A five-phase permanent magnet synchronous motor position sensorless control method

Abstract

This invention discloses a sensorless control method for a five-phase permanent magnet synchronous motor, relating to the field of sensorless motor control technology. The method includes: establishing a mathematical model of the five-phase permanent magnet synchronous motor; analyzing the influence of inverter nonlinearity on position estimation in the d1-q1 subspace to obtain the estimated position error signal; determining the harmonic frequency corresponding to the harmonic error, and extracting and suppressing the harmonic error components of the high-frequency signal in real time based on an error feedforward compensation structure based on a second-order generalized integrator; introducing the observation into an improved high-order phase-locked loop structure, using an extended state observer stage, and introducing angular acceleration as an extended state variable; setting structural parameters, and feeding back the compensated estimated angle to the vector control system. This invention effectively eliminates the influence of high-order harmonics caused by inverter nonlinearity, significantly improving the steady-state accuracy, dynamic performance, and robustness of the sensorless control system for the five-phase permanent magnet synchronous motor.

Description

Technical Field

[0001] This invention relates to the field of sensorless motor control technology, specifically to a sensorless control method for a five-phase permanent magnet synchronous motor. Background Technology

[0002] With the development of high-performance electric drive technology, five-phase permanent magnet synchronous motors (PMSMs) have been widely used in new energy transportation, industrial servo systems, and avionics drives due to their higher fault tolerance, smoother torque output, and lower phase current harmonic content. Compared to traditional three-phase systems, five-phase PMSMs can maintain stable operation when any one or more phases fail, thus offering significant advantages in high-reliability applications. However, under complex operating conditions, high-order harmonic currents are inevitably generated in the system due to inverter dead-time effects and switching device nonlinearities. This leads to increased electromagnetic torque ripple and operating noise, especially in the low-speed region, where these nonlinear factors significantly affect motor control accuracy.

[0003] To improve system robustness and reduce sensor costs, sensorless control technology has gradually become an important research direction for multiphase permanent magnet synchronous motors (e.g., CN105915130A). This technology estimates rotor position information by detecting electrical quantities such as stator voltage and current, using an observer or signal injection algorithm. Conventional methods often employ phase-locked loop (PLL)-based structures to synchronize and track motor position, but traditional PLLs have shortcomings in dynamic response and anti-interference performance. When the motor is operating at low speeds, inverter nonlinearity introduces periodic position estimation disturbances, causing phase delays and steady-state errors in the PLL output, thus affecting the control accuracy and stability of the system. Summary of the Invention

[0004] To overcome the problems in existing technologies where five-phase permanent magnet synchronous motors are affected by inverter nonlinearity and dead zone effects under sensorless control, leading to high-frequency position signal distortion and increased position estimation errors, this invention proposes a sensorless control method for five-phase permanent magnet synchronous motors. This method effectively eliminates the influence of high-order harmonics caused by inverter nonlinearity, and significantly improves the steady-state accuracy, dynamic performance, and robustness of the sensorless control system for five-phase permanent magnet synchronous motors.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a sensorless control method for a five-phase permanent magnet synchronous motor, comprising the following steps: S1, Establish the mathematical model of the five-phase permanent magnet synchronous motor; S2, in the d1-q1 subspace, analyze the impact of inverter nonlinearity on position estimation and obtain the estimated position error signal; S3, determine the harmonic frequency corresponding to the harmonic error, and extract and suppress the harmonic error component of the high-frequency signal in real time according to the error feedforward compensation structure based on the second-order generalized integrator. S4 is introduced into the observation of the improved high-order phase-locked loop structure, using the extended state observer stage, and introducing angular acceleration as the extended state variable; S5 sets the structural parameters and feeds back the compensated estimated angle to the vector control system.

[0006] Based on the principle of high-frequency voltage injection, this technical solution first establishes a high-frequency mathematical model of a five-phase permanent magnet synchronous motor, analyzing the impact of inverter nonlinearity and dead-zone effect on the high-frequency response signal and the accuracy of electrical angle estimation. Subsequently, an error feedforward compensation structure based on a second-order generalized integrator is designed to achieve adaptive filtering of the high-frequency signal and real-time extraction of the 10th harmonic component of the electrical angular frequency. The feedforward compensation effectively suppresses the position estimation deviation caused by inverter nonlinearity. Furthermore, an extended state observer is introduced into the phase-locked loop structure to replace the traditional proportional-integral filter. By using the derivative term of the electrical angular velocity as the extended state variable, a dynamic observation model including angular acceleration is established, achieving highly dynamic and accurate estimation of motor speed and electrical angle. Finally, the compensated estimated angle is fed back to the vector control system, realizing online feedforward suppression of inverter nonlinearity error and high-precision estimation of rotor position.

[0007] The present invention is further configured such that step S1 includes: S11. A high-frequency injection mathematical model for a five-phase permanent magnet synchronous motor is established. This model includes the d1-axis voltage equation, q1-axis voltage equation, d3-axis voltage equation, and q3-axis voltage equation, which can describe the electrical characteristics of the motor in the fundamental and third harmonic subspaces. S12 represents the dynamic characteristics of the motor under high-frequency injection as equivalent to a linear resistor-inductor network composed of stator resistors and inductors.

[0008] The present invention is further configured such that step S2 includes: Based on the high-frequency mathematical model of the five-phase permanent magnet synchronous motor established by S1, a high-frequency voltage signal is injected into the d1 axis of the motor to derive its current response characteristics under high-frequency conditions. In the d1-q1 subspace, the influence of the inverter's nonlinear effect on the high-frequency current response and position estimation accuracy is analyzed. The analysis results show that the inverter's nonlinear characteristics introduce a 10th harmonic error in the high-frequency current, and form an estimated angle error through the demodulation process.

