Motor torque ripple suppression method based on band separation extended state observer

Abstract

The application discloses a motor torque ripple suppression method based on a frequency band separation extended state observer, and comprises the following steps: calculating the error between a target rotating speed and a feedback rotating speed, outputting a speed PI regulator output through a speed PI regulator, inputting the feedback rotating speed and a q-axis feedback current into a low-frequency extended state observer LF-ESO, and obtaining a compensation current through low-frequency disturbance estimation of the LF-ESO; obtaining a q-axis current command value under the compensation effect of the compensation current through the speed PI regulator output; calculating the error between the q-axis current command value and the q-axis feedback current, outputting a q-axis current PI regulator output through a q-axis current PI regulator, inputting the q-axis current PI regulator output and the q-axis feedback current into a high-frequency extended state observer HF-ESO, and obtaining a q-axis compensation voltage through high-frequency disturbance estimation of the HF-ESO. Through the construction of the LF-ESO and the HF-ESO and the cooperation of frequency band separation filtering, frequency band observation and channel compensation are realized, so that the motor torque stability and the dynamic response capability are improved.

Description

Technical Field

[0001] This invention relates to the field of high-precision motor drive and control technology, specifically to a motor torque ripple suppression method based on a frequency band separation extended state observer (FP-ESO), which is particularly suitable for permanent magnet synchronous arc motors. Background Technology

[0002] In specialized direct-drive applications such as industrial automation, precision servo systems, and robot joints, traditional drive systems mostly consist of a rotating permanent magnet motor combined with mechanical transmission. This method is not only structurally complex but also suffers from mechanical losses due to frictional transmission, resulting in poor transmission stiffness and a tendency for rigidity to occur. To address these shortcomings and defects, the permanent magnet synchronous arc motor (hereinafter referred to as the arc motor) has emerged. The arc motor features a simple structure, fast dynamic response, and high torque density. Compared to traditional permanent magnet synchronous motors, the arc motor's stator is composed of multiple arc-shaped segments. These segmented stators are easier to manufacture, install, disassemble, and maintain, significantly reducing manufacturing costs and system size. Considering the direct-drive characteristics of the arc motor, it offers advantages over traditional drive systems, including fewer intermediate transmission links and higher transmission stiffness.

[0003] Due to the unique stator structure of the arc motor, compared to traditional permanent magnet synchronous motors, in addition to the inherent cogging torque, it also suffers from end torque caused by uneven magnetic permeability distribution at the stator ends due to stator segmentation. Furthermore, the discontinuity of the stator magnetic circuit results in varying mutual inductances between the three-phase windings of individual stator sections, leading to a large number of high-order harmonics in the three-phase current and consequently, torque fluctuations. During the operation of the arc motor, external interferences, such as changes in load torque and frictional torque disturbances, can also cause mechanical vibration and noise, affecting the performance of the arc motor servo system.

[0004] Based on the mechanism of pulsation and the implementation location of the control strategy, existing torque pulsation suppression methods can be broadly classified into three categories: electromagnetic side suppression methods, disturbance observation and compensation methods, and system mechanical side suppression methods. Regarding electromagnetic side suppression methods, these methods directly act on the electromagnetic model of the motor, suppressing torque fluctuations by improving current tracking or weakening electromagnetic harmonics. The main methods include: one is improving current loop performance by optimizing the sampling period, control period, PWM period, and PI parameters to increase the bandwidth and dynamic response capability of the current loop, thereby reducing current errors and high-frequency disturbances introduced by the inverter; however, this has limited effect on low-frequency pulsations caused by the motor structure. Another method is harmonic suppression control, which constructs a resonant controller at specific harmonic frequencies to achieve targeted compensation, such as PR controllers, internal model control, and repetitive control; however, its performance significantly degrades in scenarios with large speed variations. A third method is harmonic current injection control, which injects current harmonics of corresponding amplitude and phase based on the motor's harmonic model or identification results, causing it to generate reverse compensation torque to offset electromagnetic torque pulsations; however, accurate harmonic parameters are required. Regarding disturbance observation and compensation methods, this type of method treats torque pulsations as a unified system disturbance and estimates and compensates for them in real time through an observer or model. The main methods include: one is a disturbance observer, which estimates the disturbance by constructing a back EMF model, a motor voltage model, or a bandwidth-based equivalent model and performs feedforward compensation. Its implementation is simple, but it is somewhat sensitive to parameter changes. Another method is an extended state observer, which treats unmodeled parts, cogging forces, flux linkage / inductance changes, PWM voltage errors, etc., as a unified "total disturbance," estimates it in real time through an ESO, and compensates for it in the control law. Torque suppression can be achieved through several methods. One approach is the extended Kalman filter (EPF), which uses a PMSM extended state model to estimate flux linkage parameters, current harmonics, or mechanical load disturbances, thus indirectly suppressing torque. This method can handle noise and parameter variations, but is computationally complex and requires an accurate noise model. Another approach is model predictive control (MMC), which includes torque error and harmonic weights in the cost function and suppresses torque ripple through optimal voltage vector selection. This directly affects the torque generation mechanism, resulting in good suppression, but requires significant computation and high-performance hardware. Regarding mechanical-side suppression methods, these methods primarily suppress speed fluctuations and output vibrations caused by torque ripples. These are system-level compensation methods, including: one is speed loop enhancement and filtering control, which improves speed disturbances caused by torque ripples through speed feedforward, speed filtering, and servo vibration suppression, significantly improving speed smoothness and servo performance, but not eliminating torque ripples at their source; the other is iterative learning control, which learns and compensates for periodic speed fluctuations to achieve high-precision speed stabilization, but is sensitive to changes in speed fluctuation frequency.

