Dual linear extended state observer assisted sensorless control method for permanent magnet synchronous motor

Abstract

The application discloses a kind of double linear expansion state observer assisted permanent magnet synchronous motor position sensorless control method, belongs to motor control field.The application is aimed at the problem that existing permanent magnet synchronous motor position sensorless control method is weak in robustness under motor parameter variation and external interference.The application comprises: designing effective flux linkage observer, calculating αβ axis back electromotive force based on αβ axis voltage and current, obtaining αβ axis stator flux linkage in combination with αβ axis feedback compensation voltage, obtaining αβ axis effective flux linkage in combination with q axis inductance, and outputting rotor position observation value and electric angular velocity observation value by phase-locked loop;Design second-order linear extended state observer for position error compensation to obtain position estimation error;Design second-order linear extended state observer for disturbance compensation, obtain feedforward disturbance compensation current based on electric angular velocity observation value and dq axis current.The application significantly improves rotor position estimation accuracy and system anti-interference ability in full-speed domain.

Description

Technical Field

[0001] This invention relates to a sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer, belonging to the field of motor control. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industrial drives, electric vehicles, aerospace, and other fields due to their significant advantages such as high power density, high efficiency, and wide speed range. To achieve high-performance control, accurate rotor position information is typically required in real time. Traditional control methods rely on mechanical position sensors (such as encoders and resolvers) for position detection; however, these sensors suffer from drawbacks such as large size, high cost, complex installation, and susceptibility to environmental interference, reducing system reliability and economy. Therefore, sensorless control technology, which estimates rotor position in real time through control algorithms without the need for additional position sensors, has become a core research direction for improving the performance of PMSM control systems.

[0003] Currently, sensorless control methods applicable to medium- and high-speed operating ranges are mainly based on motor mathematical models, including flux linkage observer methods, back EMF observer methods, and model reference adaptive methods. Among these, flux linkage observation-based methods have attracted much attention due to their clear structure and simple implementation, and can be divided into voltage model methods and current model methods. Voltage model methods solve for flux linkage directly using the motor voltage equations, resulting in fast dynamic response, but they are sensitive to sampling circuit nonlinearity, integral drift, and parameter changes. Current model methods estimate flux linkage using the intrinsic relationship between motor current and flux linkage, offering a simple structure, but their accuracy is significantly affected by inductance and permanent magnet parameters, resulting in weak robustness. To combine the advantages of both, a hybrid model flux linkage observer has been proposed, improving the stability and accuracy of position estimation by combining the strengths of voltage and current models.

[0004] Although hybrid model flux linkage observers improve position estimation accuracy to some extent, non-ideal factors such as model errors and parameter variations result in discrepancies between the estimated rotor position and the actual rotor position. Existing rotor position error compensation techniques mainly fall into two categories: error model-based compensation and error estimation-based compensation. Error model-based compensation schemes model specific error sources and make local corrections. However, when the motor operates at high speeds, the fundamental frequency is high, and various non-ideal factors can lead to non-negligible rotor position estimation errors. Compensating only for a single or partial factor is insufficient to achieve ideal results. Error estimation-based compensation schemes directly compensate for rotor position errors without considering the specific causes.

[0005] Furthermore, sensorless control systems are prone to speed fluctuations and dynamic performance degradation under disturbances such as sudden load changes and parameter perturbations, and their speed loop bandwidth is typically lower than that of systems with encoders. To improve anti-interference capabilities, various disturbance observation and compensation strategies have been studied, such as disturbance estimation methods based on sliding mode control, linear observers, or nonlinear filters. However, these methods often suffer from problems such as complex design, high computational cost, tight coupling with the controller, or insufficient dynamic response, limiting their application in real-time high-performance control systems.

[0006] Therefore, in order to improve the position estimation accuracy, anti-interference ability and overall robustness of the sensorless control system of permanent magnet synchronous motor under complex working conditions, and to enhance the reliability and dynamic response performance of the sensorless control system of permanent magnet synchronous motor in high-end fields, it is of great theoretical significance and engineering application value to study a sensorless control method that can simultaneously achieve multi-factor position error compensation and effective disturbance suppression. Summary of the Invention

[0007] To address the problem that existing sensorless control methods for permanent magnet synchronous motors have weak robustness under changes in motor parameters and external disturbances, this invention provides a sensorless control method for permanent magnet synchronous motors assisted by a bilinear extended state observer.

[0008] The present invention provides a sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer, comprising:

[0009] Design an effective flux linkage observer. Calculate the αβ-axis back EMF based on αβ-axis voltage and current, obtain the αβ-axis stator flux linkage by combining it with the αβ-axis feedback compensation voltage, and then calculate the effective αβ-axis flux linkage by combining it with the q-axis inductance. Output the rotor position observation value via a phase-locked loop. Electric angular velocity observations The αβ-axis feedback compensation voltage is obtained from the αβ-axis stator flux linkage through Park transformation, current model, and iPark transformation.

