Dead-time compensation method for permanent magnet synchronous motor based on nonlinear flux linkage observer

Abstract

This invention belongs to the field of AC motor drive control technology, and relates to a dead-zone compensation method for permanent magnet synchronous motors based on a nonlinear flux linkage observer. The method involves measuring the induced current of the motor in the natural coordinate system and transforming it to obtain the αβ-axis current; using a nonlinear flux linkage observer in the αβ coordinate system as a position observation model to obtain the estimated actual rotor position, forming a speed loop to achieve sensorless control of the permanent magnet synchronous motor; constructing a q-axis voltage disturbance observer by measuring the phase voltage output of the inverter; using the output of the q-axis disturbance observer as the input of the dead-zone time calculation module to obtain the estimated dead-zone time; calculating and obtaining the dead-zone compensation voltage based on the estimated value to compensate the inverter output phase voltage, thus achieving dead-zone compensation. Based on the nonlinear flux linkage observer, a positionless control closed-loop structure is constructed, and the command voltage is corrected, reducing the impact of the inverter dead time on the permanent magnet synchronous motor and improving the positionless control performance.

Description

Technical Field

[0001] This invention belongs to the field of AC motor drive control technology, and relates to a method for dead zone compensation of permanent magnet synchronous motors based on a nonlinear flux linkage observer. Background Technology

[0002] Airborne pump loads encompass various pump devices, primarily used for aircraft propulsion, life support, engine operation, and maintenance. They generally require high power, light weight, small size, fast response time, and high control precision. With the rapid development of aerospace, high-power-density, low-energy-consumption permanent magnet synchronous motors (PMSMs) have become a research hotspot for airborne pump loads. However, existing airborne pump loads all use mechanical position / speed sensors to acquire the motor's position or speed signals. During actual aircraft operation, airborne pump loads operate in high-temperature, high-pressure, and high-electromagnetic-interference environments, which can easily cause mechanical sensors to fail, leading to traction system malfunctions, large torque surges, and in severe cases, damage to motor components, resulting in insufficient output and endangering aviation safety. Sensorless drive technology fundamentally eliminates this safety hazard and offers advantages such as strong anti-interference capabilities, high integration, and long service life. Compared to conventional flux linkage observers, nonlinear flux linkage observers, due to their state variables being independent of rotational speed, also have the characteristic of being applicable to a wide speed range and are simple in structure and easy to implement.

[0003] During flight, aircraft require different types of pumps at different altitudes and speeds, and the operational requirements of the same type of pump also vary. Due to inverter nonlinearity, the utilization rate of the bus voltage cannot be maximized, leading to a decrease in motor control performance, which is particularly noticeable when the motor operates in alternating forward and reverse directions. When a dead zone exists, the motor response current waveform deteriorates, affecting the performance of the nonlinear flux linkage observer and resulting in poorer rotor position estimation. Therefore, in permanent magnet traction systems using permanent magnet synchronous motors as aircraft pump loads, using a nonlinear flux linkage observer as a position observer, combined with dead zone compensation methods, has significant practical implications for improving the performance of sensorless control. Summary of the Invention

[0004] Purpose of the invention

[0005] The purpose of this invention is to provide a sensorless dead-time compensation method for permanent magnet synchronous motors based on a nonlinear flux linkage observer. By estimating the stator flux linkage using the αβ axis current, the estimated rotor position angle and speed are calculated, thus achieving sensorless control of the permanent magnet synchronous motor. Furthermore, by acquiring the phase voltages of the three phases (A, B, and C) in the natural coordinate system, the dead-time is calculated in real time, and then the phase voltages of the three phases (A, B, and C) are compensated based on the dead-time, improving the response current waveform, enhancing rotor position estimation performance, and optimizing the sensorless control performance of the permanent magnet synchronous motor based on the nonlinear flux linkage observer.

[0006] Technical solution

[0007] The dead-zone compensation method for permanent magnet synchronous motors based on nonlinear flux observers is implemented according to the following steps:

[0008] Step 1: Measure the induced current of the motor in the ABC coordinate system and obtain the αβ axis current through Clark transformation;

[0009] Step 2: Using a nonlinear flux linkage observer in the αβ coordinate system as a position observation model to obtain the actual rotor position estimate, thereby forming a speed loop and realizing sensorless control of the permanent magnet synchronous motor.

[0010] Step 3: Construct a q-axis voltage disturbance observer by measuring the phase voltage output of the inverter;

[0011] Step 4: Use the output of the q-axis perturbation observer as the input to the dead time calculation module to obtain the dead time estimate;

[0012] Step 5: Calculate and obtain the dead time compensation voltage based on the dead time estimate, and compensate the inverter output phase voltage to realize sensorless dead time compensation for permanent magnet synchronous motor based on nonlinear flux observer.

