Permanent magnet synchronous motor sensorless control method based on parameter mismatch compensation

Abstract

The invention discloses a permanent magnet synchronous motor sensorless control method based on parameter mismatch compensation. The method comprises the following steps: firstly, analyzing the problem of parameter mismatch of a permanent magnet synchronous motor sensorless under the condition of using a non-linear flux linkage observer, after analyzing the problem of parameter mismatch of a traditional flux linkage model, compensating disturbance brought by parameter mismatch by designing an extended state observer, and then analyzing the influence of the bandwidth of the extended state observer on the observation performance; and completing the whole permanent magnet synchronous motor sensorless control based on parameter mismatch compensation. According to the invention, the structure complexity of the control system is effectively reduced, the hardware cost is reduced, and the system robustness is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of motor drive control, and more particularly to a sensorless control method for a permanent magnet synchronous motor with parameter mismatch compensation. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are used in many applications, including electric vehicles, aircraft, nuclear power plants, submarines, robotic applications, medical, and industrial servo drives. Vector control of PMSM drives requires rotor position / speed and phase current. Rotor position / speed sensors used to control PMSM drives increase size and cost, reduce reliability, and require shaft extensions and mounting. To overcome these drawbacks, sensorless control is a useful solution that provides higher reliability without expensive and bulky mechanical sensors. Several methods for sensorless speed control of permanent magnet synchronous motors have been studied and applied to sensorless speed control of permanent magnet synchronous motors.

[0003] Traditional non-linear flux models have good stability but are very sensitive to uncertainties in the flux and resistance. Online adaptation of these parameters should be considered. Since the uncertain parameters enter the observer multiplicatively, this poses a challenging non-linear parametric adaptation problem.

[0004] Researching a sensorless control algorithm for a high-performance non-linear flux model is not only beneficial for simplifying the system structure and reducing hardware costs, but also for eliminating problems such as sensor cable breakage and poor interface contact, and improving system robustness. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides a sensorless control method for a permanent magnet synchronous motor based on parameter mismatch compensation, which improves the rotor position observation accuracy and the dynamic response speed of the drive system.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention proposes a sensorless control method for a permanent magnet synchronous motor based on parameter mismatch compensation, the method comprising the following steps:

[0008] S1: Analyze the problem of parameter mismatch of the sensorless permanent magnet synchronous motor using a non-linear flux observer.

[0009] S2: Compensate for the disturbance caused by parameter mismatch by designing an extended state observer.

[0010] S3: Analyze the influence of the designed extended state observer bandwidth on the observation performance.

[0011] S4: Compensate the original magnetic flux with the observed disturbance of the extended observer.

[0012] Furthermore, in step S1, the sensorless model of the permanent magnet synchronous motor using the non-linear magnetic flux observer is:

[0013] First, the stator voltage equation of the permanent magnet synchronous motor in the αβ coordinate system is:

[0014]

[0015] where v α and v β are the stator voltages of the motor in the αβ coordinate system, i α and i β are the stator currents of the motor in the αβ coordinate system, R s is the stator resistance, L d and L q are the inductance values of the motor in the dq coordinate system, ω r is the rotor electrical angular velocity, ψ f is the permanent magnet flux linkage, L0 = (L d + L q ) / 2, L1 = (L d - L q ) / 2.

[0016] Transform it into the following form

[0017]

[0018] where, L Σ = 2L0, L Δ = 2L1, e α = -ψ f ω r sin(θ r ), e β = ψ f ω r cos(θ r ).

[0019] Further transform it into:

[0020]

[0021] where

[0022]

[0023] i αβ = [i α i β T , v αβ = [v α v​β T 。

[0024] The inductance matrix of the above equation can be written in the following form:

[0025]

[0026] The stator flux linkage of the IPMSM can be written in the following form:

[0027]

[0028] By taking the derivative of the above equation, we get:

[0029]

[0030] The form of the non - linear flux observer is:

[0031]

[0032] where, is the observed value of the stator flux linkage, γ is the observer gain, and ||·|| is the Euclidean norm.

[0033] When there is a parameter mismatch, we have: Substituting it into the observer, we get:

[0034]

[0035] Further transformation gives:

[0036]

[0037] d is an additional disturbance term caused by the parameter mismatch.

