Adaptive sliding mode observation method based on variable boundary layer under low carrier wave ratio

Abstract

The invention relates to a self-adaptive sliding mode observation method based on a variable boundary layer under a low carrier wave ratio. The invention relates to the technical field of motor control, the parameter value can change in real time along with the rotating speed and the switching frequency, and the system stability, the dynamic performance and the small steady-state error under different working conditions are ensured. In addition, because the high-frequency buffeting is well suppressed, the use of filters such as LPF is cancelled, and the system complexity is reduced. And moreover, the problems of amplitude attenuation and phase delay of the back electromotive force estimated value of the motor are solved after a low-pass filter is used for filtering the estimated back electromotive force, and the accuracy of rotor position estimation is improved.

Description

Technical Field

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

[0002] Permanent magnet synchronous motor position sensorless control technology can achieve closed-loop control without physical position sensors by estimating the rotor position and speed of the motor in real time, effectively avoiding the cost, volume, complexity and reliability issues caused by sensor installation, and is widely used in the field of motor control. In the medium and high-speed motion range, permanent magnet synchronous motors usually adopt position sensorless control methods based on back-EMF observers, including sliding mode observers, Romberg observers, extended Kalman filters, etc. Among various back-EMF observers, sliding mode observers are widely used due to their simple structure and strong anti-interference ability.

[0003] Traditional sliding mode observers based on sign functions usually have obvious characteristics such as jitter. In order to reduce the jitter caused by the discontinuous switching characteristics of the sign function, the approach rate is usually changed to a saturation function to suppress high-frequency jitter. The sliding mode gain is usually determined according to the results derived from the stability of the Lyapunov equation, while the boundary layer thickness is usually selected by empirical parameter adjustment. The parameter selection is uncertain, and if the empirical parameter adjustment is not selected appropriately, it is very easy to cause instability in the system. In addition, for different working conditions or switching frequencies, the appropriate sliding mode gain and boundary layer thickness are different. If the observer is to be stable at high speed, the sliding mode gain and boundary layer thickness are usually selected to be larger. However, if the sliding mode gain is too large, it will cause excessive jitter at low speed. If the boundary layer thickness is too large, it will cause slow dynamic response and large current error in the low speed area. In addition, most literatures use a saturation function instead of a sign function and add a low-pass filter (LPF), but adding the LPF will cause a certain degree of delay, which is particularly obvious under low carrier ratio conditions. Summary of the invention

[0004] In view of the shortcomings of the prior art, the parameter values ​​of the present invention can change in real time with the rotational speed and switching frequency, ensuring the system stability, dynamic performance and small steady-state error under different working conditions. In addition, since high-frequency jitter is well suppressed, the use of filters such as LPF is eliminated, reducing the complexity of the system. And after avoiding the use of a low-pass filter to filter the estimated back EMF, the amplitude attenuation and phase delay problems of the estimated value of the motor back EMF are improved, and the accuracy of the rotor position estimation is improved. The present invention provides an adaptive sliding mode observation method based on a variable boundary layer under a low carrier ratio.

[0005] The present 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 accurate discrete sliding mode observer: The accurate discrete sliding mode observer builds a sliding mode observer based on the accurate discretization model of PMSM, and replaces the sign function with a saturation function;

[0008] Parameter adjustment: According to the steady-state trajectory of the current error on the sliding surface, the adaptive selection method of the sliding gain and the boundary layer thickness is obtained, so that the parameters can be changed in real time with the motor speed and switching frequency, ensuring the system stability and dynamic performance under different working conditions and reducing the steady-state error.

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

[0010] The precise discretization model of SPMSM is:

[0011]

[0012] Among them, i αβ 、u αβ 、e αβ are the current, voltage and back EMF components of the two-phase stationary coordinate system respectively; R s is the stator resistance, L s is the stator inductance, T s is the PWM switching period, ω e is the motor electrical angular velocity.

[0013] Preferably, the SMO is designed to:

[0014]

[0015] Among them, the symbol “^” indicates that the physical quantity is an estimated quantity, k is the sliding mode gain, z αβ The saturation function control rate is:

[0016]

[0017] Where Z0 is the boundary layer width.

