinding capacitance, and Cs is the winding self-capacitance. In the present invention, the windings are connected in a Y-shape, with terminals U2, V2, and W2 connected at a single point. Therefore, the three interwinding capacitors on the right side can be eliminated.

[0114] The cable between the drive port and the motor can be modeled as an RLC network. The output port of the drive is modeled as an SPDT switch. Since the signal under investigation is the response to the rising edge of Phase A, the other two phases are grounded. Figure 4 The equivalent circuit of the system is shown.

[0115] exist Figure 4 In the diagram, Rc is the series resistance of the cable; Lc is the inductance of the cable. In the figure, the three capacitors Ci are connected in a triangle. They can be combined with the three Cs capacitors. The lamp capacitor is labeled Cw. Furthermore, the winding capacitors Cw are accompanied by equivalent series resistors. These resistors are labeled Rw. Thus, an EMI signal transmission model is established, as shown in the figure. Figure 5 shown.

[0116] exist Figure 5 The values of Rw and Lw are found in the motor specifications; in this case, they are 15Ω and 10mH, respectively. Therefore, the cutoff frequency of the branch circuit formed by Rw and Lw is 239Hz. Since the frequency of the current oscillation signal captured on the cable is approximately 6MHz, it cannot pass through the Rw and Lw branch.

[0117] In this circuit, only Cw can transmit high-frequency AC signals. The 6MHz oscillation signal is generated by the LC circuit, which is composed of the equivalent inductance of the cable (L C ) and the parasitic capacitors (Cw) of the windings, and pass through the high-frequency path. The high-frequency path consists of Rc, Lc, Resr, and Cw. Therefore, Lw and Rw can be removed from the diagram without any impact on the analysis of high-frequency oscillation. The AC equivalent circuit is as follows Figure 6 shown.

[0118] Figure 6 The circuit shown can be converted into a simple RLC equivalent circuit as Figure 7 shown.

[0119] exist Figure 7 In the circuit, the value of C is equal to two-thirds of Cw. The value of R is 1.5 times the sum of Rc and Resr, and the value of L is 1.5 times Lc. i(t) is the current in response to the step function of Vin. In the actual circuit, i(t) is the oscillation on phase A, as shown in Figure 2 shown.

[0120] Therefore, two models are established. One is the RLC model, such as Figure 7 As shown in Figure 2, it is used to analyze AC signals. The other is the EMI signal transmission model, such as Figure 5 As shown, it is used to analyze AC and DC signals simultaneously.

[0121] Determination of RLC model and EMI signal transmission model parameters

[0122] In the RLC model, the values of R, L, and C are difficult to measure in a real system. However, since i(t) can be measured by an oscilloscope, the values of R, L, and C can be calculated using the waveform of i(t), as shown in the following example: Figure 2 shown.

[0123] According to Kirchhoff’s voltage law (KVL), the loop of an RLC circuit can be expressed as Equation 1:

[0124]

[0125] Where i(t) or i(x) is a function of current and Vin is the input value, switching from 0V or 30V.

[0126] Differentiating both sides of the equation and dividing them by L forms a standard second-order differential equation:

[0127]

[0128] Its characteristic equation is s 2 +(R / L)*s+1 / LC=0, the two solutions of the characteristic equation can be calculated using the quadratic formula:

[0129]

[0130] where α is the Neper frequency in rad / s, which describes the damping rate and can be expressed as

[0131]

[0132] ω0 is the resonant radian frequency in rad / s, which can be expressed as:

[0133]

[0134] review Figure 3 , the step response is underdamped, which means that α 2 Less than ω0 2 Its radian frequency ω d Expressed as:

[0135]

[0136] The solution to equation (3) has the following form:

[0137] i(t)=B1·e -αt ·Cos(ω d t)+B3·i -αt ·Sin(ω d t) (7)

[0138] In the present invention, a step function input is performed by turning the switch from 0V to 30V, and two initial conditions should be met:

[0139] (1) When t = 0, the current i(t) is zero;

[0140] (2) When t = 0, the voltage on L is Vin, that is, 30 V, which can be expressed as L·(di(t)) / dt.

