A sensorless control method for medium- and high-speed applications based on the extended back EMF method

Abstract

This invention belongs to the field of permanent magnet synchronous motor control, and proposes a sensorless control method for medium and high speed ranges based on the extended back EMF method. It establishes the PMS voltage equation in a three-phase coordinate system, assumes the difference Δω between the estimated speed and the actual speed to be 0, obtains the rotor position estimation error, and fits the self-inductance affected by the magnetic field saturation effect and the mutual inductance affected by the cross-coupling effect into the equivalent saturated inductance, simplifying the voltage equation for actual sensorless control. The equivalent d-axis saturated inductance and equivalent q-axis saturated inductance are expressed using d-axis and q-axis currents, yielding the flux linkage equation and voltage equation. The equivalent saturated inductance is identified, and compensation can be applied to traditional sensorless control to complete the compensation of the estimated rotor position. The calculated L... dq The current curve is fitted and compensated for in traditional sensorless control. Using a Romberg observer, sensorless control in the medium and high speed range considering the cross saturation effect is realized.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control, specifically relating to a sensorless control method for medium and high speed ranges based on the extended back EMF method. Background Technology

[0002] A permanent magnet synchronous motor (PMSM) is a type of motor in which the rotor, excited by permanent magnets, rotates synchronously with the stator's spatial magnetic field. Due to its excellent performance, PMSM is widely used in various fields. High-precision control of modern PMSM typically requires rotor position feedback. Traditional methods for rotor position feedback include incremental encoders mounted on the rotor shaft, photoelectric encoders, or Hall effect elements mounted on the stator. In sensorless control systems for PMSMs, nonlinear factors such as magnetic circuit saturation and cross-coupling effects significantly impact system performance, posing greater challenges to the implementation of sensorless control technology. Therefore, selecting algorithms that account for the impact of nonlinear factors on system performance and simplifying the algorithms as much as possible have become current research hotspots in the field of motor control. Summary of the Invention

[0003] To achieve the above objectives, the present invention provides a sensorless control method for medium- and high-speed regions based on the extended back EMF method.

[0004] The present invention adopts the following technical solution:

[0005] A sensorless control method for medium- and high-speed applications based on the extended back EMF method includes the following steps:

[0006] 1) Establish the PMSM voltage equation in the three-phase coordinate system considering the cross-coupling effect;

[0007] 2) The voltage equations of the permanent magnet synchronous motor in the three-phase coordinate system are simplified to the voltage equations in the αβ two-phase stationary coordinate system through Clark transformation;

[0008] 3) The voltage equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system is simplified to the voltage equation in the dq two-phase rotating coordinate system considering the cross saturation effect by Park transformation;

[0009] 4) Based on the voltage equation considering the cross saturation effect in the dq two-phase rotating coordinate system, the difference Δω between the estimated speed and the actual speed is assumed to be 0, and the rotor position estimation error Δθ is obtained.

[0010] 5) Based on the dq two-phase rotating coordinate system, considering the cross-coupling effect and neglecting the differential operator and the inductance product term pL reflecting the cross-coupling effect. dqThe voltage equation at that time is analyzed, and the error introduced by the cross-saturation effect in position estimation originates from... Where p is the differential operator. The rotor's electric angular velocity, To account for the q-axis component of the stator inductance due to magnetic circuit saturation, L qd With L dq To reflect the cross-coupling effect, the inductance is generally considered to be equal to that of the other two.

[0011] 6) To identify the error introduced by the cross-saturation effect in position estimation, a motor model based on an equivalent saturated inductance is established. This model can fit the self-inductance affected by the magnetic field saturation effect and the mutual inductance affected by the cross-coupling effect into the equivalent saturated inductance, and the coupled inductance L... dq As a disturbance term, it is equivalently converted into the self-inductance under the influence of magnetic field saturation effect to obtain the saturated inductance equation;

[0012] 7) When the d-axis and q-axis currents of the motor are small, it has not yet entered the saturation region. Ignoring the magnetic circuit saturation effect, we obtain another form of the conversion relationship of the saturated inductance equation.