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

[0019] The low carrier ratio accurate discretization SMO contains two parameters, namely the observer gain k and the saturation function boundary layer width Z0. In order to force the state trajectory to move from the initial state to the sliding surface, the following two conditions need to be met at the same time:

[0020]

[0021] The a and b parameters are:

[0022]

[0023] Preferably, the parameter selection principle is: take Z0 as small as possible and k in the compromise range, that is, the online parameter adaptation method of SMO based on the saturation function is as follows:

[0024]

[0025] Among them, k z >1.

[0026] Preferably, the larger the slope k is, the better the system is at tracking dynamic responses, but the more sensitive it is to high-frequency noise interference signals. As a compromise, k is taken as a middle value within the range.

[0027] Preferably, the method eliminates the use of a low-pass filter LPF in the observation link, and directly uses the observed back EMF for phase-locked loop speed angle extraction to improve the amplitude attenuation and phase delay of the motor back EMF estimation value, thereby improving the accuracy of rotor position estimation.

[0028] The invention discloses an adaptive sliding mode observer based on a variable boundary layer under a low carrier ratio. The observer is realized based on an adaptive sliding mode observation method based on a variable boundary layer under a low carrier ratio.

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

[0030] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, an adaptive sliding mode observation method based on a variable boundary layer under a low carrier ratio is implemented.

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

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

[0033] At present, the boundary layer selection of the sliding mode observer based on the saturation function under low carrier ratio is generally determined by multiple simulations or experiments, and no effective selection method and selection criteria are given, and the workload is increased. In view of the shortcomings in the selection of sliding mode gain and boundary layer thickness parameters, the present invention uses a saturation function instead of a sign function on the basis of a low carrier ratio precise discrete sliding mode observer, and derives an adaptive selection method for sliding mode gain and boundary layer thickness, whose values ​​can change in real time with the speed and switching frequency, ensuring the system stability, dynamic performance and small steady-state error under different working conditions. In addition, since high-frequency jitter is well suppressed, the use of filters such as LPF is eliminated, the amplitude attenuation and phase delay problems of the estimated value of the motor back electromotive force are improved, and the accuracy of rotor position estimation is improved.

[0034] The invention has a simple structure and a definite parameter selection principle, which can reduce the workload caused by empirical parameter adjustment and ensure system stability, dynamic performance and small steady-state error under different working conditions. At the same time, the use of LPF is eliminated, the amplitude attenuation and phase delay problems of the motor back electromotive force estimation value are improved, and the accuracy of rotor position estimation can be further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0036] Figure 1 Shown is a block diagram of an adaptive sliding mode observer based on a variable boundary layer at a low carrier ratio of the present invention;

[0037] Figure 2 It is a schematic diagram showing the quasi-sliding mode state trajectory condition 1 of the observer of the present invention;

[0038] Figure 3 It is a schematic diagram showing the quasi-sliding mode state trajectory condition 2 of the observer of the present invention;

[0039] Figure 4 It shows the observed back-EMF waveforms of the conventional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention under the condition of the carrier ratio being 30 by using the adaptive sliding mode observer based on the variable boundary layer under the low carrier ratio of the present invention;

[0040] Figure 5It shows the observed back-EMF waveforms of the conventional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention under the condition of the carrier ratio of 12.5 by using the adaptive sliding mode observer based on the variable boundary layer under the low carrier ratio of the present invention;

[0041] Figure 6 It shows a schematic diagram of the motor angular velocity observation of the conventional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention when the carrier ratio changes from 30 to 12.5 using the adaptive sliding mode observer based on the variable boundary layer under the low carrier ratio of the present invention;

[0042] Figure 7 It shows a schematic diagram of the change of PLL observation angle error of the traditional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention when the carrier ratio changes from 30 to 12.5 using the adaptive sliding mode observer based on the variable boundary layer under low carrier ratio of the present invention. DETAILED DESCRIPTION

[0043] The present invention is described in detail below in conjunction with specific embodiments. Specific embodiment one:

[0045] The present invention adopts an adaptive sliding mode observer based on a variable boundary layer under a low carrier ratio. The method includes an accurate discrete sliding mode observer and a parameter adjustment link. The accurate discrete sliding mode observer builds a sliding mode observer based on the accurate discretization model of the permanent magnet synchronous motor, and replaces the sign function with a saturation function, which greatly reduces the system jitter while ensuring the simplicity of the observer structure. Since high-frequency jitter is well suppressed, the observation link cancels the use of filters such as LPF, and directly uses the observed back electromotive force for phase-locked loop speed angle extraction to improve the amplitude attenuation and phase delay problems of the motor back electromotive force estimate, and improve the accuracy of rotor position estimation. The parameter adjustment link 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 working conditions, and greatly reduces the workload of empirical parameter adjustment.

