Low speed sensorless control method for induction motor based on lower bridge arm sampling

Abstract

This application provides a low-speed sensorless control method for induction motors based on lower arm sampling, comprising: establishing a mathematical model of the induction motor; constructing rotor position equations using the average voltage vector and current change during the first half of the PWM cycle; obtaining stator current sampling values ​​through the lower arm sampling resistor at the beginning and middle of the PWM cycle by reconstructing the zero vector allocation method, and calculating the average current slope during the first half of the PWM cycle; constructing a system of equations using the average voltage vector and average current slope of two adjacent PWM cycles, and solving for rotor position-related parameters; normalizing the rotor position-related parameters and sending them into a phase-locked loop to obtain an estimated rotor flux linkage position angle for control. This application solves the lower arm sampling blind zone through the above method and constructs a complete current sampling window without adding additional hardware sensors through an improved PWM modulation strategy.

Description

Technical Field

[0001] This application relates to the field of electrical engineering technology, and more specifically, to a sensorless control method, system and terminal for low-speed induction motors based on lower arm sampling. Background Technology

[0002] Electric motors are widely used in industry due to their robust structure and low cost. To improve system reliability and reduce costs, sensorless control technology has become a research hotspot. In the medium-to-high speed range, methods based on fundamental wave models are relatively mature; however, in the zero-speed and low-speed regions, traditional model methods fail due to the weak back electromotive force. Currently, the mainstream low-speed sensorless control methods are mainly divided into two categories: 1. High-frequency signal injection method: Utilizing the salient pole effect of the motor, the rotor position is extracted by injecting a high-frequency voltage signal. The disadvantage is that it introduces additional torque ripple and high-frequency noise, increasing system losses and being limited by the bandwidth design of the filter. 2. Fundamental wave PWM waveform excitation method: Directly using the PWM harmonics generated by the inverter switching action as excitation, the position is calculated by measuring the current response. Compared with the high-frequency injection method, this method has no additional noise and a fast dynamic response.

[0003] Currently, sensorless control technology based on fundamental PWM waveform excitation has become a research hotspot for zero-speed and low-speed control of AC motors. Most existing implementations are based on the hardware foundation of directly acquiring stator phase current. Specifically, these schemes typically install Hall current sensors or current transformers at the inverter output to directly measure the three-phase current of the motor stator. Since Hall sensors or transformers can provide continuous and complete current signals, the control system can acquire current values ​​in real time regardless of the inverter's switching state. Therefore, existing PWM excitation algorithms (such as those based on the instantaneous current slope method or the INFORM method) typically utilize this convenient hardware to trigger sampling and calculate the current derivative at any given time, thereby extracting the inductance anisotropy characteristics containing rotor position information.

[0004] Application publication number CN117081449A discloses a method for estimating the rotor position of an AC motor based on inverter pulse width modulation (PWM) excitation. This method employs space vector voltage modulation (SVM) for a two-level voltage source inverter, calculating the average voltage vector value during the zero and non-zero vector action periods in two adjacent PWM cycles. Simultaneously, by measuring the current during the zero voltage vector action period at the beginning / half of each cycle, the average current slope within the "first half of the PWM cycle" of each cycle is calculated, resulting in a rotor position calculation formula that estimates the rotor position of the AC motor from zero speed to high speed. However, this technical solution lacks any adaptation design for low-cost lower bridge arm resistance sampling in industry, relying on expensive phase current acquisition hardware such as Hall sensors and current transformers, leading to high hardware costs and limited engineering application.

[0005] In existing technologies, the traditional instantaneous current slope method requires multiple high-frequency samplings within an extremely short PWM pulse period to calculate the differential. This places extremely high demands on the sampling rate, conversion speed, and bandwidth of the signal conditioning circuit of the ADC, making it difficult to promote in low-cost industrial frequency converters.

[0006] Instantaneous differential operations amplify high-frequency switching noise, resulting in a low signal-to-noise ratio for position estimation signals.

[0007] The industry widely adopts low-cost lower-arm resistance sampling schemes. However, under standard seven-segment SVPWM modulation, the lower arm is turned off at the midpoint of the PWM cycle (when the zero vector is applied), and no phase current can flow. This results in the inability to obtain the complete current information required by the PWM excitation method, i.e., there is a sampling blind zone, causing the algorithm to fail. Summary of the Invention

[0008] In view of one of the defects in the prior art, the purpose of this application is to provide a sensorless control method for low-speed induction motors based on lower arm sampling.

[0009] A first aspect of this application provides a low-speed sensorless control method for an induction motor based on lower arm sampling, comprising: A mathematical model of an induction motor considering the anisotropy of stator leakage inductance is established, and the rotor position solution equation is constructed using the average voltage vector and current change during the first half of the PWM cycle. By improving the PWM waveform excitation strategy and reconstructing the zero vector allocation method, the stator current sampling value is obtained through the lower bridge arm sampling resistor at the beginning and middle of the PWM cycle, and the average current slope in the first half of the PWM cycle is calculated. By substituting the average current slope and the average voltage vector within two adjacent cycles into the constructed rotor position solution equation, the rotor position-related parameters are obtained. After normalizing the rotor position-related parameters, the data are fed into a phase-locked loop to obtain an estimated rotor flux linkage position angle, enabling sensorless control of the induction motor in the zero-speed and low-speed regions.

[0010] Optionally, establishing a mathematical model of the induction motor that considers the anisotropy of stator leakage inductance includes: By using the equivalent circuit of the induction motor when the stator leakage inductance changes, the voltage equation on the stator winding in two-phase stationary coordinates is obtained. Based on the voltage equation, a coordinate transformation is performed to obtain the stator leakage inductance matrix in a two-phase stationary coordinate system. By neglecting the effects of stator resistance voltage drop and back electromotive force during the low-speed operation of the induction motor, the voltage equation in the two-phase stationary coordinate system is simplified, and the mathematical model of the induction motor is established.

[0011] Optionally, the average voltage vector is obtained by weighting the non-zero voltage vector acting in the first half of the PWM cycle and its acting time, and then decomposed into voltage components of the α-axis and β-axis in a two-phase stationary coordinate system.

