A Control Method for Permanent Magnet Synchronous Motors Based on Pulsed High-Frequency Voltage Injection

Abstract

This invention belongs to the field of permanent magnet synchronous motor (PMSM) control, specifically relating to a PMSM control method based on pulsed high-frequency voltage injection. The method includes: establishing a mathematical model of the PMSM in a three-phase coordinate system, and obtaining a mathematical model in a two-phase rotating coordinate system through Clark and Park transformations. The rotor position error angle Δθ is then addressed using the pulsed high-frequency voltage injection method. A high-frequency voltage signal is injected into the estimated direct-axis coordinate system, and a high-frequency current signal is extracted through a bandpass filter to obtain the high-frequency current equation corresponding to the estimated direct axis. This equation is then multiplied by a modulation signal of the same frequency and passed through a low-pass filter to obtain f(Δθ). When the rotor position error is sufficiently small, when f(Δθ) = 0, Δθ = 0. At this point, the amplitude f(Δθ) = 0 is fed into the PI controller, which outputs an estimated rotational speed. An algorithm is used to predict the electrical angle, thus replacing the traditional Hall sensor.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control, specifically relating to a permanent magnet synchronous motor control method based on pulsed high-frequency voltage injection. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in motor control due to their relatively simple structure, high power density, strong reliability, and high efficiency. The most common control method for PMSMs is vector control. The core of this method is to perform Clark and Park transformations on voltage and current, decomposing the three-phase current into quadrature-axis and direct-axis currents in a two-phase rotating coordinate system. To achieve vector control, the rotor's electrical angle is needed. Traditionally, Hall effect sensors are used to detect the rotor's electrical angle in real time. However, in harsh environments, the effectiveness of Hall effect sensors may be significantly reduced. Furthermore, to save costs and reduce size, current research focuses on using algorithms to predict the electrical angle, thus replacing traditional Hall effect sensors. Therefore, choosing the right algorithm to achieve this goal and simplifying the algorithm as much as possible has become one of the current research hotspots in the field of motor control. Summary of the Invention

[0003] To address the problems in the aforementioned related technologies, this invention provides a control method for permanent magnet synchronous motors based on pulsed high-frequency voltage injection.

[0004] The technical solution adopted in this invention is as follows:

[0005] A control method for a permanent magnet synchronous motor based on pulsed high-frequency voltage injection includes the following steps:

[0006] 1) Establish the voltage equations for the three-phase coordinate system of the permanent magnet synchronous motor (PMSM);

[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 equations of the permanent magnet synchronous motor in the two-phase stationary coordinate system are simplified to the voltage equations in the dq two-phase rotating coordinate system through the Park transformation;

[0009] 4) Simplify the voltage equation in the dq two-phase rotating coordinate system to another form with the current derivative as the left-hand side, and obtain the mathematical model of the permanent magnet synchronous motor in the dq two-phase rotating coordinate system.

[0010] 5) By using the coordinate relationship diagram, the conversion relationship between the estimated voltage and current of the permanent magnet synchronous motor and the actual voltage and current in the dq two-phase rotating coordinate system is obtained;

[0011] 6) Combining the mathematical model of the permanent magnet synchronous motor in the dq two-phase rotating coordinate system, the estimated voltage and current of the permanent magnet synchronous motor, the conversion relationship between the actual voltage and current, a conversion relationship between the estimated current and the estimated voltage of the permanent magnet synchronous motor in the two-phase rotating coordinate system is obtained with the derivative of the estimated current as the left term.

[0012] 7) Substitute the formulas for the average inductance on the quadrature and direct axes and the half-difference inductance on the quadrature and direct axes into the conversion formula for the estimated current and voltage of the permanent magnet synchronous motor in the two-phase rotating coordinate system with the derivative of the estimated current as the left term, to obtain another form of conversion formula;

[0013] 8) Inject a high-frequency voltage signal into the estimated rectangular coordinate system and solve for the corresponding current relationship;

[0014] 9) Extract the high-frequency current equation that estimates the response of the direct axis from the current relationship. The high-frequency current equation contains information about Δθ.