[0013] Furthermore, step 1 specifically involves:

[0014] Step 1.1, the three-phase induced current i of the permanent magnet synchronous motor a i b i c Sampling is performed, and the Clarke transform is applied to obtain the α-axis current i. α and β-axis current i β Then perform a Park transformation on it to obtain the d-axis current i. d and q-axis current i q For the d-axis current i d and q-axis current i q Perform PI control to obtain the d-axis voltage command value u. d and q-axis voltage command value u qThen, perform an inverse Park transform to obtain the α-axis voltage command value u. α and β-axis voltage command value u β .

[0015] Furthermore, step 2 specifically involves:

[0016] Step 2.1, establish the mathematical model of the surface-mounted permanent magnet synchronous motor in the αβ coordinate system, as shown in equation (1);

[0017]

[0018] Among them, L and R s These are the stator inductance and stator resistance, ω and θ, respectively. r These are the motor angular velocity and the rotor position angle, ψ. m For permanent magnet flux linkage, T e Where P is the electromagnetic torque and P is the number of poles of the motor.

[0019] Step 2.2, define the state variable x and the output y, as shown in equations (2) and (3);

[0020]

[0021] Differentiating equation (2) yields the relationship between equation (2) and equation (3), as shown in equation (4).

[0022]

[0023] Step 2.3, define the vector function η(x), as shown in equation (5);

[0024]

[0025] Combining equation (3), the norm of η(x) is shown in equation (6);

[0026]

[0027] Step 2.4, combining equations (4), (5), and (6), construct the nonlinear flux observer model, as shown in equation (7);

[0028]

[0029] in, and are the state variables and their derivatives, respectively, of the nonlinear flux observer, where γ is the observer gain and γ>0;

[0030] Step 2.5, transform equation (3) to obtain equation (8);

[0031]

[0032] Therefore, the sine and cosine components containing the estimated rotor position are obtained by the observer, as shown in equation (9);

[0033]

[0034] In the formula, To estimate the rotor position.

[0035] Step 2.6: After normalizing the sine and cosine components containing the estimated rotor position, the estimated rotor position is obtained through phase-locked loop calculation. and estimated rotational speed This forms a speed ring.

[0036] Furthermore, step 3 specifically involves:

[0037] Step 3.1, establish the motor voltage equation in the dq coordinate system, as shown in equation (10);

[0038]

[0039] Among them, u dd =-ωLi q u qd =ω(Li d +K E ), K E It is the back potential constant.

[0040] When dead-time compensation is not applied, the command voltage u d and u q There will be a disturbance voltage, as shown in equation (11);

[0041]

[0042] After dead zone compensation is performed, equation (11) will change to equation (12);

[0043]

[0044] in, These are the d-axis and q-axis disturbance voltages, respectively. These are the dead zone compensation voltages for the d-axis and q-axis, respectively.

[0045] Step 3.2, since the q-axis disturbance voltage change is very small and can be ignored, its derivative is always zero, as shown in equation (13);

[0046]

[0047] Therefore, the state equation of the permanent magnet synchronous motor after adding the disturbance voltage The output equation y1 is shown in equation (14);

[0048]

[0049] Step 3.3, construct the q-axis perturbation observer as shown in Equation (15);

[0050]

[0051] in, G2 = -Lγ1γ2, where γ1 and γ2 are the observer poles.

[0052] Furthermore, step 4 specifically involves:

[0053] Step 4.1, in order to compensate for the dead zone, in the ABC coordinate system, the command voltage of the three phases ABC is increased by the dead zone compensation voltage, where the dead zone compensation voltage of phase A is shown in equation (16).

[0054]

[0055] In the formula, For phase A dead zone compensation voltage, T c For dead time, T s U is the sampling period time. dc Bus voltage.

[0056] Step 4.2, define the transformation matrix from the ABC coordinate system to the rotating coordinate system as shown in equation (17);

[0057]

[0058] Because the q-axis dead zone compensation voltage fluctuates periodically, the maximum q-axis dead zone compensation voltage... From equations (16) and (17), we can obtain the result as shown in equation (18);

[0059]

[0060] Its average value The result is obtained through integration, as shown in equation (19);

[0061]

[0062] Replace the maximum value with the average value, as shown in equation (20);

[0063]

[0064] Step 4.3, transform equation (20) to obtain the dead time T. c As shown in equation (21);

[0065]

[0066] Furthermore, step 5 specifically involves:

[0067] Step 5.1, let the output of the q-axis perturbation observer in step 3 be... Equal to the q-axis average dead zone compensation voltage in step 4 Obtain the estimated dead time As shown in equation (22);

[0068]

[0069] Step 5.2, substitute equation (22) into equation (16) to obtain the estimated dead zone compensation voltage of phase A, as shown in equation (22-1);

[0070]

[0071] Similarly, the estimated dead zone compensation voltages for phases B and C are shown in equations (23) and (24).