[0012] Optionally, the improved PWM waveform excitation strategy includes either a single zero vector modulation strategy based on full substitution or a hybrid zero vector modulation strategy based on center reconstruction. Both the single zero-vector modulation strategy based on full substitution and the hybrid zero-vector modulation strategy based on center reconstruction adjust the duration of the zero vector while maintaining the volt-second balance principle.

[0013] Optionally, the single zero vector modulation strategy based on full substitution is as follows: all zero vectors in the standard seven-segment SVPWM are replaced with zero vectors, while keeping the action sequence and timing of each non-zero voltage vector unchanged, so that the start, middle and end times of the PWM cycle are all zero vector action stages, and the lower bridge arm is still in the conducting state at the middle time of the PWM cycle, thus forming single zero vector modulation.

[0014] Optionally, the hybrid zero-vector modulation strategy based on center reconstruction is as follows: retaining the standard seven-segment SVPWM in the regions on both sides of the cycle and most of the middle region, inserting a zero-vector window at the exact middle moment of the PWM cycle, dividing the original middle time of the PWM cycle into four equal parts for sampling, and forming hybrid zero-vector modulation.

[0015] Optionally, the average current slope is calculated as follows: the stator current collected at the beginning and middle of the PWM cycle is used to calculate the difference to obtain the current change during the non-zero voltage vector action period; after Clarke coordinate transformation, the current change of the α-axis and β-axis in the two-phase stationary coordinate system is obtained, and then the average current slope is calculated in combination with the PWM half-cycle duration.

[0016] Optionally, it also includes a step of compensating for the inverter dead-time effect, wherein the compensation method includes voltage-based compensation or time-based pulse width compensation, wherein:

[0017] The voltage-based compensation method is as follows: calculate the dead zone voltage error vector in the three-phase stationary coordinate system according to the polarity of the stator phase current, obtain the voltage error components on the α-β axis through Clarke transformation, use the voltage error components to correct the reference voltage, and use the corrected reference voltage to participate in the calculation of the average voltage vector.

[0018] The time-based compensation method is as follows: the conduction time of each phase switching device calculated by the SVPWM modulation stage is compensated according to the polarity of the stator phase current. When the current flows from the inverter to the motor, the compensation time is added to the ideal conduction time, and when the current flows from the motor to the inverter, the compensation time is subtracted from the ideal conduction time, directly correcting the count value of the PWM comparator register.

[0019] A second aspect of this application provides a system for a low-speed sensorless control method for an induction motor based on lower arm sampling, comprising: The equation building module is used to establish a mathematical model of an induction motor that considers the anisotropy of stator leakage inductance. The rotor position solution equation is constructed using the average voltage vector and current change during the first half of the PWM cycle. The calculation module is used to reconstruct the zero vector allocation method by improving the PWM waveform excitation strategy. At the beginning and middle of the PWM cycle, the stator current sampling value is obtained through the sampling resistor of the lower bridge arm, and the average current slope in the first half of the PWM cycle is calculated. The solution module is used to input the average current slope and the average voltage vector obtained in two adjacent PWM cycles into the constructed rotor position solution equation to obtain the rotor position related parameters. The control module is used to normalize the rotor position-related parameters and then send them into the phase-locked loop to obtain an estimated rotor flux linkage position angle, and to perform sensorless control of the induction motor in the zero-speed and low-speed regions.

[0020] A third aspect of this application provides a terminal, the terminal comprising: a memory, a processor, and a sensorless control program for a low-speed induction motor based on lower arm sampling, stored in the memory and executable on the processor, wherein when the processor executes the sensorless control program for a low-speed induction motor based on lower arm sampling, the terminal controls the implementation of the steps of the sensorless control method for a low-speed induction motor based on lower arm sampling.

[0021] The low-speed sensorless control method for induction motors based on lower arm sampling provided in this application employs a combination of average current slope and improved PWM waveform excitation strategies. By utilizing the average current slope in the first half of the PWM cycle (i.e., the current increment in the first half of the cycle) to replace the instantaneous current slope, the rotor position of the induction motor is extracted, reducing the dependence on high-frequency hardware sampling. Simultaneously, through the improved PWM waveform excitation strategy, the sampling blind zone of standard SVPWM is eliminated by reconstructing the zero vector sequence for the lower arm resistance sampling circuit, realizing full-cycle current monitoring under low-cost hardware. Compared with the traditional PWM excitation method that requires Hall sensors or high-bandwidth ADCs, this method is compatible with general low-cost lower arm sampling inverter solutions. It does not require high-frequency injection or expensive phase current sensors, and can achieve a fully closed-loop sensorless control system for induction motors using only the lower arm resistance and a conventional DSP ADC.

[0022] Other technical effects resulting from the additional features will be further illustrated in the corresponding embodiments. Attached Figure Description

[0023] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart of a low-speed sensorless control method for an induction motor based on lower arm sampling, according to one embodiment of this application. Figure 2 This is an equivalent model of an induction motor considering stator leakage inductance variations in one embodiment of this application; Figure 3 This is a schematic diagram of average current slope sampling in one embodiment of this application; Figure 4 This is a block diagram of a phase-locked loop in one embodiment of this application; Figure 5 This is a schematic diagram of the sampling circuit of the lower bridge arm in one embodiment of this application; Figure 6 This is a single-zero vector modulation waveform in one embodiment of this application; Figure 7 This is a hybrid zero-vector modulation waveform in one embodiment of this application; Figure 8 This is a waveform diagram showing the effect of the dead-time effect on the output voltage in one embodiment of this application; Figure 9 This is a block diagram of the closed-loop structure for estimating flux linkage angle in torque control mode according to one embodiment of this application; Figure 10 This is a closed-loop steady-state estimation angle waveform in one embodiment of this application. Detailed Implementation

[0024] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application, and these all fall within the protection scope of the present application. Parts not described in detail in the following embodiments can be implemented using existing technology.

[0025] In existing technologies, the traditional instantaneous current slope method requires multiple high-frequency samples within an extremely short PWM pulse cycle to calculate the derivative. This places extremely high demands on the sampling rate, conversion speed, and bandwidth of the ADC and signal conditioning circuit, making it difficult to promote in low-cost industrial frequency converters. Instantaneous derivative calculations amplify high-frequency switching noise, resulting in a low signal-to-noise ratio for position estimation signals. Under standard seven-segment SVPWM modulation, the lower bridge arm is turned off at the midpoint of the PWM cycle (when the zero vector is applied), preventing the flow of phase current. This leads to the inability to obtain the complete current information required by the PWM excitation method, resulting in a sampling blind zone and algorithm failure. To address these issues, this application provides a sensorless low-speed control method for induction motors based on lower bridge arm sampling, thereby resolving these problems.