[0010] A second-order linear extended state observer is designed for position error compensation. Based on α and β axis voltages and currents, the position error caused by multiple factors is treated as a lumped error for observation to obtain the position estimation error. ;

[0011] Design a second-order linear extended state observer for disturbance compensation, based on electric angular velocity observations. And the dq-axis current, to obtain the feedforward disturbance compensation current. ;

[0012] Position estimation error and feedforward disturbance compensation current Used in the sensorless control process of permanent magnet synchronous motors.

[0013] The method for obtaining the αβ axis stator flux linkage using the bilinear extended state observer-assisted sensorless control method for permanent magnet synchronous motors according to the present invention is as follows:

[0014] ,

[0015] In the formula The back electromotive force is α-axis. This is the back electromotive force along the β axis. The voltage along the α-axis. For β-axis voltage, For stator resistance, For the α-axis current, For β-axis current;

[0016] ,

[0017] In the formula For the α-axis stator flux linkage, For β-axis stator flux linkage, This is the α-axis feedback compensation voltage. This is the β-axis feedback compensation voltage. For time.

[0018] The method for obtaining the effective flux linkage along the αβ axis using the bilinear extended state observer-assisted sensorless control method for permanent magnet synchronous motors according to the present invention is as follows:

[0019] ,

[0020] In the formula For the effective flux linkage along the α axis, For the effective flux linkage along the β axis, It is the q-axis inductance.

[0021] According to the bilinear extended state observer-assisted sensorless control method for permanent magnet synchronous motors of the present invention, the α-axis feedback compensation voltage... and β-axis feedback compensation voltage The method to obtain it is as follows:

[0022] α-axis stator flux and β-axis stator flux The d-axis stator flux linkage is obtained by performing the Park transformation. and q-axis stator flux The d-axis current observations were obtained using a current model. and q-axis current observations :

[0023] ,

[0024] In the formula For d-axis inductance, For permanent magnet flux linkage;

[0025] d-axis current observations and q-axis current observations The α-axis stator current and β-axis stator current are obtained by performing the iPark transformation, and then the α-axis feedback compensation voltage is calculated. and β-axis feedback compensation voltage .

[0026] According to the sensorless control method for permanent magnet synchronous motors assisted by the bilinear extended state observer of the present invention, in the second-order linear extended state observer used for position error compensation, the rotor position observation is used as the basis for the control method. Position estimation error compared to the actual rotor position The dq-axis voltage equation considering the observation position error is obtained as follows:

[0027] ,

[0028] In the formula For the d-axis voltage that takes into account the observation position error, For the q-axis voltage that takes into account the observation position error, To account for the d-axis current of the observation position error, For the q-axis current that takes into account the observation position error, For differential operators, The effective flux linkage amplitude; where:

[0029] ;

[0030] By estimation Achieve position estimation error Correction.

[0031] According to the sensorless control method for permanent magnet synchronous motors assisted by the bilinear extended state observer of the present invention, the second-order linear extended state observer for position error compensation is designed as follows:

[0032] ,

[0033] In the formula For current observation error, For observing the current vector along the dq axis, For the estimated value of the observed current vector, For the system matrix, For the input matrix, For the voltage vector observed along the dq axis, Let be the coupling matrix. The position error estimate is given by the total disturbance being... , The first-order observer gain matrix is... This is the gain matrix of the second-order observer;

[0034] , ,

[0035] , ;

[0036] In the formula This is an estimated value for the stator resistance. It is the identity matrix;

[0037] This yields the transfer function matrix of the second-order linear extended state observer used for position error compensation. for:

[0038] ,

[0039] In the formula For the Laplace operator.

[0040] According to the sensorless control method for permanent magnet synchronous motors assisted by a bilinear extended state observer of the present invention, the first-order observer gain matrix... and the second-order observer gain matrix for:

[0041] ,

[0042] In the formula The gain coefficient of the first-order observer gain matrix is ​​1. The gain coefficient of the first-order observer gain matrix is ​​2. The gain coefficient of the second-order observer gain matrix is ​​1. The gain coefficient of the second-order observer gain matrix is ​​2;

[0043] ,

[0044] In the formula The damping coefficient is... For bandwidth.

[0045] According to the sensorless control method for permanent magnet synchronous motors assisted by the bilinear extended state observer of the present invention, the second-order linear extended state observer for disturbance compensation is designed as follows:

[0046] ,

[0047] In the formula For angular velocity estimation error, For the observed angular velocity of the effective flux linkage observer, This is an estimate of the angular velocity. The damping ratio coefficient, For system input, The coupling coefficient is... Total disturbance The estimated value, For the first-order gain of the observer, The observer's second-order gain;

[0048] , ,

[0049] In the formula As an intermediate variable, As an intermediate variable, For d-axis current, This is the q-axis current;

[0050] ,

[0051] In the formula This represents the number of pole pairs of the motor. The moment of inertia of the motor. The coefficient of friction;

[0052] ,

[0053] In the formula This represents the load torque.