[0015] 10) Pass the quadrature-axis current obtained by the Park transform in the system into a bandpass filter and extract the high-frequency current signal. Multiply the high-frequency current signal with the modulation signal of the same frequency, and then pass it through a low-pass filter to obtain f(Δθ). The amplitude of f(Δθ) is half of that of the high-frequency current signal.

[0016] 11) When the rotor position error is small enough, sin(Δθ) is replaced by Δθ. When f(Δθ) = 0, sin(Δθ) = 0, that is, Δθ = 0, and the actual angle of the rotor is consistent with the estimated angle.

[0017] 12) The amplitude f(Δθ) is fed into the PI controller, which outputs the estimated speed. The estimated angle is then obtained by integration. The estimated angle is applied to the coordinate transformation to form the entire closed-loop system, thereby realizing the vector control of the permanent magnet synchronous motor.

[0018] Furthermore, the voltage equations for the permanent magnet synchronous motor in the three-phase coordinate system established in step 1) are as follows:

[0019]

[0020] 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; Ea 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.

[0021] 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:

[0022]

[0023] 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.

[0024] 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 using the Park transformation. The equation is as follows:

[0025]

[0026] u d For direct-axis voltage, u q R is the quadrature-axis voltage, R is the resistance value, and i is the cross-axis voltage. d For direct-axis current, i q For quadrature axis current, L d For direct-axis inductors, L q For quadrature axis inductance, ω e Angular velocity, ψ f It is a permanent magnet flux linkage.

[0027] Further, step 4) simplifies the voltage equation in the dq two-phase rotating coordinate system to:

[0028]

[0029] Furthermore, the conversion relationship between the estimated voltage and current and the actual voltage and current shown in step 5) is as follows:

[0030]

[0031] For direct-axis voltage estimates, For the quadrature axis voltage estimate, For the direct-axis current estimate, This is the estimated value of the quadrature axis current.

[0032] Furthermore, in step 6), the conversion relationship between the estimated value of the permanent magnet synchronous motor current and the estimated value of the voltage in the two-phase rotating coordinate system, with the derivative of the estimated current as the left-hand side, is as follows:

[0033]

[0034] Further, in step 7), substituting the formulas for the average inductance and the half-difference inductance on the quadrature and direct axes into the conversion relationship between the estimated current and voltage of the permanent magnet synchronous motor in the two-phase rotating coordinate system, with the derivative of the estimated current as the left-hand side, we get:

[0035]

[0036] L is the average inductance on the quadrature and direct axes, and ΔL is the half-differential inductance on the quadrature and direct axes.

[0037] Further, in step 8), the estimated high-frequency voltage signal injected into the rectangular coordinate system and the corresponding current relationship are respectively:

[0038]

[0039] in To estimate the high-frequency voltage signal injected into the rectangular coordinate system, U mh For estimating the voltage amplitude and ω along the direct axis h To estimate the angular velocity of the voltage along the direct axis, To calculate the direct-axis current value when estimating the voltage signal injected into the direct-axis coordinate system, This is to calculate the quadrature-axis current value when estimating the voltage signal injected into the direct-axis coordinate system.

[0040] Furthermore, in step 9), the high-frequency current equation for the direct-axis response in the current relationship is estimated as follows:

[0041]

[0042] In step 10), the high-frequency current signal is multiplied by the modulation signal of the same frequency, and then passed through a low-pass filter to obtain f(Δθ):

[0043]

[0044] The equivalent substitution formula mentioned in step 11) is approximately:

[0045]

[0046] This method establishes a mathematical model of the PMSM in a three-phase coordinate system, and obtains a mathematical model in a two-phase rotating coordinate system through Clark and Park transformations. To achieve more accurate predictions, the difference between the estimated rotor position and the actual rotor position needs to be minimized, even approaching zero. To extract the rotor position error angle Δθ, a pulsed high-frequency voltage injection method is introduced. A high-frequency voltage signal is injected into the estimated direct-axis coordinate system, and a high-frequency current signal is extracted through a bandpass filter to obtain the high-frequency current equation corresponding to the estimated direct axis. This equation is then multiplied by a modulation signal of the same frequency and passed through a low-pass filter to obtain f(Δθ). When the rotor position error is sufficiently small, when f(Δθ) = 0, Δθ = 0. At this point, the amplitude f(Δθ) = 0 is fed into the PI controller, which outputs the estimated speed. After integration, the estimated angle is obtained, and this estimated angle is applied to the coordinate transformation, forming a closed-loop vector control system. Attached Figure Description

[0047] Figure 1 This is an equivalent circuit diagram of a permanent magnet synchronous motor in the prior art of this invention.