[0005] Permanent magnet synchronous arc motors are simultaneously affected by mechanical and electromagnetic disturbances during operation, including load variations, friction, back EMF harmonics, PWM switching harmonics, and current distortion caused by inverter nonlinearity. These disturbances exhibit different characteristics at different frequency bands, but existing control methods often fail to differentiate and process disturbances at different frequency bands within a unified framework, leading to a series of technical shortcomings, including:

[0006] First, the traditional single ESO is used to observe all disturbances. Since a single ESO by default unifies all disturbances into a single total disturbance, its observation bandwidth needs to take into account both low-frequency loads and high-frequency electromagnetic harmonics. This can lead to the amplification of current sampling noise and switching ripples when the ESO bandwidth is increased to ensure that high-frequency disturbances are observable, resulting in unstable estimation. When the ESO bandwidth is decreased to reduce the impact of noise, high-frequency electromagnetic disturbances cannot be captured. A single ESO cannot take into account both at the same time, resulting in disturbance aliasing and an increase in estimation error.

[0007] Secondly, disturbances in the speed loop are reflected in speed changes, while high-frequency disturbances in the current loop affect current transients. The traditional approach is to estimate and compensate for both disturbances in a unified manner. This results in the speed loop compensating for high-frequency disturbances, causing insufficient speed loop response bandwidth and delays in compensation. The current loop compensates for low-frequency disturbances, causing overcompensation and introducing additional disturbances and oscillations. Ultimately, this leads to a decrease in overall system stability and poor torque ripple suppression.

[0008] Third, velocity loop disturbances and current loop disturbances possess different dynamic characteristics. Velocity loop mechanical disturbances change slowly and are low-frequency disturbances. Current loop electromagnetic disturbances change rapidly and are high-frequency disturbances. Traditional control methods struggle to simultaneously capture both types of disturbances at different time scales within a unified observation model. This leads to estimation lag for slowly changing disturbances and a lack of capture for rapidly changing disturbances, ultimately resulting in compensation signals being effective only for one type of disturbance but ineffective for the other.

[0009] Therefore, it is necessary to improve the existing technology to address its shortcomings, enhance the observation accuracy of disturbances in various frequency bands, and improve the torque stability and dynamic response capability of the permanent magnet synchronous arc motor. Summary of the Invention

[0010] To address the problems existing in the prior art, the present invention aims to provide a torque ripple suppression control method for permanent magnet synchronous arc motors based on a frequency band separation extended state observer. This method solves the frequency band aliasing problem of traditional single ESOs by establishing LF-ESOs and HF-ESOs under different frequency bands, combined with frequency band separation filtering, to independently observe and compensate for disturbances under different frequency bands, thereby improving the observation accuracy of disturbances under each frequency band. This provides an effective solution for improving the torque smoothness and operational stability of permanent magnet synchronous arc motor drive systems.

[0011] To achieve the above objectives, the technical solution provided by the present invention is as follows:

[0012] A method for suppressing motor torque ripple based on a frequency band separation extended state observer, the method comprising the following steps:

[0013] S1. Calculate the target rotational speed and feedback speed The error between them is output by the speed PI controller. ;

[0014] S2, Feedback speed and q-axis feedback current The input is a low-frequency extended state observer (LF-ESO), which performs low-frequency disturbance estimation and calculates the compensation current. Speed ​​PI regulator output In compensation current The q-axis current command value is obtained under the compensation effect. ;

[0015] S3. Calculate the q-axis current command value. and q-axis feedback current The error between them is then processed by the q-axis current PI controller to output the q-axis current PI controller output. ;

[0016] S4. Adjust the output of the q-axis current PI regulator. and q-axis feedback current The input is a high-frequency extended state observer (HF-ESO), which performs high-frequency disturbance estimation to obtain the q-axis compensation voltage. ;

[0017] S5, q-axis current PI regulator output q-axis compensation voltage The compensated q-axis voltage is obtained under the compensation effect. ;

[0018] S6, the q-axis voltage After Park transformation, the signal is provided to the Space Vector Pulse Width Modulation (SVPWM) adjustment module;

[0019] The S7 and SVPWM control modules control the operation of the controlled motor through PWM switching signals.

[0020] Furthermore, the LF-ESO uses band filtering for torque compensation during low-frequency disturbance estimation, and the HF-ESO uses band filtering for q-axis voltage compensation during high-frequency disturbance estimation. The output filters of the LF-ESO and HF-ESO use complementary filters, making the low-frequency estimation and high-frequency estimation approximately orthogonal in the frequency domain energy, thereby achieving band decoupling of the disturbance components.

[0021] Furthermore, the complementary filter is: ,in The low-pass filter is used to filter the output of the LF-ESO. Filter the output of the HF-ESO using a high-pass or band-pass filter;

[0022] ;

[0023] For frequency band decomposition, select the frequency that satisfies , For LF-ESO bandwidth parameters, This refers to the bandwidth parameters of HF-ESO.

