Robust dual three-phase motor dead-beat current control method

Abstract

The invention discloses a robust dual three-phase motor dead-beat current control method, and the method comprises the steps: building a dual three-phase permanent magnet synchronous motor model, and carrying out the discretization processing; extracting a plurality of groups of inductances under different complex working conditions as inductance parameters of the vertex model; deducing a corresponding adaptive law based on the convex inclusion property, and distributing the weight of each group of inductance parameters through the adaptive law; calculating through the discretized voltage equation to obtain an incremental prediction model, and performing delay compensation on the incremental prediction model; corresponding current values are obtained through the incremental prediction model subjected to delay compensation on each group of inductance parameters subjected to weight distribution; and performing weighted fusion on each group of current values. According to the method, the dual three-phase permanent magnet synchronous motor model is established, the multi-model adaptive law is introduced to distribute the weight of each vertex model, and the incremental dead-beat current control strategy is combined, so that dead-beat current control of the dual three-phase motor is realized, the robustness is good, and the performance deterioration of the motor under parameter mismatch can be effectively reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and more specifically to a robust deadbeat current control method for dual three-phase motors. Background Art

[0002] With the rapid development of electronic technology, automobiles are gradually turning to electrification and intelligence. L3 autonomous driving technology is the future development direction of automobiles, and it has higher requirements for steering control. Therefore, the steer-by-wire (SBW) system is an integral part of autonomous driving. The steering execution module of the SBW system is mainly composed of an actuator motor and a reduction mechanism. Compared with the traditional three-phase permanent magnet synchronous motor (PMSM), the dual three-phase PMSM has the advantages of low torque pulsation, high power output, high control flexibility and high fault tolerance. Dual three-phase PMSM has gradually been used in rail transit and electric vehicles, which have relatively high requirements for reliability, power level and power density. Motor control performance is particularly important for SBW systems. In order to improve the reliability and safety of SBW systems, the control method of the motor must be considered.

[0003] Deadbeat current control is a commonly used control method for permanent magnet synchronous motors. It mainly uses the current value at the current moment, combined with the motor's voltage prediction model, to predict the expected command voltage acting on the control system at the next moment, and then generates a switching signal through the PWM modulation method to pass it to the inverter to ensure that the actual output current can track the reference current without deadbeat. However, this deadbeat current control method will be affected by the motor's operating temperature and magnetic saturation factors under actual working conditions. For example, in the case of parameter mismatch, the motor control performance will deteriorate. To this end, we provide a robust deadbeat current control method for dual three-phase motors. Summary of the invention

[0004] The present invention provides a robust deadbeat current control method for dual three-phase motors, so as to solve the shortcomings of the existing deadbeat current control being affected by temperature and magnetic saturation factors, thereby affecting the control performance of the motor.

[0005] The present invention adopts the following technical solution:

[0006] A robust dual three-phase motor zero-beat current control method comprises the following steps: S1, establishing a dual three-phase permanent magnet synchronous motor model, and discretizing the dual three-phase permanent magnet synchronous motor model; S2, extracting several groups of inductances under different complex working conditions as inductance parameters of a vertex model; S3, deriving a corresponding adaptive law based on the convex inclusion property, and allocating weights of each group of inductance parameters through the adaptive law; S4, calculating an incremental prediction model through the voltage equation after the discretization process in step S1, and performing delay compensation on the incremental prediction model; S5, respectively obtaining corresponding current values ​​through the incremental prediction model after delay compensation in step S4 for each group of inductance parameters after weights are allocated in step S3; S6, weighted fusion of each group of current values ​​obtained in step S5.

[0007] The above dual three-phase permanent magnet synchronous motor model is simplified to the following formula:

[0008] In the formula, u s 、i s and ψ s They represent the motor stator voltage vector, stator current vector and stator flux vector respectively; Rs is the stator resistance; L s is the stator inductance matrix; ψ f is the permanent magnet flux amplitude; θ is the rotor electrical angle; the distribution function F(θ) is:

[0009]

[0010] The above step S1 discretizes the dual three-phase permanent magnet synchronous motor model by using the VSD method to decouple the voltage and current space vectors into three two-dimensional orthogonal subspaces. The VSD transformation matrix is ​​as follows:

[0011]

[0012] The corresponding voltage and torque equations can be simplified by the VSD matrix in (10):

[0013]

[0014] T e =3P n i q [i d (L d -L q )+ψ f ] (12)

[0015] Where L d and L q are the d-axis inductance and q-axis inductance respectively; L ls is the stator leakage inductance; P n is the extreme logarithm.

