Permanent magnet synchronous motor rotor information observation method and system

Abstract

The application provides a permanent magnet synchronous motor rotor information observation method and system, the method comprises the following steps: taking the stator voltage and current of the permanent magnet synchronous motor in the stationary coordinate system as the input variables of the high-order sliding mode observer, and calculating the observation value of the extended back electromotive force through the observation equation of the high-order sliding mode observer; taking the observation value of the extended back electromotive force as the input of the SOGI module, and obtaining the more stable observation value of the extended back electromotive force through the transfer function of the SOGI module; taking the more stable observation value of the extended back electromotive force as the input of the PLL module, and obtaining the observation value of the rotor electric angle and the electric angular velocity through the PLL module; iteratively performing the above steps until the system reaches the sliding mode surface and stably operates on the sliding mode surface, and taking the observation value of the rotor electric angle and the electric angular velocity obtained at this time as the observed permanent magnet synchronous motor rotor information. The application can effectively improve the rotor information observation precision.

Description

Technical Field

[0001] This invention belongs to the field of sensorless control of permanent magnet synchronous motors. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have advantages such as simple structure, high power factor, and small size, and are widely used in industrial manufacturing, home appliances, and other fields. Traditional PMSM control strategies use mechanical encoders to obtain rotor position information, which increases manufacturing costs and reduces reliability and durability. Sensorless PMSM control strategies, by collecting current and voltage variables related to speed, estimate rotor position and speed information instead of mechanical encoders. This offers advantages such as high reliability and strong environmental adaptability, thus demonstrating promising application prospects.

[0003] Sensorless control strategies for PMSMs are mainly divided into active control with high-frequency signal injection and passive control without signal injection. Active control methods are suitable for embedded permanent magnet synchronous motors. Utilizing the salient pole effect of the motor, high-frequency signals are injected into the stator windings to process the high-frequency response in the current signal, extracting the rotor's position and speed information. This method is suitable for low-speed and zero-speed starts. Passive control methods mainly include the flux linkage observer method and the back-EMF observer method. The flux linkage observer obtains rotor position information through rotor flux linkage. This method requires accurate rotor flux linkage components and is relatively sensitive to motor parameters. The back-EMF observer is suitable for medium- and high-speed operation stages where the motor's back EMF is significant. This method calculates the motor's back EMF using signals such as voltage and current, and estimates rotor position information through a nonlinear observer. Commonly used back-EMF observers include the model reference adaptive method, the extended Kalman filter algorithm, and the sliding-mode observer (SMO) algorithm. Kalman filter algorithms are computationally complex and have high hardware requirements; Model Reference Adaptive (MRA) methods require accurate motor reference mathematical models, and changes in internal parameters such as inductance during long-term motor operation can affect the estimation accuracy of the algorithm; Sliding mode observers are insensitive to parameter changes and have advantages such as strong robustness, fast convergence speed, and wide speed range, and are widely used in sensorless control strategies for permanent magnet synchronous motors (PMSMs). However, because traditional sliding mode observers use sign functions as switching functions, they suffer from severe chattering, resulting in low accuracy of rotor information observation for PMSMs and reducing the control accuracy of the PMSM sensorless control system.

[0004] To address the problems existing in the above-mentioned sensorless control strategy for PMSM, it is necessary to design a new method for observing rotor position and speed information to improve the accuracy of rotor information observation, thereby improving the control accuracy of the PMSM sensorless control system. Summary of the Invention

[0005] The technical problem solved by this invention is to provide a method and system for observing rotor information of a permanent magnet synchronous motor, which can effectively improve the accuracy of rotor information observation.

[0006] On one hand, the present invention provides a method for observing rotor information of a permanent magnet synchronous motor, comprising:

[0007] Step 1: Initialization;

[0008] Step 2: Convert the stator voltage and current i in the stationary coordinate system of the permanent magnet synchronous motor. α i β u α u β As input variables to the higher-order sliding mode observer, the observed value of the extended back potential is calculated through the observation equation of the higher-order sliding mode observer.

[0009] Step 3: Calculate the observed values ​​of the extended back potential. As input to the SOGI module, more stable extended back potential observations are obtained through the SOGI module's transfer function.

[0010] Step 4: Calculate more stable extended back potential observations. As input to the PLL module, the observed values ​​of rotor electrical angle and electrical angular velocity are obtained through the PLL module. and

[0011] Step 5: Iterate through steps 1-4 until the system reaches the sliding surface and operates stably on it (at this point, the observed current approximates the actual current). and (It will converge to the actual value), stop the iteration, and take the result at this time. and This information is obtained from observations of the permanent magnet synchronous motor rotor.

[0012] As one implementation, the permanent magnet synchronous motor is a surface-mounted permanent magnet synchronous motor, and the corresponding observation equation of the aforementioned high-order sliding mode observer is:

[0013]

[0014] In the formula, To account for the error between the observed current and the actual current; u α u β i represents the stator voltage in the stationary coordinate system. α i β R represents the stator current in the stationary coordinate system. sL is the stator resistance. d For stator inductance, p is the differential operator, e is the stator inductance. α e β For extended back electromotive force in stationary coordinate system; i α i β e α e β ω e The observed value; m is the gain of the extended back EMF observer;

[0015] In the formula, The adaptive sliding mode gain coefficient is calculated using the following formula:

[0016]

[0017] In the formula, k min The minimum sliding mode gain; l is the adaptive gain adjustment parameter, l > 0; k min Both l and are empirical parameters;

[0018] In the formula, sigmoid(x) is the switching function. Where a is a positive real number and x is the system state variable error.