[0009] In this technical solution, the above analysis results reveal that inverter nonlinearity introduces additional harmonic components into the high-frequency current, and forms an estimated angle error through the demodulation process, providing a theoretical basis for the design of subsequent error compensation structures.

[0010] The present invention is further configured such that step S3 includes: A feedforward filter based on a second-order generalized integrator is introduced into the signal channel; The extracted high-frequency component is multiplied and modulated with a reference signal of the same frequency. The DC component of the resulting signal is the position estimation error information. The preliminary position estimation error signal is then extracted by passing it through a first-order low-pass filter. ; A second-order generalized integrator is used to suppress the harmonic components at the 10th electrical angular frequency. The position signal error information obtained after processing by the second-order generalized integrator is... .

[0011] In this technical solution, a feedforward circuit based on a second-order generalized integrator is introduced to reduce the influence of harmonics in the position error signal on the high-frequency position signal.

[0012] The present invention is further configured such that: step S4 specifically involves: introducing the high-frequency position signal obtained in S3 after filtering and compensation by a second-order generalized integrator into an improved high-order phase-locked loop structure for position observation; obtaining the error equations of each state variable of the observer based on the extended state observer and the motor position expression, and obtaining the transfer function of the motor speed estimation error and disturbance d based on the error equations of each state variable of the observer, and finally obtaining the transfer function of the improved high-order phase-locked loop.

[0013] The present invention is further configured such that step S5 includes: Based on the results of S3 and S4, the key parameters of the improved high-order phase-locked loop are set, and the compensated estimated angle is fed back to the motor vector control system in real time.

[0014] The present invention is further configured such that the d1-axis voltage equation, q1-axis voltage equation, d3-axis voltage equation and q3-axis voltage equation each include the following parts: stator resistance voltage drop, self-inductance induced voltage and cross-coupling voltage generated by incoming current and inductance; the q1-axis voltage equation and q3-axis voltage equation also include back electromotive force.

[0015] In this technical solution, the d1-axis voltage equation and the d3-axis voltage equation each include three parts: the stator resistance voltage drop, the voltage induced by the self-inductance, and the cross-coupling voltage generated by the incoming current and the inductance. The q1-axis voltage equation and the q3-axis voltage equation each include four parts: the stator resistance voltage drop, the voltage induced by the self-inductance, the cross-coupling voltage generated by the incoming current and the inductance, and the back electromotive force.

[0016] The present invention is further configured such that the second-order generalized integrator consists of one proportional element and two integral elements, and the numerator of its transfer function is composed of the squared terms of the Laplace operator. With the square of the angular frequency of the gating signal The sum is constituted; the denominator consists of the squared terms of the Laplace operator. The proportionality coefficient k and The product term and Together they constitute.

[0017] In this technical solution, the second-order generalized integrator includes one proportional element and two integral elements, and the angular frequency parameter of the gating signal... The filter center frequency can be determined to ensure that the system responds only to specific frequency components. The proportional coefficient k can adjust the filtering performance of the system. The larger the value, the wider the filtering bandwidth and the faster the response speed, but at the same time, the ability to suppress high-frequency noise is relatively weakened.

[0018] The present invention is further configured such that the numerator of the transfer function of the improved high-order phase-locked loop is , as well as The sum of these terms, whose denominator is a third-order polynomial, is derived from... , , as well as They are formed by adding them one by one. , , is the gain coefficient of the extended state observer, and s is the Laplace operator.

[0019] In this technical solution, , , It can adjust the system's damping, bandwidth, and error convergence characteristics.

[0020] The present invention is further configured such that step S5 includes: transforming the transfer function of the improved high-order phase-locked loop to obtain the corresponding characteristic equation, the characteristic equation being... , , as well as The sum of these parameters equals the sum of s and c, where c is a parameter of the improved high-order phase-locked loop.

[0021] In this technical solution, the parameters c of the improved high-order phase-locked loop are related to the values ​​of β1, β2, and β3.

[0022] The present invention can bring the following beneficial effects: This invention relates to a sensorless control method for a five-phase permanent magnet synchronous motor. It introduces an extended state observer into a high-order phase-locked loop (PLL) structure to replace the traditional proportional-integral (PI) filter. A second-order generalized integrator is added to the system to achieve real-time extraction and compensation of harmonic errors in high-frequency signals. By introducing angular acceleration as an extended state variable into the PLL, a multi-state dynamic model including electrical angle, speed, and angular acceleration is established, thereby achieving highly dynamic and accurate estimation of speed and phase. Compared with traditional PLLs, the improved high-order PLL structure proposed in this invention significantly improves dynamic response speed and disturbance rejection performance. Furthermore, combined with the feedforward compensation structure of the second-order generalized integrator, this method can effectively suppress the 10th harmonic error caused by inverter nonlinearity and dead-zone effects, achieving high-precision rotor position estimation without mechanical sensors and improving the system's low-speed operation stability. This invention eliminates the need for complex motor parameter identification, has a simple structure, is easy to implement, and is suitable for digital control platform applications. Simulation results show that this method can effectively eliminate the influence of high-order harmonics caused by inverter nonlinearity, and significantly improve the steady-state accuracy, dynamic performance and robustness of the sensorless control system for a five-phase permanent magnet synchronous motor. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the five-phase permanent magnet synchronous motor drive system in this invention.

[0024] Figure 2 This is a schematic diagram of the windings of the five-phase permanent magnet synchronous motor in this invention.

