Permanent magnet synchronous motor rotating speed estimation method based on sliding mode expansion state observer

Abstract

The invention discloses a permanent magnet synchronous motor rotating speed estimation method based on a sliding mode expansion state observer. The method specifically comprises the following steps: step 1, constructing a permanent magnet synchronous motor state equation; step 2, constructing a sliding mode expansion state observer through the state equation obtained in the step 1 to estimate an expansion counter electromotive force; and step 3, estimating the rotor position and the rotating speed of the permanent magnet synchronous motor through a phase-locked loop according to the extended back electromotive force obtained in the step 2. According to the method, the problem that the estimated rotor position is severely lagged behind the actual rotor position due to the fact that the existing extended state observer is difficult to accurately estimate the rapidly changing counter electromotive force is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet synchronous motor control and relates to a permanent magnet synchronous motor speed estimation method based on a sliding mode expansion state observer. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) offer advantages such as high efficiency, high power density, high reliability, a wide speed regulation range, and a simple structure. They hold broad application prospects in a wide range of fields, including household appliances, rail transportation, industrial manufacturing, and aerospace. High-performance PSM drive systems are key to leveraging these advantages. Their implementation relies on position sensors to obtain accurate rotor position and speed information. However, position sensors are costly, difficult to maintain, and reduce system reliability. Therefore, sensorless control technology for PSMs offers unique advantages.

[0003] Currently, in sensorless control of medium- and high-speed permanent magnet synchronous motors, the back-EMF signal-to-noise ratio is sufficiently large to be used for rotor position estimation. The extended state observer (ESO) treats the nonlinear dynamics, parameter uncertainty, and external disturbances in the system as a total disturbance, observing the total disturbance as an extended state variable. Because it does not rely on a precise mathematical model of the controlled object and exhibits strong disturbance immunity, it has been widely studied and applied. However, the traditional ESO suffers from a low-pass filtering characteristic, resulting in a significant phase lag when estimating rapidly changing back-EMF, causing the estimated rotor position to lag significantly behind the actual rotor position. Summary of the Invention

[0004] The purpose of the present invention is to provide a permanent magnet synchronous motor speed estimation method based on a sliding mode extended state observer, which solves the problem that the existing extended state observer is difficult to accurately estimate the rapidly changing back electromotive force, thereby causing the estimated rotor position to lag seriously behind the actual rotor position.

[0005] The technical solution adopted by the present invention is a permanent magnet synchronous motor speed estimation method based on a sliding mode extended state observer, which specifically includes the following steps: Step 1, constructing the state equation of the permanent magnet synchronous motor; Step 2, constructing a sliding mode extended state observer based on the state equation obtained in step 1 to estimate the extended back electromotive force; Step 3: Estimate the rotor position and speed of the permanent magnet synchronous motor using the expanded back electromotive force obtained in step 2 through a phase-locked loop.

[0006] The present invention is also characterized in that: The specific process of step 1 is: The voltage equation in the permanent magnet synchronous motor coordinate system is shown in the following formula (1): (1); in, yes α Axis and β Shaft voltage, R s is the stator resistance, yes α Axis and β The shaft current, yes α Axis and β Shaft extension back EMF, p is the differential operator; and: (2); in, yes d Shaft inductance, yes q Shaft inductance, yes d Shaft current, is the actual rotor electrical angular frequency, is the permanent magnet flux, is the actual rotor position; The differential equation of current obtained by formula (1) is shown in the following formula (3): (3); The back electromotive force term in formula (3) is treated as an unknown disturbance and written as the state equation as shown in the following formula (4): (4); in, , , , , ; The unknown interference in the extended formula (4) As a new state variable, the constructed permanent magnet synchronous motor state equation is shown in the following formula (5): (5); in, , .

[0007] The specific process of step 2 is: Step 2.1, establish a sliding mode extended state observer using the state equation obtained in step 1; Step 2.2, design the sliding surface and control rate of the sliding mode extended state observer in step 2.1; Step 2.3, obtain the final sliding mode extended state observer to estimate the extended back electromotive force through steps 2.1 and 2.2.

[0008] The specific process of step 2.1 is: The sliding mode expansion state observer is constructed by formula (5) as shown in the following formula (6): (6); in, yes The estimated value of yes α Shaft current The estimated value of yes β Shaft current The estimated value of yes The estimated value of yes α Axis extension back EMF The estimated value of yes β Axis extension back EMF The estimated value of represents the stator current estimation error, and and , yes The estimated value of and is the gain of the extended state observer, is the terminal sliding mode control rate, K m is the terminal sliding mode gain.