[0048] Figure 2 This is a block diagram of the control principle of a permanent magnet synchronous motor based on the pulse high-frequency voltage injection method provided in an embodiment of the present invention;

[0049] 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.

[0050] Figure 4 These are (a) the error diagram of the actual speed versus the estimated speed of the motor rotor and (b) the error diagram of the motor rotor position provided in the embodiments of the present invention. Detailed Implementation

[0051] 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.

[0052] This invention is used for, for example Figure 1 In the equivalent circuit of the permanent magnet synchronous motor shown, see... Figure 2 A control method for a permanent magnet synchronous motor based on pulsed high-frequency voltage injection includes the following steps:

[0053] 1) Establish the voltage equations for the three-phase coordinate system of the permanent magnet synchronous motor (PMSM);

[0054] 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;

[0055] 3) The voltage equations of the permanent magnet synchronous motor in the two-phase stationary coordinate system are simplified to the voltage equations in the dq two-phase rotating coordinate system through the Park transformation;

[0056] 4) Simplify the voltage equation in the dq two-phase rotating coordinate system to another form with the current derivative as the left-hand side, and obtain the mathematical model of the permanent magnet synchronous motor in the dq two-phase rotating coordinate system.

[0057] 5) By using the coordinate relationship diagram, the conversion relationship between the estimated voltage and current of the permanent magnet synchronous motor and the actual voltage and current in the dq two-phase rotating coordinate system is obtained;

[0058] 6) Combining the mathematical model of the permanent magnet synchronous motor in the dq two-phase rotating coordinate system, the estimated voltage and current of the permanent magnet synchronous motor, the conversion relationship between the actual voltage and current, a conversion relationship between the estimated current and the estimated voltage of the permanent magnet synchronous motor in the two-phase rotating coordinate system is obtained with the derivative of the estimated current as the left term.

[0059] 7) Substitute the formulas for the average inductance on the quadrature and direct axes and the half-difference inductance on the quadrature and direct axes into the conversion formula for the estimated current and voltage of the permanent magnet synchronous motor in the two-phase rotating coordinate system with the derivative of the estimated current as the left term, to obtain another form of conversion formula;

[0060] 8) Inject a high-frequency voltage signal into the estimated rectangular coordinate system and solve for the corresponding current relationship;

[0061] 9) Extract the high-frequency current equation that estimates the response of the direct axis from the current relationship. The high-frequency current equation contains information about Δθ.

[0062] 10) Pass the quadrature-axis current obtained by the Park transform in the system into a bandpass filter and extract the high-frequency current signal. Multiply the high-frequency current signal with the modulation signal of the same frequency, and then pass it through a low-pass filter to obtain f(Δθ). The amplitude of f(Δθ) is half of that of the high-frequency current signal.

[0063] 11) When the rotor position error is small enough, sin(Δθ) is replaced by Δθ. When f(Δθ) = 0, sin(Δθ) = 0, that is, Δθ = 0, and the actual angle of the rotor is consistent with the estimated angle.

[0064] 12) The amplitude f(Δθ) is fed into the PI controller, which outputs the estimated speed. The estimated angle is then obtained by integration. The estimated angle is applied to the coordinate transformation to form the entire closed-loop system, thereby realizing the vector control of the permanent magnet synchronous motor.

[0065] 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:

[0066]

[0067] 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.

[0068] The mathematical model of the permanent magnet synchronous motor in the αβ two-phase stationary coordinate system is as follows:

[0069]

[0070] 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.

[0071] The voltage equation for the permanent magnet synchronous motor dq in the two-phase rotating coordinate system is as follows:

[0072]

[0073] Among them, u d For direct-axis voltage, u q R is the quadrature-axis voltage, R is the resistance value, and i is the cross-axis voltage. d For direct-axis current, i q For quadrature axis current, L d For direct-axis inductors, L q For quadrature axis inductance, ω e Angular velocity, ψ f It is a permanent magnet flux linkage.