[0025] Figure 3 This is a block diagram of the position signal error feedforward compensation structure based on a second-order generalized integrator in this invention.

[0026] Figure 4 This is a block diagram of the improved high-order phase-locked loop structure in this invention.

[0027] Figure 5 This is a block diagram of the sensorless control system for a five-phase permanent magnet synchronous motor based on the pulsed high-frequency voltage injection method in this invention.

[0028] Figure 6 The figure shows the position estimation results of the sensorless control method for a five-phase permanent magnet synchronous motor based on a traditional phase-locked loop at 200 r / min.

[0029] Figure 7 The figure shows the position estimation results of the sensorless control method for a five-phase permanent magnet synchronous motor based on an improved high-order phase-locked loop at 200 r / min. Detailed Implementation

[0030] Example 1 To overcome the problems in existing technologies where five-phase permanent magnet synchronous motors under sensorless control are affected by inverter nonlinearity and dead-zone effects, leading to high-frequency position signal distortion and increased position estimation errors, this embodiment proposes a sensorless control method for five-phase permanent magnet synchronous motors. (Refer to...) Figures 1 to 5 It mainly includes the following steps.

[0031] Step S1: Establish a mathematical model of the five-phase permanent magnet synchronous motor; analyze the voltage, current and position response relationship of the motor under high-frequency signal injection conditions, and provide a theoretical basis for subsequent error signal extraction.

[0032] Step S1 mainly includes the following sub-steps.

[0033] Step S11: First, construct a high-frequency injection mathematical model for a five-phase permanent magnet synchronous motor. The high-frequency injection mathematical model mainly includes the d1-axis voltage equation, q1-axis voltage equation, d3-axis voltage equation, and q3-axis voltage equation.

[0034] Among them, the d1-axis voltage equation, q1-axis voltage equation, d3-axis voltage equation, and q3-axis voltage equation describe the electrical characteristics of the motor in the fundamental and third harmonic subspaces. The d1-axis voltage equation, q1-axis voltage equation, d3-axis voltage equation, and q3-axis voltage equation all include the following parts: stator resistance voltage drop, self-inductance induced voltage, and cross-coupling voltage generated by incoming current and inductance; the q1-axis voltage equation and q3-axis voltage equation also include back electromotive force.

[0035] In this technical solution, the d1-axis voltage equation and the d3-axis voltage equation each include three parts: the stator resistance voltage drop, the voltage induced by the self-inductance, and the cross-coupling voltage generated by the incoming current and the inductance. The q1-axis voltage equation and the q3-axis voltage equation each include four parts: the stator resistance voltage drop, the voltage induced by the self-inductance, the cross-coupling voltage generated by the incoming current and the inductance, and the back electromotive force.

[0036] More specifically, the d1-axis voltage equation consists of three parts, namely the voltage drop R caused by the stator resistance. s i d1 The induced voltage L caused by the d1-axis inductance d1 pi d1 And the cross-coupling voltage -ω generated by the q1-axis current and inductance e L q1 i q1 The q1-axis voltage equation consists of four parts, namely the voltage drop R caused by the stator resistance. s i q1 The induced voltage L caused by the q1-axis inductance q1 pi q1 The cross-coupled voltage ω generated by the d1-axis current and inductancee L d1 i d1 and back electromotive force ω e ψ f1 The d3-axis voltage equation consists of three parts: the voltage drop R caused by the stator resistance. s i d3 The induced voltage L caused by the d3-axis inductance d3 pi d3 And the cross-coupling voltage -3ω generated by the q3 axis current and inductance. e L q3 i q3 The q3-axis voltage equation consists of four parts, namely the voltage drop R caused by the stator resistance. s i q3 The induced voltage L caused by the q3 axis inductance q3 pi q3 The cross-coupled voltage 3ω generated by the d3-axis current and inductance e L d3 i d3 and back electromotive force 3ω e ψ f3 .

[0037] Where p is the differential operator, u d1 u q1 u d3 u q3 R represents the voltages of the d1 axis, q1 axis, d3 axis, and q3 axis in the d1-q1 and d3-q3 synchronous rotating coordinate systems of the five-phase permanent magnet synchronous motor, respectively. s This represents the phase resistance of a five-phase permanent magnet synchronous motor. d1 i q1 i d3 i q3 These represent the d1-axis current, q1-axis current, d3-axis current, and q3-axis current in the d1-q1 and d3-q3 synchronous rotating coordinate systems of the five-phase permanent magnet synchronous motor, respectively. d1 L q1 L d3 L q3 Let ω represent the d1-axis inductance, q1-axis inductance, d3-axis inductance, and q3-axis inductance in the d1-q1 and d3-q3 synchronous rotating coordinate systems of a five-phase permanent magnet synchronous motor, respectively. e ψ represents the electrical angular velocity of a permanent magnet synchronous motor. f1 ψ f3 These are the actual values ​​of the fundamental flux linkage and the third harmonic flux linkage of the permanent magnet.

[0038] In step S12, the dynamic characteristics of the motor under high-frequency injection are then equivalent to a linear resistor-inductor network composed of stator resistance and inductance. After injecting a high-frequency voltage signal to excite the high-frequency response of the stator current and ignoring the change in the main flux linkage, the high-frequency characteristics of the motor are equivalent to a linear resistor-inductor network model, thereby obtaining the analytical relationship between high-frequency voltage and current, providing a theoretical basis for the extraction of position error signals.