[0019] As one implementation scheme, The center frequency is fed back to the SOGI module, and the transfer function of the SOGI module is as follows:

[0020]

[0021]

[0022] In the formula, q = e -π / 2j ;k s For system gain, k s These are empirical parameters. From equation (27), we know that D(s) is a second-order bandpass filter, and Q(s) is a second-order low-pass filter. The back potential after SOGI filtering; express or express or s represents the complex variable in the Laplace transform.

[0023] In this implementation scheme, Feedback is sent to the SOGI module as its center frequency, enabling adaptive tracking of the SOGI module's frequency.

[0024] As one implementation scheme, the calculation formula of the above PLL module is as follows:

[0025]

[0026]

[0027]

[0028] Where ε is the position error signal in the phase-locked loop, k p and k i These are the parameters of the PI controller in the PLL module.

[0029] On the other hand, the present invention provides a sensorless control method for permanent magnet synchronous motors, which uses the above-mentioned rotor information observation method of permanent magnet synchronous motors to obtain the rotor speed and position information, and combines it with the FOC algorithm to realize sensorless control of permanent magnet synchronous motors.

[0030] On the other hand, the present invention provides a rotor information observation system for a permanent magnet synchronous motor, comprising:

[0031] Initialize the template for parameter initialization;

[0032] A high-order sliding mode observer is used to measure the stator voltage and current i in the stationary coordinate system of a permanent magnet synchronous motor. α i β u α u β As input variables, the observed value of the extended back potential is obtained through iterative calculation of the observation equation of the higher-order sliding mode observer.

[0033] The SOGI module is used to extend the observations of the back potential. As input, a more stable extended back potential observation is obtained through its transfer function.

[0034] The PLL module is used to provide more stable extended back potential observations. As input, observations of rotor position and velocity are obtained. and

[0035] The judgment module is used to determine whether the system has reached the sliding surface and is running stably on the sliding surface. If so, the iteration stops, and the result obtained at this time is... and This information is obtained from observations of the permanent magnet synchronous motor rotor.

[0036] On the other hand, the present invention provides a sensorless control system for a permanent magnet synchronous motor, including the aforementioned permanent magnet synchronous motor rotor information observation system, for acquiring rotor speed and position information.

[0037] Beneficial effects:

[0038] The technical solution provided by this invention firstly designs an adaptive sliding mode gain coefficient that varies with rotational speed, based on the characteristic that the back electromotive force of the motor in a Higher Order Sliding Mode Observer (HSMO) changes with rotational speed. By constructing a higher order sliding mode observer with an adaptive gain tracking algorithm, the phase lag and amplitude attenuation problems caused by the introduction of a low-pass filter in traditional sliding mode observers are solved, reducing the impact of chattering on observation accuracy. Secondly, an adaptive bandpass filter is designed using an SOGI structure, feeding back the rotor angular frequency to the SOGI module as its center frequency to filter harmonics caused by load disturbances and dead-zone effects in the system, reducing harmonic and noise pollution caused by load disturbances and dead-zone effects. A normalized quadrature phase-locked loop (PLL) is used to obtain position and velocity information, realizing closed-loop observation of position information. The stability of the system can be proven using Lyapunov's stability theorem. A sensorless control system for a permanent magnet synchronous motor was built. Through simulation and experiments, the results show that, compared with traditional methods and traditional sliding mode observers, the novel rotor information observer proposed in this invention can effectively improve the accuracy of rotor position information observation and suppress sliding mode chattering and harmonics, proving the effectiveness of the method. Attached Figure Description

[0039] Figure 1 This is a block diagram of the SOGI structure in one embodiment of this application;

[0040] Figure 2 This is a Bode plot of D(S) for different values ​​in one embodiment of this application;

[0041] Figure 3 This is a block diagram of the PLL structure in one embodiment of this application;

[0042] Figure 4 This is a block diagram of a rotor information extraction structure based on SOGI-PLL in one embodiment of this application;

[0043] Figure 5 This is a block diagram of a sensorless control system for a permanent magnet synchronous motor in one embodiment of this application;

[0044] Figure 6 This application presents rotor observation position and error based on different control strategies in one embodiment; wherein, Figure 6 (a) The rotor observation position and error based on the HSMO control strategy at 1000 r·min⁻¹; Figure 6(b) Rotor observation position and error based on HSMO-SIG control strategy at 1000 r·min⁻¹; Figure 6 (c) The rotor observation position and error based on the AD-HSMO control strategy at 1000 r·min⁻¹; Figure 6 (d) represents the rotor observation position error based on the AD-HSMO-SOGI control strategy at 1000 r·min⁻¹;

[0045] Figure 7 This application presents rotor observation position and error based on different control strategies in one embodiment; wherein, Figure 7 (a) Rotor observation position and error based on HSMO control strategy at 400 r·min⁻¹; Figure 7 (b) Rotor observation position and error based on HSMO-SIG control strategy at 400 r·min⁻¹; Figure 7 (c) The rotor observation position and error based on the AD-HSMO control strategy at 400 r·min⁻¹; Figure 7 (d) shows the rotor observation position and error based on the AD-HSMO-SOGI control strategy at 400 r·min⁻¹;

[0046] Figure 8 This is a comparison of rotor observation phases at a rotational speed of 400 r·min⁻¹ in one embodiment of this application;

[0047] Figure 9 This is a comparison diagram of the back EMF before and after SOGI filtering in one embodiment of this application;

[0048] Figure 10 This is a waveform diagram of the estimated speed and error based on the HSMO control strategy in one embodiment of this application, with current disturbance.

