Design method of permanent magnet synchronous motor resonance current regulator

Abstract

The invention belongs to the technical field of motion control, and particularly relates to a design method of a permanent magnet synchronous motor resonance current regulator, and the method mainly comprises the steps: 1) constructing a zero point which is the same as a stator time constant so as to offset a large inertia link in an actual motor model; (2) a fundamental wave frequency order reduction integrator is introduced, and zero-static-error tracking of fundamental wave current is achieved; and 3) giving a gain parameter analytical calculation formula of the regulator. The reduced-order resonance current regulator is researched by referring to the design principle of a traditional PI current regulator, the regulator only needs to carry out one-time rotation coordinate transformation on a reference current instruction, and the calculated amount is relatively small. Meanwhile, in order to facilitate practical application, the invention provides a gain parameter analytical calculation formula. Under the condition that model parameters are accurate, the resonance current regulator has the dynamic performance similar to that of a traditional PI current regulator, but when errors exist in the parameters, the resonance current regulator has the better decoupling control performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of motion control, and particularly relates to a design method for a resonant current regulator of a permanent magnet synchronous motor. Background Art

[0002] The permanent magnet synchronous motor has the advantages of high efficiency, high torque control accuracy, and high power density, and is widely used in motion control systems. The vector control system of the permanent magnet synchronous motor usually implements current closed-loop control by using a proportional integral (PI) regulator in the synchronous rotating coordinate system. This algorithm requires rotational coordinate transformation of the stator current and the reference voltage command respectively, and the calculation amount is relatively large. At the same time, there is a dq-axis current coupling problem in the PI current regulator, and the conventional feedforward decoupling depends on accurate motor parameters, which seriously affects the control quality of the system when there are errors in the model. Therefore, it is necessary to study a high-performance current regulator with good parameter robustness and decoupling performance. Summary of the Invention

[0003] (1) Technical Problems to be Solved

[0004] The technical problem to be solved by the present invention is: in order to achieve current loop decoupling while simplifying the calculation, the present invention proposes a reduced-order resonant controller in the stationary coordinate system. The proposed controller constructs a zero point with the same stator time constant to cancel the large inertia link in the actual motor model, so it has a good dynamic response speed. At the same time, a fundamental frequency reduced-order integrator is introduced, which can achieve static error-free tracking of the fundamental current. The vector control system based on this regulator only needs to perform a coordinate transformation on the reference current command, reducing the calculation burden. Finally, a method for designing the gain parameters of the proposed regulator is given.

[0005] (2) Technical Solutions

[0006] To solve the above technical problems, the present invention provides a design method for a resonant current regulator of a permanent magnet synchronous motor, and the method includes the following steps:

[0007] Step 1: Establish the mathematical model of the permanent magnet synchronous motor in the two-phase stationary coordinate system;

[0008] Step 2: Design the resonant current regulator, where a zero point with the same stator time constant is constructed and a fundamental frequency reduced-order integrator is introduced;

[0009] Step 3: Design the gain parameters of the regulator.

[0010] Among them, in the above Step 1: in the two-phase stationary coordinate system, the electrical mathematical model of the surface-mounted permanent magnet synchronous motor is represented by a complex vector as:

[0011]

[0012] Among them, L and R s , and ψ f represent the stator inductance, stator resistance, and permanent magnet flux linkage of the motor; u s , i s represent the stator voltage vector and stator current vector; ω r and θ r represent the electrical speed and rotor position; j represents the imaginary part of a complex number;

[0013] Ignoring the back electromotive force term, the transfer function of the permanent magnet synchronous motor is expressed as:

[0014]

[0015] F c (s) is the transfer function of the permanent magnet synchronous motor;

[0016] i s (s) is the Laplace transform result of the stator current vector;

[0017] u s (s) is the Laplace transform result of the stator voltage vector;

[0018] Among them, s is the Laplace operator, τ s = L / R s is the stator time constant;

[0019] In practical applications, in order to anti-alias and reduce noise sensitivity, a low-pass filter is set in the current sampling feedback link; assuming the time constant of the low-pass filter is τ c , then the low-pass filter link is simplified as:

[0020]

[0021] F f (s) is the transfer function of the low-pass filter;

