Discrete speed control method for permanent magnet synchronous motor

Abstract

The present application belongs to the technical field of motor control, and particularly relates to a discrete rotating speed control method for a permanent magnet synchronous motor. The method comprises the following steps: S1: constructing a mechanical dynamics model of the permanent magnet synchronous motor, and constructing a lumped disturbance model based on the mechanical dynamics model; S2: constructing an augmented state space model based on the mechanical dynamics model and the lumped disturbance model, and constructing a discrete-time multi-frequency extended state observer based on the augmented state space model; S3: designing an error feedback control law, and using the error feedback control law to feedback compensate the lumped disturbance observed by the discrete-time multi-frequency extended state observer, so as to realize the discrete rotating speed control of the permanent magnet synchronous motor. In the discrete time domain, the present application can synchronously and accurately observe and effectively suppress the non-periodic slowly varying disturbance and the multi-frequency periodic harmonic, and avoids the increase of system complexity and the decline of overall performance caused by the discretization of continuous time design.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, and in particular relates to a discrete speed control method for a permanent magnet synchronous motor. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs), with their high efficiency and high power density, have become the preferred solution in modern high-performance drive applications. However, in actual operation, the motor is highly susceptible to the combined effects of aperiodic and periodic disturbances, resulting in speed pulsations and severely degrading the system's operational quality. To achieve smooth and stable speed control, extended state observers have been widely used in the field of interference suppression. However, limited by system bandwidth, traditional extended state observers can only achieve good estimations of aperiodic or low-frequency disturbances, and are unable to cope with high-frequency periodic harmonic disturbances. Although embedding a resonant controller in the observer can enhance the observation performance at specific frequencies, the continuous-time domain design inevitably introduces discretization errors during digital implementation, thereby weakening the disturbance suppression effect. Summary of the Invention

[0003] In view of this, the present invention aims to provide a discrete speed control method for permanent magnet synchronous motors to solve the problem that the existing continuous-time domain design inevitably produces discretization errors when digitally implemented, thereby weakening the suppression effect on disturbances. The present invention can synchronously and accurately observe and effectively suppress non-periodic slowly varying disturbances and multi-frequency periodic harmonics in the discrete-time domain, avoiding the increase in system complexity and the decrease in overall performance caused by the discretization of continuous-time design.

[0004] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A discrete speed control method for a permanent magnet synchronous motor specifically includes the following steps: S1: Construct a mechanical dynamics model of a permanent magnet synchronous motor, and construct a lumped disturbance model based on the mechanical dynamics model; S2: Construct an augmented state-space model based on the mechanical dynamics model and the lumped disturbance model, and construct a discrete-time multi-frequency extended state observer based on the augmented state-space model; S3: Design an error feedback control law to compensate for the lumped disturbances observed by the discrete-time multi-frequency extended state observer, thereby achieving discrete speed control of the permanent magnet synchronous motor.

[0005] Furthermore, in step S1, the mechanical dynamics model of the permanent magnet synchronous motor is as follows: ; ; ; ; ; in, For the first Mechanical angular velocity at each sampling time, and They are respectively and The nominal value, The coefficient of friction, For rotational inertia, , These are actual values ​​related to the coefficient of friction and moment of inertia. , These are actual values ​​related to the flux linkage and moment of inertia of the permanent magnet. For the first Mechanical angular velocity at each sampling time, Let q be the reference current at the k-th sampling time. For the first Lumped disturbance at each sampling time Actual value Compared with nominal value The error between them Let q be the q-axis current at the k-th sampling time. For the load torque disturbance at the k-th sampling time, Let be the q-axis current tracking error at the k-th sampling time. For the first Load torque at each sampling time, For the first Torque pulsation at each sampling time, The number of rotor pole pairs, It is a permanent magnet flux linkage. The sampling period.

[0006] Furthermore, in step S1, the lumped disturbance model is: ; in, For the first A lumped perturbation model for each sampling time. For the non-periodic perturbation at the k-th sampling time, For the first Periodic harmonic disturbances at each sampling time, The harmonic order is... The total harmonic order is denoted as .