[0049] Figure 11 This is a waveform diagram of the estimated speed and error based on the AD-HSMO-SOGI control strategy in one embodiment of this application, with current disturbance.

[0050] Figure 12 This application provides an embodiment of the extended back EMF experimental waveform and back EMF harmonic analysis based on different control strategies. Figure 12 (a) shows the experimental waveforms of the extended back EMF based on the HSMO control strategy and the AD-HSMO-SOGI control strategy; Figure 12 (b) is the back potential harmonic analysis based on the HSMO control strategy; Figure 12 (c) is the back potential harmonic analysis based on the AD-HSMO-SOGI control strategy;

[0051] Figure 13This application presents waveforms of no-load operating current and rotor position at 800 r·min⁻¹ based on different control strategies in one embodiment; wherein, Figure 13 (a) shows the waveforms of the no-load operating current and rotor position based on the HSMO control strategy at 800 r·min⁻¹. Figure 13 (b) shows the waveforms of the no-load operating current and rotor position based on the AD-HSMO-SOGI control strategy at 800 r·min⁻¹.

[0052] Figure 14 This application presents waveforms of operating current and rotor position at a load of 800 r·min⁻¹ based on different control strategies in one embodiment; wherein, Figure 14 (a) shows the waveforms of operating current and rotor position at a load of 800 r·min⁻¹ based on the HSMO control strategy; Figure 14 (b) shows the waveforms of operating current and rotor position at a load of 800 r·min⁻¹ based on the AD-HSMO-SOGI control strategy;

[0053] Figure 15 This is the result of multi-speed segment operation based on different control strategies in one embodiment of this application; wherein, Figure 15 (a) shows the multi-speed segment operation results based on the HSMO control strategy; Figure 15 (b) shows the multi-speed segment operation results based on the AD-HSMO-SOGI control strategy. Detailed Implementation

[0054] The technical solutions in the embodiments of this application will now be described with reference to the accompanying drawings.

[0055] In some embodiments, a method for observing rotor information of a permanent magnet synchronous motor is provided, including:

[0056] Step 1: Initialization;

[0057] Step 2: Convert the stator voltage and current i in the stationary coordinate system of the permanent magnet synchronous motor. α i β u α u β As input variables to the higher-order sliding mode observer, the observed value of the extended back potential is calculated through the observation equation of the higher-order sliding mode observer.

[0058] In some embodiments, at the start of the iteration and The initial value can be set to zero.

[0059] Step 3: Calculate the observed values ​​of the extended back potential. As input to the SOGI module, more stable extended back potential observations are obtained through the SOGI module's transfer function.

[0060] Step 4: Calculate more stable extended back potential observations. As input to the PLL module, the observed values ​​of rotor electrical angle and electrical angular velocity are obtained through the PLL module. and

[0061] Step 5: Iterate through steps 1-4 until the system reaches the sliding surface and operates stably on it (at this point, the observed current approximates the actual current). and (It will converge to the actual value), stop the iteration, and take the result at this time. and This information is obtained from observations of the permanent magnet synchronous motor rotor.

[0062] In some embodiments, a sensorless control method for a permanent magnet synchronous motor uses the aforementioned permanent magnet synchronous motor rotor information observation method to obtain the rotor speed and position information, and combines it with the FOC algorithm to achieve sensorless control of the permanent magnet synchronous motor.

[0063] In some embodiments, a permanent magnet synchronous motor rotor information observation system includes:

[0064] Initialize the template for parameter initialization;

[0065] A high-order sliding mode observer is used to measure the stator voltage and current i in the stationary coordinate system of a permanent magnet synchronous motor. α i β u α u β As input variables, the observed value of the extended back potential is obtained through iterative calculation of the observation equation of the higher-order sliding mode observer.

[0066] The SOGI module is used to extend the observations of the back potential. As input, a more stable extended back potential observation is obtained through its transfer function.

[0067] The PLL module is used to provide more stable extended back potential observations. As input, observations of rotor position and velocity are obtained. and

[0068] The judgment module is used to determine whether the system has reached the sliding surface and is running stably on the sliding surface. If so, the iteration stops, and the result obtained at this time is... and This information is obtained from observations of the permanent magnet synchronous motor rotor.

[0069] In some embodiments, a sensorless control system for a permanent magnet synchronous motor includes the aforementioned permanent magnet synchronous motor rotor information observation system, used to acquire rotor speed and position information.

[0070] The concept and performance of the above embodiments will be described in detail below.

