Periodic torque disturbance suppression method of permanent magnet synchronous motor

Abstract

The invention discloses a periodic torque disturbance suppression method of a permanent magnet synchronous motor, and belongs to the field of permanent magnet synchronous motors. In order to solve the problem that a low-frequency periodic load is introduced due to the fact that a motor continuously drives a complex mechanical structure to move periodically and repeatedly, a novel rotating speed controller is designed, and a four-order expansion state observer is introduced into a permanent magnet synchronous motor control system considering disturbance. A bandwidth tuning method is adopted to set observer gain parameters to achieve observation of torque disturbance, a frequency analysis method is adopted to optimize and design an observer gain matrix, an optimized four-order extended state observer is obtained, and torque disturbance compensation is achieved in the mode that estimated torque is converted into feed-forward current. According to the method, the influence of torque disturbance on the rotating speed stability is effectively suppressed, and the anti-interference performance and the anti-noise performance of the four-order extended state observer are synchronously improved.

Description

Technical field:

[0001] The present invention relates to the field of permanent magnet synchronous motors, and in particular to a method for suppressing periodic torque disturbance of a permanent magnet synchronous motor. Background technology:

[0002] With the vigorous development of the aviation industry, the performance standards for electromechanical actuation servo systems have also been improved. However, permanent magnet synchronous motor servo systems often face the challenges of multi-source disturbances and uncertainties in practical applications. When the motor continuously drives a complex mechanical structure (such as a transmission system composed of gears, connecting rods, rocker arms, etc.) to perform periodic repetitive motion, mechanical components at different positions will apply varying load forces to the motor, thereby introducing low-frequency periodic load disturbances. In addition, the inherent characteristics of the motor, such as cogging torque, flux harmonics, and dead zone effects, further exacerbate the complexity of periodic disturbances. These periodic load disturbances directly cause periodic fluctuations in the motor speed. Excessive speed pulsation not only seriously weakens the stability and accuracy of the motor control system, but also accelerates the wear of mechanical components and shortens the service life of the overall system. Therefore, effectively suppressing periodic load disturbances in permanent magnet synchronous motor servo systems is of vital importance to improving the control performance of the entire system and extending the life of the equipment.

[0003] In order to effectively suppress periodic disturbances, the academic community has explored and developed a variety of efficient control algorithms. These algorithms can be roughly classified into two directions: repetitive control and resonant control based on the internal model principle, and disturbance observers and active disturbance rejection control based on disturbance estimation. Among them, the extended state observer, as an important disturbance observation technology, has the advantages of easy parameter setting and simple structure. The extended state observer treats the internal factors of the motor, external disturbances and unmodeled nonlinear disturbances as total disturbances, and uses state variables for real-time estimation and compensation. It is the core component of active disturbance rejection control. Although active disturbance rejection control has been widely used in industrial practice, it is still difficult for the extended state observer to ensure accurate estimation when dealing with time-varying periodic disturbances. The high-order extended state observer increases the order of the observer to obtain faster dynamic response and stronger anti-interference ability. In theory, it can provide higher estimation accuracy, but there is a contradiction between anti-interference performance and anti-noise performance in parameter design. Summary of the invention:

[0004] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art. The present invention proposes a method for suppressing periodic torque disturbances of a permanent magnet synchronous motor. A high-order extended state observer is introduced and the estimated torque is converted into a feedforward current to achieve compensation, so that the influence of torque disturbances on speed stability is suppressed; the observer gain matrix is ​​optimized and designed by the frequency analysis method, so as to simultaneously improve the anti-disturbance performance and anti-noise performance of the high-order extended state observer.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A method for suppressing periodic torque disturbance of a permanent magnet synchronous motor comprises the following steps:

[0007] Step S1, considering the load torque as a part of the disturbance torque, and establishing a mathematical model of the permanent magnet synchronous motor when considering the disturbance;

[0008] Step S2, writing the mechanical motion equation of the permanent magnet synchronous motor in the form of a state equation, establishing a high-order extended state observer mathematical model, and selecting a fourth-order extended state observer taking into account both the observer order and noise sensitivity;

[0009] Step S3: Use the traditional bandwidth tuning method to adjust the observer gain parameters to achieve the motor torque disturbance T d Observation of

[0010] Step S4, rewriting the characteristic equation of the extended state observer to obtain a new gain matrix β′ based on the optimal design;

[0011] Step S5: Improve the gain matrix design value λ of the extended state observer 1 and λ 2 , use frequency analysis to analyze λ 1 With λ 2 The influence of the anti-disturbance and anti-noise performance of the observer is studied, and the appropriate gain matrix design value is selected to obtain the fourth-order extended state observer based on the gain matrix optimization design;

[0012] Step S6: Through observer feedback control, the observed torque is converted into a feedforward current to achieve torque disturbance compensation.

