Rotating speed loop active disturbance rejection control method based on disturbance observation error lead correction

Abstract

The invention relates to a rotating speed loop active-disturbance-rejection control method based on disturbance observation error lead correction, and belongs to the technical field of permanent magnet synchronous motor rotating speed control. Aiming at the problem that the rotating speed control performance is reduced due to insufficient medium-high frequency disturbance observation precision of an extended state observer ESO in the traditional active-disturbance-rejection control, the invention provides a reconstructed ESO feedback mechanism: a disturbance observation error is used for replacing a traditional rotating speed observation error as a feedback correction item; meanwhile, a series lead correction network is introduced to process the total disturbance observation value, and corrected total disturbance is generated. The method is realized by updating an extended state observer equation set, and the key comprises an observation value updating rule based on a disturbance observation error and a lead correction parameter setting mechanism. According to the method, traditional limitation is broken through, the rotating speed steady-state error under slope disturbance is effectively eliminated, the rotating speed error under parabola disturbance is restrained from infinity to a finite small value, and the dynamic response speed and the anti-interference recovery capacity under step, slope and parabola load disturbance are comprehensively improved.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor speed control technology, and relates to a speed loop active disturbance rejection control method based on disturbance observation error advance correction. Background Technology

[0002] This invention relates to the field of speed control technology for permanent magnet synchronous motors (PMSMs). In motor control systems, Active Disturbance Rejection Control (ADRC) is a widely used method to improve anti-interference capabilities. The core of this method lies in the Extended State Observer (ESO), which is used to observe the total system disturbance in real time and compensate for external disturbances. Through the operation of the ESO, ADRC can effectively resist external disturbances, thereby improving the stability and dynamic response performance of speed control. This technology has been verified in industrial practice, and it is particularly valuable in high-precision drive systems such as permanent magnet synchronous motors.

[0003] While active disturbance rejection control (ADRC) has theoretical advantages, its practical performance is highly dependent on the disturbance observation capability of the extended state observer. The extended state observer in traditional linear ADRC suffers from significantly insufficient observation accuracy in the mid-to-high frequency range. This directly leads to a decline in speed control performance; for example, the system may experience speed fluctuations or response delays when facing rapidly changing load disturbances. To improve disturbance observation capability, a common approach is to increase the observer bandwidth, but this is strictly constrained by hardware limitations. Bandwidth cannot be increased indefinitely because high bandwidth can lead to system instability issues, such as oscillations or increased noise sensitivity. These shortcomings limit the effectiveness of traditional methods in complex industrial environments.

[0004] To overcome these problems, researchers have attempted to introduce resonant or quasi-resonant controllers to enhance the observation capability of specific frequency harmonics. While these approaches can partially improve disturbance suppression, such as eliminating periodic disturbances, their overall improvement capability for complex and variable disturbances is very limited. Resonant controllers can only optimize performance at specific frequency points and cannot effectively handle broadband disturbances or nonlinear disturbances. This results in existing methods still suffering from slow observation speed and low accuracy when facing diverse disturbance scenarios such as ramp loads and parabolic loads. Therefore, current technologies cannot fully meet the requirements for high-dynamic-performance permanent magnet synchronous motor speed control.

[0005] Given the limitations of existing extended state observers and the shortcomings of resonant controller schemes, an innovative method is urgently needed to comprehensively improve the speed and accuracy of disturbance observation. This invention is based on this motivation, aiming to develop an improved extended state observer structure. This structure not only effectively improves the ability to observe mid-to-high frequency disturbances, but also significantly enhances speed control performance under various disturbance conditions, thereby breaking through the technical bottleneck of traditional active disturbance rejection control. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a speed loop active disturbance rejection control method based on disturbance observation error advance correction. This paper replaces the traditional speed observation error with disturbance observation error and employs a series feedforward correction network to further improve the mid-to-high frequency disturbance observation performance. Furthermore, based on the speed control steady-state error tuning parameters, the speed error of the PMSM under ramp and parabolic disturbances is significantly improved compared to previous methods.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A speed loop active disturbance rejection control method based on disturbance observation error lead correction, applied to the speed control of a permanent magnet synchronous motor (PMSM), includes the following steps:

[0009] Establish the state-space equation of the permanent magnet synchronous motor, and define the motor mechanical angular velocity as the first state variable x1 and the total system disturbance as the second state variable x2.

[0010] Design an Extended State Observer (ESO) to estimate the first state variable x1 and the second state variable x2, and obtain the angular velocity observation value z1 and the total disturbance observation value z2. The update of the total disturbance observation value z2 is based on the disturbance observation error of the total disturbance of the system and is corrected by feedback.