[0026] Reference Figure 1 As shown in one embodiment of this application, a low-speed sensorless control method for an induction motor based on lower arm sampling includes: S100. Establish a mathematical model of the induction motor considering the anisotropy of stator leakage inductance, and construct the rotor position solution equation using the average voltage vector and current change in the first half cycle of PWM. S200: By improving the PWM waveform excitation strategy and reconstructing the zero vector allocation method, the stator current sampling value is obtained through the lower bridge arm sampling resistor at the beginning and middle of the PWM cycle, and the average current slope in the first half of the PWM cycle is calculated. S300. Substitute the average voltage vector and average current slope of the two adjacent PWM cycles into the constructed rotor position solution equation to obtain the rotor position related parameters. S400: After normalizing the rotor position-related parameters, the data is sent to the phase-locked loop to obtain an estimated rotor flux linkage position angle, enabling sensorless control of the induction motor in the zero-speed and low-speed regions.

[0027] Specifically, rotor position estimation at low speeds or even zero speeds is achieved by coordinating the anisotropic characteristics of the stator leakage inductance of the induction motor, an improved PWM excitation strategy, and a lower arm current sampling mechanism. A mathematical model of the induction motor considering the anisotropic stator leakage inductance is established. Based on this, the rotor position solution equation is constructed using the coupling relationship between the average voltage vector and current change in the first half-cycle of the PWM, thus avoiding dependence on the instantaneous current differential. To address the blind zone problem of "lower arm turn-off during the zero vector period in the middle moment" in standard seven-segment SVPWM sampling, the PWM waveform excitation strategy is improved by employing modulation methods such as all-zero vector substitution or center zero vector reconstruction, thereby achieving rotor position estimation at low speeds or even zero speeds. Replace with Or embedded at the center of the cycle The window is reconstructed to reconstruct the zero vector allocation logic, ensuring that the bridge arm sampling resistor can reliably obtain the instantaneous value of the stator current at the beginning and middle of the PWM cycle, and then calculate the average current slope within half a cycle. Using the two sets of average voltage and average current slope data provided by two adjacent PWM cycles, a set of overdetermined equations about the sine and cosine of the rotor position angle is formed. The position characteristic is directly obtained by analytical solution. Finally, the characteristic parameter is normalized and sent to the phase-locked loop to output the estimated value of the rotor flux position angle in real time, thereby realizing sensorless closed-loop control of the induction motor in the zero-speed and low-speed regions.

[0028] The low-speed region refers to the operating conditions where the motor speed is 10% lower than the rated speed or the stator frequency is lower than 5Hz.

[0029] The embodiments described above in this application reduce the requirements for ADC sampling rate and signal conditioning bandwidth by introducing an average current slope instead of an instantaneous current slope, avoiding the problems of high hardware cost and noise sensitivity caused by high-frequency sampling in the traditional instantaneous slope method. At the same time, by using an improved PWM modulation strategy, the sampling blind zone in the lower bridge arm resistance sampling scheme of the standard seven-segment SVPWM is eliminated, enabling low-cost industrial frequency converters to achieve full-cycle current monitoring using only conventional sampling resistors and DSP built-in ADC. No high-frequency signal injection is required, no additional torque ripple or high-frequency noise is generated, and stable position estimation accuracy can still be maintained under low-speed and zero-speed conditions. It has the advantages of low cost, low noise, and high reliability, and is suitable for induction motor drive systems that are cost-sensitive and require high-performance sensorless control.

[0030] It should be noted that the average voltage vector and average current slope used in the formula for calculating the rotor position refer to the quantities in the first half of the PWM cycle; the two adjacent PWM cycles refer to the first half of the current cycle and the first half of the next cycle, that is, the first half of each of the two adjacent PWM cycles.

[0031] In some specific embodiments of this application, the mathematical model for establishing an induction motor that considers the anisotropy of stator leakage inductance includes: By using the equivalent circuit of the induction motor when the stator leakage inductance changes, the voltage equation on the stator winding in the two-phase stationary coordinate system is obtained. Based on the voltage equation, the coordinate transformation is performed to obtain the stator leakage inductance matrix in the two-phase stationary coordinate system. By ignoring the influence of stator resistance voltage drop and back electromotive force in the low-speed operation state of the induction motor, the voltage equation in the two-phase stationary coordinate system is simplified to obtain the voltage equation, and the mathematical model of the induction motor is established.

[0032] The embodiments described above in this application derive the voltage equation of the stator winding in a two-phase stationary coordinate system by relying on the equivalent circuit of the induction motor when the stator leakage inductance changes. Then, coordinate transformation is performed on this voltage equation to obtain the stator leakage inductance matrix in this coordinate system. Simultaneously, considering the operating characteristics of the induction motor at low speeds, the influence of stator resistance voltage drop and back electromotive force is ignored, and the voltage equation in the two-phase stationary coordinate system is reasonably simplified, ultimately establishing the mathematical model of the induction motor. Through targeted simplification and coordinate transformation, negligible interference factors at low speeds are eliminated, making the established mathematical model more closely match the characteristics of the induction motor at low speeds. This simplifies the subsequent rotor position calculation process and lays a precise and suitable theoretical model foundation for rotor position estimation based on the average current slope. By reasonably ignoring the influence of stator resistance voltage drop and back electromotive force during low-speed operation, the voltage equation is significantly simplified, reducing the computational complexity of the control system.

[0033] Specifically, the stator leakage inductance of an induction motor changes periodically with the rotor position. Taking a delta-connected three-phase induction motor as an example, its equivalent circuit considering the change in stator leakage inductance is as follows: Figure 2 As shown.

