Mtpa control method for permanent magnet synchronous motor based on double virtual direct current signal injection

Abstract

The application discloses a permanent magnet synchronous motor MTPA control method based on double virtual direct current signal injection, and particularly relates to a motor control method, in particular to a control method of a permanent magnet synchronous motor under a high-speed low-carrier ratio working condition. β A pair of virtual direct current signals with the same amplitude and opposite polarity are injected into a current vector angle, an electromagnetic torque containing the pair of signals is Taylor expanded, subtraction operation is performed on the two to obtain an approximate value of a first-order partial derivative of the torque to the current vector angle, the approximate value is input into an integral regulator, and when the input is controlled to be 0, an optimal current vector angle can be obtained β mtpa , and MTPA control is realized. In order to simultaneously improve dynamic performance and steady-state performance of the control, the method selects virtual direct current signals with different amplitudes to be injected under different working conditions, so that the motor can quickly approach an optimal current vector angle working state, and fluctuation of the current vector angle under a stable state is reduced.

Description

Technical Field

[0001] This invention relates to the field of motor control, and in particular to control strategies for built-in permanent magnet synchronous motors. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are characterized by high power density and high power factor. Based on their structure, they can be divided into surface-mounted PMSMs and internally mounted PMSMs. The latter embeds the permanent magnets inside the rotor, resulting in unequal direct-axis and quadrature-axis inductances. Therefore, internally mounted PMSMs contain a reluctance torque component. Maximum torque-to-current ratio control maximizes the combined output torque of the reluctance torque and electromagnetic torque under constant current conditions, and is a commonly used control strategy.

[0003] Due to the influence of temperature, magnetic saturation, and salient pole effects, the optimal current vector angle varies with the load. Methods for determining the optimal current vector angle in MTPA control are currently divided into offline and online identification methods. Offline identification involves obtaining parameters of the motor under different operating conditions through numerous experiments, and then creating tables of this data for later lookup. However, this table lookup method requires significant time for preliminary experiments and lacks universality across different motors. Online identification methods include model reference adaptation, sliding mode observers, and extended Kalman oscillators, which significantly reduce the workload at each stage compared to offline identification. However, these methods are theoretically complex, computationally intensive, and place high demands on the controller's performance. In recent years, signal injection methods for MTPA have received widespread attention from researchers. By injecting actual high-frequency signals, the difference between the ideal and actual current angles can be extracted. However, this method increases unnecessary power losses and torque ripple in the motor. Virtual signal injection methods, on the other hand, do not rely on the actual power response and therefore do not inject actual current signals, obtaining the optimal current vector angle solely from a computational perspective. Virtual signals can generally be selected from high-frequency sine waves, high-frequency square waves, and DC signals. Injecting a high-frequency sine wave requires passing it through a bandpass filter and a low-pass filter to extract the effective signal, inevitably leading to recognition lag. High-frequency square waves offer a better bandwidth, but the approximation process involves high-frequency oscillations. Compared to the former two, the traditional virtual DC signal injection method (hereinafter referred to as VDSIC) has better overall control performance, but its performance deteriorates with increasing load. To improve this issue, this application proposes a bipolar virtual DC signal injection method (hereinafter referred to as DVDSIC), which simultaneously injects both positive and negative virtual DC signals. The difference between these signals is used to obtain the final optimal current vector angle through PI control. Summary of the Invention

[0004] The purpose of this application is to propose a dual-virtual DC signal injection MTPA control method for built-in permanent magnet synchronous motors. This method is applicable to a wider range of operating conditions and is less affected by load changes compared to traditional virtual DC signal injection methods. The specific scheme is as follows:

[0005] Injecting a pair of DC signals d1(t)=A and d2(t)=-A of opposite polarity into the stator current vector angle can effectively reduce β under all loads. mtpa This reduces fluctuations in dq current and output torque, thus lowering dq current and output torque ripple. Furthermore, DVDSIC offers advantages over VDSIC in... / Fewer higher-order components are ignored during the extraction process, resulting in higher control precision. Details are as follows:

[0006] First, establish the stator voltage equation in the dq coordinate system of the built-in permanent magnet synchronous motor:

[0007] ;

[0008] In the formula, u d u q For the dq-axis components of the stator voltage; i d i q L represents the dq-axis component of the stator current. d L q For direct-axis and quadrature-axis inductors; Ψ f For permanent magnet flux linkage; ω e ω is the electric angular velocity.