[0024] Furthermore, in step S2, low-frequency disturbances are estimated using an LF-ESO and compensated within the velocity loop. A second-order linear LF-ESO is designed as follows:

[0025] ;

[0026] in The derivative of the velocity estimate, For speed estimation, The derivative of the mechanical side disturbance estimate. For mechanical side disturbance estimation, b T For LF-ESO control gain, B is the coefficient of viscous friction, and J is the moment of inertia. For electromagnetic torque, ,in For the measurement output of LF-ESO, x is the motor speed. L1 For motor feedback speed, , For the observer gain of LF-ESO, , For LF-ESO bandwidth parameters;

[0027] The perturbation estimate of the LF-ESO output is denoted as .

[0028] In step S4, the HF-ESO estimates the high-frequency disturbance and applies it to the current loop. A second-order linear HF-ESO is designed as follows:

[0029] ;

[0030] in The derivative of the current estimate. For current estimation, The derivative of the high-frequency disturbance estimate. For high-frequency disturbance estimation, ,in, This is an estimated value for the d-axis current. Here is an estimate of the electric angular velocity, R is the stator resistance, and L is... d For the d-axis inductance, L q It is the q-axis inductance. For motor magnetic flux, For HF-ESO control gain, , This is the q-axis voltage. ,in For the measurement output of HF-ESO, X H1 For q-axis feedback current, For q-axis current, For the observer gain of HF-ESO, , For the bandwidth parameters of HF-ESO;

[0031] The disturbance estimate of the HF-ESO output is denoted as .

[0032] Preferred, .

[0033] Furthermore, step S6 also includes: obtaining the d-axis voltage based on the d-axis current id and the d-axis current PI regulator calculation. , and the q-axis voltage The voltage u in the two-phase stationary coordinate system is provided after Park transformation. α and u β Adjust the SVPWM module.

[0034] The present invention also provides a control system for a permanent magnet synchronous motor, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor executes the computer program to implement the above-described method.

[0035] The present invention also provides a computer-readable storage medium comprising a stored computer program, wherein the computer program, when executed, controls the device containing the computer-readable storage medium to perform the above-described method.

[0036] The beneficial effect of this invention is that the proposed solution creatively solves the frequency band aliasing problem of a single ESO:

[0037] (1) Compared with the prior art, the present invention introduces a dual ESO mechanism with a frequency band separation mechanism into the vector control system. By constructing LF-ESO and HF-ESO under a unified control framework, it specifically models and compensates for low-frequency disturbances on the mechanical side and high-frequency disturbances on the electromagnetic side, respectively. This overcomes the shortcomings of traditional single ESO with one observer that cannot take into account disturbances across the entire frequency band.

[0038] (2) In order to balance load disturbances and switching harmonic disturbances, the bandwidth configuration of a traditional single ESO must be a compromise between "high bandwidth leading to noise amplification and low bandwidth leading to loss of high frequency disturbances", making it difficult to simultaneously guarantee low frequency accuracy and high frequency suppression effect. However, this invention divides the total disturbance into low frequency disturbances and high frequency disturbances in the frequency domain, and uses LF-ESO and HF-ESO in conjunction with complementary filters for observation and compensation, so that each observer only focuses on its own target frequency band, realizing disturbance decoupling compensation, taking into account both low frequency mechanical performance and high frequency electromagnetic performance, and improving the torque stability and dynamic response capability of permanent magnet synchronous arc motor.

[0039] The proposed solution constructs LF-ESO and HF-ESO and combines them with frequency band separation filtering. This allows the low-frequency disturbances output by LF-ESO to be used for speed loop compensation, and the high-frequency disturbances output by HF-ESO to be used for current loop feedforward compensation. Simultaneously, it addresses mechanical and electromagnetic disturbances, enabling independent observation and channel-specific compensation of low-frequency and high-frequency disturbances. This improves the observation accuracy of disturbances in each frequency band and enhances the torque stability and dynamic response capability of the permanent magnet synchronous arc motor. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of a permanent magnet synchronous arc motor structure provided in an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the stator phase sequence connection of a permanent magnet synchronous arc motor according to an embodiment of the present invention;

[0042] Figure 3 This is a block diagram of torque ripple suppression control for a permanent magnet synchronous arc motor provided in an embodiment of the present invention;

[0043] Figures 4(a) and 4(b) are the Bode diagrams of LF-ESO and HF-ESO respectively, provided in an embodiment of the present invention.

[0044] Figures 5(a) and 5(b) correspond to the performance test diagrams of PI control, PI+ESO control, and PI+FPESO control of the motor provided in an embodiment of the present invention when running at 400 r / min.

[0045] Figure 6(a) shows the motor operating stably at 2 degrees Celsius according to an embodiment of the present invention. The electromagnetic torque output curve under PI control under load is shown in Figure 6(b), which is an enlarged view of the blue box in Figure 6(a), and Figure 6(c) is the corresponding spectrum analysis diagram.

[0046] Figure 7(a) shows the motor operating stably at 2 degrees Celsius according to an embodiment of the present invention. The electromagnetic torque output curve under PI+ESO control under load is shown in Figure 7(b), which is an enlarged view of the blue box in Figure 7(a), and Figure 7(c) is the corresponding spectrum analysis diagram.