[0007] Furthermore, in step S2, the expression for the augmented state-space model is: ; ; ; ; in, This is the state vector at the (k+1)th sampling time. Let k be the state vector at the k-th sampling time. Let q be the reference current at the k-th sampling time. The motor system outputs the sampled value at the k-th sampling time. A The system state matrix, B For the input matrix, C For the output matrix, and They are respectively and The nominal value, , These are actual values ​​related to the coefficient of friction and moment of inertia. , These are actual values ​​related to the flux linkage and moment of inertia of the permanent magnet. The total harmonic order is 0, and the matrix is ​​zero. Here is the perturbation matrix. For harmonic matrices, The coefficient of friction, For rotational inertia, The number of rotor pole pairs, It is a permanent magnet flux linkage. The sampling period.

[0008] Furthermore, in step S2, the discrete-time multi-frequency extended state observer is: ; in, This is the estimated value of the state variable at the (k+1)th sampling time. The state estimation matrix is... This is the estimated value of the state variable at the k-th sampling time. As the input estimation matrix, Let q be the reference current at the k-th sampling time. Here is the gain matrix of the discrete-time multi-frequency extended state observer. The sampled value of the motor system at the k-th sampling time is... This is the estimate of the discrete-time multi-frequency extended state observer at the k-th sampling time. This is the output matrix of the discrete-time multi-frequency extended state observer. For the lumped disturbance observed at the k-th sampling time, This is the output matrix for perturbation observations.

[0009] Furthermore, the characteristic equation of the discrete-time multi-frequency extended state observer is: ; Here, det() is the function for solving the determinant of a matrix. For discrete complex variables, It is the identity matrix. The state estimation matrix is... Here is the gain matrix of the discrete-time multi-frequency extended state observer. This is the output matrix of the discrete-time multi-frequency extended state observer. To improve the characteristic equation of harmonic disturbance, The location of the pole. , For the bandwidth of the discrete-time multi-frequency extended state observer, The sampling period is This is the characteristic equation for the harmonic disturbance of the variable structure.

[0010] Furthermore, n Desired characteristics of a discrete-time multi-frequency extended state observer for subharmonics: ; Here, det() is the function for solving the determinant of a matrix. For discrete complex variables, It is the identity matrix. The state estimation matrix is... Here is the gain matrix of the discrete-time multi-frequency extended state observer. This is the output matrix of the discrete-time multi-frequency extended state observer. To improve the characteristic equation of harmonic disturbance, The location of the pole. , For the bandwidth of the discrete-time multi-frequency extended state observer, The sampling period is The characteristic equation for variable structure harmonic disturbance is given. This represents the current harmonic order. This represents the total harmonic number.

[0011] Furthermore, in step S3, the error feedback control law is: ; in, This is the q-axis reference current at the (k+1)th sampling time. and They are respectively and The nominal value, , These are actual values ​​related to the coefficient of friction and moment of inertia. , These are actual values ​​related to the flux linkage and moment of inertia of the permanent magnet. The coefficient of friction, For rotational inertia, The number of rotor pole pairs, It is a permanent magnet flux linkage. The sampling period is For controller gain, , For controller bandwidth, This is the reference value of the mechanical angular velocity at the k-th sampling time. This is the estimated mechanical angular velocity at the k-th sampling time. This represents the lumped disturbance observed at the k-th sampling time.

[0012] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) The discrete speed control method for permanent magnet synchronous motors described in this invention proposes a discrete speed control strategy for motors based on a discrete-time multi-frequency extended state observer. This observer can not only achieve high-precision synchronous estimation of aperiodic disturbances and multiple periodic harmonics, but also effectively reduce the interaction between different disturbance components, greatly simplifying the engineering implementation and parameter tuning process of the observer. In addition, this invention adopts a discrete-time design, fundamentally avoiding the potential performance degradation problem caused by the discretization of continuous-domain design. Simulation results show that this invention can significantly suppress electrode speed pulsation and achieve high-precision, smooth speed control of the motor under complex load torque and harmonic interference conditions.

[0013] (2) The discrete speed control method for permanent magnet synchronous motors described in this invention, compared with traditional proportional-integral control and traditional active disturbance rejection control, maintains excellent dynamic response quality and steady-state control accuracy in both transient conditions with sudden load changes and steady-state conditions with superimposed multi-frequency harmonic interference. This invention provides new ideas and technical support for the design and implementation of high-performance permanent magnet synchronous motor drive systems. Attached Figure Description