[0034] exist Figure 1 In this case, we can assume that the stator leakage inductance changes according to the following formula: (1) In equation (1), To average stator leakage inductance, The magnitude of the stator leakage inductance change caused by anisotropy is given, considering the salient pole effect caused by motor saturation. In a two-phase stationary coordinate system, the voltage equations on the stator windings are as follows: (2) In equation (2), The stator voltage vector, The stator current vector, It is the back potential vector. The expression for the stator leakage inductance matrix in a two-phase stationary coordinate system is shown below, and its coordinate transformation derivation process is as follows: (3) After simplification, the stator leakage inductance matrix in the two-phase stationary coordinate system can be obtained: (4) At low speeds, the voltage drop across the resistance and the back electromotive force can be ignored, and the voltage equation can be expressed as: (5) In equation (5), , However, the parameters of the motor are often difficult to know in advance, i.e., in equation (5) , Generally, the values ​​are unknown. Therefore, a certain mathematical transformation is needed for equation (5). In order to eliminate the coupling between the inductance parameter and the current slope, the variables shown in the following equation are defined: (6) Equation 6 is an intermediate parameter matrix used to simplify Equation 5; Multiplying equation (6) on the left by both sides of equation (5), we obtain the voltage equation after left multiplication as follows: (7) Expanding and simplifying equation (7) yields the rotor position solution equation as shown below: (8) Equations (2) to (5) together constitute the mathematical model of the induction motor used in this application. In the two-phase stationary coordinate system, the voltage equation on the stator winding is shown in equation (2), which constitutes the core foundation of the mathematical model of the induction motor. Equation (5) is the simplified mathematical model of the induction motor established in this application under low-speed operating conditions, which is used for the subsequent extraction of rotor position information.

[0035] In some specific embodiments of this application, the average voltage vector is obtained by weighted averaging of the non-zero voltage vector acting in the first half cycle of the PWM and its acting time, and then decomposed into voltage components of the α-axis and β-axis in a two-phase stationary coordinate system.

[0036] In the above embodiments of this application, the average voltage vector is obtained by weighted averaging of the non-zero voltage vector and its duration in the first half of the PWM cycle, and decomposed into voltage components on the α and β axes in a two-phase stationary coordinate system. Based on the known non-zero voltage vector and duration parameters in the SVPWM algorithm, the specific value of the average voltage vector can be calculated. Furthermore, it is transformed into the component form on the α and β axes through coordinate decomposition, which is compatible with the coordinate system analysis system of the mathematical model of the induction motor and improves the stability and accuracy of rotor position calculation.

[0037] Specifically, in SVPWM modulation, the average voltage vector... , This can be obtained by weighting the non-zero voltage vectors acting within the cycle and their duration. Assume that in the first half of the PWM cycle, the two non-zero voltage vectors acting are... and The action time is respectively and , The average voltage was obtained at , The components on the axis are: (9) in, The projection values ​​of the basic voltage vector in the two-phase stationary coordinate system are shown in Table 1. Since... and In the SVPWM algorithm, the current is a known quantity, therefore the average voltage vector can be calculated accurately. A schematic diagram of current sampling is shown below. Figure 3 As shown, the first sampling occurs at the beginning of the PWM cycle, i.e., the first zero vector. The sampling is triggered at the start of the action, and the second sampling occurs in the middle of the PWM cycle, i.e., at the zero vector. Sampling is triggered at the center of the action. By obtaining the difference between these two sample values, the change in current during the non-zero voltage vector action can be accurately calculated. After the coordinate transformation shown in equation (10), the coordinates of the first half of the PWM cycle can be obtained. shaft and The change in current along the shaft.

[0038] (10) Table 1. Basic voltage vector in , Components of the axis like Figure 3 As shown, equation (8) contains two unknowns. and The solution cannot be obtained using data from only one PWM cycle; a system of equations needs to be constructed using data from two adjacent PWM cycles. Assume the average voltage of the first half of the k-th PWM cycle is... , its in , The components on the axis are , average current slope , its in , The components on the axis are , The average voltage of the first half of the (k+1)th PWM cycle is , its in , The components on the axis are , average current slope , its in , The components on the axis are , Substituting the above data into equation (10), we can obtain the result. and The analytical expression: (11) (12) Based on obtaining equations (11) and (12), by adjusting... and Normalization eliminates parameters Then and The estimated rotor flux position angle can be obtained by feeding the data into a phase-locked loop (PLL). The principle block diagram of PLL is as follows: Figure 4 As shown.

[0039] The rotor position estimation method based on average current slope described above effectively reduces the hardware sampling bandwidth requirements by utilizing the average value within the first half of the PWM cycle. In practical industrial drive applications, especially in cost-sensitive situations, to further reduce system costs, expensive Hall current sensors are often not used. Instead, current information is obtained by connecting sampling resistors in series in the lower arm of the three-phase inverter. Traditional seven-segment SVPWM modulation strategies cannot meet the sampling requirements based on average current slope. To address this issue, this section proposes a lower arm current sampling strategy based on changing the PWM waveform excitation. By reconstructing the zero vector allocation method, it ensures accurate acquisition of the current at key moments within the PWM cycle using the lower arm sampling circuit without increasing additional hardware costs, thereby completing the estimation of the rotor flux linkage position.

[0040] The sampling circuit of a three-phase voltage source inverter typically consists of a sampling resistor connected in series with the emitter of each of the three lower arms. A schematic diagram of a single-phase lower arm is shown below. Figure 5 As shown.

[0041] In some specific embodiments of this application, the improved PWM waveform excitation strategy includes either a single zero vector modulation strategy based on full substitution or a hybrid zero vector modulation strategy based on center reconstruction.

[0042] Among them, the single zero vector modulation strategy based on full substitution and the hybrid zero vector modulation strategy based on center reconstruction both adjust the action period of the zero vector while maintaining the volt-second balance principle.

[0043] It should be noted that the rotor position estimation algorithm based on average current slope proposed in this application refers to the aforementioned method of solving for rotor position using the average voltage vector and current change within a half-cycle of the PWM. This requires calculation at the beginning of each PWM cycle ( ) and intermediate time ( Two current samples are taken separately to calculate the change in current. In conventional seven-segment SVPWM modulation, to reduce switching losses and harmonics, one switching cycle typically includes two zero vectors, i.e. and With the first Taking sectors as an example, the typical sequence of vector actions is as follows: At the initial time ( ), the action vector is At this time, all three lower bridge arms are conducting, and the motor stator current freewheels through the lower bridge arms. The current flowing through the sampling resistor is the current that flows in the opposite direction to the three-phase current, and can be directly sampled at this time. At the intermediate moment ( ), the action vector is At this point, the upper three-phase bridge arms are conducting, while the lower three-phase bridge arms are all off. The motor stator current freewheels through the upper bridge arms, bypassing the sampling resistors in the lower bridge arms. If current sampling is to be performed without altering the PWM waveform, an additional current measurement circuit would need to be connected to the inverter's output, incurring additional hardware costs. Therefore, the hardware structure based on lower bridge arm sampling, when using standard seven-segment SVPWM, will prevent the aforementioned rotor position estimation algorithm based on average current slope from acquiring effective current data at the midpoint of the PWM cycle, rendering the average current slope method ineffective.