[0141] Under these two conditions, find the coefficients B1 and B2:

[0142]

[0143] Therefore, the current oscillation can be expressed as:

[0144] i(t)=B2·e -αt ·Sin(ω d t) (9)

[0145] Figure 8 The figure shows a typical step response of an RLC series circuit, which is an underdamped oscillation consisting of several pulses. Each pulse is a sine wave that starts at zero, rises to a positive peak, falls to a negative peak, and then returns to zero. The amplitude of these pulses decreases over time.

[0146] exist Figure 8 In the figure, the vertical axis is the current amplitude. The horizontal axis is time. d is the period of oscillation. d , coefficient ω d It is derived from the following formula:

[0147]

[0148] Figure 8 The coordinates in the waveform do not exist in the actual waveform. Measuring the absolute amplitude is inaccurate. Instead, measure the peak-to-peak amplitude of the pulse because the peak point is easier to locate on an oscilloscope.

[0149] like Figure 8 As shown, the time point when the nth pulse has a positive peak is defined as t n The time point at which the nth pulse has a negative peak value is defined as t' n t' n t n Add T d Half of t' n =t n +π / ω d .

[0150] The peak-to-peak value of the nth pulse is defined as i p-pn

[0151]

[0152] Select the nth pulse and the mth pulse to be measured, where "m" is the sequence number later than "n".

[0153] i p-pn and i p-pm The ratio can be expressed as:

[0154]

[0155] Therefore, "α" is solved:

[0156]

[0157] Figure 9 The measurements of the 3rd and 5th pulses in one example are shown.

[0158] Once the "ω d ” and “α”, only one coefficient B2 in equation (9) is unknown. According to equation (11), B2 can be expressed as t n function.

[0159]

[0160] It looks like t n As has been determined, B2 can be calculated. However, since it is impossible to accurately locate the starting point of the oscillation, t n It is difficult to measure directly on an oscilloscope.

[0161] exist Figure 9 The waveform of the oscillation signal is amplified. It can be seen that the starting pulse is not neat. This is because the driver needs a very short time, usually tens of nanoseconds, to reduce the output resistance from R off Switch to R on The series resistor is unstable over short periods of time. Furthermore, small oscillations caused by parasitic capacitors and inductors on the board occur briefly at the start of the PWM pulse and are superimposed on the oscillating signal. These small oscillations distort the initial pulse. This is why the first one or two pulses cannot be selected for measurement.

[0162] It can be calculated that t n The oscillating current is expressed by equation (9), and all peak points have extreme values. Therefore, when t=t n When , the derivative of equation (9) should be zero and can be expressed as:

[0163]

[0164] therefore

[0165]

[0166] Thus, t n This can be obtained by formula 17:

[0167]

[0168] Once you get t n , B2 can be calculated by equation (14).

[0169] Therefore, ω d , B2 and t n By T d 、i p-pn and i p-pm The measurement results are solved.

[0170] Once you know d , α and B2, the values of R, L, and C can be determined.

[0171] According to equation (8), the calculation formula of L is

[0172]

[0173] Where V in is the PWM swing voltage, which in this case is 30 volts.

[0174] According to equation (4), R can be calculated by the following formula

[0175] R=2·L·α (19)

[0176] According to equations (5) and (6), the calculation formula for C is

[0177]

[0178] Next, the calculation process in the actual project is explained.

[0179] In the captured waveform, T d It is measured using the vertical cursors in the oscilloscope, such as Figure 9 shown.

[0180] exist Figure 9 The duration of the five pulses is 770ns, T d It is 154ns.

[0181] Select the 3rd and 5th pulses for measurement. Use the horizontal cursors to measure their peak-to-peak amplitudes. In the actual signal, i p-p3 174mA, i p-p5 It is 82mA.

[0182] According to T d =154ns, i p-p3 =174mA, i p-p5 =82mA and V in =30V, the coefficients in equation (9) are obtained from equations (10), (13), (14) and (17).