[0071] 1. Mathematical Model of PMSM and Design of Traditional Sliding Mode Observer

[0072] 1.1 Mathematical Model of Permanent Magnet Synchronous Motor

[0073] Based on field-oriented vector control technology, the mathematical model of the surface-mounted permanent magnet synchronous motor in the two-phase stationary coordinate system (α, β) is as follows:

[0074]

[0075]

[0076] In the formula: u α u β i represents the stator voltage in the stationary coordinate system. α i β R represents the stator current in the stationary coordinate system. s L is the stator resistance. d For stator inductance, p is the differential operator, e is the stator inductance. α e β For the extended back potential in the stationary coordinate system, Ψ f ω represents the flux linkage of a permanent magnet. e θ represents the electric angular velocity of the motor rotor. e This indicates the electrical angle of the motor rotor.

[0077] 1.2 Design of Traditional Sliding Mode Observer

[0078] As can be seen from equations (1) and (2), the back EMF of the motor is directly related to the rotor position and speed information. By designing a sliding mode observer to reconstruct the mathematical model of the permanent magnet synchronous motor, the back EMF observation value close to the actual value can be observed through the error of the stator current and feedback current of the motor, thereby obtaining the rotor position and speed information.

[0079] When designing the sliding mode observer, the voltage equation (1) in the stationary coordinate system is first transformed into equation (3):

[0080]

[0081] In the design of traditional sliding mode observers, a symbolic switching function is used to reconstruct the mathematical model of a permanent magnet synchronous motor. The mathematical model of a traditional sliding mode observer in a sensorless PMSM control system is as follows:

[0082]

[0083] In the formula, Indicate i α i β The observed values. k is the sliding mode gain.

[0084] Therefore, the estimated value of the back electromotive force is:

[0085]

[0086] In the formula, e α e β The observed values.

[0087] The rotor position and speed information can be calculated from the estimated back EMF using the arctangent function:

[0088]

[0089] Traditional sliding mode observers use discontinuous switching functions, which leads to severe high-frequency chattering in the extended back EMF observations. A low-pass filter is needed to filter these observations, resulting in phase delay. The arctangent function involves segmentation operations, which further amplifies rotor position observation errors, especially when the back EMF observations are low. To address these problems with sliding mode observers, this application proposes an improved rotor information observer based on the sliding mode observer.

[0090] 2. Improve the rotor information observer

[0091] 2.1 Adaptive High-Order Sliding Mode Observer

[0092] Under normal motor operation, the system's mechanical time constant is much larger than its electromagnetic time constant. Within one sampling period, the rotor's angular velocity can be considered a constant, i.e., pω. e =0, therefore, from equation (2), we know that the back potential satisfies the following relationship:

[0093]

[0094] To eliminate the phase delay and amplitude attenuation problems caused by low-pass filtering in traditional sliding mode observers, a high-order sliding mode observer with stator current and back EMF as state variables is constructed using equations (1), (2), and (7):

[0095]

[0096] In the formula, Represents ω e The observed values.

[0097] During the high-speed operation of the motor, a large sliding mode gain is required to ensure the system's robustness and fast response. However, excessive gain can cause additional chattering, leading to distortion of the back EMF estimate and reducing the accuracy of the permanent magnet synchronous motor control system. To ensure good performance at different speeds, this application proposes an adaptive sliding mode gain coefficient, as shown in equation (9).

[0098]

[0099] In the formula, k min The minimum sliding mode gain ensures that the system remains robust even when the motor speed is low; l is the adaptive gain adjustment parameter (l>0) to give the observer ideal gain during the speed change phase.

[0100] When the motor operates at variable speeds, the sliding mode observation error is not zero, and the adaptive gain k v Increase. When the estimation error reaches the sliding mode switching surface. Then, to reduce the interference of disturbances on the system, the gain k v The sliding mode gain is reduced until the sliding mode equilibrium state is disrupted, meaning the error deviates from the sliding surface again. The sliding mode gain will then be adjusted again using an adaptive algorithm based on the system state to ensure k... v The value can adapt to the wide speed range operating requirements of the motor.

[0101] The traditional sign function sign(x) is discontinuous at zero, leading to a decrease in the observation accuracy of the sliding mode observer. To address this, this embodiment uses a saturated switching control function sigmoid(x) that is continuous at zero, as shown in equation (10). The function value is zero at zero and the control is continuous within the boundary layer, allowing the system state variables to pass through the sliding surface at low speed, avoiding high-speed switching of the sign function and effectively reducing observation errors of rotor information caused by chattering. Outside the boundary layer, the sign function is still selected as the switching function based on the saturation characteristics of sliding mode control, ensuring the stability of the system.

[0102]

[0103] In the formula, a is a positive real number, and x is the system state variable error. The magnitude of a determines the boundary layer thickness of the sigmoid(x) function. A larger value of a results in more jitter near the zero point, causing the function to change too quickly near the zero point and affecting the control effect. If the value of a is too small, the function takes a longer time to stabilize, which reduces the control accuracy. Therefore, in this embodiment, a smoother sigmoid(x) with a=2 is selected as the new switching function.

[0104] Combining equations (8), (9), and (10), we finally obtain the improved high-order sliding mode observer algorithm:

[0105]

[0106] In the formula The error between the observed current and the actual current.