[0014] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic flowchart of the discrete speed control method for a permanent magnet synchronous motor described in an embodiment of the present invention; Figure 2The control system structure block diagram of the permanent magnet synchronous motor based on the discrete-time multi-frequency extended state observer described in the embodiment of the present invention; Figure 3 The structural block diagram of the discrete-time multi-frequency extended state observer described in the embodiment of the present invention; Figure 4 The structural block diagram of the two-degree-of-freedom discrete current controller described in the embodiment of the present invention; Figure 4 (a) Different embodiments of the invention described herein Bode plot of the sensitivity function under the given conditions; Figure 4 (b) Different embodiments of the present invention Bode plot of the sensitivity function under the given conditions; Figure 4 (c) Different embodiments of the present invention Bode plot of the sensitivity function under the given conditions; Figure 4 (d) Different embodiments of the present invention Bode plot of the sensitivity function under the given conditions; Figure 5 The simulation waveform diagram of speed tracking under proportional-integral control as described in the embodiment of the present invention; Figure 6 The simulation waveform diagram of speed tracking under the conventional active disturbance rejection controller described in the embodiment of the present invention; Figure 7 The speed tracking simulation waveform obtained by the discrete speed control method based on permanent magnet synchronous motor described in the embodiment of the present invention; Figure 8 The simulation waveform of motor speed change obtained by the discrete speed control method based on permanent magnet synchronous motor described in the embodiment of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0017] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0018] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0019] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] like Figures 1-2 As shown, this invention proposes a discrete speed control method for a permanent magnet synchronous motor, which specifically includes the following steps: S1: Construct a mechanical dynamics model of a permanent magnet synchronous motor, and construct a lumped disturbance model based on the mechanical dynamics model; S2: Construct an augmented state-space model based on the mechanical dynamics model and the lumped disturbance model, and construct a discrete-time multi-frequency extended state observer based on the augmented state-space model; S3: Design an error feedback control law to compensate for the lumped disturbances observed by the discrete-time multi-frequency extended state observer, thereby achieving discrete speed control of the permanent magnet synchronous motor.

[0021] It should be noted that the specific steps of this invention are as follows: First, a mechanical dynamics model of the permanent magnet synchronous motor is constructed, and the composition of the lumped disturbance is analyzed, laying the foundation for the subsequent design of a discrete-time multi-frequency extended state observer. Second, based on the mechanical dynamics model and the lumped disturbance model, an augmented state-space model is constructed, and then a discrete-time multi-frequency extended state observer is designed to simultaneously observe non-periodic slowly varying disturbances and multi-frequency periodic harmonics, and reduce the interaction between different disturbances. Finally, an error feedback control law is designed to feed back the lumped disturbance observed by the discrete-time multi-frequency extended state observer to the control loop, thereby completing the design of the discrete speed controller and counteracting the influence of the disturbance on the permanent magnet synchronous motor.

[0022] Furthermore, in Figure 2 In this context, Inverter is a three-phase inverter, and SVPWM is Space Vector Pulse Width Modulation. It is the DC power supply for a three-phase inverter. This is the α-axis voltage command. This is a β-axis voltage command. , and The currents are for the three phases a, b, and c.

[0023] Step 1: Construct a mechanical dynamics model of the permanent magnet synchronous motor and analyze the composition of the lumped disturbance. The mechanical dynamics of a permanent magnet synchronous motor can generally be modeled in the following discrete-time form: (1); in, The mechanical angular velocity at the (k+1)th sampling time. Let be the mechanical angular velocity at the k-th sampling time. Let q be the q-axis current at the k-th sampling time. The sampling period is For mechanical angular velocity, For rotational inertia, The coefficient of friction, The number of rotor pole pairs, It is a permanent magnet flux linkage. It is the load torque. It is torque pulsation caused by periodic disturbances. It is a magnetic flux harmonic. Indicates voltage harmonics. It is cogging torque. and These are current offset error and scaling error, respectively.

[0024] definition , Considering parameter mismatch and current tracking error, the mechanical dynamics of a permanent magnet synchronous motor can be rewritten as a nominal model: (2); in,

[0025] , , , , , , and They are and The nominal value, For the first Lumped disturbance at each sampling time.

