A method for suppressing rotational speed harmonics under steady-state conditions based on the gradient descent method

Abstract

The present invention relates to a method for suppressing rotational speed harmonics under steady-state conditions based on the gradient descent method. The method includes the following steps: First, measure the rotational speed value of the motor, and extract the amplitude of the rotational speed harmonics through low-pass filtering and rotational coordinate transformation; Second, inject a voltage harmonic into the system, and the injected voltage harmonic is reconstructed into an injected voltage signal in the angular domain and added to the voltage command; Third, change the phase of the injected voltage harmonic, observe the change in the amplitude of the rotational speed harmonics, and use the gradient descent method to find the optimal phase of the injected voltage harmonic that minimizes the amplitude of the rotational speed harmonics; Fourth, use the optimal voltage harmonic phase found, change the amplitude of the injected voltage harmonic, observe the change in the amplitude of the rotational speed harmonics, and use the gradient descent method to find the optimal amplitude of the injected voltage harmonic that minimizes the amplitude of the rotational speed harmonics; Fifth, set the amplitude and phase of the injected voltage harmonic to the optimal values found in steps three and four respectively, and the rotational speed harmonics can be effectively suppressed.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and particularly relates to a method for suppressing rotational speed harmonics under steady-state conditions for permanent magnet synchronous motor control based on the gradient descent method. Background Art

[0002] Permanent magnet synchronous motors (hereinafter referred to as PMSMs) have outstanding advantages such as stable operation, high energy efficiency, diverse shapes, simple structures, and light weight. Currently, they have been widely used in daily life, modern industrial production, and national defense, such as in household appliances, automotive electronics, turntable systems, and aerospace systems. However, factors such as spatial harmonics of the magnetic field, time harmonics of the armature current, cogging torque, and phase imbalance cause obvious torque ripple in permanent magnet synchronous motors. In order to meet the requirements of these systems for servo accuracy and low-speed smoothness, low torque ripple has become an important design requirement for high-precision servo motors. Therefore, researching methods for suppressing torque ripple in permanent magnet synchronous motors has great practical significance.

[0003] At present, the means of suppressing motor torque ripple are mainly divided into two types. One is to improve the mechanical design of the motor, and the other is to actively control the stator current by applying control algorithms. Technical literature (Wu Z, Yang Z, Ding K, et al. Order-Domain-Based harmonic injection method for multiple speed harmonics suppression of PMSM[J]. IEEE Transactions on Power Electronics, 2020, 36(4): 4478-4487.) (Feng G, Lai C, Tian J, et al. Multiple reference frame based torque ripple minimization for PMSM drive under both steady-state and transient conditions[J]. IEEE Transactions on Power Electronics, 2018, 34(7): 6685-6696.) designed a harmonic injection algorithm to suppress torque ripple by suppressing speed harmonics, but did not consider the influence of the change of the relationship between the injected voltage harmonics and the speed harmonics. (Yan L, Liao Y, Lin H, et al. Torque ripple suppression of permanent magnet synchronous machines by minimal harmonic current injection[J]. IET Power Electronics, 2019, 12(6): 1368-1375.) adopted the gradient descent method to find the optimal injected current harmonics that minimize the speed harmonics, but it requires an increase in the control of the injected current harmonics, which is relatively complex and computationally intensive. Summary of the Invention

[0004] The object of the present invention is to solve problems such as speed ripple and structural fatigue damage caused by torque ripple; a method for suppressing speed harmonics under steady-state conditions based on the gradient descent method is proposed; it can reduce the control difficulty, does not require controlling current harmonics, and does not require deriving complex correlation formulas for injected voltage harmonics and speed harmonics.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for suppressing rotational speed harmonics under steady-state conditions based on the gradient descent method, which includes the following steps:

[0007] Step 1: When the permanent magnet synchronous motor is running stably, measure the rotational speed value ω r (t) of the motor, and obtain the amplitude A ωk of the k-th order rotational speed harmonic through low-pass filtering and formula calculation;

[0008] Step 2: Inject a q-axis voltage harmonic into the system. The injected voltage harmonic is reconstructed into an injected voltage signal in the angular domain and added to the voltage command;

[0009] Step 3: Keep the amplitude of the injected voltage harmonic unchanged and change its phase. The amplitude of the rotational speed harmonic changes. Use the gradient descent method to find the optimal phase θ ωk of the injected voltage harmonic that makes the amplitude A uqkM of the rotational speed harmonic reach the minimum;