[0046] The parameter values ​​of the present invention can be changed in real time with the rotation speed and switching frequency, ensuring the system stability, dynamic performance and small steady-state error under different working conditions. In addition, since high-frequency jitter is well suppressed, the use of filters such as LPF is eliminated, reducing the complexity of the system. And after avoiding the use of a low-pass filter to filter the estimated back electromotive force, the amplitude attenuation and phase delay problems of the estimated value of the motor back electromotive force are improved, and the accuracy of the rotor position estimation is improved.

[0047] according to Figures 1 to 4As shown, the specific optimization technical solution adopted by the present invention to solve the above technical problems is: the present invention relates to an adaptive sliding mode observation method based on a variable boundary layer under a 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 accurate discrete sliding mode observer: The accurate discrete sliding mode observer builds a sliding mode observer based on the accurate discretization model of PMSM, and replaces the sign function with a saturation function;

[0050] Parameter adjustment: According to the steady-state trajectory of the current error on the sliding surface, the adaptive selection method of the sliding gain and the boundary layer thickness is obtained, so that the parameters can be changed in real time with the motor speed and switching frequency, ensuring the system stability and dynamic performance under different working conditions and reducing the steady-state error. Specific embodiment 2:

[0052] The difference between the second embodiment of the present application and the first embodiment is that:

[0053] A sliding mode observer is built based on the precise discretization model of PMSM, and the sign function is replaced by a saturation function, specifically:

[0054] The precise discretization model of SPMSM is:

[0055]

[0056] Among them, i αβ 、u αβ 、e αβ are the current, voltage and back EMF components of the two-phase stationary coordinate system respectively; R s is the stator resistance, L s is the stator inductance, T s is the PWM switching period, ω e is the motor electrical angular velocity. Specific embodiment three:

[0058] The difference between the third embodiment of the present application and the second embodiment is that:

[0059] Design SMO to:

[0060]

[0061] Among them, the symbol “^” indicates that the physical quantity is an estimated quantity, k is the sliding mode gain, z αβ The saturation function control rate is:

[0062]

[0063] Where Z0 is the boundary layer width. Specific embodiment four:

[0065] The difference between the fourth embodiment of the present application and the third embodiment is that:

[0066] According to the steady-state trajectory of the current error on the sliding surface, the adaptive selection method of the sliding gain and the boundary layer thickness is obtained to achieve real-time changes of the parameters with the motor speed and switching frequency. Specifically:

[0067] The low carrier ratio accurate discretization SMO contains two parameters, namely the observer gain k and the saturation function boundary layer width Z0. In order to force the state trajectory to move from the initial state to the sliding surface, the following two conditions need to be met at the same time:

[0068]

[0069] The a and b parameters are:

[0070] Specific embodiment five:

[0072] The difference between the fifth embodiment of the present invention and the fourth embodiment is that:

[0073] The principle of parameter selection is: take Z0 as small as possible and k in the compromise range, that is, the online parameter adaptation method of SMO based on the saturation function is as follows:

[0074]

[0075] Among them, k z >1. Specific embodiment six:

[0077] The difference between the sixth embodiment of the present invention and the fifth embodiment is that:

[0078] The larger the slope k is, the better the system tracks dynamic responses, but the more sensitive it is to high-frequency noise interference signals. As a compromise, k is taken as a middle value within the range. Specific embodiment seven:

[0080] The difference between the seventh embodiment of the present invention and the sixth embodiment is that:

[0081] The method eliminates the use of a low-pass filter LPF in the observation link, and directly uses the observed back electromotive force for phase-locked loop speed angle extraction, so as to improve the amplitude attenuation and phase delay of the motor back electromotive force estimation value, thereby improving the accuracy of rotor position estimation. Specific embodiment eight:

[0083] The difference between the eighth embodiment of the present invention and the seventh embodiment is that:

[0084] The invention provides an adaptive sliding mode observer based on a variable boundary layer under a low carrier ratio. The observer is realized based on an adaptive sliding mode observation method based on a variable boundary layer under a low carrier ratio. Specific embodiment nine:

[0086] The difference between the ninth embodiment of the present invention and the eighth embodiment is that:

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

[0089] The difference between the tenth embodiment of the present invention and the ninth embodiment is that:

[0090] The present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, an adaptive sliding mode observation method based on a variable boundary layer under a low carrier ratio is implemented. Specific embodiment eleven:

[0092] The difference between the eleventh embodiment of the present invention and the tenth embodiment is that:

[0093] Figure 1 This is an implementation mode of the present invention: the method includes an accurate discrete sliding mode observer and a parameter adjustment link. The accurate discrete sliding mode observer builds a sliding mode observer based on the accurate discretization model of the permanent magnet synchronous motor, and replaces the sign function with a saturation function, which greatly reduces the system jitter while ensuring the simplicity of the observer structure. Since high-frequency jitter is well suppressed, the observation link cancels the use of filters such as LPF, and directly uses the observed back EMF for phase-locked loop speed angle extraction to improve the amplitude attenuation and phase delay problems of the motor back EMF estimate and improve the accuracy of rotor position estimation. The parameter adjustment link 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 working conditions.

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

[0095] The precise discretization model of SPMSM is:

[0096]

[0097] Where i αβ 、u αβ 、e αβ They are the current, voltage and back EMF components of the two-phase stationary coordinate system respectively. s is the stator resistance, L s is the stator inductance, Ts is the PWM switching period, ω e is the motor electrical angular velocity.

[0098] Design SMO to:

[0099]

[0100] The symbol “^” indicates that the physical quantity is an estimated quantity, k is the sliding mode gain, z αβ is the saturation function control rate, and its expression is as follows:

[0101]

[0102] Its essence is to establish a buffer boundary layer, use linear control inside the boundary layer, and use switch discontinuous control outside the boundary layer.

[0103] The sliding surface is:

[0104]

[0105] The current error equation is:

[0106]

[0107] The precise discrete SMO contains two parameters, namely the observer gain k and the saturation function boundary layer width Z0, which are crucial to the performance of the observer. If the parameters are selected appropriately, the observer will exhibit quasi-sliding mode behavior after a finite time step. In order to force the state trajectory to move from the initial state to the sliding surface, the following two conditions need to be met at the same time, as shown in the schematic diagrams. Figure 2 and Figure 3 shown.

[0108] State trajectory condition 1: If Figure 2 As shown in Figure 2, 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, there should be S αβ (k+1) αβ (k)

[0110] but:

[0111]

[0112] Right now:

[0113]

[0114] Because S αβ (k)>Z0, so (1-a)i ～ ​αβ (k)>(1-a)Z0

[0115] Further simplification:

[0116]

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

[0118] but:

[0119]

[0120] Right now:

[0121]

[0122] Because S αβ (k)<-Z0, so -(1-a)i ～ αβ (k)>(1-a)Z0

[0123] Further simplification:

[0124]

[0125] In summary, the value range of kZ0 is:

[0126]

[0127] Because 1-a=1-exp(-R s / L s *T s )>0 always holds true, so the enhanced conditions of the above two equations are:

[0128]

[0129] Right now:

[0130] kZ0>|e αβ (k)|

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

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

[0133] but:

[0134]

[0135] Right now:

[0136]

[0137] Because S αβ (k)>Z0, so (1+a)i ～ αβ(k)>(1+a)Z0

[0138] Further simplification:

[0139]

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

[0141] but:

[0142]

[0143] Right now:

[0144]

[0145] Because S αβ (k)<-Z0, so -(1+a)i ～ αβ(k)>(1+a)Z0 can be further simplified to:

[0146]

[0147] In summary, the value range of k and Z0 is:

[0148]

[0149] Simplified to:

[0150]

[0151] The two conditions of comprehensive state trajectory condition 1 and state trajectory condition 2 are:

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

[0153]

[0154] Simplified

[0155]

[0156] Therefore, the value range of parameters k and Z0 is:

[0157]

[0158] The principle of parameter selection is: take the smallest possible Z0,

[0159] Take Z0 as:

[0160]

[0161] where k z >1.