[0183]

[0184] Then, according to equations (18), (19), and (20), the values of R, L, and C in the RLC model can be calculated:

[0185]

[0186] As mentioned above, in the EMI signal transmission model, Cw is 1.5 times C, Lc is 1 / 1.5 of L, and Resr + Rc is 1 / 1.5 of R. Therefore, Cw is 267pF, Lc is 2.24μH, and Resr + Rc is 10.9 ohms. Rc can be measured directly on the cable and is 0.2 ohms. Then, Resr is calculated to be 10.7 ohms. Therefore, based on these determined values, a simulation schematic of the EMI signal transmission model was established and tested in the simulation tool. The layout is carried out in Figure 10 Shown on the left.

[0187] A signal generator is used to simulate a 30 kHz PWM signal on phase A. Switches S1 and S2 are placed in the simulation circuit to change the initial states of phases B and C. A current probe is placed on the wire of phase A to measure the current oscillation. An RLC model is also laid out on the right for comparison with the EMI signal transmission model.

[0188] The simulation results are displayed on a virtual oscilloscope. Channel B shows the current oscillation in the EMI signal transmission model, while Channel C shows the oscillation in the RLC model.

[0189] Comparing the waveforms of channel B and channel C, we find that the oscillations in the RLC model and the EMI signal transmission model are the same. This verifies the equivalence of the RLC model and the EMI signal transmission model in terms of AC. The simulated waveforms are also consistent with Figure 9 The actual waveforms shown are the same. It verifies the analysis and calculation.

[0190] Next, an EMI suppression filter was designed using the EMI signal transmission model and simulation tools.

[0191] Design of EMI Suppression Filters

[0192] The purpose of establishing the two models and determining all parameters within them is to facilitate the design of EMI suppression filters. Using the EMI signal transmission model and its parameters, all filter components can be modified and tested using simulation software. Otherwise, the design process would require extensive measurement, analysis, testing, and modification of the actual circuit. Sometimes, miscalculations can damage the motor.

[0193] As mentioned above, the EMI generated in an RLC network is an oscillation in response to the switching signal. To reduce this oscillation, a low-pass filter (LPF) is typically used to filter the high-frequency components of the switching signal, thereby reducing the dv / dt ratio. LC circuits, consisting of inductors and capacitors, are ideal for LPFs due to their simple structure, minimal components, and low excess power consumption.

[0194] This type of LC filter always produces two oscillations: a natural oscillation at the frequency determined by the filter inductor and capacitor; and a forced oscillation at the frequency determined by the PWM. If the natural frequency is close to the operating frequency, resonance may occur in circuits with excessively high voltages and currents. If resonance occurs, the filter's natural frequency should be designed to be significantly higher or lower than the PWM frequency. Generally, a frequency difference of three is a safe value. Since the PWM frequency in this case is 30kHz, the filter's natural frequency should be higher than 100kHz or lower than 10kHz. As an LPF, a lower frequency is preferred to reduce noise. Therefore, the LC filter's natural frequency should be lower than 10kHz, which is also the cutoff frequency of a low-pass filter.

[0195] On the other hand, the motor's response frequency is 238Hz, which is determined by the inductance and resistance of the winding. To avoid affecting the control characteristics, the minimum frequency of the LC filter is specified to be 2.5K, which is about 10 times the motor's response frequency.

[0196] The natural oscillation frequency (f0) in the LC circuit is also the cutoff frequency (f C ), which is determined by the following formula:

[0197]

[0198] Where L is the value of the inductor in the LC filter and C is the value of the capacitor of the LC filter.

[0199] The inductor of the LC circuit is connected in series with the winding. Its inductance cannot be too large so as not to affect the characteristics of the winding. Experimentally, in this case, the inductor cannot exceed one tenth of the winding inductance, that is, 1mH.

[0200] Inductors always have parasitic capacitance. For a 1mH / 1A inductor, its parasitic capacitance is typically tens of pF. The parasitic capacitance of the inductor in an LC circuit cannot be ignored, as it can bypass transient signals. The transient signal originates from the switch, passes through the parasitic capacitance of the inductor in the LC filter, and then reaches two branches: the capacitor in the LC filter and the cable and winding. Although the transient signal passing through the cable is small, it still poses the risk of electromagnetic interference problems. Therefore, the capacitor in the LC filter should be large enough to shunt most of the transient current before it is transmitted to the cable. As a rule of thumb, the value of the filter capacitor should be at least 100 times the value of the parasitic capacitance in the winding. In this case, the minimum value of the filter capacitor is set to 27nF.