[0107] Subtracting equation (11) from equation (3) yields the equation for estimating the stator current of the motor:

[0108]

[0109] Similarly, subtracting equation (11) from equation (7) yields the equation for estimating the back potential:

[0110]

[0111] In the formula To observe the error between the extended back potential and the actual extended back potential.

[0112] As shown in equations (11), (12), and (13), compared to traditional sliding mode observers, higher-order sliding mode observers have two basic components: prediction and correction. The back EMF observation equation is the prediction component, and the feedback of the observed back EMF to the current observer constitutes the correction component. As shown in equation (13), the observed value of the extended back EMF is obtained through integration and is a continuously differentiable function, thus yielding a smooth estimated signal. The aforementioned higher-order sliding mode observer has the function of reducing errors, eliminating the low-pass filter in traditional sliding mode observers and avoiding the problem of phase delay.

[0113] 2.2 Stability Analysis of Adaptive Higher-Order Sliding Mode Observer

[0114] The improved high-order sliding mode observer consists of two second-order observers: a current sliding mode observer and an extended back-potential sliding mode observer. The current sliding surface s is defined. i for:

[0115]

[0116] To prove the reachability and stability of sliding mode motion, and to ensure that the system operates stably on the sliding surface after reaching it, the stability of the aforementioned observer is analyzed. The Lyapunov function of the current is defined as:

[0117]

[0118] From the reachability condition of sliding mode motion and the Lyapunov stability proof theorem, it can be seen that V i The derivative must be negative definite. It should meet the following requirements:

[0119]

[0120]

[0121] In the formula s iα s iβ The derivative of express The derivative of .

[0122] Combining equations (12), (13), and (14), we can deduce that:

[0123]

[0124]

[0125] To satisfy equations (16) and (17), and combining equations (18) and (19), we know that the adaptive sliding mode gain k v Must meet:

[0126] k v >max{|e α |,|e β |} (20)

[0127] When the stator current reaches the sliding mode surface, the observed stator current value will converge to the actual value. and From equation (12), we can obtain:

[0128]

[0129] Combining equations (13) and (21), we can obtain the state equation with back electromotive force error as the variable:

[0130]

[0131] By solving the differential equation (22), its characteristic equation can be obtained as follows:

[0132]

[0133] In the formula, s is the Laplace operator, and the characteristic roots of the above formula are calculated as follows:

[0134]

[0135] As can be seen from the above equation, the characteristic roots of the characteristic equation (23) are a pair of conjugate complex roots, both located in the left half-plane of s. Therefore, it can be determined that the system is stable. To satisfy the observer stability condition analyzed above and ensure the convergence speed of the back EMF observation error, in some embodiments of this application, the observer gains are selected as k min =1.2, l=0.002, m=0.3.

[0136] 2.3 Rotor Information Extraction Method Based on SOGI-PLL Structure

[0137] The back EMF obtained via an adaptive advanced sliding mode observer contains rotor position information, but due to inverter dead-time effects and rotor space harmonics, it still contains a large number of fifth and seventh harmonics. This application's embodiment employs an SOGI-PLL structure to extract rotor position information from the back EMF. SOGI reduces interference caused by harmonics, and PLL calculates the rotor position information from the SOGI-filtered back EMF. Extended back EMF It still contains harmonic components. The extended back electromotive force in the stationary coordinate system is rewritten as e = e f +e h

[23] .

[0138]

[0139] In the formula, e f =[e fα e fβ T, e h =[e hα e hβ ] T These are the fundamental wave and the 6k±1st harmonic in the extended back electromotive force, E1 and E2, respectively. 6k±1 The amplitudes of the fundamental frequency and the 6k±1st harmonic are given. The rotor position information is obtained through a phase-locked loop (PLL), and the position error signal ε in the PLL is expressed as:

[0140]

[0141] In the formula, θ e1 The initial angle of the rotor.

[0142] As can be seen from equation (26), when the PLL converges, the position error signal ε contains harmonic interference, which reduces the observation accuracy of rotor information.

[0143] To reduce the impact of harmonics on the phase-locked loop, embodiments of this application introduce SOGI to filter the back EMF acquired by the adaptive high-order sliding mode observer, thereby obtaining a more stable extended back EMF observation value. The structural block diagram of SOGI is as follows: Figure 1 As shown.

[0144] Its transfer function is shown in equation (27):

[0145]

[0146] In the formula, q = -π / 2j ;k s For system gain; Let be the angular frequency of the motor rotor. From equation (27), we know that D(s) is a second-order bandpass filter, and Q(s) is a second-order low-pass filter. This is the back potential after SOGI filtering.

[0147] Figure 1 The amplitude-frequency and phase-frequency characteristics of the system shown are as follows:

[0148]

[0149]

[0150] In the formula, ω is the center frequency of the system, when When |D|=|Q|, the center frequency achieves error-free tracking of the angular frequency. From equations (28) and (29), it can be seen that qE αβ E αβ Lag 90°.

[0151] The typical transfer function of a second-order bandpass filter can be expressed as:

[0152]

[0153] In the formula, A0 is the zero-frequency gain of the filter, and Q is the quality factor.