[0044] To address the blind zone issue in the aforementioned sampling without introducing additional hardware sampling circuitry, this application proposes an improved PWM waveform excitation generation strategy. The core idea of ​​this strategy is to modify the zero vector allocation logic while maintaining the volt-second balance principle, enabling current sampling using the lower bridge arm sampling resistor at both the beginning and middle of a PWM cycle. Specifically, depending on the generated PWM form, it can be divided into two methods: a single zero vector modulation strategy based on full substitution and a hybrid zero vector modulation strategy based on center reconstruction.

[0045] The single-zero vector modulation strategy based on full substitution is as follows: the zero vector in the standard seven-segment SVPWM is... Replace all with zero vector By maintaining the order and timing of action of each non-zero voltage vector, the start, middle, and end times of the PWM cycle are all zero vectors. During the active phase, the lower bridge arm remains in the conducting state at the midpoint of the PWM cycle, forming a single zero vector modulation.

[0046] To ensure that current can be sampled through the lower bridge arm resistor at the beginning and middle of the PWM cycle, the most direct method is to eliminate the SVPWM sequence. Vector. This strategy uses a full vector. The substitution method involves all segments of the standard seven-segment SVPWM. Vector replaced with At the same time, the order and timing of the action of each voltage vector remain unchanged. Still using the first... Taking sectors as an example, the vector order after adopting this strategy is as follows: The corresponding PWM waveform diagram is shown below. Figure 6 As shown.

[0047] like Figure 6 As shown, under this modulation method, the zero vector within one PWM cycle This occurred three times, at the beginning, middle, and end of the cycle. In this case, the PWM waveform of the upper bridge arm of one phase will always be a low-level signal. The advantage of this method is its simple implementation logic, and the fact that the lower bridge arm remains on throughout the entire zero-vector period provides sufficient sampling settling time. Although this method concentrates all the switching losses during the zero-vector period on a few bridge arms, the uneven thermal distribution of switching losses in the low-speed operating region of the motor, which is the focus of this paper, is still within an acceptable range.

[0048] Another approach, namely the hybrid zero-vector modulation strategy based on center reconstruction, involves retaining the standard seven-segment SVPWM on both sides of the cycle. and most of the intermediate areas Insert a zero vector at the exact middle of the PWM cycle. The window will be in the middle of the original PWM cycle. Duration of action The sample is divided into four equal parts and sampled to form a hybrid zero vector modulation.

[0049] Based on the center Reconstructed Hybrid Zero Vector Modulation Strategy In the above embodiments of this application, based on the whole Alternative modulation strategies address the sampling problem, but may increase current ripple or lead to excessive concentration of switching losses under certain high duty cycles or specific operating conditions. To achieve mid-moment sampling while maintaining the original harmonic characteristics of SVPWM, a center-based modulation method is proposed. The reconstructed hybrid zero-vector modulation strategy, based on the center The core idea of ​​the reconstructed hybrid zero-vector modulation strategy is to retain the standard seven-segment SVPWM on both sides of the cycle. and most of the intermediate areas Only at the very middle of the PWM cycle is a segment inserted. A window used for current sampling. Still using the first... Taking sectors as an example: the vector order after adopting the hybrid zero-vector modulation strategy is as follows: The corresponding PWM waveform diagram is shown below. Figure 7 As shown.

[0050] like Figure 7 As shown, the original continuous action It is segmented, with a width of [missing information] embedded in the center. of Vectors are used for easier analysis, reducing the time difference between the original PWM cycle and the data in the middle. Duration of action Divide into four equal parts, each with a duration of [length missing]. ,Right now This hybrid modulation method ensures that the two sampling data points required for the average current slope method can be obtained from the lower bridge arm, while also preserving the maximum amount of data. The vector effect makes the PWM waveform characteristics closer to the standard SVPWM, thus achieving a better balance between sampling feasibility and control performance.

[0051] In the sensorless control method described above in this application, the position information needs to be calculated using the average voltage of a single PWM cycle. However, in a voltage source inverter, to prevent the simultaneous conduction of two power devices on the same bridge arm, which could lead to a short circuit on the DC bus, a dead time must be set in the drive signal. [2, 3] During the dead time, the switches in the upper and lower arms of the same phase are both in the off state. At this time, the output potential is no longer determined by the control signal of the switch, but depends on the direction of the load current and the conduction state of the freewheeling diode. The average voltage at this time will be affected by the dead time effect and needs to be compensated.

[0052] In some specific embodiments of this application, the average current slope is calculated as follows: the stator current collected at the beginning and middle of the PWM cycle is used to calculate the difference to obtain the current change during the non-zero voltage vector action period; after Clarke coordinate transformation, the current change of the α-axis and β-axis in the two-phase stationary coordinate system is obtained, and then the average current slope is calculated in combination with the PWM half-cycle duration.

[0053] Specifically, when calculating the average current slope, this application first collects the stator current at two key moments at the beginning and middle of the PWM cycle, performs a difference calculation on the current values ​​collected twice, and obtains the current change during the non-zero voltage vector action phase; then, the current change is transformed into the current change on the α axis and β axis in the two-phase stationary coordinate system through Clarke coordinate transformation; finally, combined with the duration of the PWM half-cycle, the average current slope is obtained through calculation.

[0054] The embodiments described above in this application obtain effective data by sampling the current at two key nodes within the PWM cycle, and combine Clarke coordinate transformation to decompose the current change in a unified analysis coordinate system. At the same time, the average value is calculated based on the half-cycle duration of the PWM, replacing the high-frequency sampling differential calculation of the instantaneous current slope. This reduces the hardware requirements for the ADC sampling rate and conversion speed, effectively suppresses the interference of high-frequency switching noise, and improves the stability of the current slope data.