[0022] i f (s) is the Laplace transform result of the filtered current;

[0023] In summary, in the two-phase stationary coordinate system, the electrical mathematical model block diagram of the permanent magnet synchronous motor can be expressed as Figure 1 shown;

[0024] In the synchronous rotating coordinate system, there is a cross-coupling term jω r i dq, and the static coordinate system model shown in formula (2) does not have cross-coupling terms. Therefore, it is expected that better decoupling control performance can be achieved by designing the current resonance regulator based on formula (2). Especially when the parameters are inaccurate, it is difficult for the traditional feedforward decoupling control to achieve the exact cancellation of the cross-coupling terms, resulting in poor parameter robustness;

[0025] Among them, in step 2: drawing on the zero-pole cancellation principle of the traditional PI regulator, the zero point of this resonance current regulator should be able to cancel the stator time constant inertia link shown in formula (2); secondly, in order to achieve the static error-free tracking of the fundamental wave current, the gain of the regulator at the angular frequency ω r should be infinite. Therefore, the designed resonance current regulator is as follows:

[0026]

[0027] In the above formula, represents the Laplace transform result of the reference voltage command, represents the current tracking error, and k c > 0 is the regulator gain parameter; F cc represents the transfer function of the resonance current regulator; represents the Laplace transform result of the command reference current;

[0028] In addition, considering the one-beat delay during digital implementation and the zero-order hold effect of the modulation link, the relationship between the actual output voltage and the reference voltage command is modeled by the following small inertia link, that is:

[0029]

[0030] In the above formula, T sc is the sampling period;

[0031] F u (s) is the transfer function between the actual output voltage and the reference voltage command;

[0032] To sum up, the main links in the current control loop are as Figure 3 shown; from the figure, the open-loop transfer function of the current control loop is:

[0033]

[0034] F open (s) is the open-loop transfer function;

[0035] Since the PWM delay and the equivalent filter time constant of the current detection are usually very small, the above two links are combined and equivalent to a small inertia link, and formula (6) is simplified to:

[0036]

[0037] Among them, τ cc = 1.5T sc + τ c .

[0038] Among them, in step 3: According to formula (7), it can be known that F open (s) is a typical type-I system. When the condition formula (8) is satisfied, the adjustment time of the current control loop is the shortest;

[0039]

[0040] Solving the above formula, the regulator gain parameter can be obtained as:

[0041]

[0042] Substituting formula (9) into formula (7) and arranging, the closed-loop transfer function of the current control loop is obtained as:

[0043]

[0044] F cl (s) is the closed-loop transfer function of the current control loop;

[0045] According to the above formula, the amplitude-frequency response of the closed-loop transfer function of the current control loop at the fundamental wave is obtained as:

[0046] F cl (s) = 1 (11)

[0047] It can be seen that using this resonant current regulator can achieve static-error-free tracking control of the fundamental current.

[0048] Among them, the method designs a current regulator in the two-phase stationary coordinate system, constructs a zero point identical to the stator time constant through formula (4) to cancel the large inertia link in the actual motor model, and designs a fundamental frequency reduced-order integrator through formula (8).

[0049] Among them, the method sets the current sampling feedback link as a low-pass filter through formula (3), models the one-beat delay during digital implementation and the zero-order hold effect of the modulation link as a first-order inertia link through formula (5), combines and equivalent the above two links into a small inertia link through formula (7), and calculates the gain parameter according to the shortest adjustment time of the closed-loop system through formula (9).

[0050] Among them, the designed resonant current regulator of the method only needs to perform a coordinate transformation on the reference current command, reduces the calculation burden, has a good dynamic response speed, and can achieve static-error-free tracking of the fundamental current.

[0051] Among them, the gain parameter analysis and calculation process of the resonant current regulator can quickly obtain the optimal gain parameter, avoiding repeated trial and error.

[0052] (III) Beneficial effects

[0053] Compared with the prior art, the present invention provides a design method for a resonant current regulator of a permanent magnet synchronous motor, having the following beneficial effects:

[0054] The proposed resonant current regulator has excellent dynamic and static performance. Especially when the model parameters are inaccurate, it has better decoupling control performance compared with the traditional PI current regulator.