[0026] Based on the preceding analysis, the lumped disturbance can be modeled as a non-periodic, slowly varying disturbance. With n periodic harmonic components The superposition, that is (3); in, The changes between adjacent sampling times are small, that is... For angular frequency of The independent harmonic components of the harmonic essentially obey the dynamic characteristics of an undamped second-order oscillatory system. Using the internal mode principle, the discrete-time expression of this harmonic can be constructed as: (4); From equation (4), the characteristic equation of the harmonic system can be obtained. for: Its poles lie on the unit circle, corresponding to a critical stable state. To enhance system stability, it is reconstructed as a pole with a magnitude of . ( For constant damping, The stable model of ) has its difference equation modified as follows: (5); To express equation (5) in the standard first-order vector state-space form required for the design of a discrete-time multi-frequency extended state observer, a two-dimensional state vector needs to be introduced. This is achieved by introducing an auxiliary state... A single-frequency harmonic can be dynamically transformed into a subsystem consisting of two first-order equations: (6); in, Let be the augmented perturbation matrix at the k-th sampling time. Let h be the perturbation coefficient matrix of the h-th harmonic. Let be the augmented perturbation matrix at the (k+1)th sampling time, with the subscript representing the h-th frequency.

[0027] Define the augmented state vector of the lumped perturbation as external disturbances The augmented internal model can be uniformly described as: (7); in, Let be the augmented lumped perturbation matrix at the (k+1)th sampling time. For harmonic matrices, Let be the augmented lumped perturbation matrix at the k-th sampling time. The disturbance coefficient matrix for the first harmonic is... The disturbance coefficient matrix for the second harmonic is... Let be the disturbance coefficient matrix of the nth harmonic. , , , It is the identity matrix. To improve the characteristic equation of the harmonic system, namely the first polynomial equation related to z, The characteristic equation of a harmonic system is... Let cosine function variables be used. This is the lumped perturbation matrix.

[0028] Step 2: Based on the mechanical dynamics model and lumped disturbance model in Step 1, construct an augmented state space model, and then design a discrete-time multi-frequency extended state observer to achieve simultaneous observation of non-periodic slowly varying disturbances and multi-frequency periodic harmonics, and reduce the interaction between different disturbances.

[0029] By fusing the tracking error dynamics (as in Equation (2)) with the internal disturbance model (as in Equation (7)), external disturbance information can be explicitly embedded into the system description, thereby constructing the following augmented state-space model: (8); The state vector and the system matrix are defined as follows: (9); Although Equation (9) rigorously describes the system dynamics under disturbance, if a conventional observer is built directly based on this model, severe cross-coupling will occur between different frequency components, thereby deteriorating the harmonic suppression performance. In order to achieve smooth observation of disturbances and avoid the performance degradation caused by discretization, a discrete-time multi-frequency extended state observer was invented.

[0030] Without loss of generality, definition , , Let h be the frequency, where h represents the harmonic order. , and , , , , , and These are intermediate parameters with no physical meaning. Let be the transpose of the augmented perturbation matrix of the first harmonic. This is the transpose of the augmented perturbation matrix of the second harmonic. Let be the transpose of the augmented perturbation matrix of the nth harmonic. and These are intermediate parameters with no physical meaning. The disturbance coefficient matrix for the first harmonic is... The disturbance coefficient matrix for the second harmonic is... Let be the disturbance coefficient matrix of the nth harmonic. Combining equation (8), to achieve independent estimation of disturbances at different frequencies, unlike conventional observers, (Aperiodic perturbation, subscripts represent frequencies of 0) and The observations of (periodic perturbations, where the subscript represents the frequency of the h-th harmonic) should use inputs from different frequency ranges; therefore, the Discrete-Time Multi-Frequency Extended State Observer, or MFESO for short, is constructed as follows: (10); (11); in, For the state variables of a discrete-time multi-frequency extended state observer, For the estimated aperiodic disturbance, For the estimated mechanical angular velocity, Let r be the estimated value of the variable. Let h be the estimated value of the variable. For auxiliary matrix, For harmonic auxiliary matrix, For the perturbation auxiliary matrix, For auxiliary diagonal matrix, The state estimation matrix is... The input is the estimated matrix.

[0031] To achieve parallel decoupled feedforward and series step-by-step filtering, the matrix The submatrices in the design are as follows: (12); (13); in, For auxiliary matrix, For harmonic auxiliary matrix, For non-periodic disturbance observation gain coefficients, These are intermediate parameters, specifically matrices.

[0032] In particular, matrix The structure is an upper triangular coupling form: (14); in, , and These are all intermediate parameters and have no physical meaning. The disturbance coefficient matrix for the first harmonic is... The disturbance coefficient matrix for the second harmonic is... This is the disturbance coefficient matrix for the third harmonic. Let be the perturbation coefficient matrix of the h-th harmonic.