[0009] The torque equation of the motor is:

[0010] ;

[0011] After the motor reaches a steady state, i d and i q The differential term L in the stator voltage equation (1) above will not change over time. d (di d / dt) and L q (di q The terms / dt can be ignored, and the steady-state stator voltage equation can be rewritten for parameter decoupling:

[0012] ;

[0013] Substituting (3) into (1) yields:

[0014] ;

[0015] The relationship between the current vector, the dq-axis components of the stator current, and the current vector angle β is as follows:

[0016] ;

[0017] By injecting both positive and negative DC signals into the current vector angle through mathematical operations, the current containing the DC signal is represented as:

[0018] ;

[0019] Taking the injected DC signal A as an example, the electromagnetic torque T containing the injected signal is obtained. e d (β+A):

[0020] ;

[0021] In the formula i d (β+A), i q (β+A) is the dq-axis current after injecting a DC signal into the stator current vector angle β, i d i q This represents the actual dq-axis current.

[0022] T e d (β+A) can be obtained by Taylor expansion at β:

[0023] ;

[0024] Similarly, for T e d (β-A):

[0025] ;

[0026] Since the amplitude A of the injected DC signal is much less than 1 and its value is small, the odd-order terms of A are extremely small and can be ignored. Subtracting equation (9) from equation (8) yields:

[0027] ;

[0028] Introducing the current vector angle (denoted as β) used to calculate the output current vector angle of the DVDSIC algorithm. do The parameter σ d :

[0029] ;

[0030] DVDSIC controls As it continuously approaches 0, β can be made do Continuously approaching the optimal β mtpa β is expressed in integral form. do We can obtain:

[0031] ;

[0032] Where k ’ The integral coefficient is σ. d Due to the proportionality of A, theoretically, the smaller the amplitude A of the injected signal in the algorithm, the better the control effect. However, a smaller A will cause the algorithm to converge slowly. Therefore, a variable amplitude dual virtual signal algorithm is used to balance steady-state performance and dynamic performance, so that the amplitude of the injected signal A is controllable.

[0033] Compared with the traditional VDSIC method, the DVDSIC proposed in this application has smaller tracking error and higher control accuracy when tracking the MTPA point. Furthermore, the algorithm has a simple structure, low computational cost, and achieves a higher β value when tracking the MTPA point under heavy load. mtpa The fluctuations are smaller. Attached Figure Description

[0034] Figure 1 MTPA curve;

[0035] Figure 2 : Block diagram of dual virtual DC signal injection MTPA control;

[0036] Figure 3 : Amplitude-variable DVDSIC algorithm block diagram;

[0037] Figure 4 : Relationship between VDSIC torque and current vector angle under multiple load conditions;

[0038] Figure 5 : Relationship between DVDSIC torque and current vector angle under multiple load conditions;

[0039] Figure 6 : 5Nm load VDSIC and DVDSIC current and β m Simulation results;

[0040] Figure 7 : 10Nm load VDSIC and DVDSIC current and β m Simulation results;

[0041] Figure 8 DVDSIC simulation results of amplitude variation when the load increases from 5Nm to 10Nm. Detailed Implementation

[0042] like Figure 1 As shown, when the built-in permanent magnet synchronous motor outputs constant torque, the corresponding input current has a minimum value. The current vector angle corresponding to this minimum value is the optimal current vector angle, i.e., β. mtpa The embodiment aims to identify β using a dual virtual signal injection method. mtpaThis enables MTPA control, and the control flowchart and schematic diagram are as follows: Figure 2 , Figure 3 As shown below. The specific implementation method is as follows.

[0043] After Clark and Park transformations, the three phases abc of a permanent magnet synchronous motor will yield the following voltage equations:

[0044] ;

[0045] The torque equation of the motor is:

[0046] ;

[0047] The relationship between the current vector, the dq-axis components of the stator current, and the current vector angle β is as follows:

[0048] ;

[0049] Where ω e R is the electric angular velocity; s The stator resistance is L; the right-angle inductors are respectively represented by L. d and L q Indicates; Ψ f It is a permanent magnet flux linkage. Ψ can be... f Write about i d i q The function compensates for the effects of load, temperature, and other factors on Ψ in actual situations. f The influence of the differential term L when the motor reaches steady state. d (di d / dt) and L q (di q The two terms / dt) can be ignored, therefore Ψ f and i d i q The relationship can be represented as follows:

[0050] ;

[0051] Injecting small-amplitude virtual DC signals d1(t)=A and d2(t)=﹣A with opposite polarities into the current vector angle β yields two virtual current signals:

[0052] ;

[0053] Obtain the electromagnetic torque T including the injected DC signal e d (β+A) and T e d (β-A):

[0054] ;

[0055] Further obtain T e d (β+A) and T e d Taylor expansion of (β-A):

[0056] ;

[0057] Subtraction yields the following result:

[0058] ;

[0059] Introducing the current vector angle β (denoted as β) used to calculate the output current vector angle of the DVDSIC algorithm. do The parameter σ d :

[0060] ;

[0061] DVDSIC controls As it continuously approaches 0, β can be made do Continuously approaching the optimal β mtpa β is expressed in integral form. do We can obtain:

[0062] ;

[0063] Where k ’ is the integral coefficient.

[0064] like Figure 4 As shown, let β mtpa For β m .when When T is negative, e (β) monotonically decreasing, β>β m At this point, the value of β should be decreased to approach β. m ;when When T is positive, e (β) monotonically increasing, β < β m At this point, the value of β should be increased to approach β. m Based on the above characteristics, when the obtained signal σ d The current vector angle β is obtained by inputting it into the integral regulator. do When the output value of the differential controller remains essentially unchanged, it indicates that the input value approaches 0, thus indicating that σ... d When it approaches 0, the β obtained is... do It can be regarded as and β m Approximately equal. β will be updated in real time. doSubstituting the value into equation (3), we obtain the reference current for the dq axis and complete the control closed loop.

[0065] Because of T e d (β+A) and T e d (β-A) cannot be equal in a mathematical sense, σ d In reality, it's an approximation of the difference between the two. Therefore, the signal input to the integral regulator is always changing and not zero, which also leads to the identified β... m Fluctuations exist. A comparative analysis of the fluctuations generated when the VDSIC and DVDSIC algorithms reach steady state is shown in the following formula:

[0066] ;

[0067] Introducing the parameter σ used to calculate the current vector angle β output by the VDSIC algorithm, which is numerically similar to... Equal to the parameter σ used to calculate the current vector angle β output by the DVDSIC algorithm. d Numerically and Equal. By Figure 5 It can be seen , Much larger After the control system reaches steady state, the fluctuation of σ in VDSIC is much greater than that in DVDSIC. d The fluctuation amount, DVDSIC for σ d β after integration do The fluctuation value is naturally smaller. This suppression of fluctuation is particularly noticeable under heavy load conditions, as explained in the previous section. When the motor operates under a large load, T... e The characteristic of (β) as a convex function is amplified, that is, in (0,β) m ) and (β) m , Two intervals T e The slope of (β) will increase accordingly, when the amplitude of the injected signal A remains constant. There will be an increase, and and The values ​​are similar under any load. It remains largely unchanged with load variations, making DVDSIC more adaptable to high-load conditions.

[0068] According to σ dDue to the proportionality of A, theoretically, a smaller injected signal amplitude A in the algorithm results in better control. However, a smaller A leads to slower convergence and a longer time for the system to reach steady state. Therefore, a variable amplitude dual virtual signal algorithm is used to balance steady-state and dynamic performance, making the amplitude of the injected signal A controllable. Based on the motor model used in the simulation section of this application, a dual virtual DC signal with an amplitude of A = 0.05 rad is injected when the DVDSIC control algorithm starts, and β... do Rapidly approaching β m When the motor reaches near the MTPA operating point, simulations show that β is the maximum load steady-state value of the motor under DVDSIC control. m Fluctuation θ steady Less than 1°, therefore when When the angle is less than 1°, the control system has entered a steady state. At this point, the primary objective of the control algorithm is to reduce β. m To mitigate fluctuations, the amplitude A of the injected signal was changed from 0.05 rad to 0.005 rad, thereby further reducing β while maintaining the dynamic performance of the control system. m Fluctuations improve control stability. When the load changes, β... m It will track new real beta m This results in a significant change, at which point the control algorithm detects β. m Change When the angle exceeds 1°, the injected signal amplitude A is changed from 0.005 rad to 0.05 rad to quickly track the MTPA operating point under the new load, thus completing the control flow of variable amplitude DVDSIC. The method for determining the value of A is shown in the table below:

[0069] ;

[0070] Finally, to verify the method proposed in this application, a simulation based on the IPMSM model was built. The parameters of the motor used in the simulation are listed in Table 2:

[0071] ;

[0072] Figure 6 The β derived from DVDSIC compared to VDSIC m The angle was increased from 94.2° to 94.4°, improving control precision, while β... m The volatility decreased from 0.9° to 0.5°, a decrease of 0.4°, and with β... m The volatility has decreased. Figure 7 DVDSIC i d The volatility decreased from 0.69A to 0.62A. Figure 6 in i qThe fluctuation decreased from 0.43A to 0.42A, demonstrating that DVDSIC can suppress β. m Fluctuations, thereby reducing current and output torque fluctuations.