[0016] Preferably, in the above step S2, inductances under four different working conditions are extracted as inductance parameters of the vertex model.

[0017] The specific formula of the vertex model in step S2 above is as follows: Among them A s (L d , L q ) and B s (L d , L q ) is the uncertain state matrix, whose uncertainty depends on the parameter L d and L q ; The uncertainty matrix of the four sets of inductance parameters as the vertex model is expressed as: [A s (L d , L q )B s (L d , L q )]∈Co{[A i B i ]:i=1,…,4}(7), where Co{·} represents a convex inclusion of a matrix set; each vertex i∈{1,…,4} of the convex inclusion has a fixed parameter dynamic model as follows:

[0018] The above adaptive law is as follows: where w i (t) represents the weight of each vertex model at time t, satisfying: and w i (t)≥0(10).

[0019] The above step S3 introduces a linear parameter model when allocating weights, which is as follows: Where s represents the differential operator, λ is a constant design parameter; the estimation error of each vertex model is defined as: ε i (t) = z(t) - Θ i Φ(t), i = 1, ..., 4 (12); Based on the gradient descent method, the adaptive law of weight estimation is designed as:

[0020] The incremental prediction model of the dual three-phase permanent magnet synchronous motor in the above step S4 is shown as follows: After delay compensation, it is expressed as: in and represents the one-step delay compensation current at time k+1, and Represents the current measured at time k.

[0021] It can be seen from the above description of the present invention that, compared with the prior art, the present invention has the following advantages:

[0022] The present invention establishes a dual three-phase permanent magnet synchronous motor model, extracts several groups of inductances as inductance parameters of the vertex model under different complex working conditions, introduces a multi-model adaptive law to allocate the weights of each vertex model, and combines the incremental zero-beat current control strategy to achieve zero-beat current control of the dual three-phase motor. The present invention has good robustness, can effectively reduce the performance deterioration of the motor under parameter mismatch, and ensure the control performance of the motor. After testing, when the inductance of the present invention increases by 50%, the amplitude of the iq ripple current in the MM-DPCC is 1.66A, which is 22.87% lower than that of the traditional DPCC. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a block diagram of the deadbeat current control of the present invention.

[0024] Figure 2 This is a diagram showing the effect of the MM-DPCC of the present invention under parameter mismatch.

[0025] Figure 3 This is the effect diagram of PI under parameter mismatch. DETAILED DESCRIPTION

[0026] The specific implementation of the present invention is described below with reference to the accompanying drawings. In order to fully understand the present invention, many details are described below, but for those skilled in the art, the present invention can be implemented without these details. For well-known components, methods and processes, they are not described in detail below.

[0027] Reference Figure 1 , a robust dual three-phase motor deadbeat current control method provided in this embodiment includes the following steps:

[0028] 1. Establish a dual three-phase permanent magnet synchronous motor model.

[0029] By ignoring the magnetic saturation effect, mutual leakage inductance between windings and hysteresis loss, the model of the dual three-phase permanent magnet synchronous motor can be simplified as follows:

[0030]

[0031] In the formula, u s 、i s and ψ s They represent the motor stator voltage vector, stator current vector and stator flux vector respectively. Rs is the stator resistance; L s is the stator inductance matrix; ψ fis the permanent magnet flux amplitude; θ is the rotor electrical angle. Among them, the distribution function F(θ) is:

[0032]

[0033] Considering that the dual three-phase permanent magnet synchronous motor is a high-order nonlinear system, it is difficult to directly analyze and control it. Therefore, the VSD method is used to decouple its voltage and current space vectors into three two-dimensional orthogonal subspaces: α-β (torque subspace), xy (harmonic subspace) and o1-o2. The VSD transformation matrix is ​​shown as follows:

[0034]

[0035] Since a dual three-phase permanent magnet synchronous motor with an isolated neutral point is used, the corresponding voltage and torque equations can be simplified by the VSD matrix in (16):

[0036]

[0037] T e =3P n i q [i d (L d -L q )+ψ f ] (18);

[0038] Among them, L d and L q are the d-axis inductance and q-axis inductance respectively; L ls is the stator leakage inductance; P n is the extreme logarithm.