[0154] Comparing equations (27) and (30), we can see that the quality factor corresponding to equation (27) is:

[0155]

[0156] As can be seen from equation (31), the quality factor of the system is only related to k. s The relevant amplitude-frequency and phase-frequency characteristic curves of the system are as follows: Figure 2 As shown.

[0157] As can be seen from the Bode plot, k sA larger value results in a faster response speed but a worse filtering effect. To meet the requirements for both system response speed and filtering effect, the embodiments of this application select... As the resonance coefficient

[19] .

[0158] Considering that the arctangent function amplifies errors, leading to a significant difference between the estimated rotor information and the actual information, this embodiment uses a normalized orthogonal phase-locked loop (PLL) to obtain rotor position and speed information. The back EMF error signal ε is adjusted by a PI controller to obtain the rotor speed, and then the rotor position is obtained through integration. The block diagram of the PLL is shown below. Figure 3 As shown.

[0159] After SOGI filtering, the high-order harmonic components in the back EMF are relatively small and can be ignored. The error function of the phase-locked loop (PLL) can be rewritten as equation (26):

[0160]

[0161] The error signal first passes through a PI controller to obtain the rotor's electrical angular velocity, and then is integrated to obtain the rotor's electrical angle, i.e.:

[0162]

[0163]

[0164] Where, k p and k i These are the parameters of the PI controller in the PLL module.

[0165] As shown above, the rotor position and velocity can be estimated using phase-locked loop (PLL) technology. Combined with the characteristic analysis of second-order generalized integrators, a SOGI-PLL structure is constructed to analyze and filter the extended back EMF observations obtained from the improved sliding mode observer. Figure 4 As shown.

[0166] Higher-order sliding mode observers with i α i β u α u β Using the observer equation as the input variable, the observed value of the extended back potential is obtained through iterative calculation. The extended back EMF observation is used as the input to the SOGI module. Its bandpass filtering characteristics are used to eliminate high-frequency noise and harmonic interference on the extended back EMF observation. The rotor angle and frequency are obtained through a phase-locked loop. The angular frequency is fed back to the SOGI module as its center frequency, realizing adaptive frequency tracking of the SOGI module.

[0167] 3. Simulation and Experimental Verification

[0168] 3.1 Design of Sensorless Control System for Permanent Magnet Synchronous Motor

[0169] The block diagram of the improved sensorless control system for permanent magnet synchronous motor is as follows: Figure 5 As shown, the system adopts the field-oriented control (FOC) algorithm, and its structure includes a Clark transform module, a Park transform module, a Park inverse transform module, a PI control module, a sinusoidal space vector modulation (SVPMM) module, an inverter module, and a rotor information observer.

[0170] This application embodiment establishes an improved rotor information observer to acquire rotor speed and position information, and combines it with the FOC algorithm to achieve sensorless control of a permanent magnet synchronous motor. The rotor information observer acquires the estimated electrical angular velocity of the rotor and feeds it back to the speed outer loop and the sliding mode observer to complete the speed closed loop and sliding mode gain adaptation, adopting i d =0 control, establishing a dual closed-loop control structure for speed and current.

[0171] 3.2 System Simulation and Analysis

[0172] To verify the effectiveness of the improved sliding mode observer proposed in this application, a sensorless control system for a permanent magnet synchronous motor was simulated using MATLAB / Simulink software. The simulated motor parameters are shown in Table 1, and the parameters of the high-order sliding mode observer are as follows: k min =1.2, l=0.002, m=0.3.

[0173] Table 1 Simulation Motor Parameters

[0174]

[0175] 3.2.1 Comparison and Analysis of Steady-State Performance

[0176] The motor speed was set to 1000 r·min. -1 and 400r·min -1 The accuracy of rotor position estimation is compared with that of traditional high-order sliding mode observer (HSMO), saturated switching function sliding mode observer (HSMO-SIG), adaptive gain saturated switching function sliding mode observer (AD-HSMO), and improved sliding mode observer (AD-HSMO-SOGI) which introduces SOGI module on the basis of AD-HSMO structure. Figure 6 , 7 Four sliding mode observers at 1000 r·min -1 and 400r·min -1 Rotor position information under operating conditions, including the comparison results of actual rotor position and observed rotor position, as well as observation error.

[0177] A comparative experiment was conducted to evaluate the observation performance of the four observers at 1000 r·min. -1 At different rotational speeds, the observation results of HSMO are as follows: Figure 6 As shown in (a), the maximum rotor position error is 0.095 rad, the maximum rotor error of HSMO-SIG is 0.091 rad, the error value of AD-HSMO is smaller at 0.089 rad, while the observation error of AD-HSMO-SOGI is the smallest at only 0.087 rad. Moreover, the rotor runs more smoothly and the observation error is smoother, which is beneficial for the observation of rotor position.

[0178] contrast Figure 6 and Figure 7 It can be seen that the fixed-gain HSMO at 400 rpm -1 The observation error fluctuation at the speed is significantly greater than that at 1000 r·min -1 The error fluctuations were reduced, but AD-HSMO-SOGI maintained its performance at 1000 r·min. -1 It exhibits similar good performance. Therefore, the adaptive gain sliding mode observer has a stronger ability to suppress jitter, and compared to the traditional sliding mode observer, the gain-adaptive sliding mode observer has better steady-state performance over a wide speed range.

