An adaptive sliding mode observer method based on variable boundary layer under low carrier ratio

Abstract

The application is a low carrier ratio based on variable boundary layer adaptive sliding mode observation method. The application relates to the technical field of motor control. The parameter value of the application can change in real time with the rotating speed and the switching frequency, thereby guaranteeing the system stability, dynamic performance and small steady-state error under different working conditions. In addition, since the high-frequency chattering is well inhibited, the use of filters such as LPF is cancelled, thereby reducing the system complexity. Moreover, after the estimated back electromotive force is filtered by avoiding the use of the low-pass filter, the amplitude attenuation and phase delay problems of the motor back electromotive force estimation value are improved, and the accuracy of the rotor position estimation is improved.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, and is an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio. Background Technology

[0002] Sensorless control technology for permanent magnet synchronous motors (PMSMs) achieves closed-loop control by estimating the rotor position and speed in real time, eliminating the need for physical position sensors. This effectively avoids the cost, size, complexity, and reliability issues associated with sensor installation and is widely used in motor control. In medium- to high-speed applications, PMSMs typically employ sensorless control methods based on back-EMF observers, including sliding mode observers, Romberg observers, and extended Kalman filters. Among various back-EMF observers, sliding mode observers are widely used due to their simple structure and strong anti-interference capabilities.

[0003] Traditional sliding mode observers based on sign functions typically suffer from significant chattering. To reduce chattering caused by the discontinuous switching characteristics of the sign function, the approach rate is usually modified to be a saturation function to suppress high-frequency chattering. The sliding mode gain is usually determined based on the stability derivation of the Lyapunov equations, while the boundary layer thickness is usually selected empirically. Parameter selection is uncertain, and inappropriate empirical tuning can easily lead to system instability. Furthermore, suitable sliding mode gain and boundary layer thickness vary depending on the operating conditions or switching frequency. To ensure observer stability at high speeds, larger values ​​are typically chosen for both sliding mode gain and boundary layer thickness. However, excessively large sliding mode gain can cause excessive chattering at low speeds, while excessively large boundary layer thickness can lead to slower dynamic response and larger current errors in the low-speed region. In addition, most literature replaces the sign function with a saturation function and adds a low-pass filter (LPF), but adding an LPF introduces a certain degree of delay, which is particularly noticeable under low carrier ratio conditions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the parameter values ​​of this invention can be changed in real time with rotational speed and switching frequency, ensuring system stability, dynamic performance, and small steady-state error under different operating conditions. Furthermore, since high-frequency chattering is effectively suppressed, the use of filters such as LPFs is eliminated, reducing system complexity. Moreover, by avoiding the use of low-pass filters to filter the estimated back EMF, the amplitude attenuation and phase delay problems of the motor back EMF estimate are improved, thus increasing the accuracy of rotor position estimation. This invention provides an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratios.

[0005] This invention provides the following technical solutions:

[0006] An adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio, the method comprising the following steps:

[0007] Design of Precise Discrete Sliding Mode Observer: The precise discrete sliding mode observer is built on the basis of the precise discretization model of PMSM, and the saturation function is used to replace the sign function;

[0008] Parameter adjustment: Based on the steady-state trajectory of the current error on the sliding surface, an adaptive selection method for sliding gain and boundary layer thickness is obtained, enabling parameters to change in real time with motor speed and switching frequency, ensuring system stability, dynamic performance and reducing steady-state error under different operating conditions.

[0009] Preferably, a sliding mode observer is built based on the PMSM precise discretization model, and the saturation function is used instead of the sign function, specifically:

[0010] The exact discretization model of SPMSM is as follows:

[0011]

[0012] Among them, i αβ u αβ e αβ These represent the current, voltage, and back EMF components in a two-phase stationary coordinate system, respectively; R s L is the stator resistance. s For stator inductance, T s ω is the PWM switching period. e This represents the electric angular velocity of the motor.

[0013] Preferably, the SMO is designed as follows:

[0014]

[0015] Where the symbol “^” indicates that the physical quantity is an estimated quantity, k is the sliding mode gain, and z αβ For the saturation function control law:

[0016]

[0017] Where Z0 is the boundary layer width.

[0018] Preferably, based on the steady-state trajectory of the current error on the sliding surface, an adaptive selection method for the sliding mode gain and boundary layer thickness is obtained, enabling the parameters to change in real time with the motor speed and switching frequency, specifically:

[0019] The low carrier ratio precisely discrete SMO involves two parameters: the observer gain k and the saturation function boundary layer width Z0. To force the state trajectory to move from the initial state to the sliding surface, the following two conditions must be satisfied simultaneously:

[0020]

[0021] Where parameters a and b are:

[0022]

[0023] Preferably, the parameter selection principle is to take the smallest possible Z0 and a compromise range of k. That is, the online parameter adaptation method of SMO based on the saturation function is as follows:

[0024]

[0025] Where, k z >1.