[0010] Step 4: Keep the phase of the injected voltage harmonic as the optimal phase θ uqkM found in Step 3, change the amplitude of the injected voltage harmonic, and use the gradient descent method to find the optimal amplitude A ωk of the injected voltage harmonic that makes the amplitude A uqkM of the rotational speed harmonic reach the minimum;

[0011] Step 5: Set the amplitude and phase of the injected voltage harmonic to the optimal values A uqkM and θ uqkM found in Steps 3 and 4 respectively, and the rotational speed harmonics can be effectively suppressed. When the operating conditions of the motor change, repeat Steps 3 and 4 to find the optimal injected voltage harmonic under the new operating conditions.

[0012] Further, in the above solution, the algorithm for calculating the amplitude A ωk of the k-th order rotational speed harmonic in Step 1 is as follows:

[0013] Multiply the rotational speed measurement value ω r (t) of the permanent magnet synchronous motor by sin(kθ) and cos(kθ) respectively, then perform low-pass filtering, multiply the obtained DC component by 2, and finally take the 1 / 2 power of the sum of the squares of the two values:

[0014]

[0015] where ω r (t) is the rotational speed measurement value of the motor, LPF( ) is the low-pass filtering operation, A ωk is the amplitude of the k-th order rotational speed harmonic, θ is the motor rotation angle, and k is the order of the rotational speed harmonic to be suppressed.

[0016] Further, in the above solution, the formula for obtaining the angular domain reconstruction signal of the k-th order q-axis injected voltage harmonic in step two is:

[0017]

[0018] where A uqk and θ uqk are respectively the amplitude and phase of the k-th order q-axis injected voltage harmonic.

[0019] Further, in the above solution, the gradient descent algorithm used to find the optimal phase of the injected voltage harmonic that minimizes the amplitude of the speed harmonic in step three is as follows:

[0020] 1). The objective function is:

[0021] ;

[0022] 2). According to the amplitudes of the speed harmonics and the phases of the voltage harmonics at the i-th moment and the (i - 1)-th moment, calculate the gradient of the function at the i-th moment, so as to adjust the injected voltage harmonic at the (i + 1)-th moment to reduce the amplitude of the speed harmonic; through the iterative process of the function, the optimal phase of the injected voltage harmonic will eventually be found to minimize the change in the amplitude of the speed harmonic; the gradient calculation of the function f is:

[0023]

[0024] 3). The update function of the phase of the injected voltage harmonic is:

[0025]

[0026] where α 1 is the step size factor.

[0027] Further, in the above solution, the gradient descent algorithm used to find the optimal amplitude of the injected voltage harmonic that minimizes the amplitude of the speed harmonic in step four is as follows:

[0028] 1) The objective function is:

[0029] ;

[0030] 2) According to the amplitudes of the speed harmonics and the amplitudes of the voltage harmonics at the i-th moment and the (i - 1)-th moment, calculate the gradient of the function at the i-th moment, so as to adjust the injected voltage harmonic at the (i + 1)-th moment to reduce the amplitude of the speed harmonic; through the iterative process of the function, the optimal amplitude of the injected voltage harmonic will eventually be found to minimize the amplitude of the speed harmonic; the gradient calculation of the function f is:

[0031]

[0032] 3) The update function of the injection voltage harmonic amplitude is as follows:

[0033]

[0034] where α 2 is the step factor.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1). The gradient descent optimization method (GDO) is adopted to find the optimal injection voltage harmonic that minimizes the rotational speed harmonic amplitude, without the need to know in advance the relationship between the injection voltage harmonic and the rotational speed harmonic; it avoids the difficulties brought to harmonic control by the change of the relationship between the injection voltage harmonic and the rotational speed harmonic with different working conditions;

[0037] (2). The rotational speed harmonic is directly suppressed by the injection voltage harmonic, without the need to add a current harmonic controller, and without the need to deduce complex correlation formulas for the injection voltage harmonic and the rotational speed harmonic, which can reduce the control difficulty and the calculation amount. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the block schematic diagram of the present invention;

[0039] Figure 2 is the simulation model of the PMSM-VC drive system constructed in MATLAB Simulink software;

[0040] Figure 3 is the 24th-order rotational speed harmonic amplitude;

[0041] Figure 4 is the time-domain curve of the 24th-order motor rotational speed. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] The following will further illustrate the concept, specific structure and technical effects of the present invention with reference to the drawings, so as to fully understand the purpose, features and effects of the present invention.