[0054] According to the sensorless control method for permanent magnet synchronous motors assisted by the bilinear extended state observer of the present invention, the motion equation of the permanent magnet synchronous motor is as follows:

[0055] ,

[0056] In the formula This is the actual value of the electric angular velocity;

[0057] Load torque and electromagnetic torque in rotating reference frame equal:

[0058] .

[0059] The sensorless control method for permanent magnet synchronous motors assisted by a bilinear extended state observer according to the present invention comprises... and The difference is obtained by subtraction: ,

[0060] In the formula As an intermediate variable; the feedforward disturbance compensation current is calculated. .

[0061] The beneficial effects of this invention are as follows: The method of this invention is used to achieve coordinated observation and compensation of position errors and load disturbances, significantly improving the rotor position estimation accuracy and system anti-interference capability across the entire speed domain. This method can perform real-time lumped correction of multi-factor coupled position errors, effectively suppressing steady-state and dynamic position deviations; simultaneously, through disturbance observation and feedforward compensation, it significantly reduces speed fluctuations during sudden load changes, enhancing the system's dynamic response. The observation structure of this invention is simple and easy to implement, improving the position estimation accuracy, anti-interference capability, and robustness of the sensorless control system for permanent magnet synchronous motors under complex operating conditions, and significantly enhancing the dynamic performance and operational reliability of the sensorless control system for permanent magnet synchronous motors in high-end applications.

[0062] This invention constructs an improved effective flux linkage observer based on a voltage-current hybrid model. It achieves smooth correction of flux linkage observations through current error feedback and reveals the causes of position errors from multiple perspectives, including observer structure, phase-locked loop, and parameter mismatch. Next, a compensation structure assisted by a bilinear extended state observer is proposed: a second-order linear extended state observer for position error compensation actively estimates and feeds forward to compensate for lumped position errors, significantly improving estimation accuracy; a second-order linear extended state observer for disturbance compensation observes and suppresses speed fluctuations caused by external disturbances, enhancing the system's dynamic response and anti-interference capability. Furthermore, Lyapunov stability theory can be used to identify stator resistance online, enhancing the system's robustness to parameter changes. This invention's method is applied to a sensorless control system for permanent magnet synchronous motors, exhibiting high position and speed estimation accuracy, good dynamic tracking performance, and anti-interference capability under various operating conditions such as speed changes, disturbances, and stator resistance mismatch, achieving high-precision, highly robust, and stable operation of the sensorless permanent magnet synchronous motor system.

[0063] While ensuring the simplicity and feasibility of the sensorless control system structure, the method of this invention significantly improves the position estimation accuracy, dynamic response performance, and anti-interference capability through the collaborative design of an improved hybrid model effective flux observer and a bilinear extended state observer. This enhances practicality and robustness, providing an innovative technical solution for the application of sensorless control of high-performance, high-reliability permanent magnet synchronous motors in high-end equipment. Attached Figure Description

[0064] Figure 1 This is an overall schematic diagram of the sensorless control method for permanent magnet synchronous motors assisted by the bilinear extended state observer described in this invention;

[0065] Figure 2 This is a block diagram of the effective flux linkage observer;

[0066] Figure 3This is a block diagram of a second-order linear extended state observer used for position error compensation;

[0067] Figure 4 This is a block diagram of a second-order linear extended state observer used for disturbance compensation;

[0068] Figure 5 This is a schematic diagram of the experimental results observed using an existing effective flux linkage observer under the change of rotational speed command in Example 1;

[0069] Figure 6 This is a schematic diagram of the experimental results observed using the method of the present invention under the change of rotational speed command in Example 1;

[0070] Figure 7 This is a schematic diagram of the experimental results observed using an existing effective magnetic flux observer under load changes in Example 2;

[0071] Figure 8 This is a schematic diagram of the experimental results observed using the method of the present invention under load changes in Example 2;

[0072] Figure 9 This is a schematic diagram of the experimental results observed using an existing effective flux linkage observer when the motor speed is 1000 rpm and the resistance parameters are mismatched in Example 3.

[0073] Figure 10 This is a schematic diagram of the experimental results observed using the method of the present invention when the motor speed is 1000 rpm and the resistance parameters are mismatched in Example 3. Detailed Implementation

[0074] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] Specific Implementation Method 1: Combination Figures 1 to 4 As shown, this invention provides a sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer, comprising:

[0076] Design an effective flux linkage observer. Calculate the αβ-axis back EMF based on αβ-axis voltage and current, obtain the αβ-axis stator flux linkage by combining it with the αβ-axis feedback compensation voltage, and then calculate the effective αβ-axis flux linkage by combining it with the q-axis inductance. Output the rotor position observation value via a phase-locked loop. Electric angular velocity observations The αβ-axis feedback compensation voltage is obtained from the αβ-axis stator flux linkage through Park transformation, current model, and iPark transformation.