[0047] Figure 8(a) shows the motor operating stably at 2 degrees Celsius according to an embodiment of the present invention. The electromagnetic torque output curve under PI+FPESO control under load is shown in Figure 8(b), which is an enlarged view of the blue box in Figure 8(a), and Figure 8(c) is the corresponding spectrum analysis diagram. Detailed Implementation

[0048] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0049] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0050] The permanent magnet synchronous arc motor structure described in this article is as follows: Figure 1 As shown. The stator consists of three modules, all with the same curvature. Each module comprises six slots for winding the coils and auxiliary teeth at both ends. The rotor is composed of alternating, complementary front and rear motor rotors. Figure 1 (Only the front rotor is shown). The front side has 20 N-type permanent magnets and the rear side has 20 S-type permanent magnets, which together form 20 pairs of poles. Figure 2The diagram shows the corresponding stator phase sequence connection. The final wiring connects C3-, A3-, and B3- together to form the motor neutral point N. A1+, B1+, and C1+ are the wiring for phases A, B, and C, respectively.

[0051] according to Figure 2 After the phase sequence connections between the stator modules are completed, the final wiring of the permanent magnet synchronous arc motor is phase A, phase B, phase C, and the motor neutral point N. Therefore, traditional drive control strategies for permanent magnet synchronous motors can be adopted, such as those generally based on... Vector control strategy.

[0052] To address the problems of existing technologies, this invention is based on... Based on the vector control strategy, an extended state observer under frequency band separation is added, and a control block diagram for torque ripple suppression of permanent magnet synchronous arc motor based on frequency band separation extended state observer (FP-ESO) is proposed, as shown in the figure. Figure 3 As shown, it includes 1-speed proportional-integral (PI) controller, 2-low-frequency extended state observer (LF-ESO), 3a-d-axis current proportional-integral controller, 3b-q-axis current proportional-integral controller, 4-high-frequency extended state observer (HF-ESO), 5-Park converter module, 6-SVPWM controller module, 7-Clarke converter module, 8-inverter, 9-permanent magnet synchronous arc motor (PMAM), 10-encoder module, S1~S6 are 6-channel pulse signals, U dc DC voltage θ is the electrical angle, θ is the mechanical angle, and the modules are connected as follows: Figure 3 .

[0053] The specific implementation process of the control strategy proposed in this invention will be described below, including the following:

[0054] The mechanical motion equation of the permanent magnet synchronous arc motor is as follows:

[0055] (1);

[0056] in For rotational inertia, Let ω be the rotational angular velocity. For electromagnetic torque, For load torque, It is the coefficient of viscous friction.

[0057] Load disturbances and unmodeled friction disturbances are collectively referred to as total mechanical disturbances, defined as follows:

[0058] (2);

[0059] in This represents unmodeled disturbances caused by nonlinear friction, structural vibration, etc., in which case equation (1) can be rewritten as

[0060] (3);

[0061] in

[0062] (4);

[0063] The stator dq-axis current equation of a permanent magnet synchronous arc motor is:

[0064] (5);

[0065] in , For the d-axis inductance and q-axis inductance, , Let be the stator voltages along the d-axis and q-axis. , For the d-axis current and q-axis current, Electric angular velocity, For motor magnetic flux, , This represents the equivalent voltage disturbance caused by inverter non-ideality, voltage dead zone, PWM switching harmonics, current sampling errors, etc.

[0066] In particular, high-frequency disturbances on the electromagnetic side can be uniformly written as...

[0067] (6);

[0068] Taking the q-axis as an example, the q-axis stator current equation is rewritten as follows:

[0069] (7);

[0070] in

[0071] (8);

[0072] This invention provides a unified model for slowly varying disturbances caused by load changes, friction, and low-frequency structural vibrations. The LF-ESO is used to estimate it in real time and compensate it in the velocity loop. The design and construction of the LF-ESO will be described in detail below.

[0073] Select extended state

[0074] (9);

[0075] Then the extended system is constructed using equation (3).

[0076] (10);

[0077] Assumption If it is a slowly varying disturbance, then Bounded and relatively small.

[0078] Design a second-order linear LF-ESO as follows:

[0079] (11);

[0080] in The derivative of the velocity estimate, For speed estimation, The derivative of the mechanical side disturbance estimate. For mechanical side disturbance estimation, b T For LF-ESO control gain, B is the coefficient of viscous friction, and J is the moment of inertia. For electromagnetic torque, ,in For the measurement output of LF-ESO, This refers to the motor speed.

[0081] ESO gain depends on bandwidth parameters Selected as

[0082] (12);

[0083] , For the observer gain of LF-ESO, and satisfying

[0084] (13);

[0085] That is, LF-ESO bandwidth and speed loop bandwidth It remains at the same magnitude and is only sensitive to low-frequency disturbances.

[0086] The perturbation estimate of the LF-ESO output is denoted as

[0087] (14);

[0088] Furthermore, this invention models the mid-to-high frequency electromagnetic disturbances introduced by inverter switching frequency, voltage dead zone, PWM harmonics, etc., as follows: The design and construction of the HF-ESO will be described in detail below.

[0089] According to equation (7), select the extended state.

[0090] (15);

[0091] The extended system can then be written as

[0092] (16);

[0093] Assumption The rate of change is limited.

[0094] Design a second-order linear HF-ESO as

[0095] (17);

[0096] in The derivative of the current estimate. For current estimation, The derivative of the high-frequency disturbance estimate. For high-frequency disturbance estimation, ,in, This is an estimated value for the d-axis current. Here is an estimate of the electric angular velocity, R is the stator resistance, and L is... d For the d-axis inductance, L q It is the q-axis inductance. For motor magnetic flux, For HF-ESO control gain, , This is the q-axis voltage. ,in For the measurement output of HF-ESO, For q-axis current,

[0097] ESO gain depends on bandwidth parameters Selected as

[0098] (18);

[0099] For the observer gain of HF-ESO, and satisfying

[0100] (19);

[0101] That is, the HF-ESO bandwidth and the current loop bandwidth By maintaining the same magnitude, HF-ESO becomes more sensitive to medium- and high-frequency electromagnetic disturbances, but less responsive to slow-changing load disturbances.