[0179] To more clearly compare the improvement in observation accuracy, 400 r·min -1 The rotor speed observation errors were compared. For example... Figure 8 As shown, the improved rotor position observation error proposed in this application embodiment is significantly smaller than that of the traditional high-order sliding mode observer, effectively improving the observation accuracy and exhibiting good steady-state performance.

[0180] 3.2.2 Analysis of SOGI Harmonic Suppression Effect

[0181] To verify the impact of the SOGI module on the system, a random number within ±0.3A was applied to the motor current as a disturbance current to simulate the harmonics and noise caused by current fluctuations under actual operating conditions. The waveform comparison of the back EMF before and after SOGI filtering is shown in the figure below. Figure 9 As shown in the figure. The back potential before filtering. E is the back potential after SOGI filtering. fα E fβ This is the back electromotive force after being filtered by a low-pass filter. (By...) Figure 9 It is evident that SOGI effectively reduces the harmonic content in the back EMF and does not suffer from problems such as phase v-position hysteresis and amplitude attenuation, which is beneficial for estimating rotor position.

[0182] To observe the tracking performance of the improved rotor position observer for motor speed under current disturbance conditions, an external disturbance was simulated by applying a random number within ±0.3A to the motor current. The simulation results are as follows: Figure 10 , Figure 11 As shown.

[0183] Depend on Figure 10 and Figure 11 It can be seen that when the motor enters steady-state operation, the traditional high-order sliding mode observer has an estimated speed error of ±2.3 r·min⁻¹ at a motor speed of 1000 r·min⁻¹, while the improved rotor position observer has an observation error of ±1.4 r·min⁻¹ at a speed of 1000 r·min⁻¹. Compared with the traditional HSMO, AD-HSMO-SOGI shows stronger anti-harmonic interference capability.

[0184] 3.3 Experimental Verification and Result Analysis

[0185] To further verify the effectiveness of the method proposed in this application, a hardware control system platform for a surface-mounted permanent magnet synchronous motor was constructed. It mainly consists of the controlled experimental motor, control circuitry, and a host computer. Mechanical sensors are installed inside the experimental motor to verify the experimental results; the motor and observer parameters are consistent with the simulation parameters.

[0186] 3.3.1 Comparison and Analysis of Harmonic Suppression Performance

[0187] Figure 12 800 r·min -1 Experimental waveforms of back electromotive force based on HSMO and AD-HSMO-SOGI under operating conditions and their Fourier analysis.

[0188] Figure 12 (a) Comparison of back potential harmonic suppression experiments for the two observers shows that the waveform quality of the extended back potential observation is significantly improved. Figure 12 (b) and Figure 12 (c) It can be seen that the THD of the extended back EMF observed by the traditional sliding mode observer is 2.95%, while the THD of the extended back EMF observed by the improved sliding mode observer is 1.37%. It can be seen that the improved sliding mode observer control has a better effect on the harmonic suppression of the extended back EMF observation and reduces the impact of harmonics on the entire control system.

[0189] 3.3.2 Comparison and Analysis of No-Load and Load Operation Performance

[0190] Figure 13 (a) Figure 13 (b) Based on traditional HSMO and AD-HSMO-SOGI 800r·min respectively -1 The experimental results of the motor running stably under no-load conditions are shown in the figure. Figure 14 800 r·min -1 Experimental results under load conditions. (From...) Figure 13 It can be seen that at 800 r·min -1 Under no-load conditions, the three-phase current in the traditional HSMO control strategy has large harmonic interference and the rotor observation information deviation is large, at 0.18 rad. In contrast, the rotor observation error based on the AD-HSMO-SOGI control strategy is 0.12 rad, which is higher than that of the traditional HSMO. The peak fluctuation of the three-phase current is also smaller, which shows good estimation accuracy.

[0191] Depend on Figure 14 It can be seen that under motor load conditions, the observation error based on the HSMO control strategy is 0.21 rad, while the observation error of AD-HSMO-SOGI is 0.16 rad. It still has better observation effect and smaller error, lower harmonic content of current, and obvious chattering suppression effect.

[0192] 3.3.3 Comparison and Analysis of Multi-Speed ​​Range Operating Performance

[0193] To test the dynamic response capability of the proposed algorithm, different reference rotational speeds were given and the performance was compared and analyzed. Figure 15 The results show the experimental findings of sensorless control of a PMSM operating in multiple speed ranges based on HSMO and AD-HSMO-SOGI, with the motor reference speed varying from 600-1000-1400-1000-400 r·min⁻¹. Figure 15 It can be seen that both have relatively fast dynamic responses, but AD-HSMO-SOGI shows a significant advantage in reducing the impact of chattering on speed, with speed errors in each speed range being smaller than HSMO.

[0194] The experimental results are consistent with the simulation results. The AD-HSMO-SOGI-based control strategy proposed in this application can ensure the accuracy of speed and position tracking, effectively reduce harmonic interference caused by chattering, and improve the stability of system operation.