[0055] Implementation effect:

[0056] In the simulation test, the dynamic responses of the proposed resonant current regulator and the traditional PI regulator were respectively compared when the parameters were accurate and there were errors.

[0057] Figure 4a and Figure 4b are the simulation results when the q-axis current reference command steps from 0 to 1.5 times the rated value. It can be seen from the figure that the dynamic responses of the proposed resonant current regulator and the traditional PI current regulator are basically the same, and the settling time during the command step is about 2 ms. In the steady state, both current regulators can achieve static error-free tracking control. However, as mentioned above, the resonant current regulator only requires one rotation coordinate transformation, so it is easier to implement.

[0058] Figure 5a and Figure 5b are the simulation results of the traditional PI current regulator and the proposed resonant current regulator when the inductance parameter is half of the actual value and a load is suddenly applied at the rated speed. It can be seen from the figure that when the model parameters are inaccurate, when the q-axis current of the traditional PI current regulator suddenly changes, the d-axis current deviates greatly from its reference value, while the d-axis current of the proposed resonant current regulator is hardly affected when the motor model parameters are inaccurate, showing good decoupling control performance. When the inductance parameter is 2 times the actual value, it can also be found that the proposed resonant current regulator of the present invention has better transient control performance, as Figure 6a and Figure 6b shown.

[0059] In order to further verify the control performance of the proposed resonant current regulator, experimental tests were carried out based on a 2.4 kW surface-mounted permanent magnet synchronous motor speed control platform. The specific control algorithm is as Figure 2 shown. The stator three-phase current is directly measured by a current probe, and the waveforms of the motor speed, dq-axis current, and other internal variables are obtained through the on-board digital-to-analog conversion chip. To prove the superior control performance of the proposed resonant current regulator, the dynamic and static responses of the traditional PI current regulator were compared and tested under the same conditions.

[0060] Figure 7 It is the experimental test waveform of the motor starting from rest to the rated speed. It can be seen from the figure that the entire starting process is smooth without impact. The q-axis current can quickly track its command value, and at the same time, the d-axis current is not affected by the rapidly changing q-axis current and the speed, indicating that the proposed resonant current regulator has achieved good decoupling control of the dq-axis currents.

[0061] Figure 8 It is the experimental test waveform of the motor rotating forward and backward at the rated speed. It can be seen from the figure that the motor speed first drops smoothly to zero and then quickly accelerates to the reverse rated speed. During the entire transient process, the d-axis current can remain near 0, while the q-axis current can quickly track its command value, and there is no steady-state offset in the dq-axis currents, indicating that the designed resonant current regulator can achieve zero-static-error tracking control.

[0062] It can be seen from the above simulation results that compared with the traditional PI current regulator, the resonant current regulator designed in this paper has stronger robustness to the change of inductance parameters. The experimental tests also verify this conclusion. Comparing Figure 9 and Figure 10 it can be seen that when the inductance parameter in the regulator is set to half of its actual value, when the q-axis current suddenly changes, there is an obvious transient error in the d-axis current of the traditional PI current regulator, while the proposed resonant current regulator can still maintain good current tracking control ability. Comparing Figure 11 and Figure 12 it can be seen that when the inductance parameter in the regulator is set to twice its actual value, it can also be found that the proposed resonant current regulator has better parameter robustness. Description of the Drawings

[0063] Figure 1 is the block diagram of the electrical mathematical model of the permanent magnet synchronous motor;

[0064] Figure 2 is the system control block diagram;

[0065] Figure 3 is the block diagram of the control loop of the proposed resonant current regulator;

[0066] Figure 4a and Figure 4b are respectively the schematic diagrams of the stator current step responses of the traditional PI current regulator and the resonant current regulator proposed in the present invention;

[0067] Figure 5a and Figure 5b are respectively the schematic diagrams of the sudden load application responses of the traditional PI current regulator and the resonant current regulator proposed in the present invention when the inductance is 50% of the actual value;

[0068] Figure 6a and Figure 6b are respectively the schematic diagrams of the sudden load response when the inductance of the traditional PI current regulator and the resonant current regulator proposed in the present invention is 200% of the actual value;