[0026] Preferably, the larger the slope k, the better the system tracks dynamic response, but the more sensitive it is to high-frequency noise interference signals. A compromise is made by taking k as the middle value within the range.

[0027] Preferably, the observation stage of the method eliminates the use of a low-pass filter (LPF) and directly uses the observed back EMF for the extraction of phase-locked loop velocity angle, which improves the amplitude attenuation and phase delay of the estimated motor back EMF and enhances the accuracy of rotor position estimation.

[0028] An adaptive sliding mode observer based on a variable boundary layer for low carrier ratio is disclosed, wherein the observer is implemented based on an adaptive sliding mode observation method based on a variable boundary layer for low carrier ratio.

[0029] A computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement an adaptive sliding mode observation method based on a variable boundary layer at low carrier ratios.

[0030] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio.

[0031] The present invention has the following beneficial effects:

[0032] Compared with the prior art, the present invention:

[0033] Currently, for sliding mode observers based on saturation functions at low carrier ratios, the boundary layer selection is generally determined through multiple simulations or experiments, without providing an effective selection method and criteria, and increasing the workload. To address the shortcomings in the selection of sliding mode gain and boundary layer thickness parameters, this invention, based on a precise discrete sliding mode observer at low carrier ratios, replaces the sign function with a saturation function, deriving an adaptive selection method for sliding mode gain and boundary layer thickness. These values ​​can be changed in real time with rotational speed and switching frequency, ensuring system stability, dynamic performance, and small steady-state error under different operating conditions. Furthermore, because high-frequency chattering is effectively suppressed, the use of filters such as the LPF is eliminated, improving the amplitude attenuation and phase delay of the motor back EMF estimate, and increasing the accuracy of rotor position estimation.

[0034] This invention features a simple structure and well-defined parameter selection principles, reducing the workload associated with empirical parameter tuning and ensuring system stability, dynamic performance, and small steady-state errors under various operating conditions. Furthermore, by eliminating the use of the LPF, it improves the amplitude attenuation and phase delay issues of the estimated motor back EMF, further enhancing the accuracy of rotor position estimation. Attached Figure Description

[0035] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0036] Figure 1 The diagram shows the block diagram of the adaptive sliding mode observer based on a variable boundary layer under low carrier ratio according to the present invention.

[0037] Figure 2 The diagram shows the quasi-sliding mode state trajectory condition 1 of the observer of the present invention;

[0038] Figure 3 The diagram shows the quasi-sliding mode state trajectory condition 2 of the observer of the present invention;

[0039] Figure 4 The diagram shows the observed back EMF waveforms of the conventional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention at a carrier ratio of 30, using the adaptive sliding mode observer based on a variable boundary layer under low carrier ratio of the present invention.

[0040] Figure 5The diagram shows the back EMF waveforms observed by the conventional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of this invention at a carrier ratio of 12.5, using the adaptive sliding mode observer based on a variable boundary layer under low carrier ratio conditions of this invention.

[0041] Figure 6 The diagram shows the motor angular velocity observation of the traditional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention when the carrier ratio increases from 30 to 12.5 using the adaptive sliding mode observer based on variable boundary layer under low carrier ratio of the present invention.

[0042] Figure 7 The diagram shows the changes in the PLL observation angle error of the conventional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of this invention when the carrier ratio increases from 30 to 12.5, using the adaptive sliding mode observer based on a variable boundary layer under low carrier ratio of this invention. Detailed Implementation

[0043] The present invention will be described in detail below with reference to specific embodiments. Specific Implementation Example 1:

[0045] This invention employs an adaptive sliding mode observer based on a variable boundary layer under low carrier ratios. The method includes a precise discrete sliding mode observer and a parameter adjustment stage. The precise discrete sliding mode observer is built based on a precise discretized model of a permanent magnet synchronous motor, using a saturation function instead of a sign function. This significantly reduces system chattering while maintaining a simple observer structure. Since high-frequency chattering is well suppressed, the observation stage eliminates the use of filters such as LPFs, directly using the observed back EMF for PLL velocity and angle extraction. This improves the amplitude attenuation and phase delay of the motor back EMF estimate, thereby increasing the accuracy of rotor position estimation. The parameter adjustment stage adjusts the sliding mode gain and boundary layer thickness in real time according to the switching frequency and motor speed to ensure system stability, dynamic performance, and small steady-state error under different operating conditions, while greatly reducing the workload of empirical parameter tuning.