[0011] The total disturbance observation z2 is processed using a series lead compensation network to obtain the corrected total disturbance z3;

[0012] A q-axis current reference value is generated based on the observed angular velocity z1, a speed command value, and the corrected total disturbance z3 to control the speed of the permanent magnet synchronous motor.

[0013] Furthermore, the extended state observer and the cascaded lead compensator network are implemented through the following set of equations:

[0014]

[0015] Where e1 is the angular velocity observation error, e2 is the disturbance observation error, z1 is the observed angular velocity value, z2 is the observed total disturbance value, z3 is the corrected total disturbance, x1 is the actual value of the motor mechanical angular velocity, u is the system control input, i.e., the q-axis current, b0 is the system control gain, β1 and β2 are the observer error feedback coefficients, α is the correction coefficient, and T α It is the advance correction time constant, and · represents the derivative with respect to time.

[0016] Furthermore, the values ​​of the observer error feedback coefficients β1 and β2 are both set to the observer bandwidth ω0 of the extended state observer.

[0017] Furthermore, the advance correction time constant T α The value of satisfies the following formula to ensure that the steady-state speed error of the permanent magnet synchronous motor under slope disturbance is 0:

[0018]

[0019] Wherein, ω0 is the bandwidth of the observer.

[0020] Furthermore, the correction coefficient α ranges from 2 to 5.

[0021] Furthermore, the q-axis current reference value i qref Generated through the following linear error feedback control law:

[0022]

[0023] Where, k p To control the proportional gain, ω ref z1 is the rotational speed command value, z3 is the observed angular velocity value, and b0 is the corrected total disturbance.

[0024] Furthermore, the state-space equations are in the following form:

[0025]

[0026] Where x1 is the mechanical angular velocity ω of the motor. m x2 is the total system disturbance f, and u is the q-axis current i. q b0 is the system control gain, and its expression is b0 = 1.5n p ψ f / J; the n p ψ is the number of pole pairs of the motor. f J is the permanent magnet flux linkage, and J is the moment of inertia of the motor.

[0027] Furthermore, the expression for the total system disturbance f is:

[0028]

[0029] Where B is the motor damping coefficient, ω m Let T be the mechanical angular velocity of the motor. l J is the motor load torque, and J is the motor's moment of inertia.

[0030] The beneficial effects of this invention are as follows:

[0031] (1) The extended state observer in traditional active disturbance rejection control (ADDC) has insufficient ability to observe mid-to-high frequency disturbances, resulting in limited system disturbance rejection performance. This invention fundamentally optimizes the observation mechanism by reconstructing the extended state observer structure and replacing the traditional rotational speed observation error with the disturbance observation error as the feedback correction term. This design significantly broadens the effective observation bandwidth, enabling the system to maintain high-precision observation capability under mid-to-high frequency disturbances. At the same time, by introducing a series lead compensation network, the tracking sensitivity to rapidly changing disturbances is further enhanced, ensuring observation robustness under complex disturbance environments.

[0032] (2) Traditional methods suffer from steady-state speed errors under ramp disturbances, and these errors tend to become infinite under parabolic disturbances, severely limiting their application in high-precision control scenarios. This invention innovatively correlates the lead correction time constant with the observer bandwidth through a parameter tuning mechanism and optimizes the range of correction coefficient values, achieving two breakthrough effects:

[0033] Completely eliminate steady-state error under ramp disturbance, enabling the system to achieve error-free tracking under gradually changing load disturbance;

[0034] The error under parabolic disturbance is reduced from infinity to a finite minimum, breaking through the performance bottleneck of traditional active disturbance rejection control.

[0035] (3) In various disturbance tests, such as step, ramp, and parabola, this invention demonstrates excellent dynamic performance:

[0036] When faced with sudden load disturbances, it can suppress speed drops more quickly and accelerate recovery to the target value;

[0037] It maintains precise speed tracking capability even under constantly changing disturbance environments.

[0038] These advantages stem from the synergistic effect of the disturbance observation link and the lead compensation network, which makes the current compensation response faster and the system disturbance recovery time significantly shortened.

[0039] (4) This invention effectively avoids the risks of high-frequency noise sensitivity and overestimation in the mid-to-low frequency range by constraining the reasonable range of correction coefficient values ​​(2-5 recommended). This design balances accuracy improvement with system stability, ensuring reliable implementation of the solution in engineering scenarios such as motor control. Meanwhile, the parameter tuning rules are clear (e.g., This significantly reduces debugging complexity and enhances industrial applicability.