[0043] It should be noted that in the description of the present invention, the terms indicating directions or positional relationships such as "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings. This is only for convenience of description and does not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0044] Refer to Figure 1 、 2As shown in the figure, a method for suppressing rotational speed harmonics under steady-state conditions based on the gradient descent method provided by the present invention includes the following steps: First, measure the rotational speed value of the motor, and extract the amplitude of the rotational speed harmonics through low-pass filtering and rotational coordinate transformation; Second, inject a q-axis voltage harmonic into the system. The injected voltage harmonic is reconstructed into an injected voltage signal in the angular domain and added to the voltage command; Third, change the phase of the injected voltage harmonic, observe the change in the amplitude of the rotational speed harmonics, and use the gradient descent method to find the optimal phase of the injected voltage harmonic that minimizes the amplitude of the rotational speed harmonics; Fourth, use the found optimal voltage harmonic phase to change the amplitude of the injected voltage harmonic, observe the change in the amplitude of the rotational speed harmonics, and use the gradient descent method to find the optimal amplitude of the injected voltage harmonic that minimizes the amplitude of the rotational speed harmonics; Fifth, set the amplitude and phase of the injected voltage harmonic to the optimal values found in the third and fourth steps respectively, and the rotational speed harmonics can be effectively suppressed. When the operating conditions of the motor change, repeat the third and fourth steps to find the optimal injected voltage harmonic under the new operating conditions.

[0045] Specifically:

[0046] When the permanent magnet synchronous motor is running stably, measure the rotational speed value ω r (t) of the motor, and obtain the amplitude A ωk of the k-th order rotational speed harmonic through low-pass filtering and formula calculation; The algorithm for calculating the amplitude A ωk of the k-th order rotational speed harmonic is as follows:

[0047] Multiply the rotational speed measurement value ω r (t) of the permanent magnet synchronous motor by sin(kθ) and cos(kθ) respectively, and then after low-pass filtering, multiply the DC component by 2, and finally take the 1 / 2 power of the sum of the squares of the two values:

[0048]

[0049] Where ω r (t) is the rotational speed measurement value of the motor, LPF() is the low-pass filtering operation, A ωk is the amplitude of the k-th order rotational speed harmonic, θ is the motor rotation angle, and k is the order of the rotational speed harmonic to be suppressed.

[0050] Inject a q-axis voltage harmonic into the system. The injected voltage harmonic is reconstructed into an injected voltage signal in the angular domain and added to the voltage command; The formula for obtaining the angular domain reconstruction signal of the k-th order q-axis injected voltage harmonic is:

[0051]

[0052] Where, A uqk and θ uqk are the amplitude and phase of the k-th order q-axis injected voltage harmonic respectively.

[0053] Keep the harmonic amplitude of the injection voltage unchanged and change its phase. The harmonic amplitude of the rotational speed changes. Use the gradient descent method to find the optimal phase θ of the injection voltage harmonic that makes the harmonic amplitude A of the rotational speed ωk reach the minimum uqkM ; The gradient descent algorithm used to find the optimal phase of the injection voltage harmonic that makes the harmonic amplitude of the rotational speed reach the minimum is as follows:

[0054] The objective function is:

[0055] ;

[0056] According to the harmonic amplitude of the rotational speed and the phase of the voltage harmonic at the i-th moment and the (i - 1)-th moment, calculate the gradient of the function at the i-th moment, so as to adjust the injection voltage harmonic at the (i + 1)-th moment to reduce the harmonic amplitude of the rotational speed; Through the iterative process of the function, the optimal phase of the injection voltage harmonic will finally be found to make the harmonic amplitude of the rotational speed change to the minimum; The gradient of the function f is calculated as:

[0057] ;

[0058] The update function of the phase of the injection voltage harmonic is:

[0059] ;

[0060] where α 1 is the step factor.