[0046] The parameters of this invention can be changed in real time with rotational speed and switching frequency, ensuring system stability, dynamic performance, and small steady-state error under different operating conditions. Furthermore, since high-frequency chattering is well suppressed, the use of filters such as LPFs is eliminated, reducing system complexity. Moreover, by avoiding the use of low-pass filters to filter the estimated back EMF, the amplitude attenuation and phase delay of the estimated motor back EMF are improved, thus increasing the accuracy of rotor position estimation.

[0047] according to Figures 1 to 4As shown, the specific optimization technical solution adopted by the present invention to solve the above-mentioned technical problems is: The present invention relates to an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio.

[0048] An adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio, the method comprising the following steps:

[0049] Design of Precise Discrete Sliding Mode Observer: The precise discrete sliding mode observer is built on the basis of the precise discretization model of PMSM, and the saturation function is used to replace the sign function;

[0050] Parameter adjustment: Based on the steady-state trajectory of the current error on the sliding surface, an adaptive selection method for sliding gain and boundary layer thickness is obtained, enabling parameters to change in real time with motor speed and switching frequency, ensuring system stability, dynamic performance and reducing steady-state error under different operating conditions. Specific Implementation Example 2:

[0052] The only difference between Embodiment 2 and Embodiment 1 of this application is that:

[0053] A sliding mode observer is built based on the PMSM precise discretization model, and the saturation function is used to replace the sign function, specifically:

[0054] The exact discretization model of SPMSM is as follows:

[0055]

[0056] Among them, i αβ u αβ e αβ These represent the current, voltage, and back EMF components in a two-phase stationary coordinate system, respectively; R s L is the stator resistance. s For stator inductance, T s ω is the PWM switching period. e This represents the electric angular velocity of the motor. Specific Implementation Example 3:

[0058] The only difference between Embodiment 3 and Embodiment 2 of this application is that:

[0059] The SMO is designed as follows:

[0060]

[0061] Where the symbol “^” indicates that the physical quantity is an estimated quantity, k is the sliding mode gain, and z αβ For the saturation function control law:

[0062]

[0063] Where Z0 is the boundary layer width. Specific Implementation Example 4:

[0065] The only difference between Embodiment 4 and Embodiment 3 of this application is that:

[0066] Based on the steady-state trajectory of the current error on the sliding surface, an adaptive selection method for the sliding mode gain and boundary layer thickness is obtained, enabling the parameters to change in real time with motor speed and switching frequency. Specifically:

[0067] The low carrier ratio precisely discrete SMO involves two parameters: the observer gain k and the saturation function boundary layer width Z0. To force the state trajectory to move from the initial state to the sliding surface, the following two conditions must be satisfied simultaneously:

[0068]

[0069] Where parameters a and b are:

[0070] Specific Implementation Example 5:

[0072] The difference between Embodiment 5 and Embodiment 4 of the present invention lies only in:

[0073] The parameter selection principle is to take the smallest possible Z0 and a compromise range of k. Therefore, the online parameter adaptation method for SMO based on the saturation function is as follows:

[0074]

[0075] Where, k z >1. Specific Implementation Example Six:

[0077] The difference between Embodiment Six and Embodiment Five of the present invention lies only in:

[0078] The larger the slope k, the better the system tracks dynamic response, but the more sensitive it is to high-frequency noise interference signals. A compromise is to take k as the middle value within the range. Specific Implementation Example 7:

[0080] The difference between Embodiment Seven and Embodiment Six of the present invention lies only in:

[0081] The method eliminates the use of a low-pass filter (LPF) in the observation stage, and directly uses the observed back EMF for the extraction of phase-locked loop velocity angle. This improves the amplitude attenuation and phase delay of the motor back EMF estimate, thereby increasing the accuracy of rotor position estimation. Specific Implementation Example 8:

[0083] The difference between Embodiment 8 and Embodiment 7 of the present invention lies only in:

[0084] This invention provides an adaptive sliding mode observer based on a variable boundary layer under low carrier ratio, the observer being implemented based on an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio. Specific Implementation Example Nine:

[0086] The difference between Embodiment Nine and Embodiment Eight of the present invention lies only in:

[0087] The present invention provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio. Specific Implementation Example 10:

[0089] The only difference between Embodiment 10 and Embodiment 9 of the present invention is that:

[0090] The present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio. Specific Implementation Example Eleven:

[0092] The only difference between Embodiment Eleven and Embodiment Ten of this invention is that:

[0093] Figure 1 As an embodiment of the present invention: the method includes a precise discrete sliding mode observer and a parameter adjustment stage. The precise discrete sliding mode observer is built based on a precise discretized model of the permanent magnet synchronous motor, using a saturation function instead of a sign function, significantly reducing system chattering while maintaining a simple observer structure. Since high-frequency chattering is well suppressed, the observation stage eliminates the use of filters such as LPFs, directly using the observed back EMF for PLL velocity and angle extraction, thus improving the amplitude attenuation and phase delay of the motor back EMF estimate and increasing the accuracy of rotor position estimation. The parameter adjustment stage adjusts the sliding mode gain and boundary layer thickness in real time according to the switching frequency and motor speed to ensure system stability, dynamic performance, and small steady-state error under different operating conditions.

[0094] The specific principles and implementation steps are as follows:

[0095] The exact discretization model of SPMSM is as follows:

[0096]

[0097] In the formula i αβ u αβ e αβ These represent the current, voltage, and back EMF components in a two-phase stationary coordinate system, respectively. R s L is the stator resistance. s For stator inductance, Ts ω is the PWM switching period. e This represents the electric angular velocity of the motor.

[0098] The SMO is designed as follows:

[0099]

[0100] In the formula, the symbol "^" indicates that the physical quantity is an estimated quantity, k is the sliding mode gain, and z αβ The saturation function control law is expressed as follows:

[0101]

[0102] In essence, it involves setting up a buffer boundary layer, using linear control inside the boundary layer, and using discontinuous switching control outside the boundary layer.

[0103] The sliding surface is:

[0104]

[0105] The current error equation is:

[0106]

[0107] The precisely discrete SMO includes two parameters: the observer gain k and the saturation function boundary layer width Z0, which are crucial to the observer's performance. If the parameters are chosen appropriately, the observer will exhibit quasi-sliding mode behavior after a finite time step. To force the state trajectory to move from the initial state to the sliding surface, the following two conditions must be satisfied simultaneously, as illustrated in the diagrams below. Figure 2 and Figure 3 As shown.

[0108] State trajectory condition 1: such as Figure 2 As shown, when the current error is greater than the boundary layer width, the sliding mode error should be moved toward the sliding mode surface.

[0109] (a) When S αβ When (k)>Z0, S should have αβ (k+1) αβ (k)

[0110] but:

[0111]

[0112] Right now:

[0113]

[0114] And because S αβ (k)>Z0, therefore (1-a)i ～ ​αβ (k)>(1-a)Z0

[0115] Further simplification yields:

[0116]

[0117] (b) When S αβ When (k) < -Z0, S should have αβ (k+1)>S αβ (k)

[0118] but:

[0119]

[0120] Right now:

[0121]

[0122] And because S αβ (k)<-Z0, therefore -(1-a)i ～ αβ (k)>(1-a)Z0

[0123] Further simplification yields:

[0124]

[0125] In summary, the range of values ​​for kZ0 is:

[0126]

[0127] Because 1-a=1-exp(-R) s / L s *T s The condition that ) > 0 always holds true; therefore, the strengthened condition for the above two equations is:

[0128]

[0129] Right now:

[0130] kZ0>|e αβ (k)|

[0131] State trajectory condition 2: such as Figure 3 As shown, the current error should not move too much at a time to avoid the current error exceeding the boundary layer.

[0132] (a) When S αβ When (k)>Z0, S should have αβ (k)+S αβ (k+1)>0

[0133] but:

[0134]

[0135] Right now:

[0136]

[0137] And because S αβ (k)>Z0, therefore (1+a)i ～ αβ(k)>(1+a)Z0

[0138] Further simplification

[0139]

[0140] (b) When S αβ When (k) < -Z0, S should have αβ (k)+S αβ (k+1)<0

[0141] but:

[0142]

[0143] Right now:

[0144]

[0145] And because S αβ (k)<-Z0, therefore -(1+a)i ～ Further simplification of αβ(k)>(1+a)Z0 gives:

[0146]

[0147] In summary, the range of values ​​for k and Z0 is as follows:

[0148]

[0149] Simplified to:

[0150]

[0151] Combining the two conditions, condition 1 and condition 2, we have:

[0152] For the range to be valid, Z0 should satisfy...

[0153]

[0154] Simplify to get

[0155]

[0156] Therefore, the range of values ​​for parameters k and Z0 is:

[0157]

[0158] The principle for parameter selection is: take the smallest possible Z0.