[0040] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0042] Figure 1 The system control block diagram for C-ADRC;

[0043] Figure 2 This is the system control block diagram for DE-CLC-ADRC;

[0044] Figure 3 Bode plots for perturbations with the same ω0 but different α;

[0045] Figure 4 Bode plots of the amplitude-frequency response of speed control error under different control methods;

[0046] Figure 5 This is a structural diagram of the DE-CLC-ADRC system control model;

[0047] Figure 6 The simulation results are for a step load disturbance.

[0048] Figure 7 The simulation results are for slope load disturbance.

[0049] Figure 8 The simulation results are for a parabolic load disturbance. Detailed Implementation

[0050] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0051] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0052] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present 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. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0053] 1. Mathematical Model of Permanent Magnet Synchronous Motor

[0054] For a surface-mounted permanent magnet synchronous motor, its motion equations are as follows:

[0055]

[0056] Where J is the moment of inertia of the motor, ω m n is the mechanical angular velocity of the motor. p This represents the number of pole pairs of the motor. For permanent magnet flux linkage, i q Let B be the q-axis current, B be the motor damping coefficient, and T be the q-axis current. l This represents the motor load torque.

[0057] Rearranged into state-space equation form:

[0058]

[0059] x1 refers to ω m x2 refers to the total disturbance f, and u refers to i. q The system control gain b0 = 1.5n p ψ f / J.

[0060] 2. Speed ​​Loop Control Model

[0061] (1) Conventional Active Disturbance Rejection Control (C-ADRC)

[0062] The traditional linear ESO design is shown in Equation (3), where z1 and z2 are the estimated values ​​of x1 and x2, respectively, e1 is the angular velocity observation error, and β1 and β2 are the error feedback coefficients.

[0063]

[0064] The linear error feedback control law is:

[0065]

[0066] Where, k p To control the proportional gain, i qref This is the reference value for the q-axis current output by the speed loop.

[0067] Since the response speed of the current loop is usually much faster than that of the speed loop, the transfer function of the current loop is assumed to be 1. The control block diagram of the C-ADRC system is as follows: Figure 1 As shown.

[0068] The transfer functions of the actual and observed perturbations in C-ADRC are shown in equation (5). Generally, the "bandwidth method" is used to configure the poles of the transfer function as multiple poles on the real axis, letting β1 = 2ω0 and β2 = ω0. 2 ω0 is the observer bandwidth.

[0069]

[0070] (2) Active Disturbance Rejection Control Based on Series Lead Compensation of Disturbance Observation Error (DE-CLC-ADRC)

[0071] As can be seen from the traditional ESO equation (3), the total disturbance observation value z2 also converges with the angular velocity observation error e1, resulting in insufficient observation accuracy and rate of the disturbance. Therefore, the disturbance observation error is used as the disturbance observation feedback term. The disturbance observation error e2 = z2 - x2 is introduced.

[0072] According to (2) and (3), we get

[0073]

[0074] The perturbation observation equation is:

[0075]

[0076] The transfer functions of the actual disturbance and the observed disturbance are as shown in equation (8). The parameters are still tuned using the "bandwidth method", with β1 = β2 = ω0.

[0077]

[0078] To further enhance the disturbance observation capability, a lead compensator is connected in series with the observed disturbances. The disturbance observation transfer function after lead compensation is as follows:

[0079]

[0080] In the formula, T α α is the advance correction time constant, and α is the correction coefficient with a value > 1. By performing a time-domain transformation on equation (9) and combining it with the previous text to form a state equation, we can obtain DE-CLC-ESO as shown in equation (10).

[0081]

[0082] Where z3 is the corrected total disturbance.

[0083] The DE-CLC-ADRC system control block diagram is as follows: Figure 2 As shown.

[0084] 3. DE-CLC-ADRC parameter tuning

[0085] Depend on Figure 2 From the system control block diagram shown, we can obtain the speed control error ε = ω. ref -ω m The transfer function with respect to the total disturbance f is

[0086]

[0087] When the system faces a unit step disturbance of 1 / s, according to the Laplace Final Value Theorem (FVT), the steady-state speed control error is:

[0088]

[0089] When the system faces a unit slope disturbance of 1 / s 2 At that time, the steady-state speed control error is

[0090]

[0091] Let ε ss2 =0, at this time the advance correction time constant T α When equation (21) is satisfied, the steady-state speed error under slope disturbance can be reduced to 0.