[0039] 2. Take the simplified motor model as the vertex model, as follows:

[0040]

[0041] Among them A s (L d , L q ) and B s (L d , L q ) is the uncertain state matrix, whose uncertainty depends on the parameter L d and L q .

[0042] In order to reduce the impact of inductance changes, four groups of inductance parameters (L d , L q), i = 1, 2, 3, 4 as the quadrature and direct-axis inductances of the vertex model. Therefore, the uncertainty matrix can be expressed as:

[0043] [A s (L d , L q )B s (L d , L q )]∈Co{[A i B i ]:i=1,…,4} (7)

[0044] Where CD{·} represents the convex inclusion of the matrix set. Under different working conditions, most motor inductances can be linearly represented by four vertices. For each vertex i∈{1,…,4} of the convex inclusion in equation (7), its fixed parameter dynamic model is as follows:

[0045]

[0046] 3. Based on the convex inclusion property, the corresponding adaptive law can be derived, and the weights of each group of inductance parameters can be allocated through the adaptive law.

[0047] The above formula (8) can be rewritten as:

[0048]

[0049] where w i (t) represents the weight of each vertex model at time t, satisfying:

[0050]

[0051] Since the parameter matrix A of each vertex model i , B i is known, for unknown weight w i The estimation of is equivalent to identifying the unknown matrix A s (L d , L q ) and B s (L d , L q ). For the online identification problem, a linear parameter model is introduced, and equation (9) can be rewritten as:

[0052]

[0053] Where s represents the differential operator and λ is a constant design parameter. The estimated error of each vertex model can be defined as:

[0054] ε i (t) = z(t) - Θ iΦ(t), i = 1, ..., 4 (12)

[0055] From (10), we can see that the weight of the fourth model is According to the convex property (11), we can get the following relationship:

[0056]

[0057] The above equations lay the foundation for weight adaptive identification. By moving the term on the right side of the first equation in equation (13) to the left side and multiplying both ends by We can get:

[0058]

[0059] Based on the gradient descent method, the adaptive law for weight estimation can be designed as:

[0060]

[0061] where r is a symmetric positive definite matrix used to adjust the convergence rate.

[0062] Consider a weight w that satisfies equation (15) R (t), the estimated error is Substituting it into the first equation in (15), we get At the same time, multiply r on both sides of equation (11) and combine it with equation (15) to get the following equation:

[0063]

[0064] To prove the convergence ability of the proposed adaptive law, the Lyapunov function is defined as:

[0065]

[0066] Derivative the above equation and substitute equation (16) into it:

[0067]

[0068] Although the adaptive law can ensure the convergence of deviation and satisfy But it cannot guarantee i (t)≥0, i=1,…,4. In order to ensure the two conditions in formula (12) at the same time, the gradient projection method is introduced. The constraints in formula (12) can be expressed as:

[0069]

[0070] The function g is defined as above to ensure its constraint capability, where χ = [χ1, χ2, χ3].

[0071] Will s 0 , They are defined as the interior and boundary of the set s respectively. Applying the gradient projection method, we get the following adaptive law:

[0072] like or( and ),

[0073]

[0074] otherwise,

[0075]

[0076] Fourth, by discretizing the voltage equation in equation (4), the current at time k+1 can be predicted, and by subtracting it from the current expression at time k, the incremental prediction model can be obtained:

[0077]

[0078] Considering that the digital controller has a sampling cycle delay, the incremental DPCC must perform additional current prediction to obtain the corresponding voltage reference value, which can be expressed as:

[0079]

[0080] in, and represents the one-step delay compensation current at time k+1, and represents the current measured at time k. Formula (24) can also be rewritten as:

[0081]

[0082] 5. The four groups of inductance parameters after weights are assigned in step 3 are respectively applied to the incremental prediction model after delay compensation in step 4 to obtain corresponding current values.

[0083] 6. Perform weighted fusion on the four groups of current values ​​obtained in step 5.

[0084] The following reference Figure 2 and Figure 3 This is to illustrate that the present invention can still guarantee the control performance of the motor under parameter mismatch.

[0085] Figure 2The control effect of the MM-DPCC of the present invention is shown in Figure 1: (a) and (b) respectively describe the effect of the resistance on the current when it is reduced to 0.1 times and enlarged to 10 times; (c) and (d) show the current control performance when the flux linkage is mismatched. The current control performance when the inductance is reduced by 50% is shown in (e); on the contrary, when the inductance is increased by 100%, the current control performance is shown in (f).