[0033] Its corresponding local cross-coupling vector is defined as: (15); in, As intermediate variables defined for ease of calculation, h = 1, 2, ..., n. Let be the variables of the cosine function.

[0034] The output and disturbance extraction matrix of the discrete-time multi-frequency extended state observer are defined as follows: (16); (17); (18); in, , and These are intermediate variables used to simplify calculations.

[0035] Finally, the gain matrix of the discrete-time multi-frequency extended state observer. Defined as: (19); (20); (twenty one); in, and This is an intermediate matrix used to simplify calculations and has no physical meaning. For current observation gain coefficient, For non-periodic disturbance observation gain coefficients, , and It is an intermediate variable with no physical meaning. The gain coefficient for the first harmonic disturbance observation. The gain coefficient for second harmonic disturbance observation. The gain coefficient for the (2n-1)th harmonic disturbance observation is given. The gain coefficient for the 2nth harmonic disturbance observation.

[0036] With system status Related to, and dominates the convergence characteristics of the tracking error state. and and system status The correlation primarily determines the convergence speed of the perturbation estimation; specifically, Controlling non-periodic disturbances The estimated bandwidth, and Each harmonic component can then be configured independently. The estimation of velocity and frequency selectivity. The block diagram of the discrete-time multi-frequency extended state observer (MFESO) is shown below. Figure 3 As shown.

[0037] Define the speed estimation error Arrange equation (10) to obtain: (twenty two); in, For the estimated mechanical angular velocity, For mechanical angular velocity, It is a non-periodic, slowly varying disturbance. For harmonic disturbances, For the observation gain coefficient of non-periodic perturbation, This is the characteristic equation for harmonic disturbances. To improve the characteristic equation of harmonic disturbances, the first polynomial equation related to z is... The observed gain coefficient for the (2h-1)th harmonic is... The observation gain coefficient is the 2h harmonic.

[0038] As can be seen from equation (22), under non-periodic slowly varying disturbances In the estimation loop, the input exist It exhibits band-stop characteristics, effectively isolating high-frequency harmonics from interfering with the estimation of slowly varying DC components. Conversely, under harmonic disturbances... In the estimation loop, the system is It exhibits bandpass characteristics, enabling the extraction of specific harmonic disturbances.

[0039] The goal of any observer is to drive the estimated state to converge quickly and without steady-state error to the true state. Subtracting equation (2) from equation (10) yields: (twenty three); in, For the (k+1)th observation error, The state estimation matrix is... Here is the gain matrix of the discrete-time multi-frequency extended state observer. This is the output matrix of the discrete-time multi-frequency extended state observer. Let $\frac{k}{k}$ be the observation error at the kth sampling time. As the input estimation matrix, Let be the lumped disturbance at the k-th sampling time. For the lumped disturbance observed at the k-th sampling time, This is the output matrix for perturbation observations.

[0040] in, Its characteristic equation polynomial is To adjust the gain of a discrete-time multi-frequency extended state observer, the pole placement method can be used.

[0041] Applying equation (23) z By transformation, we can obtain: (twenty four) in, This is an estimate of the lumped disturbance in the z-domain. For the perturbation observation output matrix, For discrete complex variables, The state estimation matrix is... Here is the gain matrix of the discrete-time multi-frequency extended state observer. This is the output matrix of the discrete-time multi-frequency extended state observer. As the input estimation matrix, For the lumped perturbation in the z-domain.

[0042] Define lumped disturbance estimation error and the sensitivity function of the perturbation estimation loop Combining equation (24), we can obtain: (25); in, For sensitivity function, For current observation gain coefficient, This is an intermediate variable matrix.

[0043] It can be seen that the numerator term The existence of this makes the system have an absolute suppressive effect on non-periodic, slowly varying disturbances, while The term enables the frequency of harmonics to be at a preset harmonic frequency. At this point, the sensitivity gain is approximately zero, ensuring high-precision estimation for complex multi-frequency disturbances.

[0044] on the other hand, The extreme point depends entirely on The eigenvalue distribution. Therefore, it is necessary to rationally design the gain of the discrete-time multi-frequency extended state observer. Shaping the characteristic polynomial of the expectation is the core of optimizing the performance of MFESO perturbation estimation.