[0013] Furthermore, the mechanical motion equation of the permanent magnet synchronous motor in step S1 is:

[0014]

[0015] Where, J is the moment of inertia; T e is the electromagnetic torque; T d is the disturbance torque, and the load torque is also regarded as a part of the disturbance torque; B a is the viscous friction coefficient; ω m is the motor speed.

[0016] Furthermore, the process of establishing the mathematical model of the high-order extended state observer in step S2 includes:

[0017] Take the state variable as The control variable is The reference signal is The output signal is

[0018] Rewrite the mechanical motion equation into the form of state equation:

[0019]

[0020] On this basis, the expression of the observer is derived as follows:

[0021]

[0022] In the formula, is the estimated value of the state variable x. When the observer converges, the estimated value is equal to the value of the state variable. K T is the motor torque constant; β=[β 1 β 2 β 3 β 4 ] T is the gain matrix.

[0023] Furthermore, the process of adjusting the observer gain parameter in step S3 includes:

[0024] Defining state error From formula (2)-(3), we can get:

[0025]

[0026] The characteristic equation of the extended state observer can be obtained from the error state matrix:

[0027] det(sI-A)=s 4 +β 1 s 3 +β 2 s 2 +β 3 s+β 4 =0 (5)

[0028] The characteristic equation is configured into a multiple root form using the bandwidth tuning method, and the pole is set at -ω 0 Place, that is:

[0029] s 4 +β 1 s 3 +β 2 s 2 +β 3 s 1 +β 4 =(s+ω 0 ) 4 (6)

[0030] The gain matrix is:

[0031]

[0032] Furthermore, the control rate of the designed observer in step S3 is:

[0033]

[0034] In the formula, k p It is the proportional coefficient of the speed loop PI regulator.

[0035] Furthermore, the process of improving the new gain matrix β′ of the extended state observer in step S4 includes:

[0036] The characteristic equation of the fourth-order extended state observer is:

[0037] D′(s)=s 4 +β 1 's 3 +β′ 2 s 2 +β′ 3 s 1 +β′ 4 (9)

[0038] Decompose the characteristic equation into the form of the product of two second-order factors:

[0039]

[0040] Where λ 1 and λ 2 is the gain matrix design value, when λ 1 =λ 2 =1, the characteristic equation is equivalent to the traditional characteristic equation;

[0041] The new gain matrix β′=[β 1 ′β 2 ′β 3 ′β 4 ′] T for:

[0042]

[0043] Furthermore, the process of improving the gain matrix design value of the extended state observer in step S5 to obtain an optimized designed fourth-order extended state observer gain matrix includes:

[0044] In the speed control structure based on the fourth-order extended state observer, the system's anti-disturbance transfer function G f (s) and the noise-rejection transfer function G n (s) is:

[0045]

[0046] λ 2 Set to a fixed value λ 2 =1, change λ 1 , analyze λ 1 System anti-interference performance |G f (jω)| and noise immunity performance|G n (jω)|, we get λ 1 The value range of is:

[0047] λ 1 ∈[1,4] (14)

[0048] Similarly, we can get λ 2 The value range of is:

[0049] λ 2 ∈[0.25,1] (15)

[0050] On the basis of fixed parameter analysis, the gain design value λ is changed at the same time 1 With λ 2 , taking into account the anti-disturbance performance and anti-noise performance of the observer, the design value of the observer gain matrix is:

[0051] λ 1 =4,λ 2 =0.25 (16)

[0052] The gain matrix of the optimized fourth-order extended state observer is:

[0053]

[0054] Furthermore, the observer feedback control described in step S6 converts the observed torque into a feedforward current and introduces it into the output end of the PI controller to achieve torque disturbance compensation:

[0055] Feedforward current i com for:

[0056]

[0057] The given value of the quadrature axis current after compensation is:

[0058]

[0059] Where: is the given value of the quadrature axis current; It is the current value output by the speed controller.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] (1) The present invention designs a novel speed controller, introduces a fourth-order extended state observer into the permanent magnet synchronous motor control system to estimate the torque disturbance, and converts the estimated torque into a feedforward current to achieve compensation, thereby effectively suppressing the periodic torque disturbance and improving the speed stability.