[0039] In this embodiment, since the injected high-frequency signal frequency is much higher than the rotor frequency of the motor, the dynamic changes of the motor's main flux linkage can be ignored when analyzing the high-frequency response. At this time, the dynamic characteristics of the five-phase permanent magnet synchronous motor under high-frequency injection can be approximately equivalent to a linear resistor-inductor network composed of stator resistance and inductance. This invention injects a high-frequency voltage signal along the d1 axis of the motor; therefore, only the high-frequency components in the d1-q1 synchronous rotating coordinate system need to be analyzed. According to the equivalent model, its high-frequency voltage equation can be simplified to the following form: the high-frequency voltage equation of the motor includes the d1-axis high-frequency voltage equation and the q1-axis high-frequency voltage equation, which can describe the voltage and current relationship characteristics of the motor under high-frequency injection conditions. The d1-axis high-frequency voltage equation consists of two parts: the voltage drop R caused by the stator resistance. s i hf,d1 The induced voltage L caused by the d1-axis inductance d1 pi hf,d1 This equation can be further expressed as the product of the high-frequency equivalent impedance and the current, Z. d1 i hf,d1 The equivalent high-frequency impedance Z of the d1 axis d1 From resistor R s and resistance jω h L d1 The q1-axis high-frequency voltage equation consists of two parts: the voltage drop R caused by the stator resistance. s i hf,q1 The induced voltage L caused by the q1-axis inductance q1 pi hf,q1 This equation can be further expressed as the product of the high-frequency equivalent impedance and the current, Z. q1 i hf,q1 The equivalent high-frequency impedance Z along the q1 axis q1 From resistor R s and resistance jω h L q1 It consists of two parts.

[0040] in, , These represent the high-frequency components of the voltages along the d1 and q1 axes, respectively. , These represent the high-frequency components of the d1 and q1 axis currents, respectively. This represents the angular frequency of the injected high-frequency signal. , These represent the equivalent high-frequency impedances of the d1 and q1 axes, respectively.

[0041] Step S2: Analyze the impact of inverter nonlinearity on position estimation in the d1-q1 subspace to obtain the estimated position error signal caused by inverter dead zone effect and device nonlinearity.

[0042] For step S2, based on the high-frequency mathematical model of the five-phase permanent magnet synchronous motor established in S1, a high-frequency voltage signal is injected into the d1 axis of the motor to derive its current response characteristics under high-frequency conditions; in the d1-q1 subspace, the influence of the inverter's nonlinear effect on the high-frequency current response and position estimation accuracy is analyzed. The analysis results show that the inverter's nonlinear characteristics introduce a 10th harmonic error in the high-frequency current, and form an estimated angle error through the demodulation process.

[0043] More specifically, the rotor position estimation error Δθ is defined as the difference between the actual rotor position θ and the estimated rotor position θ of the five-phase permanent magnet synchronous motor. difference.

[0044] A high-frequency voltage is injected along the d1 axis of the estimated synchronous reference coordinate system, specifically expressed as the amplitude of the high-frequency signal. Angular frequency of the injected high-frequency signal The product of the cosine value of t.

[0045] Based on the high-frequency mathematical model of the five-phase permanent magnet synchronous motor constructed in step S1, the current response of the five-phase permanent magnet synchronous motor in the estimated synchronous reference coordinate system can be obtained, where the estimated high-frequency current values ​​of the d1 axis and q1 axis are... and It is equal to the amplitude of the high-frequency excitation voltage U. h cos(ω h t) divided by the product of the impedances of the d1 and q1 axes, Zd d1 Z q1 Then multiply by a vector related to the rotor position error angle Δθ; the d-axis component of this vector is the average impedance. Subtract differential impedance The product of the double-angle error and the cosine function, the q-axis component of which is only related to the differential impedance. It is related to the sinusoidal function of double-angle error. Average impedance This represents the average high-frequency impedance between the d1 and q1 axes. Differential impedance. This represents half of the difference between the high-frequency impedances of the d1 axis and the q1 axis.

[0046] As can be seen from the high-frequency model above, the rotor position estimation error is reflected in the high-frequency component of the estimated q1-axis current. To extract this error information, the estimated q1-axis current is first bandpass filtered to retain the narrowband component near the carrier wave; then it is multiplied with a quadrature reference signal of the same frequency; finally, a low-pass filter is used to remove the high-frequency residue, resulting in an observation signal proportional to the rotor position estimation error. .

[0047] when When it is 0, A value of zero indicates that the estimated angle is approximately consistent with the actual rotor angle. Therefore, by adjusting the control loop to bring the position error signal closer to zero, synchronization between the actual rotor position and the estimated position can be achieved, thereby obtaining accurate position information.

[0048] In a five-phase inverter, a dead time is typically set between control signals to prevent the simultaneous conduction of power switches on the same bridge arm. This dead time causes a deviation between the actual output voltage and the ideal reference voltage, distorting the stator phase current waveform. As a result, multiple harmonic components are superimposed on the fundamental current component, with harmonics that are multiples of 10 being the most significant. Taking phase A current as an example, its waveform can be represented by two parts: the first part is the fundamental current component. Its amplitude corresponds to the fundamental amplitude of the A-phase current. The frequency is equal to the electrical angular frequency of the motor. The phase is determined by the initial phase angle of phase A. The decision is made. The second part consists of harmonic current components, caused by the inverter's nonlinear characteristics and dead-zone effect. These components are mainly harmonics at frequencies of 10 times and their integer multiples. Each harmonic current component has its own amplitude and phase angle, and their superposition results in a periodic distortion of the current waveform.

[0049] , , These represent the fundamental amplitude, electrical angular frequency, and initial phase angle of phase A current, respectively. , These represent the amplitude and phase angle of the 10kth harmonic current component caused by inverter nonlinearity and dead-zone effect, respectively.