[0069] Figure 7 is the schematic diagram of the experimental test result from starting from rest to the rotational speed;

[0070] Figure 8 is the schematic diagram of the experimental test result of the forward and reverse rotation at the rated speed;

[0071] Figure 9 is the schematic diagram of the dynamic response of the traditional PI current regulator during the forward and reverse rotation at the rated speed when the inductance is 50% of the actual value;

[0072] Figure 10 is the schematic diagram of the dynamic response of the resonant current regulator proposed in the present invention during the forward and reverse rotation at the rated speed when the inductance is 50% of the actual value;

[0073] Figure 11 is the schematic diagram of the dynamic response of the traditional PI current regulator during the forward and reverse rotation at the rated speed when the inductance is 200% of the actual value;

[0074] Figure 12 is the schematic diagram of the dynamic response of the resonant current regulator proposed in the present invention during the forward and reverse rotation at the rated speed when the inductance is 200% of the actual value.

[0075] Figure 13 is the flow chart of the solution of the present invention. Detailed implementation manners

[0076] To make the objectives, contents, and advantages of the present invention clearer, the following further describes in detail the specific implementation manners of the present invention with reference to the drawings and embodiments.

[0077] To solve the above technical problems, the present invention provides a design method for a resonant current regulator of a permanent magnet synchronous motor, and the method includes the following steps:

[0078] Step 1: Establish the mathematical model of the permanent magnet synchronous motor in the two-phase stationary coordinate system;

[0079] Step 2: Design the resonant current regulator, where a zero point identical to the stator time constant is constructed and a fundamental frequency reduced-order integrator is introduced;

[0080] Step 3: Design the gain parameters of the regulator.

[0081] Among them, in the said Step 1: In the two-phase stationary coordinate system, the electrical mathematical model of the surface-mounted permanent magnet synchronous motor is represented by a complex vector as:

[0082]

[0083] Among them, L and R s , and ψ f represent the motor stator inductance, stator resistance, and permanent magnet flux linkage; u s , i s represent the stator voltage vector and the stator current vector; ω r and θ r represent the electrical speed and the rotor position; j represents the imaginary part of a complex number;

[0084] Ignoring the back electromotive force term, the transfer function of the permanent magnet synchronous motor is expressed as:

[0085]

[0086] F c (s) is the transfer function of the permanent magnet synchronous motor;

[0087] i s (s) is the Laplace transform result of the stator current vector;

[0088] u s (s) is the Laplace transform result of the stator voltage vector;

[0089] Among them, s is the Laplace operator, τ s = L / R s is the stator time constant;

[0090] In practical applications, in order to anti-alias and reduce noise sensitivity, a low-pass filter is set in the current sampling feedback link; assuming the time constant of the low-pass filter is τ c , then the low-pass filter link is simplified as:

[0091]

[0092] F f (s) is the transfer function of the low-pass filter;

[0093] i f (s) is the Laplace transform result of the filtered current;

[0094] In summary, in the two-phase stationary coordinate system, the electrical mathematical model block diagram of the permanent magnet synchronous motor can be expressed as Figure 1 shown;

[0095] In the synchronous rotating coordinate system, there is a cross-coupling term jω r i dq, while the static coordinate system model shown in formula (2) has no cross-coupling term. Therefore, it is expected that better decoupling control performance can be achieved by designing the current resonance regulator based on formula (2). Especially when the parameters are inaccurate, it is difficult for the traditional feedforward decoupling control to achieve the exact cancellation of the cross-coupling term, resulting in poor parameter robustness;

[0096] Among them, in step 2: referring to the zero-pole cancellation principle of the traditional PI regulator, the zero point of this resonance current regulator should be able to cancel the stator time constant inertia link shown in formula (2); secondly, in order to achieve the static error-free tracking of the fundamental wave current, the gain of the regulator at the angular frequency ω r should be infinite. Therefore, the designed resonance current regulator is as follows:

[0097]

[0098] In the above formula, represents the Laplace transform result of the reference voltage command, represents the current tracking error, and k c > 0 is the regulator gain parameter; F cc represents the transfer function of the resonance current regulator; represents the Laplace transform result of the command reference current;