[0009] The specific process of step 2.2 is: The terminal sliding surface in the designed sliding mode expansion state observer is shown in the following formula (7): (7); in, is the terminal sliding surface, 、 and m is a real number greater than zero, and , is a symbolic function, ; The control rate under the terminal sliding surface is shown in the following formula (8): (8); in, is the control rate, Control rate jitter term; The control rate jitter term in formula (8) is designed as shown in the following formula (9): (9); in, g and h is an adjustable parameter. Formula (9) is a low-pass filter. g The adaptive adjustment method is shown in the following formula (10): (10); in, k is the error sensitivity adjustment parameter.

[0010] The specific process of step 2.3 is: By substituting formula (8) and formula (9) into formula (6), the final sliding mode extended state observer is obtained as shown in the following formula (11): (11).

[0011] The specific process of step 3 is: The estimated extended back EMF obtained by formula (11) 、 The rotor position error signal is calculated after normalization as shown in the following formula (12): (12); in, is the normalized error signal, is the estimated rotor position.

[0012] In step 3, the error signal The estimated speed is obtained by the PI regulator as shown in the following formula (13): (13); in, is the estimated speed, is the proportional gain, is the integral gain; The estimated rotor position is obtained by integrating the estimated speed obtained by formula (13) as shown in the following formula (14): (14).

[0013] The beneficial effects of the present invention are that, compared with conventional extended state observer (ESO) methods for estimating back EMF, the sliding mode ESO employed in this invention not only expands the bandwidth of disturbance estimation but also improves its dynamic performance and robustness. Furthermore, by introducing a terminal sliding surface structure, finite-time convergence of the state estimation error is achieved, improving the system's response speed and convergence accuracy. Furthermore, the control rate designed based on this sliding surface can inherently suppress chattering. This overcomes the difficulty of existing ESOs in accurately estimating rapidly changing back EMF. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a block diagram of a vector control system used in a permanent magnet synchronous motor speed estimation method based on a sliding mode extended state observer according to the present invention; Figure 2 This is a block diagram of a sliding mode extended state observer used in a permanent magnet synchronous motor speed estimation method based on a sliding mode extended state observer according to the present invention; Figure 3 This is a simulation result diagram of the extended back-electromotive force estimated using the traditional extended state observer; Figure 4 1 is a diagram of the simulation results of the extended back electromotive force estimated by the permanent magnet synchronous motor speed estimation method based on the sliding mode extended state observer of the present invention; Figure 5 This is a diagram of the simulation results of the rotor position estimated using the traditional extended state observer; Figure 6 This is a diagram of the simulation results of the rotor position estimated by the permanent magnet synchronous motor speed estimation method based on the sliding mode expansion state observer of the present invention. DETAILED DESCRIPTION

[0015] The following describes it in detail with reference to specific implementation methods.

[0016] Example 1 The present invention is based on a permanent magnet synchronous motor speed estimation method of a sliding mode expansion state observer, wherein the vector control system block diagram is as follows: Figure 1 As shown, the specific steps are as follows: Step 1, constructing the state equation of the permanent magnet synchronous motor; Step 2: Construct the state equation obtained in step 1 as Figure 2 The sliding mode extended state observer shown estimates the extended back EMF; Step 3: Estimate the rotor position and speed of the permanent magnet synchronous motor using the expanded back electromotive force obtained in step 2 through a phase-locked loop.

[0017] Example 2 The specific process of step 1 is: permanent magnet synchronous motor The voltage equation in the coordinate system is shown in the following formula (1): (1); in, yes α Axis and β Shaft voltage, R s is the stator resistance, yes α Axis and β The shaft current, yesα Axis and β Shaft extension back EMF, p is the differential operator.

[0018] and: (2); in, L d yes d Shaft inductance, L q yes q Shaft inductance, yes d Shaft current, is the actual rotor electrical angular frequency, is the permanent magnet flux, is the actual rotor position; The differential equation of current obtained by formula (1) is shown in the following formula (3): (3); The back electromotive force term in formula (3) is treated as an unknown disturbance and written as the state equation as shown in the following formula (4): (4); in, , , , , ; The unknown interference in the extended formula (4) As a new state variable, the constructed permanent magnet synchronous motor state equation is shown in the following formula (5): (5); in, , .

[0019] Example 3 The specific process of step 2 is: Step 2.1, establish a sliding mode extended state observer using the state equation obtained in step 1; Step 2.2, design the sliding surface and control rate of the sliding mode extended state observer in step 2.1; Step 2.3, obtain the final sliding mode extended state observer to estimate the extended back electromotive force through steps 2.1 and 2.2.