[0038] Furthermore, in S2, by designing an extended observer to estimate the additional disturbance caused by the parameter mismatch, the flux observer is arranged as:

[0039]

[0040] where,

[0041] Based on this model, combined with the extended state observer, the error feedback equation with ψ s and d as state variables is as follows:

[0042]

[0043] where, β1 and β2 are the observer error feedback gains.

[0044] ​Further, in S3, the observer error feedback gains β1 and β2 are designed. The observer can be rewritten in the following form:

[0045]

[0046] where C = [1 0], The observer characteristic equation can be expressed as:

[0047] |sI - (A - DC)| = s 2 + β1s + β2

[0048] where I is the identity matrix. To make the roots of the characteristic equation all fall at -ω0, β1 and β2 are obtained as:

[0049] β1 = 2ω0

[0050]

[0051] ω0 is the bandwidth of the ESO, which determines the steady-state and dynamic performance of the observer. Directly designing an appropriate ω0 is not intuitive. In this design, the design of ω0 will be carried out in the z-domain. Discretizing the observer gives:

[0052]

[0053] where β 01 = T sc β1 and β 02 = T sc β2. The values of β 01 and β 02 affect the distribution of the system closed-loop poles, thus affecting the stability of the observer. Therefore, reasonable values of β 01 and β 02 must be selected to ensure the stability of the system and ensure that the controller achieves good control performance.

[0054] The transfer function of the ESO can be expressed as:

[0055]

[0056] Its characteristic equation:

[0057] z 2 +(β 01 - 2)z + 1 - β 01 + β 02 t sc = 0

[0058] Considering β 01 = 2ω0t sc and The poles of G(z) are solved as:

[0059] z 1,2 = 1 - ω0t sc

[0060] ω0 can be calculated from the z-domain poles as follows:

[0061]

[0062] ω0 is selected such that z 1,2 is inside the unit circle in the z-domain. Generally, if ω0 is too small (z 1,2 is close to 1), the dynamic performance of the observer will deteriorate. If ω0 is too large (z 1,2 is close to 0), it will affect the robustness of the system and may cause the system to diverge. Therefore, in the present invention, in order to achieve fast response, z 1,2 is set to 0.15. When the sampling frequency is 10 kHz, the corresponding ω0 is 8500.

[0063] Furthermore, in S4, the lumped disturbance observed in S2 is brought into the original non-linear flux linkage equation, and a non-linear flux linkage observer capable of handling parameter mismatches can be obtained:

[0064]

[0065] The observed flux linkage is obtained, and then the effective flux linkage is calculated:

[0066]

[0067] Finally, the rotor angle is obtained by taking the arctangent of the effective flux linkage, and the rotational speed is obtained by differentiating the rotor angle:

[0068]

[0069] The beneficial effects of the present invention are:

[0070] 1. The positionless control proposed by the present invention through the non-linear flux linkage model simplifies the system structure and improves the dynamic response performance.

[0071] 2. The flux linkage model with parameter mismatch compensation proposed by the present invention improves the robustness of the system and can adapt to more extreme and harsh environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 is the flowchart of the sensorless control based on the non-linear flux linkage model with parameter mismatch compensation.

[0073] Figure 2 is the structural diagram of the sensorless control based on the non-linear flux linkage model with parameter mismatch compensation.

[0074] Figure 3 It is the simulation diagram of the observed angle error when there is resistance mismatch.

[0075] Figure 4 It is the simulation diagram of the observed angle error when there is q-axis inductance mismatch.

[0076] Figure 5 It is the simulation diagram of the observed angle error when there is rotor flux linkage mismatch.

[0077] Figure 6 It is the simulation diagram of the observed angle error when compensating for resistance mismatch.

[0078] Figure 7 It is the simulation diagram of the observed angle error when compensating for q-axis inductance mismatch.

[0079] Figure 8 It is the simulation diagram of the observed angle error when compensating for rotor flux linkage mismatch. Specific implementation plan

[0080] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0081] Example 1

[0082] Figure 1 It is the control flow chart of sensorless control of a permanent magnet synchronous motor based on a nonlinear flux linkage model with parameter mismatch compensation. Figure 2 It is the control structure diagram of sensorless control of a permanent magnet synchronous motor based on a nonlinear flux linkage model with parameter mismatch compensation. This example proposes a sensorless control method, and the method includes the following steps:

[0083] S1: Analyze the problem of parameter mismatch of sensorless permanent magnet synchronous motor using a nonlinear flux linkage observer.