[0062] (2) The observer gain matrix is ​​optimized and designed by frequency analysis method, which solves the contradiction between the anti-interference performance and anti-noise performance of the extended state observer. Description of the drawings:

[0063] Attached Figure 1 A system control block diagram of a periodic torque disturbance control method for a permanent magnet synchronous motor provided by the present invention;

[0064] Attached Figure 2 Design of a fourth-order extended state observer G for traditional gain matrix and gain optimization f (s) Comparison of transfer function amplitude-frequency characteristic curves;

[0065] Attached Figure 3 Design of a fourth-order extended state observer G for traditional gain matrix and gain optimization n (s) Comparison of transfer function amplitude-frequency characteristic curves;

[0066] Attached Figure 4 This is the experimental waveform of the traditional extended state observer under 5 Hz torque disturbance when the method of the present invention is not adopted;

[0067] Attached Figure 5 This is the experimental waveform of the fourth-order extended state observer under 5Hz torque disturbance when the method of the present invention is used;

[0068] Attached Figure 6 This is the experimental waveform of the fourth-order extended state observer based on gain optimization under 5 Hz torque disturbance when the method of the present invention is adopted. Specific implementation method:

[0069] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings, and the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] Attached Figure 1 A system control structure block diagram of a method for suppressing periodic torque disturbance of a permanent magnet synchronous motor provided by the present invention, the method comprising the following steps:

[0071] Step S1, considering the load torque as a part of the disturbance torque, and establishing a mathematical model of the permanent magnet synchronous motor when considering the disturbance;

[0072] Step S2, writing the mechanical motion equation of the permanent magnet synchronous motor in the form of a state equation, establishing a high-order extended state observer mathematical model, and selecting a fourth-order extended state observer taking into account both the observer order and noise sensitivity;

[0073] Step S3: Use the traditional bandwidth tuning method to adjust the observer gain parameters to achieve the motor torque disturbance T d Observation of

[0074] Step S4, rewriting the characteristic equation of the extended state observer to obtain a new gain matrix β′ based on the optimal design;

[0075] Step S5: Improve the gain matrix design value λ of the extended state observer 1 and λ 2 , use frequency analysis to analyze λ 1 With λ 2 The influence of the anti-disturbance and anti-noise performance of the observer is studied, and the appropriate gain matrix design value is selected to obtain the fourth-order extended state observer based on the gain matrix optimization design;

[0076] Step S6: Through observer feedback control, the observed torque is converted into a feedforward current to achieve torque disturbance compensation.

[0077] Furthermore, the mechanical motion equation of the permanent magnet synchronous motor in step S1 is:

[0078]

[0079] Where, J is the moment of inertia; T e is the electromagnetic torque; T d is the disturbance torque, and the load torque is also regarded as a part of the disturbance torque; B a is the viscous friction coefficient; ω m is the motor speed.

[0080] Furthermore, the process of establishing the mathematical model of the high-order extended state observer in step S2 includes:

[0081] Take the state variable as The control variable is The reference signal is The output signal is

[0082] Rewrite the mechanical motion equation into the form of state equation:

[0083]

[0084] On this basis, the expression of the observer is derived as follows:

[0085]

[0086] In the formula, is the estimated value of the state variable x. When the observer converges, the estimated value is equal to the value of the state variable. K T is the motor torque constant; β=[β 1 β 2 β 3 β 4 ] T is the gain matrix.

[0087] Furthermore, the process of adjusting the observer gain parameter in step S3 includes:

[0088] Defining state error From formula (2)-(3), we can get:

[0089]

[0090] The characteristic equation of the extended state observer can be obtained from the error state matrix:

[0091] det(sI-A)=s 4 +β 1 s 3 +β 2 s 2 +β 3 s+β 4 =0 (5)

[0092] The characteristic equation is configured into a multiple root form using the bandwidth tuning method, and the pole is set at -ω 0 Place, that is:

[0093] s 4 +β 1 s 3 +β 2 s 2 +β 3 s 1 +β 4 =(s+ω 0 ) 4 (6)

[0094] The gain matrix is:

[0095]

[0096] Furthermore, in order to enable the observer to converge quickly, the control rate of the observer is designed in step S3 as:

[0097]

[0098] In the formula, k p It is the proportional coefficient of the speed loop PI regulator.