[0050] After coordinate transformation, the current expression in the synchronous reference coordinate system can be obtained. Here, the d1-axis current is equal to the amplitude of the d1-axis fundamental current. Including the harmonic summation term, the harmonic summation term includes: the amplitude of the d1-axis harmonic current multiplied by 10kω. e Phase angle between t and d1 axis harmonic current components The cosine of the sum is then used to sum the results. The q1-axis current is equal to the amplitude of the q1-axis fundamental current. Including the harmonic summation term, the harmonic summation term includes: the amplitude of the q1-axis harmonic current multiplied by 10kω. e Phase angle between t and d1 axis harmonic current components Find the cosine of the sum, and finally sum the results.

[0051] The 10kth harmonic current caused by inverter nonlinearity and dead-zone effect results in integer harmonics of the current in the synchronous reference coordinate system. and These represent the amplitudes of the fundamental wave current along the d1 axis and the fundamental wave current along the q1 axis in the d1-q1 synchronous rotating coordinate system, respectively. and These represent the amplitudes of the harmonic current along the d1 axis and the q1 axis in the d1-q1 synchronous rotating coordinate system, respectively. and These represent the phase angles of the d1-axis harmonic current component and the q1-axis harmonic current component in the d1-q1 synchronous rotating coordinate system, respectively.

[0052] Furthermore, the amplitude of the fundamental wave current along the d1 axis in the d1-q1 synchronous rotating coordinate system is... Multiply The sinusoidal value, the amplitude of the fundamental wave current on the q1 axis in the d1-q1 synchronous rotating coordinate system is Multiply The cosine value, the amplitude of the d1-axis harmonic current in the d1-q1 synchronous rotating coordinate system is Multiply The cosine value, the amplitude of the q1-axis harmonic current is - Multiply The sine value, , as well as equal.

[0053] The high-frequency current components of the five-phase permanent magnet synchronous motor in the d1-q1 synchronous rotating coordinate system were further estimated. These high-frequency current components include d1-axis and q1-axis high-frequency current components, which can describe the current response characteristics of the motor under high-frequency signal injection conditions. The d1-axis high-frequency current component consists of two parts. The first part is composed of coefficients... The product of the angle error cosine function and the phase angle cosine function and coefficients The product of the sine function of the angle error and the cosine function of the phase angle Together they form, and their difference is related to the high-frequency sine function. Multiplication; the second part consists of coefficients The product of the cosine function of the angle error and the sine function of the phase angle. and coefficients The product of the sine function of the angle error and the sine function of the phase angle Together they form, and their difference is related to the high-frequency cosine function. Multiply. The two parts above, when superimposed, constitute the complete d1-axis high-frequency current component. .

[0054] The q1-axis high-frequency current component also consists of two parts. The first part is composed of coefficients. The product of the sine function of the angle error and the cosine function of the phase angle and coefficients The product of the angle error cosine function and the phase angle cosine function Together they form a sum with the high-frequency sine function. Multiplication; the second part consists of coefficients The product of the sine function of the angle error and the sine function of the phase angle and coefficients The product of the cosine function of the angle error and the sine function of the phase angle. Together they form, and their sum is the high-frequency cosine function. Multiply. The two parts are superimposed to form the complete q1-axis high-frequency current component. .

[0055] in, and These are the combined amplitudes of the high-frequency current along the d1 and q1 axes, respectively. It is obtained by superimposing the amplitude of the high-frequency fundamental current on the d1 axis with the 10th harmonic high-frequency current component; It is obtained by superimposing the amplitude of the high-frequency fundamental current on the q1 axis with the corresponding 10th harmonic current component. and These represent the amplitudes of the high-frequency fundamental current along the d1 axis and the q1 axis in the d1-q1 synchronous rotating coordinate system, respectively. , These are the initial phase angles of the high-frequency fundamental current on the d1-q1 axis. and These represent the amplitudes of the high-frequency harmonic current along the d1 axis and the q1 axis, respectively, in the d1-q1 synchronous rotating coordinate system. and These represent the phase angles of the high-frequency harmonic current components along the d1 axis and the q1 axis, respectively, in the d1-q1 synchronous rotating coordinate system.

[0056] Furthermore, it can be seen that the 10kth harmonic exists in the high-frequency component of the q-axis current. Based on the general process of obtaining the rotor position using the pulsed high-frequency voltage injection method, the position estimation error information is obtained after low-pass filtering. .

[0057] Specifically, the estimated high-frequency current signal of the q1 axis is first multiplied by a quadrature reference signal of the same frequency to obtain a mixed signal containing error information. Then, a low-pass filter is used to remove the high-frequency components, retaining the low-frequency part related to the angle error. The resulting position signal observation can be expressed as follows: this signal is composed of two superimposed parts, the first part being the coefficients. The product of the sine function of the angle error and the cosine function of the phase angle The second part is the coefficient. The product of the angle error cosine function and the phase angle cosine function The sum of the two parts described above constitutes the final error signal output, which reflects the rotor position estimation error information. .

[0058] As can be seen from the above analysis, the nonlinear characteristics and dead zone effect of the inverter will introduce harmonic components containing 10 times the electrical angular frequency into the estimated position signal. These harmonic errors cause deviations in position estimation, thereby reducing the accuracy and stability of the sensorless control system. In order to improve the operating performance of the system, it is necessary to effectively identify and suppress such harmonic errors.