[0073] Next, under the given speed of 1000 r / min and a heavy load of 10 Nm, the VDSIC algorithm was used within 0-1 s, and the DVDSIC algorithm was switched after 1 s to obtain β. m The results of the current simulation are as follows Figure 5 As shown.

[0074] Figure 4-7 The β derived from DVDSIC compared to VDSIC m The angle was increased from 98.05° to 98.5°, improving control precision, while β... m The volatility decreased significantly from 1.2° to 0.6°, and this decrease was further reduced with β. m The fluctuation amount decreased, and the i of DVDSIC d The volatility decreased from 0.86A to 0.69A, i q The current fluctuation decreased from 0.5A to 0.47A, a significant reduction compared to the smaller load of 5Nm. Figure 4-6 As a result, DVDSIC suppresses β under heavy load. m The effects of fluctuations and current fluctuations are more pronounced.

[0075] Meanwhile, VDSIC increases β from a smaller load of 5 Nm to a larger load of 10 Nm. m The fluctuation increased from 0.9° to 1.2°, an increase of 0.3°; d The volatility increased from 0.69A to 0.86A, an increase of 0.17A; q The volatility increased from 0.43A to 0.5A, an increase of 0.07A, β m Fluctuations in both current and frequency increase significantly with increasing load. DVDSIC's β... m The fluctuation increased from 0.5° to 0.6°, an improvement of only 0.1°; d The volatility increased from 0.62A to 0.69A, an increase of only 0.07A; q The fluctuation increased from 0.42A to 0.47A, an increase of only 0.05A. This represents a decrease in β when DVDISC is increased from a lower load to a higher load. m The fluctuations and current fluctuations have only been slightly improved, which solves the problem that the current and output torque fluctuations of the VDSIC algorithm are aggravated as the load increases.

[0076] The variable amplitude DVDSIC method proposed in this application injects a signal amplitude A of 0.05 rad when the motor starts and the load changes, to quickly track the MTPA point. After entering the steady state, A is changed to 0.005 rad to reduce current and torque fluctuations, and β m The change amount is used as the switching criterion. Less than 1° is regarded as the steady state, and greater than 1° is regarded as the tracking state. The simulation results of the variable amplitude DVDSIC when the load is switched from 5 Nm to 10 Nm at a given speed of 1000 r / min and 1 s are as Figure 6 shown.

[0077] As Figure 6 shown, after the load suddenly increases, the fluctuation amount of β m rises from 0.15° to 0.2°, only increasing by 0.05°; the fluctuation amount of i d rises from 0.55 A to 0.61 A, only increasing by 0.06 A; the fluctuation amount of the middle i q rises from 0.42 A to 0.46 A, only increasing by 0.04 A. Compared with DVDSIC, the fluctuation amount is smaller and the steady-state control performance is better. And by using a larger injection signal amplitude A in the MTPA tracking state to quickly track the MTPA point, and then reasonably selecting a smaller A to reduce fluctuations after entering the steady state, the algorithm can complete the MTPA tracking and fluctuation suppression after the load mutation within 0.08 s, and the dynamic performance is greatly improved.

[0078] In summary, compared with VDSIC, DVDSIC can further suppress the fluctuation of β q and thus reduce the current and output torque fluctuations, and the suppression effect is more obvious under large load conditions. At the same time, the variable amplitude DVDSIC proposed based on DVDSIC has a faster response speed and better dynamic performance by reasonably switching the injection signal amplitude A during load mutation. Therefore, the variable amplitude DVDSIC has better steady-state and dynamic performance, and the comprehensive control effect is more excellent.​​