[0013] 8) Based on the equivalent d-axis saturated inductance L d_e The equivalent q-axis saturated inductance L is a function of the d-axis and q-axis currents. q_e Also a function of the d-axis and q-axis currents, we obtain another form of the motor flux linkage equation and voltage equation;

[0014] 9) Based on the flux linkage equation and voltage equation, the equivalent saturated inductance is identified, and compensation can be used in traditional sensorless control to complete the compensation of the rotor's estimated position.

[0015] 10) Employing parameter identification methods for... Identify and calculate L dq The current curve is fitted and compensated for in traditional sensorless control. Using a Romberg observer, sensorless control in the medium and high speed range considering the cross saturation effect is realized.

[0016] Furthermore, the voltage equations for the permanent magnet synchronous motor in the three-phase coordinate system established in step 1) are as follows:

[0017]

[0018] Among them, U a U b U c These are the terminal voltages of the windings in the three-phase coordinate system; i a i b i c These are the phase currents of the three-phase windings in the three-phase coordinate system; E a E bE c R is the back electromotive force of the three-phase winding in a three-phase coordinate system. s L is the phase resistance of the winding, and L is the equivalent inductance.

[0019] Further, step 2) simplifies the voltage equations in the three-phase coordinate system to the voltage equations in the two-phase stationary coordinate system αβ:

[0020] Among them, E α E β λ is the back electromotive force in the αβ two-phase stationary coordinate system; αf For permanent magnet flux linkage; ω r U is the rotor angular velocity; θ is the rotor speed. α and U β Let α and β be the voltages in the stationary coordinate system of the two phases.

[0021] Further, in step 3), the voltage equation in the two-phase stationary coordinate system is simplified to the voltage equation in the dq two-phase rotating coordinate system considering the cross-saturation effect through the Park transformation. The equation is as follows:

[0022]

[0023] in, To extend the back electromotive force, L d L is the direct-axis inductance of the motor. q For the quadrature axis inductance of the motor, and Let dq be the voltage in the two-phase rotating coordinate system. The rotor's electric angular velocity, The q-axis component of the stator inductance is given to account for magnetic circuit saturation effects, and Δθ is the rotor position estimation error.

[0024] Furthermore, step 4) ignores pL dq One step yields the rotor position estimation error Δθ as follows:

[0025]

[0026] Furthermore, in step 5), the cross-coupling effect is considered in the dq two-phase rotating coordinate system, and pL is ignored. dq The voltage equation at that time is:

[0027]

[0028] Further, in step 6), the coupling inductor L qd As a disturbance term, it is equivalently converted into the self-inductance under the influence of the magnetic field saturation effect, yielding the equation for the saturated inductance:

[0029]

[0030] Among them, L d_e L q_e It is the d-axis and q-axis saturated inductance.

[0031] Furthermore, in step 7), ignoring the magnetic circuit saturation effect, we obtain L. d_e L q_e Another form of conversion formula:

[0032]

[0033] Among them, i min This represents the minimum current when the d-axis and q-axis inductors enter the saturation region.

[0034] Furthermore, based on L obtained in step 8), d_e L q_e The conversion formula, i.e., the equivalent d-axis saturated inductance L d_e The equivalent q-axis saturated inductance L is a function of the d-axis and q-axis currents. q_e Also a function of the d-axis and q-axis currents, we obtain another form of the motor flux linkage equation and voltage equation:

[0035]

[0036] in, For the d-axis and q-axis stator flux linkages, It is a permanent magnet flux linkage.

[0037] Furthermore, the saturated inductance identified in step 9) is L. q_e .

[0038] Furthermore, in step 10), L dq The calculation equation is as follows:

[0039]

[0040] Where θ c This is the cross saturation angle.