[0020] Example 4 The specific process of step 2.1 is: The sliding mode expansion state observer is constructed by formula (5) as shown in the following formula (6): (6); in, yes The estimated value of yes α Shaft current The estimated value of yes β Shaft current The estimated value of yes The estimated value of yes α Axis extension back EMF The estimated value of yes β Axis extension back EMF The estimated value of represents the stator current estimation error, and and , yes The estimated value of and is the gain of the extended state observer, is the designed terminal sliding mode control rate, K m is the terminal sliding mode gain.

[0021] Example 5 The specific process of step 2.2 is: The terminal sliding surface in the designed sliding mode expansion state observer is shown in the following formula (7): (7); in, is the terminal sliding surface, 、 and m is a real number greater than zero, and , is a symbolic function, ; The control rate under the terminal sliding surface is shown in the following formula (8): (8); in, is the control rate, Controls the rate jitter term.

[0022] The control rate jitter term in formula (8) is designed as shown in the following formula (9): (9); in, g and his an adjustable parameter. Formula (9) is a low-pass filter. Perform smoothing to suppress chattering and make the control rate continuous. g It can be regarded as the equivalent cutoff frequency of the low-pass filter, reducing g Can reduce The chattering, but g Too small will lead to the degradation of system dynamic performance. g The adaptive adjustment method is shown in the following formula (10): (10); in, 1000, 1500, k is the error sensitivity adjustment parameter.

[0023] Example 6 The specific process of step 2.3 is: By substituting formula (8) and formula (9) into formula (6), the final sliding mode extended state observer is obtained as shown in the following formula (11): (11); Example 7 The specific process of step 3 is: The estimated extended back EMF obtained by formula (11) 、 The rotor position error signal is calculated after normalization as shown in the following formula (12): (12); in, is the normalized error signal, is the estimated rotor position.

[0024] Error signal The estimated speed is obtained by the PI regulator as shown in the following formula (13): (13); in, is the estimated speed, is the proportional gain, is the integral gain; The estimated rotor position is obtained by integrating the estimated speed obtained by formula (13) as shown in the following formula (14): (14); The vector control system block diagram of the permanent magnet synchronous motor speed estimation method based on the sliding mode expansion state observer of the present invention is as follows: Figure 1As shown in the figure, the system adopts a double closed loop structure consisting of three PI regulators, including a speed outer loop and a current inner loop. Control strategy, current command output by the speed loop PI regulator As q Input of the shaft current regulator, As d The two currents are regulated by their respective PI regulators and then output voltage control instructions for controlling the power electronic converter.

[0025] Detecting the stator current of a three-phase permanent magnet synchronous motor through a current sensor 、 、 and through Transformation to obtain the current in the two-phase stationary coordinate system 、 Then through Coordinate transformation obtains the current component in the synchronous rotating coordinate system 、 ; Two-phase voltage in two-phase stationary coordinate system 、 and two-phase current 、 As Figure 2 The input of the sliding mode expansion state observer is shown to realize the disturbance 、 Extended back-EMF estimation. 、 As the input of the phase-locked loop, the rotor position information is realized through the phase-locked loop and electrical angular velocity Extraction of the speed command With estimated speed The difference is used as the input of the speed loop PI regulator to output the torque current command. . Given the excitation current With feedback current The difference is output through the current loop PI regulator d Shaft voltage command , given torque current With feedback current The difference is output through the current loop PI regulator q Shaft voltage command .

[0026] 、 pass Transformation to obtain the two-phase voltage in the two-phase stationary coordinate system 、 The inverter outputs three-phase voltage through SVPWM modulation to drive the permanent magnet synchronous motor.

[0027] Figure 3 This is a simulation result diagram of the extended back-electromotive force estimated using the traditional extended state observer; Figure 4 1 is a diagram of the simulation results of the extended back electromotive force estimated by the permanent magnet synchronous motor speed estimation method based on the sliding mode extended state observer of the present invention; Figure 5 This is a diagram of the simulation results of the rotor position estimated using the traditional extended state observer; Figure 6 This is a diagram of the simulation results of the rotor position estimated by the permanent magnet synchronous motor speed estimation method based on the sliding mode expansion state observer of the present invention. Figures 3 to 6 The parameters of the permanent magnet synchronous motor used in the simulation are shown in Table 1. Figures 3 to 6 The speed in the simulation results is set to 1000 rpm. Figure 3 and Figure 4 It can be found that when the motor runs at rated speed, the phase of the extended back EMF estimated by the traditional extended state observer lags behind the phase of the actual extended back EMF, while the extended back EMF estimated by the present invention can track the actual extended back EMF well without amplitude attenuation and phase lag. Figure 5 and Figure 6 It can be found that when the motor is running at rated speed, the rotor position estimated by the conventional extended state observer lags behind the actual rotor position, while the rotor position estimated by the present invention can accurately track the actual rotor position. The above simulation results show that the present invention can effectively solve the problem that the rotor position estimated by the conventional extended state observer cannot accurately track the actual rotor position.