[0059] Step S3: Based on the position estimation error signal obtained in step S2, determine the harmonic frequency corresponding to the harmonic error, design an error feedforward compensation structure based on a second-order generalized integrator, and extract and suppress the harmonic error components of the high-frequency signal in real time.

[0060] Step S3 mainly includes the following process.

[0061] A feedforward filter based on a second-order generalized integrator is introduced into the signal channel.

[0062] More specifically, to effectively eliminate the 10th harmonic error caused by inverter nonlinearity and dead-zone effects, it is necessary to extract and compensate for specific harmonic components in the high-frequency position signal in real time. A second-order generalized integrator, capable of accurately tracking specific frequency components within a narrow band, is therefore introduced to construct the error feedforward compensation stage. By adjusting the integrator's center frequency and damping coefficient, selective filtering of the 10th electrical angular frequency component can be achieved, thereby extracting the harmonic signal corresponding to the position error.

[0063] To reduce the impact of harmonics in the position error signal on the high-frequency position signal, a feedforward stage based on a second-order generalized integrator is introduced. The second-order generalized integrator can effectively suppress other frequency components while preserving the target frequency component, thereby improving the purity and anti-interference capability of the position signal. The numerator of the transfer function of the second-order generalized integrator consists of the squared terms of the Laplace operator. With the square of the angular frequency of the gating signal The sum is constituted; the denominator consists of the squared terms of the Laplace operator. The proportionality coefficient k and The product term and Together they constitute the integrator; the transfer function determines the gain and phase characteristics of the integrator at the selected frequency.

[0064] A second-order generalized integrator consists of one proportional element and two integral elements, wherein the angular frequency parameter of the gating signal... The filter center frequency can be determined to ensure that the system responds only to specific frequency components; the proportional coefficient k can adjust the filtering performance of the system. A larger value results in a wider filtering bandwidth and faster response speed, but at the same time, the ability to suppress high-frequency noise is relatively weakened. By appropriately selecting the proportional coefficient k and... A balance is achieved between filtering speed and suppression effect, thereby ensuring the stability and accuracy of position signals under high-frequency injection conditions.

[0065] In this technical solution, the extracted high-frequency components are combined with... Multiplication modulation yields the DC component of the resulting signal, which represents the position estimation error information. This component simultaneously contains the position error signal and a frequency of... The high-frequency components. The position estimation error signal can be extracted using a first-order low-pass filter. .

[0066] Due to the nonlinearity of the inverter, the error signal will contain a significant 10th harmonic component. Therefore, a second-order generalized integrator is used to suppress this 10th harmonic component at the electrical angular frequency, and the angular frequency of the gating signal is set to... The position signal error information obtained after processing by the second-order generalized integrator is denoted as... This signal has effectively eliminated the 10th harmonic error, providing accurate input for subsequent high-order phase-locked loop observations.

[0067] Step S4: The observation is introduced into the improved high-order phase-locked loop structure. An extended state observer is used, and angular acceleration is introduced as the extended state variable.

[0068] Step S4 mainly includes the following processes.

[0069] The high-frequency position signal obtained in step S3, filtered and compensated by a second-order generalized integrator, is introduced into an improved high-order phase-locked loop (PLL) structure for position observation. This improved PLL structure introduces an extended state observer stage, replacing the original proportional-integral (PI) filter stage, based on the traditional PLL. By introducing angular acceleration as an extended state variable, the high-order PLL can not only quickly track changes in motor speed but also actively compensate for external disturbances and model uncertainties. This structure significantly enhances the system's anti-disturbance capability and robustness while improving the dynamic response speed of the position observer. Finally, the estimated angle, after observation and compensation, is fed back to the motor vector control system, achieving high-precision estimation and stable closed-loop control of the motor rotor position.

[0070] Based on the extended state observer and the motor position expression, the error equations of each state variable of the observer are obtained. Then, based on the error equations of each state variable of the observer, the transfer function of the motor speed estimation error and the disturbance d is obtained. Finally, the transfer function of the improved high-order phase-locked loop is obtained.

[0071] More specifically, in the extended state observer, the derivative of the rotational speed is introduced as an extended state variable, which physically represents the angular acceleration of the motor. Regardless of whether the system is in steady state or transient state, the electrical angle, rotational speed, and angular acceleration of the motor always satisfy a derivative relationship; that is, angular acceleration is the rate of change of rotational speed, and rotational speed is the rate of change of electrical angle. By introducing this variable into the state equations, more accurate modeling and real-time observation of the motor's dynamic behavior can be achieved.

[0072] The extended state observer expression is further derived, including the error e equal to the difference between the current state z1 and the expected value θ, and the rate of change of state variable z1 equal to the next state variable z2 minus a correction term β1e proportional to the error e. The rate of change of state variable z2 equals the next state variable z3 minus a correction term β2e proportional to the error e. The rate of change of state variable z3 is directly equal to a correction term −β3e inversely proportional to the error e. β1, β2, and β3 are the gain coefficients of the extended state observer.

[0073] Substituting the extended state observer expression into the motor position expression yields the error equations for each state variable of the observer. Based on these error equations, the transfer function between the speed estimation error and the disturbance d of the five-phase permanent magnet synchronous motor can be obtained. The transfer relationship between the speed estimation error and the disturbance d of the five-phase permanent magnet synchronous motor can be expressed as: its numerator is the Laplace operator s and... The sum of coefficients. Its denominator is a third-order polynomial, derived from... , , as well as It is formed by adding them one by one. , , This is the gain coefficient of the extended state observer, which can adjust the system's damping, bandwidth, and error convergence characteristics.