[0099] In addition, considering the one-beat delay during digital implementation and the zero-order hold effect of the modulation link, the relationship between the actual output voltage and the reference voltage command is modeled by the following small inertia link, that is:

[0100]

[0101] In the above formula, T sc is the sampling period;

[0102] F u (s) is the transfer function between the actual output voltage and the reference voltage command;

[0103] To sum up, the main links in the current control loop are as Figure 3 shown; from the figure, the open-loop transfer function of the current control loop is:

[0104]

[0105] F open (s) is the open-loop transfer function;

[0106] Since the PWM delay and the equivalent filter time constant of the current detection are usually very small, the above two links are combined and equivalent to a small inertia link, and formula (6) is simplified to:

[0107]

[0108] Among them, τ cc = 1.5T sc + τ c .

[0109] Among them, in the said step 3: According to formula (7), it can be known that F open (s) is a typical type I system. When the condition formula (8) is satisfied, the adjustment time of the current control loop is the shortest;

[0110]

[0111] Solving the above formula, the regulator gain parameter can be obtained as:

[0112]

[0113] Substituting formula (9) into formula (7) and arranging, the closed-loop transfer function of the current control loop is obtained as:

[0114]

[0115] F cl (s) is the closed-loop transfer function of the current control loop;

[0116] According to the above formula, the amplitude-frequency response of the closed-loop transfer function of the current control loop at the fundamental wave is obtained as:

[0117] F cl (s) = 1 (11)

[0118] It can be seen that using this resonant current regulator can achieve the static-error-free tracking control of the fundamental wave current.

[0119] Among them, the said method designs the current regulator in the two-phase stationary coordinate system, constructs a zero point with the same stator time constant through formula (4) to cancel the large inertia link in the actual motor model, and designs the fundamental wave frequency reduced-order integrator through formula (8).

[0120] Among them, the said method sets the current sampling feedback link as a low-pass filter through formula (3), models the one-beat delay during digital implementation and the zero-order hold effect of the modulation link as a first-order inertia link through formula (5), combines and equivalently transforms the above two links into a small inertia link through formula (7), and calculates the gain parameter according to the shortest adjustment time of the closed-loop system through formula (9).

[0121] Among them, the designed resonant current regulator of the said method only needs to perform a coordinate transformation on the reference current command, reduces the calculation burden, has a good dynamic response speed, and can achieve the static-error-free tracking of the fundamental wave current.

[0122] Among them, the gain parameter analysis and calculation process of the resonant current regulator can quickly obtain the optimal gain parameter, avoiding repeated trial and error.

[0123] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and deformations can be made, and these improvements and deformations should also be regarded as the protection scope of the present invention.

Claims

1. A design method for a permanent magnet synchronous motor resonant current regulator, characterized in that: The method comprises the following steps: Step 1: Establish a mathematical model of the permanent magnet synchronous motor in a two-phase stationary coordinate system; Step 2: Design a resonant current regulator, in which a zero point identical to the stator time constant is constructed and a fundamental frequency reduced-order integrator is introduced; Step 3: Design the gain parameters of the regulator.

2. The design method of the permanent magnet synchronous motor resonant current regulator according to claim 1, characterized in that: In step 1: in a two-phase stationary coordinate system, the electrical mathematical model of the surface-mounted permanent magnet synchronous motor is expressed by a complex vector as follows: Among them, L, R s , and ψ f Represents the motor stator inductance, stator resistance and permanent magnet flux; u s 、i s Represents the stator voltage vector and the stator current vector; ω r and θ r represents the electrical speed and rotor position; j represents the imaginary part of the complex number; Ignoring the back EMF term, the transfer function of the permanent magnet synchronous motor is expressed as: F c (s) is the transfer function of the permanent magnet synchronous motor; i s (s) is the Laplace transform result of the stator current vector; u s (s) is the Laplace transform result of the stator voltage vector; Among them, s is the Laplace operator, τ s =L / R s is the stator time constant; In practical applications, in order to resist aliasing and reduce noise sensitivity, a low-pass filter is set in the current sampling feedback link; assuming that the time constant of the low-pass filter is τ c , then the low-pass filtering link is simplified as: F f (s) is the transfer function of the low-pass filter; i f (s) is the Laplace transform result of the filtered current.