[0028] Table 1 Parameters of permanent magnet synchronous motor

Claims

1. A permanent magnet synchronous motor speed estimation method based on a sliding mode extended state observer is characterized by: The specific steps include: Step 1, constructing the state equation of the permanent magnet synchronous motor; Step 2, constructing a sliding mode extended state observer based on the state equation obtained in step 1 to estimate the extended back electromotive force; Step 3: Estimate the rotor position and speed of the permanent magnet synchronous motor using the expanded back electromotive force obtained in step 2 through a phase-locked loop.

2. The method for estimating the speed of a permanent magnet synchronous motor based on a sliding mode extended state observer according to claim 1, wherein: The specific process of step 1 is: permanent magnet synchronous motor αβ The voltage equation in the coordinate system is shown in the following formula (1): （1）； in, yes α Axis and β Shaft voltage, R s is the stator resistance, yes α Axis and β The shaft current, yes α Axis and β Shaft extension back EMF, p is the differential operator; and: （2）； in, L d yes d Shaft inductance, L q yes q Shaft inductance, yes d Shaft current, is the actual rotor electrical angular frequency, is the permanent magnet flux, is the actual rotor position; The differential equation of current obtained by formula (1) is shown in the following formula (3): （3）； The back electromotive force term in formula (3) is treated as an unknown disturbance and written as the state equation as shown in the following formula (4): （4）； in, , , , , ; The unknown interference in the extended formula (4) As a new state variable, the constructed permanent magnet synchronous motor state equation is shown in the following formula (5): （5）； in, , .

3. The method for estimating the speed of a permanent magnet synchronous motor based on a sliding mode extended state observer according to claim 2, wherein: The specific process of step 2 is: Step 2.1, establish a sliding mode extended state observer using the state equation obtained in step 1; Step 2.2, design the sliding surface and control rate of the sliding mode extended state observer in step 2.1; Step 2.3, obtain the final sliding mode extended state observer to estimate the extended back electromotive force through steps 2.1 and 2.

2.

4. The method for estimating the speed of a permanent magnet synchronous motor based on a sliding mode extended state observer according to claim 3, wherein: The specific process of step 2.1 is as follows: The sliding mode expansion state observer is constructed by formula (5) as shown in the following formula (6): （6）； in, yes The estimated value of yes α Shaft current The estimated value of yes β Shaft current The estimated value of yes The estimated value of yes α Axis extension back EMF The estimated value of yes β Axis extension back EMF The estimated value of represents the stator current estimation error, and and , yes The estimated value of and is the gain of the extended state observer, is the terminal sliding mode control rate, K m is the terminal sliding mode gain.

5. The method for estimating the speed of a permanent magnet synchronous motor based on a sliding mode extended state observer according to claim 4, characterized in that: The specific process of step 2.2 is as follows: The terminal sliding surface in the designed sliding mode expansion state observer is shown in the following formula (7): （7）； in, is the terminal sliding surface, 、 and m is a real number greater than zero, and , is a symbolic function, ; The control rate under the terminal sliding surface is shown in the following formula (8): （8）； in, is the control rate, Control rate jitter term; The control rate jitter term in formula (8) is designed as shown in the following formula (9): （9）； in, g and h is an adjustable parameter. Formula (9) is a low-pass filter. g The adaptive adjustment method is shown in the following formula (10): （10）； in, k is the error sensitivity adjustment parameter.

6. The method for estimating the speed of a permanent magnet synchronous motor based on a sliding mode extended state observer according to claim 5, characterized in that: The specific process of step 2.3 is as follows: By substituting formula (8) and formula (9) into formula (6), the final sliding mode extended state observer is obtained as shown in the following formula (11): （11）。 7. The method for estimating the speed of a permanent magnet synchronous motor based on a sliding mode extended state observer according to claim 6, characterized in that: The specific process of step 3 is as follows: The estimated extended back EMF obtained by formula (11) 、 The rotor position error signal is calculated after normalization as shown in the following formula (12): （12）； in, is the normalized error signal, is the estimated rotor position.

8. The method for estimating the speed of a permanent magnet synchronous motor based on a sliding mode extended state observer according to claim 7, characterized in that: In step 3, the error signal The estimated speed is obtained by the PI regulator as shown in the following formula (13): （13）； in, is the estimated speed, is the proportional gain, is the integral gain; The estimated rotor position is obtained by integrating the estimated speed obtained by formula (13) as shown in the following formula (14): （14）。

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