[0084] S2: Compensate for the disturbance caused by parameter mismatch by designing an extended state observer.

[0085] S3: Analyze the influence of the designed extended state observer bandwidth on the observation performance.

[0086] S4: Compensate the original flux linkage with the observed disturbance of the extended observer.

[0087] I. Establishment of a traditional nonlinear flux linkage model with parameter mismatch

[0088] First, the stator voltage equation of a permanent magnet synchronous motor in the αβ coordinate system is:

[0089]

[0090] Among them, v α and v β are the stator voltages of the motor in the αβ coordinate system, iα and \(i\) β are the stator currents of the motor in the αβ coordinate system, \(R\) s is the stator resistance, \(L\) d and \(L\) q are the inductance values of the motor in the dq coordinate system, \(\omega\) r is the rotor electrical angular velocity, \(\psi\) f is the permanent magnet flux linkage, \(L_0=(L\) d + \(L\) q ) / 2, \(L_1=(L\) d - \(L\) q ) / 2.

[0091] The stator flux linkage of the IPMSM can be written in the following form:

[0092]

[0093] By taking the derivative of the above equation, we get:

[0094]

[0095] The form of the nonlinear flux observer is:

[0096]

[0097] where, is the observed value of the stator flux linkage, \(\gamma\) is the observer gain, and \(\|\cdot\|\) is the Euclidean norm.

[0098] When there is a parameter mismatch, we have: Substituting into the observer, we get:

[0099]

[0100] Further transformation gives:

[0101]

[0102] d is the additional disturbance term caused by the parameter mismatch.

[0103] Figure 3 、 Figure 4 and Figure 5 are the observed rotor angle results under resistance mismatch, inductance mismatch, and flux linkage mismatch respectively. It can be seen that there are relatively large errors in the observed angles in both cases. This shows that the influence caused by the parameter mismatch conforms to the principle described above and will bring errors to the angle observation.

[0104] II. Principle of observing parameter mismatch disturbance by the extended state observer

[0105] Rearranging the flux observer gives:

[0106]

[0107] Among them,

[0108] Based on this model, combined with an extended state observer, taking ψ s and d as state variables, the error feedback equation is as follows:

[0109]

[0110] Among them, β1 and β2 are the observer error feedback gains.

[0111] The observer can be rewritten in the following form:

[0112]

[0113] C = [1 0], The observer characteristic equation can be expressed as:

[0114] |sI - (A - DC)| = s 2 + β1s + β2

[0115] Among them, I is the identity matrix. In order to make the roots of the characteristic equation all fall at -ω0, β1 and β2 are obtained as:

[0116] β1 = 2ω0

[0117]

[0118] ω0 is the bandwidth of the ESO, which determines the steady-state and dynamic performance of the observer. Directly designing an appropriate ω0 is not intuitive. In this design, the design of ω0 will be carried out in the z-domain. Discretizing the observer gives:

[0119]

[0120] Among them, β 01 = T sc β1 and β 02 = T sc β2. β 01 and β 02 The values of affect the distribution of the closed-loop poles of the system, thus affecting the stability of the observer. Therefore, reasonable values of β 01 and β 02 must be selected to ensure the stability of the system and ensure that the controller achieves good control performance.

[0121] The transfer function of the ESO can be expressed as:

[0122]

[0123] Its characteristic equation:

[0124] z 2 +(β 01 - 2)z + 1 - β 01 +β 02 t sc =0

[0125] Considering β 01 =2ω0t sc and The poles of G(z) are solved as:

[0126] z 1,2 =1 - ω0t sc

[0127] ω0 can be calculated from the z - domain poles as:

[0128]

[0129] III. Compensate the error of the original flux - linkage model according to the observed disturbance

[0130] Bringing the lumped disturbance obtained by observation into the original non - linear flux - linkage equation, a non - linear flux - linkage observer capable of handling parameter mismatch can be obtained:

[0131]

[0132] Obtain the observed flux - linkage, and then calculate the effective flux - linkage:

[0133]

[0134] Finally, use the arctangent of the effective flux - linkage to obtain the rotor angle, and the differential of the rotor angle to obtain the rotational speed:

[0135]

[0136] In the embodiment of the present invention, a position - less control method for a permanent - magnet synchronous motor based on parameter - mismatch compensation is used, and the stability of rotor - angle observation and the simplification of the control structure are improved by using the proposed method. Figure 6 、 Figure 7 and Figure 8 are the effect diagrams of angle observation after disturbance compensation. Comparing with Figure 3 、 Figure 4 and Figure 5 the uncompensated angle observation, it can be seen that the angle error decreases after disturbance compensation.