[0055] Among them, the average current slope method solves the high-frequency sampling bandwidth problem, and the improved PWM modulation solves the sampling blind zone problem of the lower bridge arm. The combination of the two realizes sensorless control under a low-cost platform.

[0056] In some specific embodiments of this application, in addition to the above method steps, a step of compensating for the inverter dead-time effect is also included, and the compensation method includes voltage-based compensation or time-based pulse width compensation.

[0057] exist Figure 8 In the diagram, the blue area represents the area where the actual output voltage is lower than the ideal reference voltage, and the orange area represents the area where the actual output voltage is higher than the ideal reference voltage. When the current... At that time, according to Figure 8 The error voltage can be obtained by subtracting the area of ​​the blue area from the area of ​​the orange area, corresponding to the waveform of the output voltage. It can be expressed by equation (13): (13) In equation (13), This indicates the duty cycle of the current ideal reference voltage output.

[0058] Similarly, when the current At that time, according to Figure 8 The error voltage can be obtained by subtracting the area of ​​the blue area from the area of ​​the orange area, corresponding to the waveform of the output voltage. It can be expressed by equation (14): (14) As can be seen from equations (13) and (14), the magnitude of the error voltage vector introduced by the inverter dead-time effect is proportional to the DC bus voltage and the dead time, while its direction depends on the polarity of the stator phase current. In the sensorless control system based on fundamental PWM excitation proposed in this paper, the extraction of rotor position information is highly dependent on the accurate analysis of the relationship between the stator voltage and current slope. In order to ensure the accuracy of rotor position estimation, an effective dead-time compensation strategy must be adopted to eliminate the influence of this nonlinear factor.

[0059] Depending on the compensation objective, inverter nonlinearity compensation can be divided into two categories: voltage-based compensation method and time-based compensation method.

[0060] In some specific embodiments of this application, the voltage-based compensation method is as follows: the dead zone voltage error vector in the three-phase stationary coordinate system is calculated according to the polarity of the stator phase current, the voltage error components on the α-β axis are obtained by Clarke coordinate transformation, the reference voltage is corrected by the voltage error components, and the corrected reference voltage is used to participate in the calculation of the average voltage vector.

[0061] Specifically, the voltage-based compensation method starts with the inverter reference voltage and eliminates the average deviation of the inverter output voltage caused by inverter nonlinearity by compensating for the inverter reference voltage. Based on the previous analysis, the dead-zone voltage error vector in the three-phase stationary coordinate system... It can be calculated using the following formula: (15) In equation (15), To represent the error voltage caused by inverter nonlinearity, equations (13) and (14) are substituted according to the different current polarities. The Clarke transform is then used to represent the three-phase voltage error. Projecting onto the two-phase stationary coordinate system, we obtain Voltage error components on the shaft and Subsequently, the reference voltage was corrected as follows: (16) By using the corrected voltage Replacement ideal reference voltage Involving it in the calculation can effectively eliminate the mismatch problem of current slope response caused by voltage distortion, thereby improving the accuracy of position estimation.

[0062] In some specific embodiments of this application, the time-based compensation method is as follows: the conduction time of each phase switching device calculated by the SVPWM modulation stage is compensated according to the polarity of the stator phase current. When the current flows from the inverter to the motor, the compensation time is added to the ideal conduction time, and when the current flows from the motor to the inverter, the compensation time is subtracted from the ideal conduction time, thereby directly correcting the count value of the PWM comparator register.

[0063] Specifically, besides the aforementioned method of correcting the reference voltage vector in a stationary coordinate system, another more direct dead-time compensation scheme is a time-based pulse width compensation strategy. This method does not change the reference voltage input to the SVPWM algorithm, but instead directly compensates and corrects the count value of the PWM comparator register after calculating the conduction time of each phase switching device in the SVPWM modulation stage.

[0064] The logic of the time-based compensation method is as follows. When At this time, current flows from the inverter to the motor. During the dead time, the current freewheels through the lower bridge arm diode, causing the A-phase output to be clamped to zero. At this time, the actual high-level pulse width is smaller than the ideal pulse width, resulting in voltage drop. Therefore, a compensation time should be added to the ideal conduction time. (17) when At this time, current flows from the motor to the inverter. During the dead time, the current freewheels through the upper bridge arm diode, causing the A-phase output to be clamped to the bus voltage. At this time, the actual output high-level pulse width is greater than the ideal pulse width, causing a voltage rise. Therefore, the compensation time should be subtracted from the ideal conduction time. (18) Compared to voltage-based compensation methods, pulse-width time-based compensation methods avoid the influence of complex coordinate transformations on error voltages and directly affect the final control signal. They have the advantages of low computational load and simple implementation, making them suitable for embedded control systems with high real-time requirements.

[0065] Based on the same inventive concept, another embodiment of this application provides a sensorless control system for a low-speed induction motor based on lower arm sampling, comprising: an equation construction module, a calculation module, a solution module, and a control module.

[0066] The equation construction module is used to establish a mathematical model of the induction motor considering the anisotropy of stator leakage inductance. It uses the average voltage vector and current change during the first half of the PWM cycle to construct the rotor position solution equation. The calculation module is used to improve the PWM waveform excitation strategy and reconstruct the zero vector allocation method. At the beginning and middle of the PWM cycle, the stator current sampling value is obtained through the sampling resistor of the lower bridge arm, and the average current slope during the first half of the PWM cycle is calculated. The solution module is used to substitute the average current slope and average voltage vector obtained in two adjacent PWM cycles into the constructed rotor position solution equation to obtain the rotor position related parameters. The control module is used to normalize the rotor position related parameters and send them to the phase-locked loop to obtain the estimated rotor flux linkage position angle for sensorless control of the induction motor in the zero-speed and low-speed regions.