[0201] Therefore, the design of the LC filter in the present invention sets three constraints:

[0202] 1) The L value should not exceed 1mH;

[0203] 2) C value should not be less than 27nF;

[0204] 3) The product of L and C should satisfy the cutoff frequency between 2.5KHz and 10KHz.

[0205] Choosing different cutoff frequencies will result in different filter characteristics. Even for a certain frequency, different combinations of L and C will produce different effects.

[0206] When the PWM signal passes through the LPF and reaches the load, the filter should absorb most of the AC current. This AC current alternately flows in and out of the filter's capacitor, charging and discharging it. While theoretically, this current does not actually contribute to power, it still dissipates some power due to the equivalent series resistor within the capacitor. This AC current also generates an AC voltage across the capacitor, which is superimposed on the DC output voltage of the load. The filter's low inductance results in high AC current; low capacitance results in high AC output voltage. Both AC current and voltage must be considered when designing the filter.

[0207] To evaluate the performance of different cutoff frequencies and different LC combinations, a lot of calculations are required. The practical approach is not to calculate, but to build a simulation circuit and try different values in a virtual environment. Figure 11 A system schematic diagram based on the EMI signal transmission model is shown.

[0208] exist Figure 11 In, L f and C f Forming an LC filter, R f It's L fThe equivalent series resistance is 1 ohm. An LC filter is placed between the switch and the cable. A signal generator generates a 30V / 30kHz square wave to simulate PWM. An analog oscilloscope is used to capture the waveforms of certain signals. Channel A of the oscilloscope is connected to the output of the PWM. Channel B measures the output current fed to phase A of the motor. Channel C measures the AC output voltage, and Channel D measures the AC current charging and discharging C. f .

[0209] Through simulation tools and EMI signal transmission models, different frequencies and different LC combinations were realized in a virtual environment. After checking all simulation results and considering several engineering issues, the filter parameters were finally determined to be L f =1000μH (rated current is 900mA), C f =330nF (rated voltage is 100V). The cutoff frequency of the LC filter is 8.76KHz. The simulation results are as follows Figure 12 shown.

[0210] exist Figure 12 In the example, the current fed to the cable has a ripple of 1.5 mA at 30 kHz (Channel B); f The charging current is 260mA (Channel C); and the AC amplitude of the output voltage is 4V at 30kHz (Channel D).

[0211] As mentioned above, EMI originates from current oscillations in the cable, which have a frequency of 6 MHz and a maximum amplitude of 350 mA. The LC filter suppresses the current oscillations to 1.5 mA, removing high-frequency components. This should effectively filter out EMI.

[0212] The control characteristics of the servo motor were also tested, and no changes were found after installing the filter. Figure 13 and Figure 14 The captured waveform of the actual signal on the circuit is shown. The test configuration is the same as Figure 1 and Figure 2 The configuration is the same as in .

[0213] contrast Figure 1 and Figure 2 、 Figure 13 and Figure 14 , it can be seen that the current oscillation has been filtered out.

[0214] The specific process of the method of the present invention is as follows: Figure 15 As shown;

[0215] In summary, the present invention eliminates the need to use network analyzers or other equipment to measure and model multiple component parameters of the motor and its driver, nor does it require consideration of internal winding resonances. Instead, it only requires measuring the system's drive current, saving time and effort. Furthermore, debugging and evaluation can be completed in a simulated environment, reducing costs.