[0045] because The frequency response determines the perturbation estimation capability of MFESO; therefore, this invention will design it from the perspective of the sensitivity function. First, to avoid structural redundancy and reduce implementation complexity, the denominator must contain... Subsequently, for the remaining 2 n The +2nd order fundamental dynamic characteristics introduce a control engineering configuration criterion based on bandwidth parameterization, uniformly configuring its closed-loop poles at the same position on the real axis. Location: (26); in, This represents the observer bandwidth. Specifically, when... n When = 0, equation (10) degenerates into a traditional discrete-time ESO, and its sensitivity function can be obtained by combining equations (25) and (26): (27); in, This is the sensitivity function of ESO.

[0046] Speed ​​estimation error and disturbance estimation error This can be deduced as: (28); According to equation (28), the discrete ESO can only achieve good estimation of slowly varying DC signals. However, due to its limited bandwidth, it cannot estimate fast-changing harmonic disturbances.

[0047] when n =1, meaning that when facing a single harmonic, according to equation (26), the observer gain can be derived as: (29); in, , , , For current observation gain coefficient, The gain coefficient for the first harmonic disturbance observation. The gain coefficient for second harmonic disturbance observation. For non-periodic disturbance observation gain coefficients, , , and These are all intermediate parameters used to simplify calculations.

[0048] Furthermore, by combining equations (29) and (25), the sensitivity transfer function can be derived as follows: (30); in, Let be the open-loop transfer function of the inner loop for perturbation suppression. Applying the Bode integral theorem to equation (30) yields: (31); in, For sensitivity function, For frequency variables, for The limit, The sampling period is As can be seen from equation (31), with The increase or The decrease, Near the zero point and The distance to the poles increases. The peak value increases at low frequencies, which means the robustness of the closed-loop system deteriorates. Furthermore, the gain in equation (29)... Includes periodic harmonic information Observation gain coefficient of first harmonic disturbance Includes non-periodic perturbation estimation gain Combining equation (22), we can see that: and There is strong mutual interference between the observation results. Changes in the relative positions of the zeros and poles can affect the performance of the observer (MFESO), therefore, fixing the poles is not a good parameter configuration method.

[0049] To mitigate the impact of changes in the relative positions of zeros and poles, the poles of the observer (MFESO) should be designed separately for aperiodic and harmonic disturbances. Based on this idea, the characteristic equation of the MFESO is designed as follows: (32); in, To improve the characteristic equation of harmonic disturbance, the first polynomial equation related to z is used to avoid structural redundancy. The two principal poles determined are retained, while the other two poles are determined by... Adjustments should be made. The characteristic equation for variable structure harmonic disturbances is the second polynomial equation related to z. The characteristic equation for harmonic disturbances is given, maintaining a fixed position relative to zero, where... , is the damping coefficient, where p is the pole location.

[0050] The observer gain of MFESO can be obtained by solving the characteristic equation (32) (as shown in equation (33)), and then the sensitivity function can be calculated (as shown in equation (34)): (33); (34); in, For current observation gain coefficient, For constant perturbation observation gain coefficient, The gain coefficient for the first harmonic disturbance observation. The gain coefficient for second harmonic disturbance observation. This represents the location of the pole.

[0051] To intuitively describe the sensitivity characteristics of MFESO, Figure 4 Different , , and Below The Bode plot shows that the MFESO proposed in this invention can observe not only aperiodic disturbances but also periodic harmonic disturbances. Figure 4 (a) Know, Increasing the value of will increase the bandwidth near the harmonic frequency, thereby enhancing robustness to frequency changes. However, it will also lead to a rise in the low-frequency range, which can be reasonably explained by equation (31). This highlights the necessity of balancing the selection of parameters. Figure 4 (b) Know, Increasing the amplitude attenuation depth at harmonic frequencies will increase the ability to suppress periodic harmonics; Figure 4 (c) It can be seen that increasing It can enhance the notch depth of the system for low-frequency and periodic harmonics; Figure 4 (d) shows the good frequency selectivity of MFESO.

[0052] Considering the real-world conditions of multiple harmonics, and combining the preceding analysis, n The expected characteristic polynomial of the subharmonic MFESO can be defined as: (35); in, To improve the characteristic equation of harmonic disturbance, the first polynomial equation related to z is... This is the characteristic equation for the variable structure harmonic disturbance, and the second polynomial equation related to z.

[0053] Accordingly, sensitivity function It can be calculated as: (36); The solution of the characteristic polynomial (36) is in n The case of ≥ 2 is more complex and requires further consideration. This paper adopts an approximate solution, as follows: (37); in, For current observation gain coefficient, For constant perturbation observation gain coefficient, The gain coefficient for the 2k-1th harmonic disturbance observation. The gain coefficient for the 2kth harmonic disturbance observation.