[0067] In the embodiments described above, the equation-building module, calculation module, solution module, and control module work collaboratively. The equation-building module establishes a mathematical model of the induction motor considering the anisotropy of stator leakage inductance, and builds a rotor position solution equation based on the average voltage vector and current change in the first half of the PWM cycle, providing a core framework for position calculation. Then, the calculation module adopts an improved PWM waveform excitation strategy and reconstructs the zero vector allocation method. At the beginning and middle of the PWM cycle, it obtains the stator current through the sampling resistor of the lower bridge arm and calculates the average current slope in the first half of the cycle, thus solving the sampling blind zone problem of low-cost sampling hardware. Subsequently, the solution module connects two adjacent PWM cycles... The average voltage vector and average current slope of the cycle are substituted into the equation to solve for the rotor position-related parameters, completing the preliminary calculation of position information. Finally, the control module normalizes the parameters and sends them to the phase-locked loop to obtain the estimated rotor flux linkage position angle, realizing sensorless control of the induction motor in the zero-speed and low-speed regions. The entire system does not require high-frequency signal injection and expensive phase current sensors, and is compatible with low-cost industrial bridge arm sampling hardware. The average current slope is used instead of the instantaneous slope, which reduces the requirements for hardware bandwidth and sampling rate. At the same time, relying on dedicated modeling, dual-cycle data solving and phase-locked loop filtering adjustment, the switching noise is effectively suppressed, and the accuracy and stability of rotor position estimation are improved. There is no additional torque pulsation and high-frequency noise, realizing high-performance and cost-effective sensorless control of induction motor in the low-speed domain.

[0068] In another embodiment of this application, a terminal is provided, comprising: a memory, a processor, and a sensorless control program for a low-speed induction motor based on lower arm sampling, stored in the memory and executable on the processor. When the processor executes the sensorless control program for a low-speed induction motor based on lower arm sampling, the terminal controls the implementation of the steps of the sensorless control method for a low-speed induction motor based on lower arm sampling.

[0069] Optionally, the memory is used to store programs; the memory may include volatile memory, such as random-access memory (RAM), such as static random-access memory (SRAM), double data rate synchronous dynamic random-access memory (DDR SDRAM), etc.; the memory may also include non-volatile memory, such as flash memory. The memory is used to store computer programs (such as application programs and functional modules that implement the above methods), computer instructions, etc., and the aforementioned computer programs and computer instructions can be partitioned and stored in one or more memories. Furthermore, the aforementioned computer programs, computer instructions, data, etc., can be accessed by the processor.

[0070] The aforementioned computer programs, computer instructions, etc., can be stored in partitions within one or more memory locations. Furthermore, the aforementioned computer programs, computer instructions, data, etc., can be accessed by a processor.

[0071] A processor is used to execute a computer program stored in memory to implement the various steps of the methods involved in the above embodiments. For details, please refer to the relevant descriptions in the preceding method embodiments.

[0072] The processor and memory can be separate structures or integrated structures. When the processor and memory are separate structures, they can be coupled together via a bus.

[0073] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0075] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0076] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0077] The preferred features in the above embodiments can be used individually in any embodiment, or in any combination thereof, provided they do not conflict with each other. Furthermore, parts not described in detail in the embodiments can be implemented using existing technologies.

[0078] The following examples and comparative examples will be used to further illustrate this application in order to better understand the above-mentioned technical solutions. It should be understood that the following are only some examples and are not intended to limit this application.

[0079] Application Example 1: This application was verified using a 2.2 kW induction motor-assisted drag test platform based on a TMS320F28335 DSP.

[0080] The experimental verification was carried out on the CCS operating platform using the TMS320F283355 board from TI's C2000 series. The parameters of the asynchronous motors involved in the experiment are shown in Table 2.

[0081] Table 2. Motor Parameters Closed-loop experimental verification of low-speed positionless control algorithm for induction motor: Conduct a sensorless closed-loop control experiment. In the closed-loop experiment, the system's feedback loop will be switched to sensorless control mode, meaning that the orientation angles required for the Park transform and inverse Park transform in the vector control system will no longer originate from the photoelectric encoder, but will directly use the estimated angles output by the position observer. At this point, the photoelectric encoder serves only as a monitoring instrument, used to compare and record the actual rotor position, and no longer participates in the control loop. Consistent with the open-loop control experimental conditions, this experiment still employs torque control mode. The motor speed is forcibly clamped by the drag platform, and the control system directly provides the excitation current. and torque current The system only includes a current inner closed loop and does not include a speed outer closed loop. The block diagram of this sensorless closed-loop control system is as follows: Figure 9 As shown.

[0082] The experimental motor speed was clamped at 30 r / min using a towing platform, i.e., the motor operated in the low-speed range. The control system provided a reference excitation current. Reference torque current Variables during stable system operation and The experimental waveforms of the stator A-phase current and rotor flux linkage angle estimation results are as follows: Figure 10 As shown.

[0083] In sensorless closed-loop mode, the estimated angle is... It directly participates in the coordinate transformation of the voltage vector. Due to the inverter's nonlinearity, dead-zone compensation residuals, and current sampling noise, small disturbances in the estimated angle are introduced into the output voltage, affecting the stator current and ultimately feeding back into the demodulated signal, resulting in a slight increase in noise. Observation of the final estimation results shows that although the input signal contains some harmonic interference, thanks to the low-pass filtering characteristics and integral regulation capability of the PLL in the position observer, these high-frequency noises are effectively filtered out, without substantially affecting the final angle output, thus ensuring the stability of the observation system.

[0084] The quality of the stator current waveform is the most direct standard for evaluating the effectiveness of sensorless control. For example... Figure 10 As shown in the first channel, under low-speed closed-loop operating conditions at a speed of 30 r / min, the stator A-phase current... It exhibits a very smooth and standard sinusoidal waveform. In a vector control system, a large deviation in the estimated angle will lead to an error in the phase of the voltage vector calculated by the inverse Park transform, which in turn causes... Axial current coupling causes distortion or low-frequency oscillations in the actual line current waveform. In the experiment, the current waveform maintained good sinusoidal characteristics and stable amplitude, strongly supporting the estimated angle. The accuracy of this technology ensures precise decoupling of the excitation and torque components in the stator current, enabling the motor to operate smoothly and efficiently at low speeds without the need for mechanical sensors. (Observation) Figure 10 The angle estimation results are used to estimate the rotor flux linkage angle. Compared with the measured angle The high consistency indicates that the algorithm can accurately lock the actual position of the rotor. Further analysis of the angle error waveform at the bottom of the figure... During steady-state operation, the angle estimation error mainly manifests as periodic narrow pulse spikes. These spikes typically appear near sector switching or current zero-crossing points, but their amplitude is limited to a small range, and the steady-state estimation error converges and stabilizes within a certain range. Within.