[0092]

[0093] The system faces a unit parabolic disturbance of 1 / s 3 The steady-state speed control error is

[0094]

[0095] When equation (14) is not satisfied, the numerator of (16) is not 0, then ε ss3 If T is ∞, then T α If equation (14) is satisfied, then

[0096]

[0097] It can be seen that by setting the advance correction parameters, not only can the steady-state speed error under slope disturbance be reduced to 0, but the steady-state speed control error under parabolic disturbance can also be reduced from ∞ to a finite value.

[0098] Bode plots of the perturbation observation transfer functions of DE-CLC-ADRC with the same bandwidth ω0 but different α are shown below. Figure 3 As shown, it can be seen that as α increases, the Bode plot curve shifts towards higher frequencies, improving the tracking accuracy for mid-to-high frequency disturbances. However, α should not be too large because: 1) Figure 5 As shown in the right figure, the larger α is, the longer the mid-to-low frequency band for disturbance estimation exceeds 0 dB, leading to "overestimation" of the mid-to-low frequency band. That is, the observed values ​​of disturbances in these frequency bands are greater than the actual values, which may cause observer oscillations and affect system stability. 2) The larger α is, the lower the amplitude attenuation in the high-frequency band, resulting in a weakened filtering effect on high-frequency noise. Therefore, the recommended value of α is 2 to 5.

[0099] In contrast, the speed control error transfer function under C-ADRC control is: Plot the Bode plots of the speed control error amplitude-frequency response under the C-ADRC and DE-CLC-ADRC control modes as follows: Figure 4 As shown, when facing low-frequency interference, the speed control error of DE-CLC-ADRC is significantly lower than that of C-ADRC, while the speed control error response in the mid-to-high frequency range is almost the same.

[0100] Table 1 shows the steady-state speed control errors of the two control methods under various orders of disturbance. It can be seen that C-ADRC has a steady-state speed error under ramp disturbance, and it becomes infinite under parabolic disturbance; while DE-CLC-ADRC, after parameter setting, can reduce the steady-state speed error under ramp disturbance to 0, and limit the steady-state speed error under parabolic disturbance to a finite value.

[0101] Table 1. Steady-state speed error of each control method under different orders of disturbance.

[0102]

[0103] Control structure block diagram as follows Figure 5 As shown, a simulation model was built in Matlab / Simulink software to verify the control effect.

[0104] The motor current loop uses PI control, and the selected current loop bandwidth is uniformly set to 1000 rad / s. In the speed loop parameters, the ADRC observer bandwidth ω0 is 100 rad / s. Generally, the observer bandwidth is 5 to 10 times the control bandwidth. k is set... p The value is 20 rad / s. Based on the parameter tuning analysis of DE-CLC-ADRC above, α is chosen as 3, and T... α The value is 0.006. The parameters of the selected permanent magnet synchronous motor are shown in Table 2.

[0105] Table 2 Parameters of Permanent Magnet Synchronous Motor System

[0106] parameter value parameter value Phase resistance R 0.5Ω <![CDATA[Number of pole pairs n p > 4 <![CDATA[Direct-axis inductance L d > 4.5mH <![CDATA[Bus voltage U dc > 150V <![CDATA[Quadrature axis inductance L q > 4.5mH <![CDATA[Rated current i n > 8A <![CDATA[Permanent magnet flux linkage ψ f > 0.135Wb <![CDATA[Control frequency f pwm > 5kHz

[0107] (1) Step load disturbance

[0108] After the motor starts under no-load and reaches 200 r / min, a step load disturbance with an amplitude of 2 Nm is added at the 2nd second. The simulation results are as follows. Figure 6 As shown, the time to reach a given speed under no-load conditions is similar for both. However, after applying a step load, the speed drop for the C-ADRC is 90.24 r / min, while for the DE-CLC-ADRC it is only 17.04 r / min. The time for the DE-CLC-ADRC to recover to 200 rpm after applying a load is 0.134 s, while for the C-ADRC it is 0.268 s. From i q As can be seen from the waveform observed by the disturbance, the DE-CLC-ADRC can track disturbance changes more quickly and output current to compensate for load disturbances.

[0109] (2) Slope load disturbance

[0110] After the motor starts under no-load and reaches 200 r / min, a ramp load disturbance with a slope of 2 Nm / s is introduced at the 2nd second, and a constant load of 2 Nm is maintained at the 3rd second. The simulation results are as follows. Figure 7 As shown, after adding a ramp load, the DE-CLC-ADRC can accurately track the ramp load disturbance and achieve error-free speed control, while the C-ADRC exhibits a steady-state speed error between 2 and 3 seconds, consistent with the analysis above. After 3 seconds, the ramp load disappears and becomes a constant load, and the C-ADRC only returns to the speed command value after adjustment.