[0216] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for designing an LC output filter in a PWM driven servo motor system, characterized in that: The following steps are included: Analyze the EMI of the three-phase servo motor system and establish an EMI signal transmission model based on the EMI characteristics; Convert the EMI signal transmission model into an RLC model; Then the RLC model is used to determine the key parameters of the EMI signal transmission model; Finally, the design of the LC output filter is verified based on the key parameters of the EMI signal transmission model; Use the RLC model to determine the key parameters of the EMI signal transmission model, including: In the captured oscillating current waveform, two pulses are selected and the period and pulse current peak are measured. Based on the measurement results, the unknown coefficients in formula (9) are calculated using formulas (10), (13), (14) and (17). Based on the calculated coefficients, the values of R, L and C in the RLC model are obtained by combining formulas (18), (19) and (20). Where R is the equivalent series resistance of the motor drive cable, L is the equivalent inductance of the motor drive cable, and C is the parasitic capacitance of the motor winding. According to Kirchhoff's voltage law, the loop of the RLC circuit is expressed by equation (1): （1） Where i(t) or i(x) is a function of current, Vin is the input value, switching between 0V and Vin; Differentiating both sides of the equation and dividing them by L forms a standard second-order differential equation: （2） Its characteristic equation is s 2 + (R / L) * s + 1 / LC = 0, the two solutions of the characteristic equation are calculated using the quadratic formula: （3） where α is the Neper frequency in rad / s, which describes the damping rate and is expressed as （4） ω0 is the resonant radian frequency in rad / s, expressed as: （5） The step response is underdamped, which means that α 2 Less than ω0 2 , whose radian frequency ω d Expressed as: （6） The solution to equation (3) has the following form: （7） A step function is applied by turning the switch from 0V to Vin, satisfying two initial conditions: (1) When t = 0, the current i(t) is zero; (2) When t = 0, the voltage on L is Vin, expressed as L∙(di(t)) / dt; Under these two conditions, find the coefficients B1 and B2: （8） The current oscillation is expressed as: （9） The vertical axis of the coordinate is the current amplitude, and the horizontal axis is time; T d is the period of oscillation, for T d , coefficient ω d It is derived from the following formula: （10） The time point at which the nth pulse has a positive peak is defined as t n The time point when the nth pulse has a negative peak value is defined as t' n ;t' n t n Add T d Half of t' n =t n +π / ω d ; The peak-to-peak value of the nth pulse is defined as i p-pn （11） Select the nth pulse and the mth pulse to be measured, where "m" is the sequence number later than "n"; i p-pn and i p-pm The ratio is expressed as: (12) α is solved for: （13） According to equation (11), B2 is expressed as t n function; （14） Calculate t n The measured value of the oscillating current is expressed by equation (9). All peak points have extreme values. Therefore, when t=t n When , the derivative of equation (9) should be zero and can be expressed as: （15） therefore （16） thereby, t n According to formula (17), we can get: （17） Once you get t n , calculate B2 by equation (14); Therefore, ω d , B2 and t n By T d 、i p-pn and i p-pm Solve the measurement results of ; Once you know d , α and B2, then determine the values of R, L, and C, where R, L, and C are the equivalent series resistance of the motor drive cable, the equivalent inductance of the motor drive cable, and the parasitic capacitance of the motor winding under the RLC model; According to equation (8), the calculation formula of L is （18） Where V in is the PWM swing voltage; According to equation (4), R is calculated by the following formula （19） According to equations (5) and (6), the calculation formula for C is （20） In the captured oscillating current waveform, T d It is measured using the vertical cursors in the oscilloscope.

2. The method for designing an LC output filter in a PWM driven servo motor system according to claim 1, wherein: The design verification of the LC output filter based on the key parameters of the EMI signal transmission model specifically includes: Based on the values of R, L, and C determined by the RLC model, a simulation circuit for the EMI signal transmission model is constructed. In the EMI signal transmission model, the sum of the winding equivalent series resistance Resr and the drive cable resistance Rc is 1 / 1.5 of R. Rc is measured directly on the drive cable. The drive cable equivalent inductance Lc is 1 / 1.5 of L, and the winding parasitic capacitance Cw is 1.5 times C. Therefore, the values of Resr, Lc, and Cw in the EMI signal transmission model are determined. Then add 1 LC filter on each phase and use equivalent series resistance; The natural oscillation frequency f0 in the LC filter circuit is also the cutoff frequency f of the LPF or low-pass filter. C On the one hand, the design is much lower than the PWM frequency, and a frequency difference of 3 times is safe; on the other hand, considering the response frequency of the motor, it can be about 10 times the response frequency of the motor. Combining these two factors, the cutoff frequency f of the system is determined. C ;f C and the inductor L in the LC filter f The value of capacitance C f The relationship between the values of is determined by the following formula: （21） Build a simulation circuit and try different L f and C f value, evaluate the filtering performance, output voltage and charging current, and determine the optimal L value of the LC filter f and C f value.

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