[0074] The steady-state error is calculated based on the final value theorem. When the angular acceleration changes slowly, the steady-state error of the extended state observer approaches zero. When the rate of change of angular acceleration is zero, the improved high-order phase-locked loop can achieve zero steady-state error tracking of the rotational speed.

[0075] After further simplification, the transfer function of the improved high-order phase-locked loop can be obtained. The numerator of the transfer function of the improved high-order phase-locked loop is: , as well as The sum of these terms, whose denominator is a third-order polynomial, is derived from... , , as well as They are formed by adding them one by one. , , is the gain coefficient of the extended state observer, and s is the Laplace operator.

[0076] Step S5: Set the structural parameters and feed back the compensated estimated angle to the vector control system.

[0077] Based on the design results of steps S3 and S4, the key parameters of the improved high-order phase-locked loop are set appropriately. While ensuring the robustness and dynamic performance of the control system, the compensated estimated angle is fed back to the motor vector control system in real time, achieving high-precision estimation of the rotor position of the five-phase permanent magnet synchronous motor and online feedforward compensation for inverter nonlinear errors.

[0078] According to the transfer function expression of the second-order generalized integrator obtained in step S3, the smaller the value of k, the better the filtering effect, but the slower the filter response speed. Considering that the harmonic frequency is relatively low and the impact of discretization control is small, the proportional coefficient k of the integrator does not need to be too large. In this invention, to avoid oscillation and ensure filtering stability, k is selected as 0.07.

[0079] Then, based on the transfer function of the improved high-order phase-locked loop obtained in step S3, the characteristic equation of the improved high-order phase-locked loop is obtained, and the characteristic equation is: , , as well as The sum is equal to the sum of s and c, where c is the parameter of the improved high-order phase-locked loop; where c is related to the values ​​of β1, β2, and β3 mentioned above, β1 is three times c, β2 is three times the square of c, and β3 is the cube of c.

[0080] Increasing the parameter c improves the bandwidth of the improved high-order phase-locked loop, thereby enhancing speed estimation accuracy. However, excessive bandwidth reduces the system's noise suppression capability, potentially causing resonance or oscillation in the mid-frequency range. To achieve a balance between performance and stability, c is chosen to be 230 in this embodiment.

[0081] This embodiment offers the following technical advantages: First, it establishes a high-frequency mathematical model of a five-phase permanent magnet synchronous motor based on the principle of high-frequency voltage injection, providing a theoretical foundation for position signal extraction. Second, through precise modeling and analysis, it comprehensively considers the impact of inverter nonlinearity, dead-zone effect, and other factors on the motor's high-frequency response and electrical angle estimation accuracy. Subsequently, based on this model, a second-order generalized integrator structure is designed to achieve adaptive filtering of high-frequency signals and real-time extraction of the 10-fold harmonic error signal at the electrical angular frequency. An error signal feedforward compensation stage is also constructed to effectively suppress position estimation deviations caused by inverter nonlinearity. Furthermore, an extended state observer stage is introduced into the phase-locked loop structure to replace the traditional proportional-integral filter. By using the derivative of the electrical angular velocity as the extended state variable, a dynamic observation model including angular acceleration is established, thereby achieving highly dynamic and accurate estimation of speed and electrical angle. Finally, the compensated position estimate is fed back to the five-phase permanent magnet synchronous motor vector control system, achieving high-precision observation of rotor position and online feedforward suppression of inverter nonlinearity errors, significantly improving the system's stability and control accuracy under low-speed and dynamic operating conditions.

[0082] Example 2 This embodiment provides a simulation example based on the method of Embodiment 1, referencing... Figure 1 This is a schematic diagram of the five-phase permanent magnet synchronous motor drive system in this embodiment. In the diagram, Vdc is the DC bus voltage, and A, B, C, D, and E represent the motor phase currents, respectively. (Reference) Figure 2 This is a schematic diagram of the windings of the five-phase permanent magnet synchronous motor in this embodiment, where a, b, c, d, and e represent the windings of each phase of the motor, respectively; (Refer to...) Figure 3 This is a block diagram of the position signal error feedforward compensation structure based on a second-order generalized integrator in this embodiment. Estimating the electrical angular velocity for a permanent magnet synchronous motor; Reference Figure 4 This is a block diagram of the improved high-order phase-locked loop structure in this embodiment; see reference. Figure 5 This is a block diagram of the sensorless control system for a five-phase permanent magnet synchronous motor based on the pulsed high-frequency voltage injection method in this embodiment; see reference. Figure 6 This is a position estimation result diagram of the sensorless control method for a five-phase permanent magnet synchronous motor based on a traditional phase-locked loop in this embodiment at 200 r / min; (Refer to...) Figure 7The figure shows the position estimation results of the sensorless control method for a five-phase permanent magnet synchronous motor based on an improved high-order phase-locked loop at 200 r / min in this embodiment.

[0083] This embodiment verifies the effectiveness of the sensorless control method based on an improved high-order phase-locked loop described in this invention through simulation on a five-phase permanent magnet synchronous motor. The system's speed loop and current loop employ conventional PI controllers for closed-loop control.

[0084] refer to Figure 6 and Figure 7 The performance of traditional phase-locked loops and the method of this invention in speed and position estimation under low-speed conditions was compared. The experimental conditions were a speed of 200 r / min and a load torque of 3 N·m.

[0085] refer to Figure 6 Under traditional phase-locked loop control, the system's rotational speed fluctuation range is (−10.7, +9.6) r / min, and the estimated position error fluctuation range is (−12.2°, +15.7°). It is evident that the traditional method is susceptible to inverter nonlinearity and dead-zone effects at low speeds, resulting in low estimation accuracy and significant dynamic response fluctuations.