[0099] Furthermore, the process of improving the new gain matrix β′ of the extended state observer in step S4 includes:

[0100] The characteristic equation of the fourth-order extended state observer is:

[0101] D′(s)=s 4 +β 1 's 3 +β 2 's 2 +β 3 's 1 +β 4 ′ (9)

[0102] Decompose the characteristic equation into the form of the product of two second-order factors:

[0103]

[0104] Where λ 1 and λ 2 is the gain matrix design value, when λ 1 =λ 2 =1, the characteristic equation is equivalent to the traditional characteristic equation;

[0105] The new gain matrix β′=[β 1 ′β 2 ′β 3 ′β 4 ′] T for:

[0106]

[0107] Furthermore, the process of improving the gain matrix design value of the extended state observer in step S5 to obtain an optimized designed fourth-order extended state observer gain matrix includes:

[0108] In the speed control structure based on the fourth-order extended state observer, the system's anti-disturbance transfer function G f (s) and the noise-rejection transfer function G n (s) is:

[0109]

[0110] λ 2 Set to a fixed value λ 2 =1, change λ 1 , analyze λ 1 System anti-interference performance |G f(jω)| and noise immunity performance|G n (jω)|. When λ 1 The larger the anti-disturbance transfer function G f Gain (s) |G f The larger the (jω)|, the better the anti-disturbance performance of the observer, but too large λ 1 Will cause G n (s) High frequency noise gain |G n (jω)| increases sharply, so λ 1 The value range of is:

[0111] λ 1 ∈[1,4] (14)

[0112] λ 1 Set to a fixed value λ 1 =1, change λ 2 , analyze λ 2 System anti-interference performance |G f (jω)| and noise immunity performance|G n The influence of (jω)|λ 2 The smaller the G n (s) high frequency gain |G n The smaller (jω)| is, the better the noise immunity of the observer is. However, too small λ 2 Will cause G f (s) The low-frequency anti-interference performance drops sharply. Therefore, λ 2 The available ranges are:

[0113] λ 2 ∈[0.25,1] (15)

[0114] On the basis of fixed parameter analysis, the gain design value λ is changed at the same time 1 With λ 2 , taking into account the anti-disturbance performance and anti-noise performance of the observer, the design value of the observer gain matrix is:

[0115] λ 1 =4,λ 2 =0.25 (16)

[0116] The gain matrix of the optimized fourth-order extended state observer is:

[0117]

[0118] Furthermore, the observer feedback control described in step S6 converts the observed torque into a feedforward current and introduces it into the output end of the PI controller to achieve torque disturbance compensation:

[0119] Feedforward current i com for:

[0120]

[0121] The given value of the quadrature axis current after compensation is:

[0122]

[0123] Where: is the given value of the quadrature axis current; It is the current value output by the speed controller.

[0124] The frequency domain characteristic curves of the transfer function of the high-order extended state observer based on the traditional gain matrix and the optimized gain matrix are shown in the attached figure. Figure 2 and attached Figure 3 As shown in the figure, the anti-interference and anti-noise performances of the HESO after optimized gain design are further improved, but there is some performance deterioration in the intermediate frequency band. Since the intermediate frequency band is narrow, it has little impact on the overall performance of the observer.

[0125] Under the same 5Hz sinusoidal torque disturbance, comparative experiments were carried out under different disturbance observers: traditional extended state observer, fourth-order extended state observer and fourth-order extended state observer based on gain optimization. The experimental results are shown in the attached figure. Figure 4 , Attachment Figure 5 and attached Figure 6 As shown in the figure. It can be seen from the figure that compared with the traditional extended state observer control strategy, the fourth-order extended state observer control strategy shows higher accuracy in observing disturbance torque and can provide effective feedforward current compensation. This improvement significantly reduces the speed fluctuation from ±30r / min to ±10r / min. On this basis, through the optimization design of the fourth-order extended state observer gain matrix, the rapidity and accuracy of disturbance torque observation are further improved, so that the observed torque error is reduced to 0.10N·m, and the speed fluctuation is further reduced to ±6r / min, so the anti-disturbance performance of the motor is significantly improved.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for suppressing periodic torque disturbance of a permanent magnet synchronous motor, characterized in that: The method comprises the following steps: Step S1, considering the load torque as a part of the disturbance torque, and establishing a mathematical model of the permanent magnet synchronous motor when considering the disturbance; Step S2, writing the mechanical motion equation of the permanent magnet synchronous motor in the form of a state equation, establishing a high-order extended state observer mathematical model, and selecting a fourth-order extended state observer taking into account both the observer order and noise sensitivity; Step S3: Use the traditional bandwidth tuning method to adjust the observer gain parameters to achieve the motor torque disturbance T d Observation of Step S4, rewriting the characteristic equation of the extended state observer to obtain a new gain matrix β′ based on the optimal design; Step S5, improving the gain matrix design values ​​λ1 and λ2 of the extended state observer, using the frequency analysis method to analyze the influence of λ1 and λ2 on the anti-interference performance and anti-noise performance of the observer, selecting a suitable gain matrix design value, and obtaining a fourth-order extended state observer based on the gain matrix optimization design; Step S6: Through observer feedback control, the observed torque is converted into a feedforward current to achieve torque disturbance compensation.