[0195] Therefore, this application proposes a sensorless control strategy for permanent magnet synchronous motors (PMSMs) based on an improved rotor information observer, effectively solving the problems of chattering and low rotor position estimation accuracy in the sliding mode observer vector control system of PMSMs. The causes of chattering in sliding mode variable structure control are analyzed, and a saturation function is used to replace the traditional sign function. An adaptive sliding mode gain is introduced to feed back the motor speed and internal system state to the sliding mode observer, improving the observation accuracy of the sliding mode observer at different speeds. Simultaneously, a SOGI-PLL structure is proposed to filter the back EMF, reducing the impact of harmonics on the system control accuracy. The angular frequency in the PLL is used as the center frequency of the SOGI to prevent phase lag and amplitude attenuation, further improving the servo performance of the sensorless vector control system for PMSMs. Simulation and experimental results also verify that the method proposed in this application can accurately estimate rotor position and speed information, improve position estimation accuracy, reduce speed chattering, enhance harmonic suppression, improve speed tracking, and increase operational stability, which is beneficial for expanding the application of PMSMs in home appliances, servo robots, electric vehicles, and other fields.

Claims

1. A method for observing rotor information of a permanent magnet synchronous motor, characterized in that, include: Step 1: Initialization; Step 2: Convert the stator voltage and current in the stationary coordinate system of the permanent magnet synchronous motor. As input variables to the higher-order sliding mode observer, the observed value of the extended back potential is calculated through the observation equation of the higher-order sliding mode observer. ; Step 3: Calculate the extended back potential observations. As input to the SOGI module, more stable extended back potential observations are obtained through the SOGI module's transfer function. ; Step 4: Calculate more stable extended back potential observations. As input to the PLL module, the observed values ​​of rotor electrical angle and electrical angular velocity are obtained through the PLL module. and ; Step 5: Iterate through steps 1-4 until the system reaches the sliding surface and runs stably on it. Stop the iteration and record the result at this point. and As observed information about the rotor of the permanent magnet synchronous motor; The permanent magnet synchronous motor is a surface-mounted permanent magnet synchronous motor, and the corresponding observation equation of the high-order sliding mode observer is: ； In the formula, To account for the error between the observed current and the actual current; This represents the stator voltage in a stationary coordinate system. This represents the stator current in a stationary coordinate system. For stator resistance, For stator inductance, For differential operators, For extended back electromotive force in stationary coordinate system; , , , , They are respectively , , Observed values; To extend the gain of the back potential observer; In the formula, The adaptive sliding mode gain coefficient is calculated using the following formula: ； In the formula, Minimum sliding mode gain; For adaptive gain adjustment parameters, ; and These are all empirical parameters; In the formula, For switching functions, ,in, It is a positive real number. This refers to the error in the system state variables.

2. The method for observing rotor information of a permanent magnet synchronous motor according to claim 1, characterized in that, The The feedback is sent to the SOGI module as its center frequency; The transfer function of the SOGI module is: ； In the formula, ; For system gain, These are empirical parameters. It is a second-order bandpass filter. It is a second-order low-pass filter. The back potential after SOGI filtering; express or , express or ; This represents a complex variable in the Laplace transform.

3. The method for observing rotor information of a permanent magnet synchronous motor according to claim 1, characterized in that, The calculation formula for the PLL module is as follows: ； ； ； in, This is the position error signal in the phase-locked loop. and These are the parameters of the PI controller in the PLL module.

4. A sensorless control method for a permanent magnet synchronous motor, characterized in that, The rotor speed and position information are obtained by using the method described in any one of claims 1 to 3, and combined with the FOC algorithm, sensorless control of the permanent magnet synchronous motor is realized.

5. A rotor information observation system for a permanent magnet synchronous motor, characterized in that, include: A high-order sliding mode observer is used to measure the stator voltage and current in the stationary coordinate system of a permanent magnet synchronous motor. As input variables, the observed value of the extended back potential is obtained through iterative calculation of the observation equation of the higher-order sliding mode observer. ; Initialize the template for parameter initialization; The SOGI module is used to extend the observations of the back potential. As input, a more stable extended back potential observation is obtained through its transfer function. ; The PLL module is used to provide more stable extended back potential observations. As input, observations of rotor position and velocity are obtained. and ; The judgment module is used to determine whether the system has reached the sliding surface and is running stably on the sliding surface. If so, the iteration stops, and the result obtained at this time is... and As observed information about the rotor of the permanent magnet synchronous motor; The permanent magnet synchronous motor is a surface-mounted permanent magnet synchronous motor, and the corresponding observation equation of the high-order sliding mode observer is: ； In the formula, To account for the error between the observed current and the actual current; This represents the stator voltage in a stationary coordinate system. This represents the stator current in a stationary coordinate system. For stator resistance, For stator inductance, For differential operators, For extended back electromotive force in stationary coordinate system; , , , , They are respectively , , Observed values; To extend the gain of the back potential observer; In the formula, The adaptive sliding mode gain coefficient is calculated using the following formula: ； In the formula, Minimum sliding mode gain; For adaptive gain adjustment parameters, ; and These are all empirical parameters; In the formula, For switching functions, ,in, It is a positive real number. This refers to the error in the system state variables.

6. A sensorless control system for a permanent magnet synchronous motor, characterized in that, The permanent magnet synchronous motor rotor information observation system as described in claim 5 is used to acquire rotor speed and position information.

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