[0086] refer to Figure 7 After adopting the control method based on the improved high-order phase-locked loop proposed in this invention, the speed fluctuation range is significantly reduced to (−2.5, +1.9) r / min, and the position estimation error fluctuation range is only (−1.7°, +2.4°). This shows that the method of this invention can effectively eliminate the high-order harmonic error caused by inverter nonlinearity, improve the position estimation accuracy, and improve the dynamic tracking performance and low-speed stability of the system.

[0087] In summary, the experimental results show that the method proposed in this invention can achieve higher speed stability and position estimation accuracy under low-speed operating conditions, verifying the superior performance of the improved high-order phase-locked loop structure in sensorless control systems.

Claims

1. A sensorless control method for a five-phase permanent magnet synchronous motor, characterized in that, Includes the following steps: S1, Establish the mathematical model of the five-phase permanent magnet synchronous motor; S2, in the d1-q1 subspace, analyze the impact of inverter nonlinearity on position estimation and obtain the estimated position error signal; S3, determine the harmonic frequency corresponding to the harmonic error, and extract and suppress the harmonic error component of the high-frequency signal in real time according to the error feedforward compensation structure based on the second-order generalized integrator. S4 is introduced into the observation of the improved high-order phase-locked loop structure, using the extended state observer stage, and introducing angular acceleration as the extended state variable; S5 sets the structural parameters and feeds back the compensated estimated angle to the vector control system.

2. The sensorless control method for a five-phase permanent magnet synchronous motor according to claim 1, characterized in that, Step S1 includes: S11. A high-frequency injection mathematical model for a five-phase permanent magnet synchronous motor is established. This model includes the d1-axis voltage equation, q1-axis voltage equation, d3-axis voltage equation, and q3-axis voltage equation, which can describe the electrical characteristics of the motor in the fundamental and third harmonic subspaces. S12 represents the dynamic characteristics of the motor under high-frequency injection as equivalent to a linear resistor-inductor network composed of stator resistors and inductors.

3. A sensorless control method for a five-phase permanent magnet synchronous motor according to claim 1 or 2, characterized in that, Step S2 includes: Based on the high-frequency mathematical model of the five-phase permanent magnet synchronous motor established by S1, a high-frequency voltage signal is injected into the d1 axis of the motor to derive its current response characteristics under high-frequency conditions. In the d1-q1 subspace, the influence of the inverter's nonlinear effect on the high-frequency current response and position estimation accuracy is analyzed. The analysis results show that the inverter's nonlinear characteristics introduce a 10th harmonic error in the high-frequency current, and form an estimated angle error through the demodulation process.

4. The sensorless control method for a five-phase permanent magnet synchronous motor according to claim 3, characterized in that, Step S3 includes: A feedforward filter based on a second-order generalized integrator is introduced into the signal channel; The extracted high-frequency component is multiplied and modulated with a quadrature reference signal of the same frequency. The DC component of the resulting signal is the position estimation error information. The preliminary position estimation error signal is then extracted by passing it through a first-order low-pass filter. ; A second-order generalized integrator is used to suppress the harmonic components at the 10th electrical angular frequency. The position signal error information obtained after processing by the second-order generalized integrator is... .

5. A sensorless control method for a five-phase permanent magnet synchronous motor according to claim 1, 2, or 4, characterized in that, Step S4 specifically involves: introducing the high-frequency position signal obtained in S3 after filtering and compensation by a second-order generalized integrator into the improved high-order phase-locked loop structure for position observation; obtaining the error equations of each state variable of the observer based on the extended state observer and the motor position expression, and obtaining the transfer function of the motor speed estimation error and disturbance d based on the error equations of each state variable of the observer, and finally obtaining the transfer function of the improved high-order phase-locked loop.

6. A sensorless control method for a five-phase permanent magnet synchronous motor according to claim 5, characterized in that, Step S5 includes: Based on the results of S3 and S4, the key parameters of the improved high-order phase-locked loop are set, and the compensated estimated angle is fed back to the motor vector control system in real time.

7. The sensorless control method for a five-phase permanent magnet synchronous motor according to claim 2, characterized in that, The d1-axis voltage equation, q1-axis voltage equation, d3-axis voltage equation, and q3-axis voltage equation all include the following parts: The voltage drop across the stator resistance, the voltage induced by its own inductance, and the cross-coupled voltage generated by the incoming current and inductance; the q1-axis voltage equation and the q3-axis voltage equation also include the back electromotive force.

8. A sensorless control method for a five-phase permanent magnet synchronous motor according to claim 4, characterized in that, The second-order generalized integrator consists of one proportional element and two integral elements, and the numerator of its transfer function is composed of the squared terms of the Laplace operator. With the square of the angular frequency of the gating signal The sum is constituted; the denominator consists of the squared terms of the Laplace operator. The proportionality coefficient k and The product term and Together they constitute.

9. A sensorless control method for a five-phase permanent magnet synchronous motor according to claim 5, characterized in that, The numerator of the transfer function of the improved high-order phase-locked loop is: , as well as The sum of these terms, whose denominator is a third-order polynomial, is derived from... , , as well as They are formed by adding them one by one. , , is the gain coefficient of the extended state observer, and s is the Laplace operator.

10. A sensorless control method for a five-phase permanent magnet synchronous motor according to claim 5, characterized in that, Step S5 includes: transforming the transfer function of the improved high-order phase-locked loop to obtain the corresponding characteristic equation, the characteristic equation being: , , as well as The sum of these parameters equals the sum of s and c, where c is a parameter of the improved high-order phase-locked loop.

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