[0077] A second-order linear extended state observer is designed for position error compensation. Based on α and β axis voltages and currents, the position error caused by multiple factors is treated as a lumped error for observation to obtain the position estimation error. ;

[0078] Design a second-order linear extended state observer for disturbance compensation, based on electric angular velocity observations. And the dq-axis current, to obtain the feedforward disturbance compensation current. ;

[0079] Position estimation error and feedforward disturbance compensation current Used in the sensorless control process of permanent magnet synchronous motors.

[0080] This implementation method is used for position error and disturbance compensation. Addressing the inherent position errors caused by non-ideal factors such as observer structure and motor parameter mismatch in sensorless control of permanent magnet synchronous motors (PMSMs), as well as the limitations imposed by load disturbance sensitivity, it achieves high-precision position estimation and high robustness. This includes establishing a sensorless control model for PMSMs based on an improved hybrid model with an effective flux linkage observer; revealing the causes of position errors from multiple perspectives, including observer structure, phase-locked loop (PLL), and parameter mismatch; proposing a second-order linear extended state observer for position error compensation, which treats position errors caused by multiple factors as lumped errors for real-time observation; proposing a second-order linear extended state observer for disturbance compensation, which observes changes caused by external loads in real-time; and combining Lyapunov stability theory to identify stator resistance online.

[0081] Figure 1 middle, This is an angular velocity command. For the estimated load torque, For the motor angle, This is the d-axis current command. This is the q-axis voltage command. This is a d-axis voltage command. This is the α-axis voltage command. This is a β-axis voltage command. This is an SVPWM switching instruction. It is a three-phase current.

[0082] Furthermore, combined with Figure 2 As shown, this embodiment establishes a sensorless control model for a permanent magnet synchronous motor based on an improved hybrid model effective flux linkage observer; including:

[0083] In the dq coordinate system, the stator voltage equation of the permanent magnet synchronous reluctance motor is:

[0084] ,

[0085] Transform the above equation to make it symmetrical:

[0086] ,

[0087] In the formula The d-axis stator voltage, This is the q-axis stator voltage. Let p be the stator resistance, and p be the differential operator. For the d-axis stator inductance, For the q-axis stator inductance, The electric angular velocity of the motor. The stator current is the d-axis current. This represents the q-axis stator current. For permanent magnet flux linkage;

[0088] Based on the above formula, the definition of effective flux linkage is obtained:

[0089] ,

[0090] In the formula For effective magnetic flux, The stator flux vectors are the d-axis and q-axis. These are the stator current vectors along the d-axis and q-axis;

[0091] Similarly, in the α-β coordinate system, the effective flux linkage is represented as:

[0092] ,

[0093] In the formula The stator flux vector, The stator current vector, The α-axis component of the stator flux linkage. The β-axis component of the stator flux linkage. This represents the α-axis component of the stator current. This represents the β-axis component of the stator current.

[0094] The method for obtaining the αβ-axis stator flux linkage is as follows:

[0095] ,

[0096] In the formula The back electromotive force is α-axis. This is the back electromotive force along the β axis. The voltage along the α-axis. For β-axis voltage, For stator resistance, For the α-axis current, For β-axis current;

[0097] In the voltage model, the effective flux linkage is obtained by calculating the stator flux linkage, which can be obtained by integrating the back electromotive force. In the α-β coordinate system, the stator flux linkage of the permanent magnet synchronous motor can be calculated by the following formula:

[0098] ,

[0099] In the formula For the α-axis stator flux linkage, For β-axis stator flux linkage, This is the α-axis feedback compensation voltage. This is the β-axis feedback compensation voltage. For time; feedback compensation , , I is the identity matrix. , This represents the gain of the PI controller.

[0100] The method for obtaining the effective flux linkage along the αβ axis based on the stator flux linkage output from the voltage model is as follows:

[0101] ,

[0102] In the formula For the effective flux linkage along the α axis, For the effective flux linkage along the β axis, It is the q-axis inductance.

[0103] Furthermore, the α-axis feedback compensation voltage and β-axis feedback compensation voltage The method to obtain it is as follows:

[0104] The design strategy for the current model uses the observation angles calculated from the stator flux linkage and voltage models as input. For the α-axis stator flux linkage... and β-axis stator flux The d-axis stator flux linkage is obtained by performing the Park transformation. and q-axis stator flux The d-axis current observations were obtained using a current model. and q-axis current observations :

[0105] ,

[0106] In the formula For d-axis inductance, For permanent magnet flux linkage;

[0107] d-axis current observations and q-axis current observations The α-axis stator current and β-axis stator current are obtained by performing the iPark transformation, and then the α-axis feedback compensation voltage is calculated. and β-axis feedback compensation voltage .