[0102] The disturbance estimate of the HF-ESO output is denoted as

[0103] (20);

[0104] To address the frequency band aliasing problem inherent in traditional single ESOs during disturbance estimation, this invention optimizes the control strategy by designing LF-ESOs and HF-ESOs for different frequency bands. To further enhance suppression performance, this invention also incorporates band separation filtering, the theory of which and its implementation will be discussed below.

[0105] From a frequency perspective, the total disturbance experienced by mechanical and electromagnetic systems The spectrum typically covers a wide bandwidth and can be formally decomposed into

[0106] (twenty one);

[0107] in, It mainly includes low-frequency components (load, friction, low-frequency vibration, etc.). It mainly includes mid-to-high frequency components (current harmonics, components near the switching frequency, etc.).

[0108] Therefore, a pair of complementary filters are constructed.

[0109] (twenty two);

[0110] in For low-pass, For high-pass or band-pass applications, a typical form is a first-order complementary filter:

[0111] (twenty three);

[0112] For frequency band decomposition, select the frequency that satisfies

[0113] (twenty four);

[0114] The frequency domain complementarity proposition is now proposed, which states that for any real frequency... ,like , If equation (22) is satisfied, then

[0115] (25);

[0116] And satisfy

[0117] when hour, ;when hour, .

[0118] In this way, the total disturbance spectrum can be approximately decomposed into:

[0119] (26);

[0120] and These represent the low-frequency and high-frequency components, respectively.

[0121] In this invention, LF-ESO and HF-ESO have been implemented using different bandwidths. , Preliminary frequency selectivity was established for the disturbances. The LF-ESO responded quickly to low-frequency disturbances but exhibited low gain for high-frequency disturbances; the HF-ESO responded quickly to mid-to-high-frequency disturbances but exhibited low gain for low-frequency disturbances. Based on this, a complementary filter was introduced to further refine the frequency band division of the ESO output, resulting in:

[0122] (27);

[0123] in, , These are the Laplace transforms of the output perturbation estimates for LF-ESO and HF-ESO, respectively. , This is an estimate of the low-frequency and high-frequency disturbances after frequency band separation.

[0124] like If equation (24) is satisfied, and the bandwidth configurations of LF-ESO and HF-ESO satisfy equations (13) and (19), then in the perturbation band of interest, there are

[0125] (28);

[0126] That is, the low-frequency estimation and the high-frequency estimation are approximately orthogonal in the frequency domain energy, thus achieving frequency band decoupling of the disturbance component.

[0127] To ensure the convergence of ESO observation errors and the stability of the actual system, Lyapunov's proof of the convergence of LF-ESO observation errors is given below, taking LF-ESO as an example.

[0128] The proof is conducted using a linearized mechanical side model as a linear approximation of the real nonlinear system near a certain operating point, assuming that the mechanical side can be approximated as a first-order linear system:

[0129] (29);

[0130] Where x1 is the system state variable characterizing the mechanical rotational speed, defined , u is the system control input characterizing the equivalent electromagnetic torque input, defined as follows: a and b are system parameters, generally constants, and w represents external disturbances caused by load, friction, etc., assumed to be constant, i.e., its derivative. ,

[0131] y represents the system output;

[0132] The system extended states are defined as follows:

[0133] (30);

[0134] here Indicates the first state. This represents the second state, upon which the standard ESO form is constructed.

[0135] Extended system is written as:

[0136] (31);

[0137] ESO structure:

[0138] (32);

[0139] in It is the first gain of the observer. It is the second gain of the observer.

[0140] Define error:

[0141] (33);

[0142] Subtracting the ESO equation from the system equation yields the error system equation.

[0143] (34);

[0144] Error system polynomial:

[0145] (35);

[0146] Where s is the Laplace variable, used to describe the system's characteristic equations and pole locations; I is the identity matrix;

[0147] The gain is designed according to the desired pole, and the dynamic convergence speed of the error is expected to be determined by the bandwidth. Decisions, for example:

[0148] (36);

[0149] Let equation (35) equal equation (36), we can obtain

[0150] (37);

[0151] The characteristic roots at this time are Double roots, i.e. It is a Hurwitz matrix with a negative real part, which guarantees the linear exponential stability of the error system.

[0152] in: ;

[0153] because For a Hurwitz matrix, there exists a unique symmetric positive definite matrix. ,make

[0154] (38);

[0155] in , where is any given symmetric positive definite matrix.

[0156] Define the Lyapunov function:

[0157] (39);

[0158] Differentiate equation (34) along the error locus

[0159] (40);

[0160] because ,exist , Let Q be the smallest eigenvalue of matrix Q, such that...

[0161] (41);

[0162] then

[0163] (42);

[0164] because There exists a constant , , Let be the smallest eigenvalue of matrix P. Let P be the largest eigenvalue of matrix P. Let the norm of the error vector be such that...

[0165] (43);

[0166] In summary

[0167] (44);

[0168] By the comparison lemma, we obtain exponential convergence:

[0169] (45);

[0170] Where k represents the exponential decay rate of error convergence;

[0171] therefore

[0172] (46);

[0173] Where c is a proportionality constant. The initial observation error is represented by , indicating that the observation error exponent of ESO converges to 0, which is the linear case where the perturbation is constant.