[0061] Keep the phase of the injection voltage harmonic as the optimal phase θ found in step three uqkM , change the amplitude of the injection voltage harmonic, and use the gradient descent method to find the optimal amplitude A of the injection voltage harmonic that makes the harmonic amplitude A of the rotational speed ωk reach the minimum uqkM ; The gradient descent algorithm used to find the optimal amplitude of the injection voltage harmonic that makes the harmonic amplitude of the rotational speed reach the minimum is as follows:

[0062] The objective function is:

[0063] ;

[0064] According to the harmonic amplitude of the rotational speed and the amplitude of the voltage harmonic at the i-th moment and the (i - 1)-th moment, calculate the gradient of the function at the i-th moment, so as to adjust the injection voltage harmonic at the (i + 1)-th moment to reduce the harmonic amplitude of the rotational speed; Through the iterative process of the function, the optimal amplitude of the injection voltage harmonic will finally be found to make the harmonic amplitude of the rotational speed reach the minimum; The gradient of the function f is calculated as:

[0065] ;

[0066] The update function of the injected voltage harmonic amplitude is as follows:

[0067] ;

[0068] where α 2 is the step factor.

[0069] Finally, set the amplitude and phase of the injected voltage harmonic to the found optimal values A uqkM and θ uqkM , then the rotational speed harmonics can be effectively suppressed. When the operating conditions of the motor change, repeat to find the optimal injected voltage harmonic under the new conditions; directly suppress the rotational speed harmonics with the injected voltage harmonic.

[0070] Embodiment:

[0071] Applied to the permanent magnet synchronous motor control system based on the traditional vector control strategy to suppress the 24th-order rotational speed harmonics. The simulation model is as Figure 2 shown. Under the operating conditions of rotational speed 1500 rpm and torque 1.3 Nm, use the proposed method to suppress the 24th-order rotational speed harmonics. After the permanent magnet synchronous motor reaches the target rotational speed and operates stably, then start this control algorithm. The steps are as follows:

[0072] Step 1: When the permanent magnet synchronous motor is operating stably, measure the rotational speed value ω r (t) of the motor, and obtain the amplitude A ω24 of the 24th-order rotational speed harmonics through low-pass filtering and formula calculation:

[0073] ;

[0074] Step 2: Inject a q-axis voltage harmonic into the system, with amplitude A uq24 = 0.5 and phase θ uq24 = π / 10. The injected voltage harmonic is reconstructed into an injected voltage signal in the angular domain and added to the voltage command:

[0075] ;

[0076] Step 3: Keep the amplitude of the injected voltage harmonic unchanged and change its phase. The amplitude of the rotational speed harmonics changes. Use the gradient descent method to find the optimal phase θ ωk of the injected voltage harmonic that makes the amplitude A uqkM of the rotational speed harmonics reach the minimum. The gradient calculation formula of the function f is

[0077] ;

[0078] The update function of the injected voltage harmonic phase is as follows:

[0079] ;

[0080] where α 1 is set to 0.2.

[0081] Step 4: Keep the phase of the injected voltage harmonic as the optimal phase θ found in Step 3 uqkM , change the amplitude of the injected voltage harmonic, and use the gradient descent method to find the optimal amplitude A of the injected voltage harmonic that minimizes the amplitude A ωk of the rotational speed harmonic. The gradient calculation formula of the function uqkM . f is as follows

[0082] ;

[0083] The update function of the amplitude of the injected voltage harmonic is:

[0084] ;

[0085] where α 2 is set to 0.02.

[0086] Step 5: Set the amplitude and phase of the injected voltage harmonic to the optimal values A uqkM and θ uqkM found in Steps 3 and 4 respectively, and the rotational speed harmonic can be effectively suppressed. The experimental results are as Figure 3 , 4 shown. When the rotational speed of the motor is stable, the amplitude of the 24th-order rotational speed harmonic is 2.3 rpm. The method proposed in the present invention starts to suppress the 24th-order rotational speed harmonic from 0.2 s, and completes the first step of suppressing the amplitude of the 24th-order rotational speed harmonic at 0.6 s, that is, the rotational speed harmonic controller based on the gradient descent method finds the optimal phase of the injected voltage harmonic, and the harmonic amplitude is suppressed to fluctuate around 1.2 rpm. At the same time, the system starts the second step of suppressing the amplitude of the 24th-order rotational speed harmonic from 1.1 s. At 1.5 s, the rotational speed harmonic controller based on the gradient descent method finds the optimal amplitude of the voltage harmonic injection command, and the amplitude of the 24th-order rotational speed harmonic is suppressed to below 0.13 rpm.