[0054] Since the speed loop of a permanent magnet synchronous motor mainly faces harmonic disturbances caused by the first and second harmonics due to current sampling errors, this invention primarily focuses on suppressing the first and second harmonics. n Take 2, corresponding to , .

[0055] Step 3: Design an error feedback control law to feed back the lumped disturbance observed by the observer (MFESO) to the controller, thereby counteracting the impact of the disturbance on the permanent magnet synchronous motor.

[0056] Based on the error feedback control principle, the lumped disturbance estimate extracted in real time by the observer (MFESO) is fed forward for compensation, and the following error feedback control law is designed: (38); in, , For controller bandwidth, For controller gain, Let be the reference mechanical angular velocity at the k-th sampling time. Let q be the reference current at the k-th sampling time. This is the estimated mechanical angular velocity at the k-th sampling time. Let be the lumped disturbance observed at the k-th sampling time. Combining equations (38) and (2), it can be seen that if the disturbance estimated by MFESO converges well, i.e. Then the system degenerates into a nominal deterministic system of pure integrals. This completely eliminates the impact of complex disturbances on speed control.

[0057] To verify the effectiveness of the proposed strategy, Figure 5 , Figure 6 and Figure 7 Simulation waveforms comparing the permanent magnet synchronous motor (PMSM) under proportional-integral (PI) control, a traditional active disturbance rejection (ADR) controller, and the strategy proposed in this invention are presented. From top to bottom, the figures show the global speed graph, the enlarged local speed graph, the q-axis current graph, the d-axis current graph, the A-phase current response, and the steady-state speed Fast Fourier Transform (FFT) analysis. Since the harmonics of the PMSM are more pronounced at low speeds, the operating parameters were set as follows: speed 150 rpm and load torque 5 N·m. It can be seen that when using PI control, significant speed overshoot occurs, with the speed dropping to 32 rpm under sudden load application and a steady-state speed pulsation of 11 rpm. The FFT analysis reveals significant first and second harmonics in the speed readings, with amplitudes of 3.62 rpm and 1.02 rpm, respectively, resulting in a total harmonic distortion (THD) of 2.54%. When using traditional active disturbance rejection control, there is no speed overshoot, the speed drops to 26 rpm under sudden load, and the steady-state speed pulsation reaches 8.2 rpm. The first and second harmonics are suppressed to some extent, but the speed pulsation is still relatively large, with a THD of 2.09%. When using the scheme proposed in this invention, speed tracking without overshoot is achieved, while the speed drop is reduced to 24 rpm, the steady-state speed pulsation is reduced to 1.5 rpm, the first and second speed harmonics are significantly attenuated, and the THD reaches 0.53%, achieving satisfactory smooth speed control.

[0058] Since this invention is related to rotational speed, it is necessary to verify the speed control performance at different speeds, such as... Figure 8 As shown, the discrete speed control method of the present invention can operate excellently at different speeds.

[0059] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0060] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A discrete speed control method for a permanent magnet synchronous motor, characterized in that: Specifically, the steps include the following: S1: Construct a mechanical dynamics model of a permanent magnet synchronous motor, and construct a lumped disturbance model based on the mechanical dynamics model; S2: Construct an augmented state-space model based on the mechanical dynamics model and the lumped disturbance model, and construct a discrete-time multi-frequency extended state observer based on the augmented state-space model; In step S2, the discrete-time multi-frequency extended state observer is: ； in, This is the estimated value of the state variable at the (k+1)th sampling time. The state estimation matrix is... This is the estimated value of the state variable at the k-th sampling time. As the input estimation matrix, Let q be the reference current at the k-th sampling time. Here is the gain matrix of the discrete-time multi-frequency extended state observer. The sampled value of the motor system at the k-th sampling time is... This is the estimate of the discrete-time multi-frequency extended state observer at the k-th sampling time. This is the output matrix of the discrete-time multi-frequency extended state observer. For the lumped disturbance observed at the k-th sampling time, Output matrix for perturbation observation; Sensitivity function for: ； ； ； in, The characteristic equation for variable structure harmonic disturbances is the second polynomial equation related to z. The characteristic equation for harmonic disturbances is... Where is the damping coefficient and p is the pole location. For discrete complex variables, Let cosine function variables be used. For constant damping, The sampling period is For periodic harmonic disturbances, This represents the current harmonic order. The total harmonic number; S3: Design an error feedback control law, and use the error feedback control law to compensate for the lumped disturbance observed by the discrete-time multi-frequency extended state observer, so as to realize the discrete speed control of the permanent magnet synchronous motor. In step S3, the error feedback control law is: ； in, This is the q-axis reference current at the (k+1)th sampling time. and They are respectively and The nominal value, , These are actual values ​​related to the coefficient of friction and moment of inertia. , These are actual values ​​related to the flux linkage and moment of inertia of the permanent magnet. The coefficient of friction, For rotational inertia, The number of rotor pole pairs, It is a permanent magnet flux chain. The sampling period is For controller gain, , For controller bandwidth, The sampling period is This is the reference value of the mechanical angular velocity at the k-th sampling time. This is the estimated mechanical angular velocity at the k-th sampling time. This represents the lumped disturbance observed at the k-th sampling time.