Claims

1. A sensorless control method for a permanent magnet synchronous motor based on parameter mismatch compensation, comprising the following steps: S1: Analyze the problem of parameter mismatch of the sensorless permanent magnet synchronous motor using a nonlinear flux observer. S2: Compensate the disturbance caused by parameter mismatch by designing an extended state observer. S3: Analyze the influence of the designed bandwidth of the extended state observer on the observation performance. S4: Compensate the original flux with the observed disturbance of the extended observer.

2. The control method according to claim 1, wherein In step S1, analyze the problem of parameter mismatch of the sensorless permanent magnet synchronous motor using a nonlinear flux observer: First, the stator voltage equation of the permanent magnet synchronous motor in the αβ coordinate system is: where v α and v β are the stator voltages of the motor in the αβ coordinate system, i α and i β are the stator currents of the motor in the αβ coordinate system, R s is the stator resistance, L d and L q are the inductance values of the motor in the dq coordinate system, ω r is the rotor electrical angular velocity, ψ f is the permanent magnet flux linkage, L0 = (L d + L q ) / 2, L1 = (L d - L q ) / 2. Transform it into the following form where L Σ = 2L0, L Δ = 2L1, e α = -ψ f ω r sin(θ r ), e β = ψ f ω r cos(θ r ). Further transform it into: Among them i αβ = [i α i β ᵀ, v αβ = [v α v β T .​ The inductance matrix of the above equation can be written in the following form: The stator flux of the IPMSM can be written in the following form: By taking the derivative of the above equation, we get: The form of the nonlinear flux observer is: wherein, is the stator flux observer value, γ is the observer gain, and ||·|| is the Euclidean norm. When there is a parameter mismatch, there is: Substituting into the observer gives: Further transform to get: d is an additional disturbance term caused by parameter mismatch.

3. The control method according to claim 1, characterized in that In step S2, estimate the additional disturbance caused by parameter mismatch by designing an extended observer, and organize the flux observer as: Among them, Based on this model, combined with an extended state observer, with ψ s and d as state variables, the error feedback equation is as follows: wherein, β1 and β2 are observer error feedback gains.

4. The control method according to claim 1, characterized in that, In step S3, design the observer error feedback gains β1 and β2. The observer can be rewritten in the following form: Among them C = [1 0], The observer characteristic equation can be expressed as: |sI-(A-DC)| = s 2 +β1s + β2 Where I is the identity matrix. To make the roots of the characteristic equation all fall at -ω0, we get β1 and β2 as: β1 = 2ω0 ω0 is the bandwidth of the ESO, which determines the steady-state and dynamic performance of the observer. Directly designing a suitable ω0 is not intuitive. In this design, the design of ω0 will be carried out in the z domain. Discretize the observer to get: Among them, β 01 = T sc β1 and β 02 = T sc β2. β 01 and β 02 The values of affect the distribution of the system closed-loop poles, thereby affecting the stability of the observer. Therefore, reasonable values of β 01 and β 02 must be selected to ensure the stability of the system and ensure that the controller achieves good control performance. The transfer function of the ESO can be expressed as: Its characteristic equation: z 2 +(β 01 -2)z + 1 - β 01 +β 02 t sc =0 Consider β 01 = 2ω0t sc and The poles of G(z) are solved as follows: z 1,2 = 1 - ω0t sc ω0 can be calculated from the z-domain poles as: The selection of ω0 makes z 1,2 inside the unit circle in the z-domain. Generally, if ω0 is too small (z 1,2 close to 1), the dynamic performance of the observer will deteriorate. If ω0 is too large (z 1,2 close to 0), it will affect the robustness of the system and may cause the system to diverge. Therefore, in the present invention, in order to achieve fast response, z 1,2 is set to 0.

15. When the sampling frequency is 10 kHz, the corresponding ω0 is 8500.

5. The control method according to claim 1, characterized in that In step S4, substitute the lumped disturbance observed in S2 into the original nonlinear flux equation to obtain a nonlinear flux observer capable of handling parameter mismatch: Obtain the observed flux, and then calculate the effective flux: Finally, use the arctangent of the effective flux to obtain the rotor angle, and differentiate the rotor angle to obtain the speed:

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