[0174] In actual operation, disturbance It is not a constant, but rather in a slowly changing process, that is...

[0175] (47);

[0176] in, This represents the rate of change of the disturbance. The upper bound of the rate of change of the disturbance, at which point the extended system becomes

[0177] (48);

[0178] The second equation for the error becomes

[0179] (49);

[0180] Write in matrix form

[0181] (50);

[0182] Where B is the channel matrix;

[0183] Repeat the Lyapunov function above ,get

[0184] (51);

[0185] In equation (51), the right side of the equation satisfies the inequality.

[0186] (52);

[0187] use And with Cauchy's inequality, we can obtain

[0188] (53);

[0189] Where c1 and c2 are both constants, c1 represents the convergence capability of the error system itself, and c2 represents the excitation of the error system by the time-varying disturbance.

[0190] Therefore, it can be deduced that the error will converge to the same value. The proportional small neighborhood, that is, when the rate of change of the disturbance is bounded and small, the observation error of ESO will converge exponentially to the neighborhood of the origin, and its radius is proportional to the upper bound of the rate of change of the disturbance. This indicates that under slowly varying disturbances, the LF-ESO error actually converges, ensuring the stability of the system.

[0191] The convergence proof of HF-ESO is similar to that of LF-ESO, so I will not go into further detail.

[0192] Furthermore, in combination Figure 3 To illustrate the implementation of this solution, the control method of the present invention includes:

[0193] S1. Calculate the target rotational speed using the first subtractor. and feedback speed The error between them is then processed by the speed PI controller 1, which outputs the speed PI controller output. ;

[0194] S2, Feedback speed and q Shaft feedback current Input the low-frequency extended state observer (LF-ESO)2, which performs low-frequency disturbance estimation and torque compensation in conjunction with band filtering to calculate the compensation current. ;

[0195] Speed ​​PI regulator output The compensation current is achieved through the second subtractor. Under the compensation effect, q Shaft current command value ;

[0196] S3, Calculate using the third subtractor q Shaft current command value and q Shaft feedback current The error between them is then processed by the q-axis current PI regulator 3b, which outputs the q-axis current PI regulator. ;

[0197] S4. Adjust the output of the q-axis current PI regulator. and q Shaft feedback current Input the high-frequency extended state observer (HF-ESO)4, which performs high-frequency disturbance estimation in conjunction with band filtering. q Shaft voltage compensation, to obtain q Shaft compensation voltage ;

[0198] S5. Adjust the output of the q-axis current PI regulator. After the fourth subtractor qShaft compensation voltage The compensated result is obtained under the compensation effect. q shaft voltage ;

[0199] S6, the above q shaft voltage After passing through the Park transformation module 5, the voltage is provided to the space vector pulse width modulation (SVPWM) adjustment module 6. The SVPWM adjustment module 6 is used to control the voltage u in the two-phase stationary coordinate system using the SVPWM control strategy. α and u β After space vector pulse width modulation, a PWM switching signal is obtained to control the on / off state of the power devices in inverter 8, which ultimately drives the operation of permanent magnet synchronous arc motor (PMAM) 9 and produces the desired torque ripple suppression effect.

[0200] The method further includes: sampling the phase currents of the U, V, and W phases of the permanent magnet synchronous arc motor 9 through a sampling circuit to obtain the three-phase current i of the permanent magnet synchronous arc motor. a i b and i c The three-phase current i is converted by Clarke conversion module 7. a i b and i c Perform a Clarke transformation to convert the three-phase current into a two-phase current i in a stationary coordinate system. α and i β Park transformation module 5 is used to transform the current i in the two-phase stationary coordinate system. α and i β Perform the Parker transformation to obtain the q-axis current i of the permanent magnet synchronous arc motor. q and d-axis current i d .

[0201] A total of 6 PWM switching signals S1-S6 are output to control the on / off state of the power devices of inverter 8, so that inverter 8 drives the permanent magnet synchronous arc motor 9 through the switching bridge.

[0202] The encoder module 10 also obtains the real-time feedback rotor position angle θ of the permanent magnet synchronous arc motor 9, and then obtains the feedback speed through differential calculation. .

[0203] Furthermore, an initial current id0=0 and a d-axis current i are injected into the fifth subtractor. d The output result is processed by the d-axis current PI controller 3a to output the d-axis voltage. , and the q-axis voltage Voltage u is provided after Park transformation module 5.α and u β 6. Adjust the SVPWM module.

[0204] The above method achieves channel-specific decoupling compensation for low- and high-frequency disturbances through a frequency band separation mechanism, avoiding frequency band aliasing and cross-compensation under a single ESO observation, thereby improving the system's torque stability and dynamic response capability.

[0205] For slowly varying disturbances caused by load changes, friction, inertial disturbances, and low-frequency structural vibrations, this method constructs a low-frequency extended state observer (LF-ESO). Based on a mechanical-side dynamics model, it treats other slowly varying disturbances such as load torque, friction, and structural vibrations as low-frequency disturbances. The estimated value is obtained through real-time estimation using LF-ESO. By employing feedforward compensation through a speed loop, the motor can promptly offset the effects of load changes, achieving smooth torque output regulation and reducing speed fluctuations caused by mechanical disturbances. For mid-to-high frequency electromagnetic disturbances caused by inverter switching, PWM voltage distortion, current sampling errors, and space harmonics, this method constructs a high-frequency extended state observer (HF-ESO). Based on a current loop model, it treats rapid disturbances such as high-frequency voltage errors, current harmonics, voltage dead zones, and sampling errors as uniform high-frequency disturbances. The HF-ESO's bandwidth is designed to be higher than the current loop bandwidth, allowing it to focus on extracting the mid-to-high frequency components of the current signal, and using a feedforward method to... Injecting current loop voltage commands enables rapid compensation on the voltage side, effectively offsetting voltage disturbances and current harmonics caused by the inverter, thereby improving current waveform quality and reducing electromagnetic torque ripple.