Claims

1. A control method for a permanent magnet synchronous motor (MTPA) based on dual virtual DC signal injection, characterized in that, include: Define the stator current vector angle β as the angle between the stator current direction and the positive d-axis. Inject a pair of DC signals d1(t)=A and d2(t)=-A with the same amplitude but opposite signs into β. For the electromagnetic torque T containing these signals... e d (β+A) and T e d (β-A) is expanded using Taylor series, T e d (β+A) and T e d Subtracting (β-A) yields... / The approximate value of β is obtained and input into the integral controller. The output of the integral controller is the updated value of β. When control / When the value approaches 0, the output value β of the integral regulator converges to the optimal current vector angle β. mtpa This enables MTPA control; in order to balance the steady-state and dynamic performance of the motor during operation, the amplitude of the injected signal A is made controllable. Based on the built-in permanent magnet synchronous motor model, a dual virtual DC signal A with a large amplitude is injected when the control algorithm starts, so as to quickly approximate β with respect to β. mtpa , reaching the vicinity of the MTPA operating point; When the β value is less than 1°, the control system is considered to have entered a steady state. At this point, the goal of the control algorithm is to reduce β. mtpa The amplitude of the injected signal, A, is reduced to decrease due to fluctuations, thereby further reducing β while ensuring the dynamic performance of the control system. mtpa Fluctuations improve control stability; The current vector angle β is set to a non-zero initial value.

2. The MTPA control method for permanent magnet synchronous motors based on dual virtual DC signal injection as described in claim 1, characterized in that, Establish a mathematical model for the dq axis of the built-in permanent magnet synchronous motor: ； In the formula, u d u q For the dq-axis components of the stator voltage; i d i q L represents the dq-axis component of the stator current. d L q For direct-axis and quadrature-axis inductors; Ψ f For permanent magnet flux linkage; ω e Electric angular velocity; The electromagnetic torque equation of the motor is: ； When the signal is subsequently injected into the current vector angle, the virtual signal only exists in the MTPA algorithm; the motor is not actually injected with a real signal. The parameter expression should remain unchanged, used to represent Ψ f dq axis current i d and i q There will be no injected signal.

3. The MTPA control method for permanent magnet synchronous motors based on dual virtual DC signal injection as described in claim 2, characterized in that, Injecting two virtual DC signals of opposite signs and equal amplitude, d1(t)=A and d2(t)=-A, into the current vector angle β yields a virtual dq-axis current containing the injected signals. ； The electromagnetic torque obtained after injecting the virtual signal is: ； In the formula i d (β+A), i q (β+A), i d (β-A), i q (β-A) is the dq-axis current after a DC signal is injected into the stator current vector angle; i d i q This represents the actual dq-axis current.

4. The MTPA control method for permanent magnet synchronous motors based on dual virtual DC signal injection according to claim 3, characterized in that, T e d (β+A) and T e d Taylor expansion of (β-A): ； From the above formula, it can be seen that T e d (β+A) and T e d Subtracting (β-A) eliminates the even-order Taylor expansion terms of the electromagnetic torque; since the amplitude of A is very small, the odd-order Taylor expansion terms can be ignored; the extracted signal is as follows: ； Introducing parameter σ d As input to the integral regulator: 。 5. The MTPA control method for permanent magnet synchronous motors based on dual virtual DC signal injection according to claim 4, characterized in that, The obtained σ d The input to the integral regulator allows β to continuously approach the optimal β. mtpa Expressing β in integral form, we get: ； Where k ’ The integral coefficient; Once the value of β stabilizes, σ d Approaching 0, thus indicating / When β approaches 0, it can be approximated as being equal to β. mtpa equal; According to σ d Due to the proportionality of A, theoretically, the smaller the amplitude A of the injected signal in the algorithm, the better the control effect. However, a smaller A will lead to a slower convergence speed of the algorithm. Therefore, to make the amplitude of the injected signal A controllable, a variable amplitude dual virtual DC signal injection algorithm is used to balance steady-state performance and dynamic performance.

6. The MTPA control method for permanent magnet synchronous motors based on dual virtual DC signal injection as described in claim 5, characterized in that, When the motor is in MTPA condition, β mtpa Represented as β m The stator current is expressed as: ； Among them Ψ f For permanent magnet flux linkage, L d L q Let these be the direct-axis inductance and the quadrature-axis inductance, respectively. Based on the above equation, the electromagnetic torque can be expressed as: ； Will / Represented as: ； When the load increases, the magnetic saturation effect of the motor intensifies, at which point |L d -L q | Decrease; it can be seen from the above formula that T at this time em With β m The slope of the curve increases, meaning that at this time T e The characteristic of (β) as a convex function is further amplified, therefore it converges to β at the identified angle β. m When the load changes, the angle fluctuation generated by the dual virtual DC signal injection permanent magnet synchronous motor MTPA control method does not change significantly.

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