[0074] The voltage equations in the two-phase rotating coordinate system dq are simplified to:

[0075]

[0076] Among them, by Figure 3 As shown, in a two-phase rotating coordinate system, the conversion relationship between the estimated voltage and current of the PMSM and the actual voltage and current is as follows:

[0077]

[0078] For direct-axis voltage estimates, For the quadrature axis voltage estimate, For the direct-axis current estimate, This is the estimated value of the quadrature axis current.

[0079] Combining the voltage equations in the dq two-phase rotating coordinate system, the conversion relationships between the estimated voltage and current of the PMSM and the actual voltage and current, the conversion relationship between the estimated current and voltage of the permanent magnet synchronous motor in the two-phase rotating coordinate system, with the derivative of the estimated current as the left-hand side, can be obtained as follows:

[0080]

[0081] The formulas for the average inductance and half-difference inductance on the direct and quadrature axes, when substituted into the conversion formula for the estimated current and voltage of a permanent magnet synchronous motor in a two-phase rotating coordinate system with the derivative of the estimated current as the left-hand side, are as follows:

[0082]

[0083] L is the average inductance on the quadrature and direct axes, and ΔL is the half-differential inductance on the quadrature and direct axes.

[0084] Among them, estimating the injected high-frequency voltage signal in the rectangular coordinate system and solving for the corresponding current relationship are as follows:

[0085]

[0086] in To estimate the high-frequency voltage signal injected into the rectangular coordinate system, U mh For estimating the voltage amplitude and ω along the direct axis h To estimate the angular velocity of the voltage along the direct axis, To calculate the direct-axis current value when estimating the voltage signal injected into the direct-axis coordinate system, This is to calculate the quadrature-axis current value when estimating the voltage signal injected into the direct-axis coordinate system.

[0087] Among them, the high-frequency current equation for estimating the direct-axis response in the current relationship is:

[0088]

[0089] The amplitude of the high-frequency current equation contains information about Δθ. The quadrature-axis current obtained from the Park transform in the system is passed through a band-pass filter (BPF) to extract the high-frequency current signal. This high-frequency current signal is multiplied by a modulation signal of the same frequency, and finally passed through a low-pass filter (LPF) to obtain f(Δθ). The formula for f(Δθ) is:

[0090]

[0091] When the rotor position error Δθ is sufficiently small, constituting an equivalent infinitesimal substitution condition, sin(2Δθ) can be replaced by 2Δθ, and the above formula can be approximated as:

[0092]

[0093] When f(Δθ) = 0, then Δθ = 0, and the actual rotor angle is equal to the estimated angle. The amplitude f(Δθ) is fed into a PI controller, which outputs the estimated rotational speed. This estimated speed is then integrated to obtain the estimated angle, which is used in the coordinate transformation to form the entire closed-loop system. When the system reaches steady state, f(Δθ) = 0, and the estimated rotor position is equal to the actual rotor position. After the Park transform, a bandpass filter is applied to extract the high-frequency signal, followed by a low-pass filter to obtain f(Δθ).

[0094] Figure 4 As shown in Figure 4(a), the electrical angle value detected by the Hall sensor is shown in Figure 4(b), and the electrical angle value estimated by the algorithm is shown in Figure 4(b). It can be seen from the figures that the error between the value estimated by the algorithm and the electrical angle value measured by the Hall sensor is within one degree, indicating that the permanent magnet synchronous motor control method based on the pulse high-frequency voltage injection method is effective.