[0086] Figure 3 The control effect of PI is shown in Figure 1. (a) and (b) respectively describe the effect of resistance on current when it is reduced to 0.1 times and enlarged to 10 times; (c) and (d) show the current control performance when flux linkage is mismatched. The current control performance when the inductance is reduced by 50% is shown in (e); on the contrary, when the inductance is increased by 100%, the current control performance is shown in (f).

[0087] Figure 2 and Figure 3 In the figure, the cyan line represents the q-axis current reference value, and the brown line represents the d-axis current reference value. The initial state of the motor is 1500r / min speed and 5N·m load. The parameter mismatch occurs at 0.05s, and the torque suddenly rises to 50N·m at 0.1s, and then drops to 25N·m at 0.15s.

[0088] The above is only a specific implementation of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial changes to the present invention using this concept shall be deemed as an infringement of the protection scope of the present invention.

Claims

1. A robust dual three-phase motor deadbeat current control method, characterized in that: The following steps are involved: S1. Establish a dual three-phase permanent magnet synchronous motor model and discretize the dual three-phase permanent magnet synchronous motor model; S2, extracting the inductances under several groups of different complex working conditions as the inductance parameters of the vertex model; S3. Based on the convex inclusion property, the corresponding adaptive law is derived, and the weights of each group of inductance parameters are allocated through the adaptive law; S4, calculating the incremental prediction model through the voltage equation after discretization in step S1, and performing delay compensation on it; S5, respectively obtain the corresponding current value of each group of inductance parameters after the weights are assigned in step S3 through the incremental prediction model after the delay compensation in step S4; S6. Perform weighted fusion on each group of current values ​​obtained in step S5.

2. A robust dual three-phase motor deadbeat current control method as claimed in claim 1, characterized in that: The dual three-phase permanent magnet synchronous motor model is simplified to the following formula: In the formula, u s 、i s and ψ s They represent the motor stator voltage vector, stator current vector and stator flux vector respectively; Rs is the stator resistance; L s is the stator inductance matrix; ψ f is the permanent magnet flux amplitude; θ is the rotor electrical angle; the distribution function F(θ) is:

3. A robust dual three-phase motor deadbeat current control method as claimed in claim 2, characterized in that: The step S1 discretizes the dual three-phase permanent magnet synchronous motor model by using the VSD method to decouple the voltage and current space vectors into three two-dimensional orthogonal subspaces. The VSD transformation matrix is ​​as follows: The corresponding voltage and torque equations can be simplified by the VSD matrix in (4): T e =3P n and q [i d (L d -L q )+ψ f ] (6) Where L d and L q are the d-axis inductance and q-axis inductance respectively; L ls is the stator leakage inductance; P n is the extreme logarithm.

4. A robust dual three-phase motor deadbeat current control method as claimed in claim 3, characterized in that: In step S2, inductances under four different working conditions are extracted as inductance parameters of the vertex model.

5. A robust dual three-phase motor deadbeat current control method as claimed in claim 4, characterized in that: The specific formula of the vertex model in step S2 is as follows: Among them A s (L d , L q ) and B s (L d , L q ) is the uncertain state matrix, whose uncertainty depends on the parameter L d and L q ; The uncertainty matrix of the four sets of inductance parameters as the vertex model is expressed as: [A s (L d , L q )B s (L d , L q )]∈Co{[A i B i ]:i=1,…,4} (7), where CD{·} represents a convex inclusion of a matrix set; each vertex i∈{1,…,4} of the convex inclusion has a fixed parameter dynamic model as follows:

6. A robust dual three-phase motor deadbeat current control method as claimed in claim 5, characterized in that: The adaptive law is specifically as follows: where w i (t) represents the weight of each vertex model at time t, satisfying:

7. A robust dual three-phase motor deadbeat current control method as claimed in claim 6, characterized in that: The step S3 introduces a linear parameter model when allocating weights, which is as follows: Where s represents the differential operator, λ is a constant design parameter; the estimation error of each vertex model is defined as: ε i (t) = z(t) - Θ i Φ(t), i = 1, ..., 4 (12); Based on the gradient descent method, the adaptive law of weight estimation is designed as:

8. A robust dual three-phase motor deadbeat current control method as claimed in claim 1, characterized in that: The incremental prediction model of the dual three-phase permanent magnet synchronous motor in step S4 is shown in the following formula: After delay compensation, it is expressed as: in and represents the one-step delay compensation current at time k+1, and Represents the current measured at time k.

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