3. The design method of the permanent magnet synchronous motor resonant current regulator according to claim 2, characterized in that: In step 2: referring to the zero-pole cancellation principle of the traditional PI regulator, the zero point of the resonant current regulator should be able to cancel the stator time constant inertia link shown in formula (2); secondly, in order to achieve zero-error tracking of the fundamental current, the regulator is at an angular frequency ω r The gain at should be infinite, so the designed resonant current regulator is as follows: In the above formula, Represents the Laplace transform result of the reference voltage command, represents the current tracking error, k c >0 is the regulator gain parameter; F cc represents the transfer function of the resonant current regulator; Represents the Laplace transform result of the command reference current; In addition, considering the one-beat delay in digital implementation and the zero-order hold effect of the modulation link, the relationship between the actual output voltage and the reference voltage command is modeled using the following small inertia link, namely: In the above formula, T sc is the sampling period; F u (s) is the transfer function between the actual output voltage and the reference voltage command; The open-loop transfer function of the current control loop is: F open (s) is the open-loop transfer function; Since the PWM delay and the equivalent filtering time constant of current detection are usually very small, the above two links are combined into a small inertia link, and formula (6) is simplified to: (7) Among them, t cc =1.5T sc +t c 。 4. The design method of the permanent magnet synchronous motor resonant current regulator as claimed in claim 3, characterized in that: In step 3: According to formula (7), F open (s) is a typical type I system. When the condition formula (8) is satisfied, the adjustment time of the current control loop is the shortest; Solving the above equation, we can get the regulator gain parameter: Substituting formula (9) into formula (7), the closed-loop transfer function of the current control loop is obtained as follows: F cl (s) is the closed-loop transfer function of the current control loop; According to the above formula, the amplitude-frequency response of the closed-loop transfer function of the current control loop at the fundamental wave is: F cl (s)=1 (11) It can be seen that the use of the resonant current regulator can achieve zero-static error tracking control of the fundamental current.

5. The design method of the permanent magnet synchronous motor resonant current regulator according to claim 4, characterized in that: The method designs a current regulator in a two-phase stationary coordinate system, and constructs a zero point identical to the stator time constant through formula (4) to cancel the large inertia link in the actual motor model, and designs a fundamental frequency reduced-order integrator through formula (8).

6. The design method of a permanent magnet synchronous motor resonant current regulator as claimed in claim 4, characterized in that: The method sets the current sampling feedback link as a low-pass filter through formula (3), models the one-beat delay during digital implementation and the zero-order hold effect of the modulation link as a first-order inertia link through formula (5), combines the above two links into a small inertia link through formula (7), and calculates the gain parameters according to the shortest adjustment time of the closed-loop system through formula (9).

7. The design method of a permanent magnet synchronous motor resonant current regulator as claimed in claim 4, characterized in that: The resonant current regulator designed by the method only needs to perform one coordinate transformation on the reference current instruction, which reduces the calculation burden, has a good dynamic response speed, and can achieve zero-static-error tracking of the fundamental current.

8. The design method of a permanent magnet synchronous motor resonant current regulator as claimed in claim 4, characterized in that: The gain parameter analytical calculation process of the resonant current regulator can quickly obtain the optimal gain parameter and avoid repeated trial and error.

9. The design method of a permanent magnet synchronous motor resonant current regulator as claimed in claim 4, characterized in that: The method proposes a reduced-order resonant controller in a stationary coordinate system; the proposed controller constructs a zero point that is the same as the stator time constant to cancel the large inertia link in the actual motor model, so it has a good dynamic response speed, and at the same time introduces a fundamental frequency reduced-order integrator to achieve zero-static error tracking of the fundamental current; the vector control system based on the regulator only needs to perform one coordinate transformation on the reference current command, reducing the calculation burden; finally, the gain parameter design method of the proposed regulator is given.

10. The design method of a permanent magnet synchronous motor resonant current regulator according to claim 4, characterized in that: The resonant current regulator proposed by the method has excellent dynamic and static performance, especially when the model parameters are inaccurate, and has better decoupling control performance than the traditional PI current regulator.

Images