[0206] A pair of complementary filters are introduced at the outputs of the LF-ESO and HF-ESO. , ,satisfy By combining the bandwidth configurations of LF-ESO and HF-ESO, frequency band decomposition of disturbances is achieved. Through frequency band separation, low-frequency disturbances only affect the velocity loop, and high-frequency disturbances only affect the current loop, forming a channel-specific decoupling compensation mechanism to avoid frequency band aliasing and cross-compensation under single ESO observation.

[0207] The dual-observer band separation structure of LF-ESO and HF-ESO proposed in this invention achieves disturbance decoupling compensation through a band separation mechanism. This system can specifically suppress mechanical disturbances and electromagnetic harmonic disturbances in different frequency bands, thereby achieving comprehensive suppression of torque ripple in permanent magnet synchronous arc motors. Through the dual-loop compensation structure, the motor's dynamic response, speed stability, and torque output smoothness are significantly improved.

[0208] The bandwidth configuration selection for LF-ESO and HF-ESO is illustrated using Figures 4(a) and 4(b). Figure 4(a) shows the Bode plot of LF-ESO, with bandwidth... As the frequency changes from 20Hz to 80Hz, the 0dB cutoff frequency gradually shifts to the right. At the same frequency, the ESO with a higher bandwidth has a smaller phase and a faster response, but the higher bandwidth also results in greater gain and greater sensitivity to noise. This can lead to the inclusion of high-frequency noise, causing the disturbance estimation curve to become more jittery. Figure 4(b) shows the Bode plot of the HF-ESO, with bandwidth... As the frequency changes from 500Hz to 1200Hz, a larger bandwidth allows for faster tracking of current harmonics around 1kHz or even 2kHz. However, this also leads to closer proximity to the sampling Nyquist frequency, posing a risk of noise amplification. Therefore, a trade-off must be made when selecting the bandwidth configuration, with 40Hz and 800Hz bandwidths being preferred.

[0209] Furthermore, to analyze and evaluate the anti-disturbance performance of the control method in this embodiment, experimental results from PI control, PI+ESO control, and PI+FPESO control were compared and analyzed. When the motor was running at 400 r / min, a sudden increase of 2... The speed response curve of the motor under load is analyzed as follows:

[0210] The disturbance rejection performance of this embodiment is evaluated using Figures 5(a) and 5(b). Figure 5(a) shows the speed response curves of PI control, PI+ESO control, and PI+FPESO control when the motor is running at 400 r / min. As can be seen from Figure 5(a), all three control methods can track the speed well, but there are slight differences in speed drop and recovery time, which are shown in Figure 5(b). As can be seen from Figure 5(b), both PI+ESO control and PI+FPESO control are superior to PI control in terms of speed drop, and PI+FPESO control has a significantly shorter recovery time than PI+ESO control. This indicates that PI+FPESO control can better suppress transient speed fluctuations caused by load disturbances and has a certain improvement in dynamic response capability, thus improving the disturbance rejection performance of the system.

[0211] To analyze and evaluate the torque ripple suppression capability of the control method in this embodiment, experimental results from PI control, PI+ESO control, and PI+FPESO control were used for comparative analysis. The analysis was conducted with the motor running at 400 r / min. The electromagnetic torque curve of the motor output under load is analyzed as follows:

[0212] Figures 6(a)-(c), 7(a)-(c), and 8(a)-(c) show the motor operating stably at 2 Under load, the electromagnetic torque output curves and corresponding spectrum analysis results are shown for PI, PI+ESO, and PI+FPESO control. The torque ripple suppression performance of this embodiment is evaluated by combining the graphical curves and analysis results. Figure 6(a) shows the torque output curves under PI control with a sudden increase of 2... The load torque output diagram shows that torque ripple is quite noticeable under this control mode; Figure 6(b) is an enlarged view of the blue box in Figure 6(a), showing that the torque ripple fluctuation remains at 0.4625. Based on this, a spectrum analysis of the torque waveform was performed, as shown in Figure 6(c). Under PI control, the amplitude of the 6th harmonic accounts for 9.1957% of the DC component.

[0213] Figure 7(a) shows the sudden addition of 2 under PI+ESO control mode. The torque output diagram of the load shows that the torque ripple is improved compared to the PI control method. Figure 7(b) is an enlarged view of the blue box in Figure 7(a), showing that the torque ripple fluctuation under this control method is 0.4112. Compared with the PI control method, it has a certain effect on suppressing torque ripple, but it is not obvious; Figure 7(c) is the torque spectrum analysis diagram under the PI+ESO control method. It can be seen that the amplitude of the 6th harmonic accounts for 9.0619% of the DC component;

[0214] Figure 8(a) shows the sudden addition of 2 under PI+FPESO in this embodiment. The torque output diagram of the load shows a significant reduction in torque ripple compared to the previous two control methods. Figure 8(b) is an enlarged view of the blue box in Figure 8(a). It can be seen that in this implementation method, the torque ripple fluctuation is reduced to 0.3128. The torque output of this embodiment is subjected to spectrum analysis, as shown in Figure 8(c). At this time, the amplitude of the 6th harmonic accounts for 5.4703% of the DC component.