[0108] The correction term for the conventional flux linkage observer is This means that current model calculations must be performed in each control cycle. Then immediately feed back to the observer output. In comparison, this structure exhibits strong instantaneous coupling. The improved hybrid model effective flux linkage observer proposed in this embodiment corrects for errors via current, rather than flux linkage. The current model is calculated based on its internal state. and The error is compared with the stator current, and the error is smoothly affected by the flux observation through a PI regulator. Therefore, the observer has a simple structure and low computational complexity.

[0109] The following sections reveal the causes of position errors from multiple perspectives, including observer structure, phase-locked loop, and parameter mismatch:

[0110] Based on the stator flux linkage calculation formula, the estimation error dynamics of the improved hybrid flux linkage observer can be derived as follows:

[0111] ,

[0112] The above equation shows that the flux linkage estimation error The dynamic characteristics are directly determined by the measured current. Current estimation with current model Driven by the differences between them. However, this structure results in its error correction characteristics exhibiting unipolar integral properties. On the one hand, this structure can effectively smooth high-frequency measurement noise by integrating the current error. But on the other hand, the integrator has high gain at low frequencies and even in the DC range, which makes the observer extremely sensitive to DC offset interference, causing the flux linkage estimate to drift and thus introducing a continuous steady-state error.

[0113] The improved hybrid flux linkage observer in this embodiment obtains the effective flux linkage and then uses a phase-locked loop (PLL) to acquire position and rotational speed information. Based on the PLL structure, the position error signal can be expressed as:

[0114] ,

[0115] In the formula For the observed rotor position, The effective flux linkage amplitude;

[0116] Based on the above formula, the error transfer function of the phase-locked loop can be obtained as follows:

[0117] ;

[0118] As can be seen, the phase-locked loop (PLL) is a type II system, which can only obtain a precise position signal under constant speed. When the motor accelerates or decelerates, the input of the PLL is a frequency ramp signal. According to the final value theorem, the PLL will produce a steady-state error, and therefore, a position error will inevitably occur.

[0119] Furthermore, it can be seen that R s and L s It was introduced to calculate the effective flux linkage. However, R s It is highly sensitive to system temperature and skin effect, L s It is highly sensitive to saturation effects. Therefore, it is necessary to analyze the impact of parameter mismatch on the accuracy of position estimation.

[0120] To evaluate the impact of parameter errors on the observer within different speed and torque ranges, a complex vector function is first selected. Then, the complex sensitivity function is constructed as follows:

[0121] ,

[0122] When considering the mismatch of motor parameters, the formula is... Transform to the α-β coordinate system and rewrite in vector form:

[0123] ,

[0124] Combining the complex sensitivity function, it can be seen that the sensitivity of the effective flux linkage amplitude is the real part of the complex sensitivity function. Therefore, the observer's sensitivity with respect to R... s and L q The parameter sensitivity can be derived as

[0125] ,

[0126] ,

[0127] In the formula The angle by which the stator current leads the q-axis;

[0128] In summary, while sensorless control has replaced mechanical position sensors in many applications due to its advantages, the observer algorithm is affected by non-ideal factors such as changes in motor parameters and the use of phase-locked loops, leading to a certain error between the estimated rotor position and the actual rotor position. Position observation errors directly cause problems such as torque ripple and efficiency reduction; excessive errors can even result in loss of synchronization. Therefore, dynamic position correction of position estimation errors can improve the steady-state performance of sensorless control systems.

[0129] Furthermore, combining Figure 3 As shown, a second-order linear extended state observer is constructed for position error compensation, which is used to observe the position error caused by multiple factors in real time as a lumped error.

[0130] There will be an error between the estimated position and the actual position of the flux linkage observer. That is, the effective flux linkage is not on the actual d-axis, but on the observed d-axis. Therefore, it is necessary to obtain the voltage equation of the permanent magnet synchronous motor in the estimated dq coordinate axis.

[0131] In a second-order linear extended state observer used for position error compensation, based on rotor position observations... Position estimation error compared to the actual rotor position The dq-axis voltage equation considering the observation position error is obtained as follows:

[0132] ,

[0133] In the formula For the d-axis voltage that takes into account the observation position error, For the q-axis voltage that takes into account the observation position error, To account for the d-axis current of the observation position error, For the q-axis current that takes into account the observation position error, For differential operators, The effective flux linkage amplitude; where:

[0134] ;

[0135] By estimation Achieve position estimation error Correction.