[0159] Let Z0 be:

[0160]

[0161] Where k z >1.

[0162] The range of values ​​for k is:

[0163]

[0164] Among these, a larger slope k results in better dynamic response tracking, but also greater sensitivity to high-frequency noise interference signals. Therefore, a compromise is made, with k taken as the middle value within the range, i.e.:

[0165]

[0166] Therefore, the online parameter adaptation method for SMO based on the saturation function is as follows:

[0167]

[0168] Figure 4 To illustrate the observation back EMF waveforms of the conventional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of this invention at a carrier ratio of 30 using the adaptive sliding mode observer based on a variable boundary layer under low carrier ratio conditions of this invention.

[0169] Figure 5 To illustrate the observation back EMF waveforms of the conventional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of this invention at a carrier ratio of 12.5 using the adaptive sliding mode observer based on a variable boundary layer under low carrier ratio conditions of this invention.

[0170] Figure 6 To observe the motor angular velocity using the adaptive sliding mode observer based on a variable boundary layer under low carrier ratio of this invention, when the carrier ratio increases from 30 to 12.5, the results are compared between the conventional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of this invention.

[0171] Figure 7 To illustrate the changes in PLL observation angle error of the traditional saturated function sliding mode (CSMO) and the sliding mode observer (ASMO) of this invention under low carrier ratio, when the carrier ratio increases from 30 to 12.5.

[0172] As can be seen from the simulation waveforms above, the adaptive sliding mode observer based on a variable boundary layer in this invention can ensure the accuracy of back EMF observation even at low carrier ratios. It eliminates the need for an LPF to address the issues of back EMF amplitude attenuation and phase delay, further improving the accuracy of rotor position estimation. Furthermore, because the parameter selection principles are predetermined, the workload of empirical parameter tuning is significantly reduced.

[0173] The above description is merely a preferred embodiment of an adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio. The scope of protection for such a method is not limited to the above embodiments; all technical solutions falling within this conceptual framework are within the scope of protection of this invention. It should be noted that for those skilled in the art, any improvements and variations made without departing from the principles of this invention should also be considered within the scope of protection of this invention.

Claims

1. An adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio, characterized by: The method includes the following steps: Design of Precise Discrete Sliding Mode Observer: The precise discrete sliding mode observer is built on the basis of the precise discretization model of PMSM, and the saturation function is used to replace the sign function; Parameter adjustment: Based on the steady-state trajectory of the current error on the sliding surface, an adaptive selection method for sliding mode gain and boundary layer thickness is obtained, enabling parameters to change in real time with motor speed and switching frequency, ensuring system stability, dynamic performance and reducing steady-state error under different operating conditions; Based on the steady-state trajectory of the current error on the sliding surface, an adaptive selection method for the sliding mode gain and boundary layer thickness is obtained, enabling the parameters to change in real time with motor speed and switching frequency. Specifically: The low carrier ratio precisely discrete SMO includes two parameters: the sliding mode gain M and the saturation function boundary layer width. Z 0. In order to force the state trajectory to move from the initial state to the sliding surface, the following two conditions must be met simultaneously: in a , b The parameters are: ； in, e αβ The back electromotive force component in a two-phase stationary coordinate system. R s For stator resistance, L s For stator inductance, T s For the PWM switching cycle, ω e This represents the electric angular velocity of the motor.

2. The method according to claim 1, characterized in that: A sliding mode observer is built based on the PMSM precise discretization model, and the saturation function is used to replace the sign function, specifically: The exact discretization model of SPMSM is as follows: in, i αβ , u αβ These represent the current and voltage in a two-phase stationary coordinate system, respectively.

3. The method according to claim 2, characterized in that: The SMO is designed as follows: Where the symbol "^" indicates that the physical quantity is an estimated quantity, and M is the sliding mode gain. z αβ For the saturation function control law: in, Z 0 represents the boundary layer width.

4. The method according to claim 3, characterized in that: The online parameter adaptation method for SMO based on the saturation function is as follows: in, k z >1.

5. The method according to claim 4, characterized in that: The method eliminates the use of a low-pass filter (LPF) in the observation stage, and directly uses the observed back EMF for the extraction of phase-locked loop velocity angle. This improves the amplitude attenuation and phase delay of the motor back EMF estimate, thereby increasing the accuracy of rotor position estimation.

6. An adaptive sliding mode observer based on a variable boundary layer under low carrier ratio, characterized in that: The observer is implemented based on any of the methods described in claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the method as claimed in any one of claims 1-5.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the method of any one of claims 1-5.

Images