[0085] The foregoing has described some specific embodiments of this application. It should be understood that this application is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the substantive content of this application. The above-described preferred features can be used in any combination without conflict.

Claims

1. A low speed position sensorless control method for induction machines based on lower bridge arm sampling, characterized in that ,include: A mathematical model of an induction motor considering the anisotropy of stator leakage inductance is established, and the rotor position solution equation is constructed using the average voltage vector and current change during the first half of the PWM cycle. By improving the PWM waveform excitation strategy and reconstructing the zero vector allocation method, the stator current sampling value is obtained through the lower bridge arm sampling resistor at the beginning and middle of the PWM cycle, and the average current slope in the first half of the PWM cycle is calculated. Substitute the average current slope and the average voltage vector obtained in two adjacent PWM cycles into the constructed rotor position solution equation to obtain the rotor position related parameters. After normalizing the rotor position-related parameters, the data are fed into a phase-locked loop to obtain an estimated rotor flux linkage position angle, enabling sensorless control of the induction motor in the zero-speed and low-speed regions.

2. The low speed position sensorless control method of an induction motor based on sampling of lower bridge arm according to claim 1, characterized in that, The establishment of the mathematical model for the induction motor considering the anisotropy of stator leakage inductance includes: By using the equivalent circuit of the induction motor when the stator leakage inductance changes, the voltage equation on the stator winding in two-phase stationary coordinates is obtained. Based on the voltage equation, a coordinate transformation is performed to obtain the stator leakage inductance matrix in a two-phase stationary coordinate system. By neglecting the effects of stator resistance voltage drop and back electromotive force during the low-speed operation of the induction motor, the voltage equation in the two-phase stationary coordinate system is simplified, and the mathematical model of the induction motor is established.

3. The low speed position sensorless control method of an induction motor based on sampling of lower bridge arm according to claim 1, characterized in that, The average voltage vector is obtained by weighting the non-zero voltage vector acting in the first half of the PWM cycle and its acting time, and then decomposes it into voltage components along the α-axis and β-axis in a two-phase stationary coordinate system.

4. The low speed position sensorless control method of an induction motor based on sampling of lower bridge arm according to claim 1, characterized in that, The improved PWM waveform excitation strategy includes either a single zero vector modulation strategy based on full substitution or a hybrid zero vector modulation strategy based on center reconstruction. Both the single zero-vector modulation strategy based on full substitution and the hybrid zero-vector modulation strategy based on center reconstruction adjust the duration of the zero vector while maintaining the volt-second balance principle.

5. The low-speed sensorless control method for an induction motor based on lower arm sampling according to claim 4, characterized in that, The single zero vector modulation strategy based on full replacement is to replace all the zero vectors in the standard seven-segment SVPWM with zero vectors , keep the action order and time position of each non-zero voltage vector unchanged, and make the starting, middle and ending moments of the PWM period be zero vectors , keep the action order and time position of each non-zero voltage vector unchanged, and make the starting, middle and ending moments of the PWM period be zero vectors action stage, so that the bridge arm is still in the on state at the middle moment of the PWM period, forming a single zero vector modulation.

6. The low-speed sensorless control method for an induction motor based on lower arm sampling according to claim 4, characterized in that, The hybrid zero-vector modulation strategy based on center reconstruction is as follows: It retains the standard seven-segment SVPWM on both sides of the cycle. and most of the intermediate areas Insert a zero vector at the exact middle of the PWM cycle. The window will be in the middle of the original PWM cycle. Duration of action The sample is divided into four equal parts and sampled to form a hybrid zero vector modulation.

7. The low-speed sensorless control method for an induction motor based on lower arm sampling according to claim 1, characterized in that, The average current slope is calculated as follows: the stator current collected at the beginning and middle of the PWM cycle is used to calculate the difference, and the current change during the non-zero voltage vector action is obtained; after Clarke coordinate transformation, the current change of the α axis and β axis in the two-phase stationary coordinate system is obtained, and then the average current slope is calculated in combination with the PWM half-cycle duration.

8. The low-speed sensorless control method for an induction motor based on lower arm sampling according to claim 1, characterized in that, It also includes steps to compensate for the inverter dead-time effect, with compensation methods including voltage-based compensation or time-based pulse width compensation, wherein: The voltage-based compensation method is as follows: calculate the dead zone voltage error vector in the three-phase stationary coordinate system according to the polarity of the stator phase current, obtain the voltage error components on the α-β axis through Clarke coordinate transformation, use the voltage error components to correct the reference voltage, and use the corrected reference voltage to participate in the calculation of the average voltage vector. The time-based compensation method is as follows: the conduction time of each phase switching device calculated by the SVPWM modulation stage is compensated according to the polarity of the stator phase current. When the current flows from the inverter to the motor, the compensation time is added to the ideal conduction time, and when the current flows from the motor to the inverter, the compensation time is subtracted from the ideal conduction time, and the count value of the PWM comparator register is directly corrected.

9. A system for a sensorless low-speed control method for an induction motor based on lower arm sampling as described in any one of claims 1-8, characterized in that, include: The equation building module is used to establish a mathematical model of an induction motor that considers the anisotropy of stator leakage inductance. The rotor position solution equation is constructed using the average voltage vector and current change during the first half of the PWM cycle. The calculation module is used to reconstruct the zero vector allocation method by improving the PWM waveform excitation strategy. At the beginning and middle of the PWM cycle, the stator current sampling value is obtained through the sampling resistor of the lower bridge arm, and the average current slope in the first half of the PWM cycle is calculated. The solution module is used to input the average current slope and the average voltage vector obtained in two adjacent PWM cycles into the constructed rotor position solution equation to obtain the rotor position related parameters. The control module is used to normalize the rotor position-related parameters and then send them into the phase-locked loop to obtain an estimated rotor flux linkage position angle, and to perform sensorless control of the induction motor in the zero-speed and low-speed regions.

10. A terminal, characterized in that, The terminal includes: a memory, a processor, and a sensorless control program for a low-speed induction motor based on lower arm sampling, stored in the memory and executable on the processor. When the processor executes the sensorless control program for a low-speed induction motor based on lower arm sampling, the terminal controls the implementation of the steps of the sensorless control method for a low-speed induction motor based on lower arm sampling as described in any one of claims 1-8.

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