[0041] This invention establishes the PMSM voltage equation in a three-phase coordinate system and, through Clark and Park transformations, obtains a mathematical model considering cross-saturation effects in a two-phase rotating coordinate system. To achieve more accurate predictions, the difference Δω between the estimated and actual speeds is assumed to be zero, yielding the rotor position estimation error. A motor model based on equivalent saturated inductance is then established, fitting the self-inductance influenced by magnetic field saturation and the mutual inductance influenced by cross-coupling effects into the equivalent saturated inductance. This simplifies the voltage equation for sensorless control. The equivalent d-axis and q-axis saturated inductances are represented by d- and q-axis currents, resulting in the flux linkage and voltage equations. The equivalent saturated inductance is identified, and compensation in traditional sensorless control can thus compensate for the estimated rotor position. A parameter identification method is used to further refine the model. Identify and calculate L dq The current curve is fitted and compensated for in traditional sensorless control. Using a Romberg observer, sensorless control in the medium and high speed range considering the cross saturation effect is realized. Attached Figure Description

[0042] Figure 1 This is the physical model of the permanent magnet synchronous motor provided in the embodiments of the present invention;

[0043] Figure 2 This is a block diagram of the sensorless control principle in the medium-to-high speed range based on the extended back EMF method provided in this embodiment of the invention.

[0044] Figure 3 This is a diagram showing the relationship between the two-phase stationary coordinate system, the two-phase rotating coordinate system, and the estimated two-phase rotating coordinate system provided in the embodiments of the present invention.

[0045] Figure 4 The present invention provides the following error in the estimation of electrical angle and rotor position when the given torque is 30 N·m and the speed is 50 Hz, without considering the cross saturation effect and with considering the cross saturation effect. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0047] like Figure 1 Combination Figure 2 As shown, a physical model of a permanent magnet synchronous motor based on the extended back EMF method is presented. The motor control method includes the following steps:

[0048] 1) Establish the PMSM voltage equation in the three-phase coordinate system considering the cross-coupling effect;

[0049] 2) The voltage equations of the permanent magnet synchronous motor in the three-phase coordinate system are simplified to the voltage equations in the αβ two-phase stationary coordinate system through Clark transformation;

[0050] 3) The voltage equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system is simplified to the voltage equation in the dq two-phase rotating coordinate system considering the cross saturation effect by Park transformation;

[0051] 4) Based on the voltage equation considering the cross saturation effect in the dq two-phase rotating coordinate system, the difference Δω between the estimated speed and the actual speed is assumed to be 0, and the rotor position estimation error Δθ is obtained.

[0052] 5) Based on the dq two-phase rotating coordinate system, considering the cross-coupling effect and neglecting the differential operator and the inductance product term pL reflecting the cross-coupling effect. dq The voltage equation at that time is analyzed, and the error introduced by the cross-saturation effect in position estimation originates from... Where p is the differential operator. The rotor's electric angular velocity, To account for the q-axis component of the stator inductance due to magnetic circuit saturation, L qd With L dq To reflect the cross-coupling effect, the inductance is generally considered to be equal to that of the other two.

[0053] 6) To identify the error introduced by the cross-saturation effect in position estimation, a motor model based on an equivalent saturated inductance is established. This model can fit the self-inductance affected by the magnetic field saturation effect and the mutual inductance affected by the cross-coupling effect into the equivalent saturated inductance, and the coupled inductance L... dq As a disturbance term, it is equivalently converted into the self-inductance under the influence of magnetic field saturation effect to obtain the saturated inductance equation;

[0054] 7) When the d-axis and q-axis currents of the motor are small, they have not yet entered the saturation region, so the magnetic circuit saturation effect can be ignored, resulting in another form of conversion formula;

[0055] 8) Based on the equivalent d-axis saturated inductance L d_e The equivalent q-axis saturated inductance L is a function of the d-axis and q-axis currents. q_e Also a function of the d-axis and q-axis currents, another form of the motor flux linkage equation and voltage equation can be obtained;

[0056] 9) Based on the flux linkage equation and voltage equation, the equivalent saturated inductance is identified, and compensation can be used in traditional sensorless control to complete the compensation of the rotor's estimated position.

[0057] 10) Employing parameter identification methods for... Identify and calculate L dqThe current curve is fitted and compensated for in traditional sensorless control. Using a Romberg observer, sensorless control in the medium and high speed range considering the cross saturation effect is realized.

[0058] Assuming the three-phase windings of the permanent magnet synchronous motor are symmetrical, and neglecting the electromagnetic hysteresis loss and eddy current loss of the permanent magnet synchronous motor, the voltage equation is:

[0059]

[0060] U a U b U c These are the terminal voltages of the windings; i a i b i c These are the phase currents of the three-phase windings; E a E b E c R is the back electromotive force of the three-phase winding; s L is the phase resistance of the winding, and L is the equivalent inductance.