2. The method for suppressing periodic torque disturbance of a permanent magnet synchronous motor according to claim 1, characterized in that: The mechanical motion equation of the permanent magnet synchronous motor in step S1 is: Where, J is the moment of inertia; T e is the electromagnetic torque; T d is the disturbance torque, and the load torque is also regarded as a part of the disturbance torque; B a is the viscous friction coefficient; ω m is the motor speed.

3. The method for suppressing periodic torque disturbance of a permanent magnet synchronous motor according to claim 1, characterized in that: The process of establishing the mathematical model of the high-order extended state observer in step S2 includes: Take the state variable as The control variable is The reference signal is The output signal is Rewrite the mechanical motion equation into the form of state equation: On this basis, the expression of the observer is derived as follows: In the formula, is the estimated value of the state variable x. When the observer converges, the estimated value is equal to the value of the state variable. K T is the motor torque constant; β=[β1β2β3β4] T is the gain matrix.

4. The method for suppressing periodic torque disturbance of a permanent magnet synchronous motor according to claim 1, characterized in that: The process of adjusting the observer gain parameter in step S3 includes: Defining state error From formula (2)-(3), we can get: The characteristic equation of the extended state observer can be obtained from the error state matrix: det(sI-A)=s 4 +β1s 3 +β2s 2 +β3s+β4=0 (5) The bandwidth tuning method is used to configure the characteristic equation into a multiple root form and set the pole at -ω0, that is: s 4 +β1s 3 +β2s 2 +β3s 1 +β4=(s+ω0) 4 (6) The gain matrix is:

5. The method for suppressing periodic torque disturbance of a permanent magnet synchronous motor according to claim 1, characterized in that: The control rate of the designed observer in step S3 is: In the formula, k p It is the proportional coefficient of the speed loop PI regulator.

6. The method for suppressing periodic torque disturbance of a permanent magnet synchronous motor according to claim 1, characterized in that: The process of improving the new gain matrix β′ of the extended state observer in step S4 includes: The characteristic equation of the fourth-order extended state observer is: D′(s)=s 4 +β1′s 3 +β2′s 2 +β3′s 1 +β4′ (9) Decompose the characteristic equation into the form of the product of two second-order factors: Where λ1 and λ2 are the design values ​​of the gain matrix. When λ1=λ2=1, the characteristic equation is equivalent to the traditional characteristic equation. New gain matrix β′=[β1′β2′β3′β4′] based on optimal design T for:

7. The method for suppressing periodic torque disturbance of a permanent magnet synchronous motor according to claim 1, characterized in that: The process of improving the gain matrix design value of the extended state observer in step S5 to obtain an optimized designed fourth-order extended state observer gain matrix includes: In the speed control structure based on the fourth-order extended state observer, the system's anti-disturbance transfer function G f (s) and the noise-rejection transfer function G n (s) is: Set λ2 to a constant value of λ2=1, change λ1, and analyze the effect of λ1 on the system anti-disturbance performance|G f (jω)| and noise immunity performance|G n The influence of (jω)|, the value range of λ1 is obtained as follows: λ1∈[1,4] (14) Similarly, the value range of λ2 is: λ2∈[0.25,1] (15) On the basis of fixed parameter analysis, the gain design values ​​λ1 and λ2 are changed at the same time, taking into account the anti-disturbance performance and anti-noise performance of the observer, and the design value of the observer gain matrix is: λ1=4,λ2=0.25 (16) The gain matrix of the optimized fourth-order extended state observer is:

8. The method for suppressing periodic torque disturbance of a permanent magnet synchronous motor according to claim 1, characterized in that: The observer feedback control described in step S6 converts the observed torque into a feedforward current and introduces it into the output end of the PI controller to achieve torque disturbance compensation: Feedforward current i com for: The given value of the quadrature axis current after compensation is: Where: is the given value of the quadrature axis current; It is the current value output by the speed controller.

Images