[0111] (3) Parabolic load disturbance

[0112] After the motor starts under no-load and reaches 200 r / min, add 2 Nm / s at the 2nd second. 2 The simulation results are as follows: A parabolic load disturbance is applied, and a constant load of 2 Nm is maintained at the 3rd second. Figure 8 As shown. Based on the parameters and equation (23), the steady-state speed error of DE-CLC-ADRC is only -2.6 × 10⁻⁶. -6The speed error is almost negligible, while the steady-state speed error of the traditional method is ∞. Therefore, during the 2-3s interval, the speed error of the DE-CLC-ADRC is almost zero, while the C-ADRC shows a linear decrease to ∞. After 3s, the parabolic load disappears and becomes a constant load, and the C-ADRC returns to the speed command value after adjustment.

[0113] In summary, based on simulation results, the proposed improved method demonstrates better speed tracking performance compared to the traditional method under step, ramp, and parabolic load disturbances.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A speed loop active disturbance rejection control method based on disturbance observation error lead correction, applied to the speed control of a permanent magnet synchronous motor (PMSM), characterized in that: Includes the following steps: Establish the state-space equation of the permanent magnet synchronous motor, and define the motor mechanical angular velocity as the first state variable x1 and the total system disturbance as the second state variable x2. Design an Extended State Observer (ESO) to estimate the first state variable x1 and the second state variable x2, and obtain the angular velocity observation value z1 and the total disturbance observation value z2. The update of the total disturbance observation value z2 is based on the disturbance observation error of the total disturbance of the system and is corrected by feedback. The total disturbance observation z2 is processed using a series lead compensation network to obtain the corrected total disturbance z3; A q-axis current reference value is generated based on the observed angular velocity z1, a speed command value, and the corrected total disturbance z3 to control the speed of the permanent magnet synchronous motor.

2. The speed loop active disturbance rejection control method based on disturbance observation error lead correction according to claim 1, characterized in that: The extended state observer and the cascaded lead compensator network are implemented through the following set of equations: Where e1 is the angular velocity observation error, e2 is the disturbance observation error, z1 is the observed angular velocity value, z2 is the observed total disturbance value, z3 is the corrected total disturbance, x1 is the actual value of the motor mechanical angular velocity, u is the system control input, i.e., the q-axis current, b0 is the system control gain, β1 and β2 are the observer error feedback coefficients, α is the correction coefficient, and T α It is the advance correction time constant, and · represents the derivative with respect to time.

3. The speed loop active disturbance rejection control method based on disturbance observation error lead correction according to claim 2, characterized in that: The values ​​of the observer error feedback coefficients β1 and β2 are both set to the observer bandwidth ω0 of the extended state observer.

4. The speed loop active disturbance rejection control method based on disturbance observation error lead correction according to claim 3, characterized in that: The advanced correction time constant T α The value of satisfies the following formula to ensure that the steady-state speed error of the permanent magnet synchronous motor under slope disturbance is 0: Wherein, ω0 is the bandwidth of the observer.

5. The speed loop active disturbance rejection control method based on disturbance observation error lead correction according to claim 2, characterized in that: The correction coefficient α ranges from 2 to 5.

6. The speed loop active disturbance rejection control method based on disturbance observation error lead correction according to claim 1, characterized in that: The q-axis current reference value i qref Generated through the following linear error feedback control law: Where, k p To control the proportional gain, ω ref z1 is the rotational speed command value, z3 is the observed angular velocity value, and b0 is the corrected total disturbance.

7. The speed loop active disturbance rejection control method based on disturbance observation error lead correction according to claim 1, characterized in that: The state-space equations are in the following form: Where x1 is the mechanical angular velocity ω of the motor. m x2 is the total system disturbance f, and u is the q-axis current i. q b0 is the system control gain, and its expression is b0 = 1.5n p ψ f / J; the n p ψ is the number of pole pairs of the motor. f J is the permanent magnet flux linkage, and J is the moment of inertia of the motor.

8. The speed loop active disturbance rejection control method based on disturbance observation error lead correction according to claim 7, characterized in that: The expression for the total system disturbance f is: Where B is the motor damping coefficient, ω m Let T be the mechanical angular velocity of the motor. l J is the motor load torque, and J is the motor's moment of inertia.

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