[0061] The mathematical model of the permanent magnet synchronous motor in the αβ two-phase stationary coordinate system is as follows:

[0062]

[0063] Among them, E α E β λ is the back electromotive force; αf For permanent magnet flux linkage; ω r θ is the rotor angular velocity; θ is the rotor speed.

[0064] Among them, by Figure 3 As shown, the voltage equation in the two-phase stationary coordinate system is simplified to the voltage equation in the dq two-phase rotating coordinate system considering the cross-saturation effect through the Park transformation. The equation is as follows:

[0065]

[0066] in, To extend the back electromotive force, L d L is the direct-axis inductance of the motor. q This is the quadrature axis inductance of the motor.

[0067] Where pL is ignored dq One step yields the following rotor position estimation error:

[0068]

[0069] In the dq two-phase rotating coordinate system, the cross-coupling effect is considered and pL is ignored.dq The voltage equation at that time is:

[0070]

[0071] Among them, the coupling inductor L qd As a disturbance term, it is equivalently converted into the self-inductance under the influence of the magnetic field saturation effect, yielding the equation for the saturated inductance:

[0072]

[0073] Among them, L d_e L q_e It is the d-axis and q-axis saturated inductance.

[0074] Neglecting magnetic circuit saturation effects, we obtain L d_e L q_e Another form of conversion formula:

[0075]

[0076] Among them, according to the equivalent d-axis saturated inductance L d_e The equivalent q-axis saturated inductance L is a function of the d-axis and q-axis currents. q_e Also a function of the d-axis and q-axis currents, we obtain the motor flux linkage equation and voltage equation:

[0077]

[0078] Based on the flux linkage equation and the voltage equation, the equivalent saturation inductance is identified as only L. q_e This compensation method can achieve the estimated rotor position compensation in traditional sensorless control. A parameter identification method is used to... Identify and calculate L dq The calculation equation is:

[0079]

[0080] Figure 3 As shown, the fitted curve about the current is compensated for in traditional sensorless control. Using a Romberg observer, sensorless control in the medium-to-high speed range considering the cross-saturation effect is achieved.

[0081] Figure 4 As shown, Figure 4 Figure (a) shows the estimation error of electrical angle and rotor position without considering the cross saturation effect when the given torque is 30 N·m and the speed is 50 Hz. Figure 4Figure (b) shows the electrical angle and rotor position estimation errors considering the cross-saturation effect when the given torque is 30 N·m and the speed is 50 Hz. Comparing the position estimation errors before and after compensation, the errors after compensation are reduced from 2.5° and 7.5° to 0°, a significant decrease. This demonstrates that the improved sensorless control strategy adopted in this invention has higher accuracy, and the sensorless control method based on the extended back EMF method in the medium-to-high speed range is effective.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sensorless control method for medium- and high-speed regions based on the extended back EMF method, characterized in that, Includes the following steps: 1) Establish the PMSM voltage equation in the three-phase coordinate system considering the cross-coupling effect; 2) The voltage equations of the permanent magnet synchronous motor in the three-phase coordinate system are simplified to the voltage equations in the αβ two-phase stationary coordinate system through Clark transformation; 3) The voltage equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system is simplified to the voltage equation in the dq two-phase rotating coordinate system considering the cross saturation effect through Park transformation; 4) Based on the voltage equation considering cross-saturation effect in the dq two-phase rotating coordinate system, the difference between the estimated velocity and the actual velocity is calculated. Assuming the value is 0, the rotor position estimation error is obtained. ; 5) Based on the dq two-phase rotating coordinate system, considering the cross-coupling effect and neglecting the product term of the differential operator and the inductance reflecting the cross-coupling effect. The voltage equation at that time is analyzed, and the error introduced by the cross-saturation effect in position estimation originates from... Where p is the differential operator, The rotor's electric angular velocity, To account for the q-axis component of the stator inductance due to magnetic circuit saturation, and Inductance to reflect cross-coupling effect; 6) To identify the error introduced by the cross-saturation effect in position estimation, a motor model based on equivalent saturated inductance is established. This model can fit the self-inductance affected by the magnetic field saturation effect and the mutual inductance affected by the cross-coupling effect into the equivalent saturated inductance, and incorporate the coupled inductance. As a disturbance term, it is equivalently converted into the self-inductance under the influence of magnetic field saturation effect to obtain the saturated inductance equation; 7) When the d-axis and q-axis currents of the motor are small, it has not yet entered the saturation region. Ignoring the magnetic circuit saturation effect, we obtain another form of the conversion relationship of the saturated inductance equation. 8) Based on the equivalent d-axis saturated inductance The inductance is a function of the d-axis and q-axis currents, and is equivalent to the q-axis saturated inductance. Also a function of the d-axis and q-axis currents, we obtain another form of the motor flux linkage equation and voltage equation; 9) Based on the flux linkage equation and voltage equation, the equivalent saturated inductance is identified, and compensation can be used in traditional sensorless control to complete the compensation of the rotor's estimated position. 10) Using parameter identification methods to... Perform identification and calculation The current curve is fitted and compensated for in traditional sensorless control. Using a Romberg observer, sensorless control in the medium and high speed range considering the cross saturation effect is realized.

2. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 1, characterized in that, The voltage equations for the permanent magnet synchronous motor in the three-phase coordinate system established in step 1) are as follows: ， Among them, U a U b U c These are the terminal voltages of the windings in the three-phase coordinate system; i a i b i c These are the phase currents of the three-phase windings in the three-phase coordinate system; E a E b E c R is the back electromotive force of the three-phase winding in a three-phase coordinate system. s L is the phase resistance of the winding, and L is the equivalent inductance.

3. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 2, characterized in that, Step 2) Simplify the voltage equations in the three-phase coordinate system to the voltage equations in the two-phase stationary coordinate system αβ: , in, , The back electromotive force is given in the αβ two-phase stationary coordinate system. For permanent magnet flux linkage; θ is the rotor angular velocity; θ is the rotor speed. and Let α and β be the voltages in the stationary coordinate system of the two phases.

4. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 3, characterized in that, Step 3) Simplify the voltage equation in the two-phase stationary coordinate system using the Park transformation to the voltage equation in the dq two-phase rotating coordinate system considering the cross-saturation effect. The equation is: ， in, , To extend the back electromotive force, For the direct-axis inductance of the motor, For the quadrature axis inductance of the motor, and Let dq be the voltage in the two-phase rotating coordinate system. The rotor's electric angular velocity, To account for the q-axis component of the stator inductance due to magnetic circuit saturation, This represents the rotor position estimation error.

5. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 4, characterized in that, Step 4) Ignore One step yields the rotor position estimation error. as follows: 。 6. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 5, characterized in that, Step 5) The cross-coupling effect is considered and ignored in the dq two-phase rotating coordinate system. The voltage equation at that time is: 。 7. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 6, characterized in that, Step 6) Couple the inductor As a disturbance term, it is equivalently converted into the self-inductance under the influence of the magnetic field saturation effect, yielding the equation for the saturated inductance: ， in, , It is the d-axis and q-axis saturated inductance.

8. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 7, characterized in that, Step 7) Ignoring magnetic circuit saturation effects, we obtain , Another form of conversion formula: ， in, This represents the minimum current when the d-axis and q-axis inductors enter the saturation region.

9. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 8, characterized in that, According to step 8), , The conversion formula, i.e., the equivalent d-axis saturated inductance. The inductance is a function of the d-axis and q-axis currents, and is equivalent to the q-axis saturated inductance. Also a function of the d-axis and q-axis currents, we obtain another form of the motor flux linkage equation and voltage equation: ， ， in, For the d-axis and q-axis stator flux linkages, It is a permanent magnet flux linkage.

10. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 9, characterized in that, The saturated inductance identified in step 9) is .

11. The sensorless control method for medium- and high-speed regions based on the extended back EMF method according to claim 10, characterized in that, Step 10) The calculation equation is as follows: ， Among them, This is the cross saturation angle.

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