[0136] The second-order linear extended state observer designed for position error compensation is as follows:

[0137] ,

[0138] In the formula For current observation error, For observing the current vector along the dq axis, For the estimated value of the observed current vector, For the system matrix, For the input matrix, For the voltage vector observed along the dq axis, Let be the coupling matrix. The position error estimate is given by the total disturbance being... , The first-order observer gain matrix is... This is the gain matrix of the second-order observer;

[0139] , ,

[0140] , ;

[0141] In the formula This is an estimated value for the stator resistance. It is the identity matrix;

[0142] Therefore, the positional error can be obtained through observation. This yields the transfer function matrix of the second-order linear extended state observer used for position error compensation. for:

[0143] ,

[0144] In the formula For the Laplace operator.

[0145] First-order observer gain matrix and the second-order observer gain matrix for:

[0146] ,

[0147] In the formula The gain coefficient of the first-order observer gain matrix is ​​1. The gain coefficient of the first-order observer gain matrix is ​​2. The gain coefficient of the second-order observer gain matrix is ​​1. The gain coefficient of the second-order observer gain matrix is ​​2.

[0148] Considering the noise sensitivity and simple parameter configuration of the linearly extended state observer, the poles of the linearly extended state observer are precisely positioned at the desired locations on the root plane by selecting the gain matrix. By comparing the characteristic polynomial with the characteristic polynomial of the target second-order system, and utilizing the equality of corresponding coefficients, the gain of the second-order linearly extended state observer can be designed as follows:

[0149] ,

[0150] In the formula The damping coefficient is... For bandwidth.

[0151] Furthermore, combining Figure 4 As shown, a second-order linear extended state observer for disturbance compensation is proposed to observe changes caused by external loads in real time.

[0152] The second-order linear extended state observer designed for disturbance compensation is as follows:

[0153] ,

[0154] In the formula For angular velocity estimation error, For the observed angular velocity of the effective flux linkage observer, This is an estimate of the angular velocity. The damping ratio coefficient, For system input, The coupling coefficient is... Total disturbance The estimated value, For the first-order gain of the observer, The observer's second-order gain;

[0155] , ,

[0156] In the formula As an intermediate variable, As an intermediate variable, For d-axis current, This is the q-axis current;

[0157] ,

[0158] In the formula This represents the number of pole pairs of the motor. For the moment of inertia of the motor, The coefficient of friction;

[0159] ,

[0160] In the formula This represents the load torque.

[0161] The equation of motion for a permanent magnet synchronous motor is:

[0162] ,

[0163] In the formula This is the actual value of the electric angular velocity;

[0164] In permanent magnet synchronous motor speed control systems, changes in external load significantly affect the actual speed. (Load torque and electromagnetic torque in the rotating reference frame are discussed.) equal:

[0165] .

[0166] Depend on and The difference is used to obtain the disturbance observation error: ,

[0167] In the formula As an intermediate variable; the feedforward disturbance compensation current is calculated. .

[0168] The q-axis current after perturbation compensation by the second-order linear extended state observer for:

[0169] In the formula This is the current after position compensation.

[0170] In this embodiment, the stator resistance is identified online using Lyapunov stability theory. The method includes:

[0171] Based on the above analysis, it can be concluded that existing improved effective flux linkage observers are susceptible to parameter variations, leading to an inability to accurately correct position errors. Among these variations, stator resistance mismatch has a significant impact. The position estimation error in vector control is addressed. Therefore, this embodiment employs an online stator resistance parameter estimation method based on Lyapunov theory, which simultaneously obtains the stability conditions of the second-order linear extended state observer.

[0172] First, construct the Lyapunov function as follows:

[0173] ;

[0174] It can be seen that V is positive definite, and the time derivative of V can be expressed as follows:

[0175] ;

[0176] In the formula The d-axis current observation error is the output of the second-order linear extended state observer used for position error compensation. This refers to the q-axis current observation error output by the second-order linear extended state observer used for position error compensation.

[0177] Formula reduce We can obtain:

[0178] ;

[0179] Substituting the above equation into the derivative formula for V, we can obtain:

[0180] ;

[0181] To satisfy the Lyapunov stability criterion < 0, let The above equation can be decomposed into the following two equations:

[0182] ;

[0183] ;

[0184] from The calculation formula clearly shows that as long as the gain ξ of the second-order linear extended state observer used for position error compensation and If it is positive, then it can be satisfied. <0. Therefore, according to The calculation formula for the stator resistance, and the online identification formula are as follows:

[0185] ;

[0186] In the formula, The stator resistance is identified online. In the formula... This is the d-axis observed current estimate output by the second-order linear extended state observer used for position error compensation. This is the q-axis observation current estimate output by the second-order linear extended state observer used for position error compensation.