[0215] In summary, compared with the three control methods, the PI+FPESO control proposed in this embodiment has the smallest torque ripple fluctuation and the harmonic amplitude is also significantly reduced. This indicates that this embodiment achieves a better torque ripple suppression effect, which can further suppress torque ripple and improve the system's anti-disturbance capability and dynamic response capability.

[0216] This invention provides a control system for a permanent magnet synchronous motor. The control system includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the control method. Furthermore, the computer program can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the invention. The control system for the permanent magnet synchronous motor can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The control system for the permanent magnet synchronous motor may include, but is not limited to, a processor and a memory.

[0217] The control system module of the permanent magnet synchronous motor, if implemented as a software functional unit and sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware.

[0218] Unless otherwise specified, the equipment components involved in the above embodiments are all conventional equipment components, and the structural settings, working methods or control methods involved are all conventional settings, working methods or control methods in the art unless otherwise specified.

[0219] Finally, it should be noted that the above are merely exemplary embodiments of this application and are not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the protection scope of this application.

Claims

1. A method for suppressing motor torque ripple based on a frequency band separation extended state observer, characterized in that, The method includes the following steps: S1, calculate target rotation speed and error between feedback rotation speed between the error, through the speed PI regulator output speed PI regulator output ; S2, Feedback speed and q-axis feedback current The input is a low-frequency extended state observer (LF-ESO), which performs low-frequency disturbance estimation and calculates the compensation current. Speed ​​PI regulator output In compensation current The q-axis current command value is obtained under the compensation effect. ; S3. Calculate the q-axis current command value. and q-axis feedback current The error between them is then processed by the q-axis current PI controller to output the q-axis current PI controller output. ; S4. Adjust the output of the q-axis current PI regulator. and q-axis feedback current The input is a high-frequency extended state observer (HF-ESO), which performs high-frequency disturbance estimation to obtain the q-axis compensation voltage. ; S5, q-axis current PI regulator output q-axis compensation voltage The compensated q-axis voltage is obtained under the compensation effect. ; S6, the above q shaft voltage After inverse Park transformation, the signal is provided to the SVPWM adjustment module (6); S7, SVPWM adjustment module (6) controls the operation of the controlled motor through PWM switching signal; The output filtering of the LF-ESO and HF-ESO uses complementary filters, making the low-frequency estimation and high-frequency estimation approximately orthogonal in the frequency domain energy, thus achieving frequency band decoupling of the disturbance components. The complementary filter is: ,in The low-pass filter is used to filter the output of the LF-ESO. Filter the output of the HF-ESO using a high-pass or band-pass filter; ； For frequency band decomposition, select the frequency that satisfies , For LF-ESO bandwidth parameters, This refers to the bandwidth parameters of HF-ESO.

2. The method for suppressing motor torque ripple according to claim 1, characterized in that: The LF-ESO also uses band filtering for torque compensation when estimating low-frequency disturbances, and the HF-ESO also uses band filtering for q-axis voltage compensation when estimating high-frequency disturbances.

3. The method for suppressing motor torque ripple according to any one of claims 1-2, characterized in that: In step S2, the low-frequency disturbance is estimated using an LF-ESO and compensated within the velocity loop. A second-order linear LF-ESO is designed as follows: ； in The derivative of the velocity estimate, For speed estimation, The derivative of the mechanical side disturbance estimate. For mechanical side disturbance estimation, b T For LF-ESO control gain, B is the coefficient of viscous friction, J is the moment of inertia, and Te is the electromagnetic torque. ,in For the measurement output of LF-ESO, x L1 For motor feedback speed, This refers to the motor speed. , For the observer gain of LF-ESO, , For LF-ESO bandwidth parameters; The perturbation estimate of the LF-ESO output is denoted as .

4. The method for suppressing motor torque ripple according to any one of claims 1-2, characterized in that: In step S4, the HF-ESO estimates the high-frequency disturbance and applies it to the current loop. A second-order linear HF-ESO is designed as follows: in: The derivative of the current estimate. For current estimation, The derivative of the high-frequency disturbance estimate. For high-frequency disturbance estimation, ,in, This is an estimated value for the d-axis current. Here is an estimate of the electric angular velocity, and R is the stator resistance. For d-axis inductance, It is the q-axis inductance. For motor magnetic flux, For HF-ESO control gain, , This is the q-axis voltage. ,in For the measurement output of HF-ESO, X H1 For q-axis feedback current, For q-axis current, , For the observer gain of HF-ESO, , For the bandwidth parameters of HF-ESO; The disturbance estimate of the HF-ESO output is denoted as .

5. The method for suppressing motor torque ripple according to claim 4, characterized in that: , This refers to the bandwidth parameters of LF-ESO.

6. The method for suppressing motor torque ripple according to any one of claims 1-2, characterized in that, Step S6 further includes: based on d-axis current The d-axis voltage is obtained by calculation with the d-axis current PI regulator. , and the q-axis voltage The voltage u in the two-phase stationary coordinate system is provided by the inverse Park transformation. α and u β Adjust the SVPWM module.

7. A control system for a permanent magnet synchronous motor, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device on which the computer-readable storage medium is located to perform the method as described in any one of claims 1-6.

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