2. The discrete speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that: In step S1, the mechanical dynamics model of the permanent magnet synchronous motor is as follows: ； ； ； ； ； in, For the first Mechanical angular velocity at each sampling time, and They are respectively and The nominal value, The coefficient of friction, For rotational inertia, , These are actual values ​​related to the coefficient of friction and moment of inertia. , These are actual values ​​related to the flux linkage and moment of inertia of the permanent magnet. For the first Mechanical angular velocity at each sampling time, Let q be the reference current at the k-th sampling time. For the first Lumped disturbance at each sampling time Actual value Compared with nominal value The error between them Let q be the q-axis current at the k-th sampling time. For the load torque disturbance at the k-th sampling time, Let be the q-axis current tracking error at the k-th sampling time. For the first Load torque at each sampling time, For the first Torque pulsation at each sampling time, The number of rotor pole pairs, It is a permanent magnet flux chain. The sampling period.

3. The discrete speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that: In step S1, the lumped disturbance model is: ； in, For the first A lumped perturbation model for each sampling time. For the non-periodic perturbation at the k-th sampling time, For the first Periodic harmonic disturbances at each sampling time, The harmonic order is... The total harmonic order is denoted as .

4. The discrete speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that: In step S2, the expression for the augmented state-space model is: ； ； ； ； in, This is the state vector at the (k+1)th sampling time. Let k be the state vector at the k-th sampling time. Let q be the reference current at the k-th sampling time. The motor system outputs the sampled value at the k-th sampling time. A The system state matrix, B For the input matrix, C For the output matrix, and They are respectively and The nominal value, , These are actual values ​​related to the coefficient of friction and moment of inertia. , These are actual values ​​related to the flux linkage and moment of inertia of the permanent magnet. The total harmonic order is 0, and the matrix is ​​zero. Here is the perturbation matrix. For harmonic matrices, The coefficient of friction, For rotational inertia, The number of rotor pole pairs, It is a permanent magnet flux chain. The sampling period.

5. The discrete speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that: The characteristic equation of the discrete-time multi-frequency extended state observer is: ； ； Here, det() is the function for solving the determinant of a matrix. For discrete complex variables, It is the identity matrix. The state estimation matrix is... Here is the gain matrix of the discrete-time multi-frequency extended state observer. This is the output matrix of the discrete-time multi-frequency extended state observer. To improve the characteristic equation of harmonic disturbance, The location of the pole. , For the bandwidth of the discrete-time multi-frequency extended state observer, The sampling period is The characteristic equation for variable structure harmonic disturbance is given. Let cosine function variables be used. For constant damping, This represents the current harmonic order. This represents the total harmonic number.

6. The discrete speed control method for a permanent magnet synchronous motor according to claim 1, characterized in that: n Desired characteristics of a discrete-time multi-frequency extended state observer for subharmonics: ； ； Here, det() is the function for solving the determinant of a matrix. For discrete complex variables, It is the identity matrix. The state estimation matrix is... Here is the gain matrix of the discrete-time multi-frequency extended state observer. This is the output matrix of the discrete-time multi-frequency extended state observer. To improve the characteristic equation of harmonic disturbance, The location of the pole. , For the bandwidth of the discrete-time multi-frequency extended state observer, The sampling period is The characteristic equation for variable structure harmonic disturbance is given. This represents the current harmonic order. The total harmonic number is 1. Let cosine function variables be used. The damping is constant.

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