[0162] Then the value range of k is:

[0163]

[0164] The larger the slope k, the better the system is at tracking dynamic responses, but the more sensitive it is to high-frequency noise interference signals. Therefore, k is taken as a compromise to be the middle value within the range, that is:

[0165]

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

[0167]

[0168] Figure 4 For the adaptive sliding mode observer based on variable boundary layer under low carrier ratio of the present invention, when the carrier ratio is 30, the observed back EMF waveforms of the traditional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention are shown;

[0169] Figure 5 For the adaptive sliding mode observer based on variable boundary layer under low carrier ratio of the present invention, the observed back EMF waveforms of the traditional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention are shown in the case of a carrier ratio of 12.5;

[0170] Figure 6 The motor angular velocity observations of the conventional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention are shown in the figure when the carrier ratio changes from 30 to 12.5 using the adaptive sliding mode observer based on variable boundary layer under low carrier ratio of the present invention;

[0171] Figure 7 In order to adopt the adaptive sliding mode observer based on variable boundary layer under low carrier ratio of the present invention, when the carrier ratio changes from 30 to 12.5, the PLL observation angle error changes of the traditional saturation function sliding mode (CSMO) and the sliding mode observer (ASMO) of the present invention are shown.

[0172] It can be seen from the above simulation waveforms that the adaptive sliding mode observer based on variable boundary layer under low carrier ratio of the present invention can ensure the accuracy of observing back EMF when the carrier ratio is relatively low, eliminate the use of LPF to solve the problem of back EMF amplitude attenuation and phase delay, and further improve the accuracy of rotor position estimation. And because the parameter selection principle is determined, the workload of empirical parameter adjustment is greatly reduced.

[0173] The above is only a preferred implementation of an adaptive sliding mode observation method based on a variable boundary layer under a low carrier ratio. The protection scope of an adaptive sliding mode observation method based on a variable boundary layer under a low carrier ratio is not limited to the above embodiment. All technical solutions under this idea belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, several improvements and changes without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. An adaptive sliding mode observation method based on a variable boundary layer under low carrier ratio, characterized by: The method comprises the following steps: Design of accurate discrete sliding mode observer: The accurate discrete sliding mode observer builds a sliding mode observer based on the accurate discretization model of PMSM, and replaces the sign function with a saturation function; Parameter adjustment: According to the steady-state trajectory of the current error on the sliding surface, the adaptive selection method of the sliding gain and the boundary layer thickness is obtained, so that the parameters can be changed in real time with the motor speed and switching frequency, ensuring the system stability and dynamic performance under different working conditions and reducing the steady-state error.

2. The method according to claim 1, characterized in that: A sliding mode observer is built based on the precise discretization model of PMSM, and the sign function is replaced by a saturation function, specifically: The precise discretization model of SPMSM is: Among them, i αβ 、u αβ 、e αβ are the current, voltage and back EMF components of the two-phase stationary coordinate system respectively; R s is the stator resistance, L s is the stator inductance, T s is the PWM switching period, ω e is the motor electrical angular velocity.

3. The method according to claim 2, characterized in that: Design SMO to: Among them, the symbol "^" indicates that the physical quantity is an estimated quantity, k is the sliding mode gain, z αβ The saturation function control rate is: Where Z0 is the boundary layer width.

4. The method according to claim 1, characterized in that: According to the steady-state trajectory of the current error on the sliding surface, the adaptive selection method of the sliding gain and the boundary layer thickness is obtained to achieve real-time changes of the parameters with the motor speed and switching frequency. Specifically: The low carrier ratio accurate discretization SMO contains two parameters, namely the observer gain k and the saturation function boundary layer width Z0. In order to force the state trajectory to move from the initial state to the sliding surface, the following two conditions need to be met at the same time: The a and b parameters are:

5. The method according to claim 4, characterized in that: The principle of parameter selection is: take Z0 as small as possible and k in the compromise range, that is, the online parameter adaptation method of SMO based on the saturation function is as follows: Among them, k z >1.

6. The method according to claim 4, characterized in that: The larger the slope k is, the better the system tracks dynamic responses, but the more sensitive it is to high-frequency noise interference signals. As a compromise, k is taken as a middle value within the range.

7. The method according to claim 6, characterized in that: The method eliminates the use of a low-pass filter LPF in the observation link, and directly uses the observed back electromotive force for phase-locked loop speed angle extraction, so as to improve the amplitude attenuation and phase delay of the motor back electromotive force estimation value, thereby improving the accuracy of rotor position estimation.

8. An adaptive sliding mode observer based on a variable boundary layer under low carrier ratio, characterized by: The observer is implemented based on the method described in claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the method according to claims 1-7.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method of claims 1-7 is implemented.

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