[0187] The beneficial effects of the method of the present invention will be verified below with reference to specific embodiments: Specific Implementation Example 1:

[0189] To verify the effectiveness of the method of the present invention, the proposed improved hybrid model effective flux linkage observer assisted by the bilinear extended state observer was verified on the experimental platform of permanent magnet synchronous motor.

[0190] The main parameters of the permanent magnet synchronous motor used are: rated power 3.8kW, rated voltage 220V, rated current 13.5A, inductance L = 1.68mH, number of pole pairs p = 4, stator resistance Rs = 0.49Ω, and permanent magnet flux linkage ψ. PM = 0.13065Wb.

[0191] like Figure 5 and Figure 6As shown, the motor speed accelerates uniformly from 1500 rpm to 2500 rpm with an acceleration of 300 rpm / s, and then decelerates back to 300 r / min. Specifically, as... Figure 5 As shown, the maximum position and velocity errors of the improved hybrid model effective flux linkage observer before compensation are 0.17 rad and 4.38 rpm, respectively, and the estimated rotor position error gradually increases with increasing motor speed. This is mainly due to the low-pass filtering characteristics of the phase-locked loop, and the higher speed leads to a larger phase delay. Subsequently, the test results of the improved hybrid model effective flux linkage observer after compensation by the bilinear extended state observer under the same conditions are shown below. Figure 6 As shown, the maximum position and velocity errors are only 0.12 rad and 3.57 rpm, respectively, and the maximum velocity error after stabilization is only 0.84 rpm. Clearly, the performance of the method of this invention is not significantly affected by changes in motor speed. This stability is due to the adaptive adjustment of the position correction effect of the second-order linear extended state observer with position error compensation. Experimental results show that the sensorless control strategy assisted by the bilinear extended state observer proposed in this invention can effectively and adaptively suppress the position and velocity errors of the flux observer, significantly reduce the estimation error, and effectively enhance the observation accuracy and dynamic performance of position and velocity estimation. Specific Implementation Example 2:

[0193] To evaluate the dynamic performance of the proposed method, performance comparisons were performed during load variations. Experimental results for different estimation schemes are shown below. Figure 7 and Figure 8 As shown.

[0194] Figure 7 and Figure 8 All results are experimental results from different estimation schemes under varying load conditions, including the motor transitioning from no-load to 4 N·m and then back to no-load. Figure 7 In the uncompensated improved hybrid model, the maximum position error of the effective flux linkage observer is 0.11 rad, and the velocity fluctuation caused by load disturbance is 22.06 rpm, resulting in a settling time of approximately 613.05 ms. In contrast, when compensated using the bilinear extended state observer proposed in this invention, due to the real-time compensation effect... Figure 8 Under the same test conditions, the position estimation error was reduced to 0.07 rad, the speed fluctuation was reduced to approximately 15.83 rpm, and the speed recovery time was approximately 251.00 ms, effectively suppressing transient speed fluctuations caused by disturbances and enhancing the system's anti-interference capability. Furthermore, Figure 7The rotor position error showed a clear re-convergence process during the load disturbance, while the position estimation error in the improved hybrid model effective flux observer after compensation by the bilinear extended state observer did not change significantly and remained at around 0.07 rad.

[0195] Experimental results show that the linear extended state observer for disturbance compensation proposed in this invention improves the system's robustness against load disturbances in the medium-to-high speed range and significantly enhances the system's dynamic response at high speeds. Simultaneously, the linear extended state observer for position error compensation proposed in this invention improves the accuracy of rotor position estimation. Therefore, the sensorless control method for permanent magnet synchronous motors assisted by the bilinear extended state observer proposed in this invention has significant advantages in disturbance suppression for position and speed estimation. Specific Implementation Example 3:

[0197] As mentioned above, mismatched resistance parameters can lead to errors in the estimated rotor position. Figure 9 and Figure 10 All results are experimental findings before and after implementing the compensation strategy when the motor speed is 1000 rpm and resistance parameter mismatch exists. The R used in this embodiment... s The value is set to 200% of the nominal value. It is worth noting that, in order to simulate the effect of parameter changes on the system, only the motor parameters in the observer are changed, while the actual physical parameters of the motor remain unchanged.

[0198] like Figure 9 As shown, when the resistance parameters are mismatched, the observer's position error is 0.07 rad, and the maximum velocity fluctuation is 4.53 rpm. However, after compensation using the bilinear extended state observer proposed in this invention, as... Figure 10 As shown, the position error was reduced to 0.05 rad, the speed fluctuation was reduced to 1.38 rpm, and the online identified R... s It can track actual nominal values. Experimental results show that the sensorless control method for permanent magnet synchronous motors assisted by the bilinear extended state observer proposed in this invention can effectively eliminate position errors caused by resistance parameter mismatch and improve parameter robustness.