[0087] The amplitude of the 24th-order rotational speed harmonic is suppressed from 2.3 rpm to below 0.13 rpm in only 1.3 s, the amplitude of the rotational speed harmonic is reduced by 94%, and at the same time the range of rotational speed fluctuation is reduced from 5.0 rpm to 0.6 rpm, a reduction of 87%.

[0088] The above-described embodiments are only descriptions of the preferred embodiments of the present invention, and do not limit the concept and scope of the present invention. Without departing from the design concept of the present invention, various variations and improvements made by others to the technical solution of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for suppressing rotational speed harmonics under steady-state conditions based on the gradient descent method, characterized in that, it includes the following steps: Step 1. When the permanent magnet synchronous motor operates stably, measure the rotational speed value ω r (t) of the motor, and obtain the amplitude A of the k-th order rotational speed harmonic through low-pass filtering and formula calculation ωk ; Step 2: Inject a q-axis voltage harmonic into the system. The injected voltage harmonic is reconstructed into an injected voltage signal in the angular domain and added to the voltage command; Step 3: Keep the amplitude of the injected voltage harmonic unchanged, change its phase, the amplitude of the rotational speed harmonic changes, and use the gradient descent method to find the optimal phase θ of the injected voltage harmonic that makes the amplitude A ωk of the rotational speed harmonic reach the minimum uqkM ; Step 4: Keep the phase of the injected voltage harmonic as the optimal phase θ found in Step 3 uqkM , change the amplitude of the injected voltage harmonic, and use the gradient descent method to find the optimal amplitude A of the injected voltage harmonic that minimizes the amplitude A ωk of the rotational speed harmonic uqkM ; Step 5: Set the amplitude and phase of the injected voltage harmonics to the optimal values A uqkM and θ uqkM found in Steps 3 and 4 respectively, which can effectively suppress the speed harmonics. When the operating conditions of the motor change, repeat Steps 3 and 4 to find the optimal injected voltage harmonics under the new conditions; Calculate the amplitude A of the k-th order rotational speed harmonic in the first step ωk The algorithm is as follows: Measured speed value ω of the permanent magnet synchronous motor r (t) is multiplied by sin(kθ) and cos(kθ) respectively, and then after low-pass filtering, the DC component is multiplied by 2, and finally the 1 / 2 power of the sum of the squares of the two values is taken: ； where ω r (t) is the measured motor speed, LPF( ) is the low-pass filtering operation, A ωk is the amplitude of the k-th order speed harmonic, θ is the motor angle, and k is the order of the speed harmonic to be suppressed; The formula for the angular domain reconstruction signal of the k-th order q-axis injected voltage harmonic obtained in Step 2 is: ； Among them, A uqk and θ uqk are respectively the amplitude and phase of the k-th order q-axis injected voltage harmonic; The gradient descent algorithm used in Step 3 to find the optimal phase of the injected voltage harmonic that minimizes the amplitude of the rotational speed harmonic is as follows: 1) The objective function is: ； 2) Calculate the gradient of the function at the $i$-th moment based on the amplitudes of the rotational speed harmonics and the phases of the voltage harmonics at the $i$-th and $(i - 1)$-th moments, so as to adjust the injected voltage harmonics at the $(i + 1)$-th moment to reduce the amplitude of the rotational speed harmonics; through the iterative process of the function, the optimal phase of the injected voltage harmonics will ultimately be found to minimize the change in the amplitude of the rotational speed harmonics; the function f The gradient is calculated as follows: ； 3) The update function of the phase of the injected voltage harmonic is: ； where α 1 is the step factor; The gradient descent algorithm used in Step 4 to find the optimal amplitude of the injected voltage harmonic that minimizes the amplitude of the rotational speed harmonic is as follows: 1) The objective function is: ； 2) Calculate the gradient of the function at the $i$-th moment based on the amplitudes of the rotational speed harmonics and voltage harmonics at the $i$-th and $(i - 1)$-th moments, so as to adjust the injected voltage harmonics at the $(i + 1)$-th moment to reduce the amplitude of the rotational speed harmonics; through the iterative process of the function, the optimal amplitude of the injected voltage harmonics will eventually be found to minimize the amplitude of the rotational speed harmonics; the function f The gradient is calculated as follows: ； 3) The update function of the amplitude of the injected voltage harmonic is: ； where α 2 is the step factor.

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