[0095] 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 control method for a permanent magnet synchronous motor based on pulsed high-frequency voltage injection, characterized in that, Includes the following steps: 1) Establish the voltage equations for the three-phase coordinate system of the permanent magnet synchronous motor (PMSM); 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 equations of the permanent magnet synchronous motor in the two-phase stationary coordinate system are simplified to the voltage equations in the dq two-phase rotating coordinate system through the Park transformation; 4) Simplify the voltage equation in the dq two-phase rotating coordinate system to another form with the current derivative as the left-hand side, and obtain the mathematical model of the permanent magnet synchronous motor in the dq two-phase rotating coordinate system. 5) By using the coordinate relationship diagram, the conversion relationship between the estimated voltage and current and the actual voltage and current of the permanent magnet synchronous motor in the dq two-phase rotating coordinate system is obtained; 6) Combining the mathematical model of the permanent magnet synchronous motor in the dq two-phase rotating coordinate system, the estimated voltage and current of the permanent magnet synchronous motor, the conversion relationship between the actual voltage and current, a conversion relationship between the estimated current and voltage of the permanent magnet synchronous motor in the two-phase rotating coordinate system is obtained, with the derivative of the estimated current as the left term: ， For direct-axis voltage estimates, For quadrature axis voltage estimates, For the direct-axis current estimate, This is an estimated value for the quadrature-axis current. It is a quadrature axis inductor. It is a direct-axis inductor; 7) Substituting the formulas for the average inductance and the half-difference inductance on the quadrature and direct axes into the conversion formula for the estimated current and voltage of a permanent magnet synchronous motor in a two-phase rotating coordinate system, with the derivative of the estimated current as the left-hand side, we obtain another form of the conversion formula: ， The average inductance on the perpendicular and perpendicular axes, It is the half-differential inductance on the direct and quadrature axes; 8) Inject a high-frequency voltage signal into the estimated rectangular coordinate system and solve for the corresponding current relationship: ， ， in To estimate the high-frequency voltage signal injected into the rectangular coordinate system, To estimate the voltage amplitude along the direct axis, To estimate the angular velocity of the voltage along the direct axis, To calculate the direct-axis current value when estimating the voltage signal injected into the direct-axis coordinate system, To calculate the quadrature-axis current value when estimating the voltage signal injected into the rectangular coordinate system; 9) Extract the high-frequency current equation that estimates the direct-axis response from the current relationship. The high-frequency current equation contains... Information; 10) The quadrature-axis current obtained by the Park transform in the system is passed into a bandpass filter to extract the high-frequency current signal. The high-frequency current signal is multiplied by the modulation signal of the same frequency, and then passed through a low-pass filter to obtain the final signal. , Its amplitude is half that of the high-frequency current signal; 11) When the rotor position error is sufficiently small, use To replace, when When =0, =0, that is =0, the actual angle of the rotor is consistent with the estimated angle; 12) Amplitude The input is fed into the PI controller, which outputs an estimated speed. This estimated speed is then integrated to obtain an estimated angle. The estimated angle is applied to the coordinate transformation to form the entire closed-loop system, thereby achieving vector control of the permanent magnet synchronous motor.

2. The permanent magnet synchronous motor control method based on pulsed high-frequency voltage injection 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: ， in , , These are the terminal voltages of the windings; , , These are the phase currents of the three-phase windings; , , This is the back electromotive force of the three-phase winding; For winding phase resistance, It is the equivalent inductance.

3. The permanent magnet synchronous motor control method based on pulsed high-frequency voltage injection 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, , It is the back electromotive force; For permanent magnet flux linkage; θ is the rotor angular velocity; θ is the rotor speed.

4. The permanent magnet synchronous motor control method based on pulsed high-frequency voltage injection according to claim 3, characterized in that, Step 3) Simplify the voltage equation in the two-phase stationary coordinate system to the voltage equation in the dq two-phase rotating coordinate system using the Park transformation. The equation is as follows: ， in, For direct-axis voltage, For quadrature axis voltage, For resistance value, For direct-axis current, For quadrature axis current, Angular velocity, It is a permanent magnet flux linkage.

5. The permanent magnet synchronous motor control method based on pulsed high-frequency voltage injection according to claim 4, characterized in that, Step 4) Simplify the voltage equation in the dq two-phase rotating coordinate system as follows: 。 6. The permanent magnet synchronous motor control method according to claim 5, characterized in that, The conversion relationship between the estimated voltage and current and the actual voltage and current shown in step 5) is as follows: ， 。 7. The permanent magnet synchronous motor control method based on pulsed high-frequency voltage injection according to claim 5, characterized in that, In step 9), the high-frequency current equation for the direct-axis response in the current relationship is estimated as follows: ； In step 10), the high-frequency current signal is multiplied by a modulation signal of the same frequency, and then passed through a low-pass filter to obtain the result. for: ； The equivalent substitution formula mentioned in step 11) is approximately: .

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