[0199] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer, characterized in that... include, Design an effective flux linkage observer. Calculate the αβ-axis back EMF based on αβ-axis voltage and current, obtain the αβ-axis stator flux linkage by combining it with the αβ-axis feedback compensation voltage, and then calculate the effective αβ-axis flux linkage by combining it with the q-axis inductance. Output the rotor position observation value via a phase-locked loop. Electric angular velocity observations The αβ-axis feedback compensation voltage is obtained from the αβ-axis stator flux linkage through Park transformation, current model, and iPark transformation. A second-order linear extended state observer is designed for position error compensation. Based on α and β axis voltages and currents, the position error caused by multiple factors is treated as a lumped error for observation to obtain the position estimation error. ; Design a second-order linear extended state observer for disturbance compensation, based on electric angular velocity observations. And the dq-axis current, to obtain the feedforward disturbance compensation current. ; Position estimation error and feedforward disturbance compensation current Used in the sensorless control process of permanent magnet synchronous motors.

2. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 1, characterized in that, The method for obtaining the stator flux linkage along the αβ axis is as follows: ， In the formula The back electromotive force is α-axis. This is the back electromotive force along the β axis. The voltage along the α-axis. For β-axis voltage, For stator resistance, For the α-axis current, For β-axis current; ， In the formula For the α-axis stator flux linkage, For β-axis stator flux linkage, This is the α-axis feedback compensation voltage. This is the β-axis feedback compensation voltage. For time.

3. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 2, characterized in that, The method for obtaining the effective flux linkage along the αβ axis is as follows: ， In the formula For the effective flux linkage along the α axis, For the effective flux linkage along the β axis, It is the q-axis inductance.

4. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 3, characterized in that, α-axis feedback compensation voltage and β-axis feedback compensation voltage The method to obtain it is as follows: α-axis stator flux and β-axis stator flux The d-axis stator flux linkage is obtained by performing the Park transformation. and q-axis stator flux ; The d-axis current observations were obtained using a current model. and q-axis current observations : ， In the formula For d-axis inductance, For permanent magnet flux linkage; d-axis current observations and q-axis current observations The α-axis stator current and β-axis stator current are obtained by performing the iPark transformation, and then the α-axis feedback compensation voltage is calculated. and β-axis feedback compensation voltage .

5. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 4, characterized in that, In a second-order linear extended state observer used for position error compensation, based on rotor position observations... Position estimation error compared to the actual rotor position The dq-axis voltage equation considering the observation position error is obtained as follows: ， In the formula For the d-axis voltage that takes into account the observation position error, For the q-axis voltage that takes into account the observation position error, To account for the d-axis current of the observation position error, For the q-axis current that takes into account the observation position error, For differential operators, The effective flux linkage amplitude; where: ； By estimation Achieve position estimation error Correction.

6. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 5, characterized in that, The second-order linear extended state observer designed for position error compensation is as follows: ， In the formula For current observation error, For observing the current vector along the dq axis, For the estimated value of the observed current vector, For the system matrix, For the input matrix, For the voltage vector observed along the dq axis, Let be the coupling matrix. The position error estimate is given by the total disturbance being... , The first-order observer gain matrix is... This is the gain matrix of the second-order observer; ， ， ， ； In the formula This is an estimated value for the stator resistance. It is the identity matrix; This yields the transfer function matrix of the second-order linear extended state observer used for position error compensation. for: ， In the formula For the Laplace operator.

7. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 6, characterized in that, First-order observer gain matrix and the second-order observer gain matrix for: ， In the formula The gain coefficient of the first-order observer gain matrix is ​​1. The gain coefficient of the first-order observer gain matrix is ​​2. The gain coefficient of the second-order observer gain matrix is ​​1. The gain coefficient of the second-order observer gain matrix is ​​2. ， In the formula The damping coefficient is... For bandwidth.

8. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 7, characterized in that, The second-order linear extended state observer designed for disturbance compensation is as follows: ， In the formula For angular velocity estimation error, For the observed angular velocity of the effective flux linkage observer, This is an estimate of the angular velocity. The damping ratio coefficient, For system input, The coupling coefficient is... For total disturbance The estimated value, For the first-order gain of the observer, The observer's second-order gain; ， ， In the formula As an intermediate variable, As an intermediate variable, For d-axis current, This is the q-axis current; ， In the formula This represents the number of pole pairs of the motor. For the moment of inertia of the motor, The coefficient of friction; ， In the formula This represents the load torque.

9. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 8, characterized in that, The equation of motion for a permanent magnet synchronous motor is: ， In the formula This is the actual value of the electric angular velocity; Load torque and electromagnetic torque in rotating reference frame equal: 。 10. The sensorless control method for a permanent magnet synchronous motor assisted by a bilinear extended state observer according to claim 9, characterized in that, Depend on and The difference is obtained by subtraction: , In the formula As an intermediate variable; the feedforward disturbance compensation current is calculated. .

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