[0072]

[0073] Step 5.3: Apply the estimated dead-zone compensation voltage of phases ABC to the three-phase output voltage of the inverter to achieve dead-zone compensation.

[0074] Furthermore, the nonlinear flux observer is constructed based on the nonlinear model of the motor, and does not depend on the back EMF model of the motor during motor startup, thus realizing zero-speed startup and load operation of the motor.

[0075] Furthermore, prior to step 1, the motor control system should satisfy at least two-phase current sampling and bus voltage sampling functions.

[0076] Furthermore, after completing step 5, the feasibility of the method can be verified through simulation modeling or experiments.

[0077] Furthermore, the verification method includes high-speed operating conditions and low-speed operating conditions.

[0078] Furthermore, the above-mentioned high-speed operating condition verification method is as follows: when the given speed is 8000 rpm, using this method, the initial load is 0.5 Nm, and the load suddenly changes to 2 Nm after 1 second. After compensating for the dead zone, the time required for the speed fluctuation caused by the sudden load change to recover to the steady state value is significantly reduced; in addition, compared with the waveform without dead zone compensation, the waveform fluctuation of the estimated speed after dead zone compensation is also improved and is closer to the actual speed.

[0079] Furthermore, the aforementioned low-speed operating condition verification method specifically involves setting a given speed of 200 rpm, with the load increasing over time, reaching its maximum at 0.35 s, with a maximum value of 2.5 Nm. Using this method, the actual rotor position waveform is better than when it was not used, and the actual rotor position curve is closer to a straight line.

[0080] The beneficial effects of this application are as follows:

[0081] The aforementioned sensorless dead-zone compensation method for permanent magnet synchronous motors (PMSMs) based on a nonlinear flux linkage observer achieves dead-zone compensation during PMSM control. By using a q-axis disturbance observer to calculate the dead-zone time in real time, the accuracy of dead-zone compensation is further ensured. This improves the sensorless control performance of PMSMs based on the nonlinear flux linkage observer and enhances position estimation accuracy. At high speeds, speed fluctuations are significantly reduced. At low speeds, rotor position observation is more stable, and load-carrying capacity is significantly improved. Dead-zone compensation increases the success rate of zero-speed starts and eliminates the need to switch to other algorithms at medium to high speeds, ensuring algorithm consistency. The dead-zone compensation method, by incorporating a q-axis disturbance observer, enhances the PMSM's ability to suppress disturbances, improving its control performance and exhibiting stronger robustness. The dead-zone compensation method also improves the performance of zero-speed switching in positionless servo control, ensuring smoother system transitions during zero-speed changes. Attached Figure Description

[0082] Figure 1 This is a block diagram illustrating the dead-zone compensation principle of a permanent magnet synchronous motor based on a nonlinear flux linkage observer, as presented in this invention.

[0083] Figure 2 This is a block diagram of a nonlinear flux linkage observer.

[0084] Figure 3 This is a block diagram of the dead zone compensation principle;

[0085] Figure 4 This is a waveform comparison between the estimated rotational speed and the actual rotational speed after adding dead time at a given rotational speed of 8000 rpm.

[0086] Figure 5 This is a waveform comparison between the estimated rotational speed and the actual rotational speed after dead zone compensation at a given rotational speed of 8000 rpm (initially 0.5 Nm, abruptly changing to 2 Nm in 1 second).

[0087] Figure 6 This is the current waveform diagram of the present invention after adding dead time at 200 rpm;

[0088] Figure 7This is a waveform comparison of the estimated rotor position and the actual rotor position at 200 rpm after adding dead time according to the present invention.

[0089] Figure 8 This is the current waveform diagram after the dead zone is compensated at 200 rpm according to the present invention;

[0090] Figure 9 This is a waveform comparison between the estimated rotor position and the actual rotor position after dead zone compensation at 200 rpm, according to the present invention. Detailed Implementation

[0091] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar components or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of this invention. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The embodiments of this invention will be described in detail below with reference to the accompanying drawings.

[0092] This invention relates to a method for dead-zone compensation of permanent magnet synchronous motors based on a nonlinear flux linkage observer, the principle of which is shown in the following block diagram. Figure 1 As shown, this method constructs a speed loop based on a nonlinear flux linkage observer to realize a sensorless closed-loop structure for a permanent magnet synchronous motor. The structure of the nonlinear flux linkage observer is as follows: Figure 2 As shown. Considering the impact of dead time on sensorless control, a dead time compensation method for permanent magnet synchronous motors based on a nonlinear flux linkage observer is designed. The detailed calculation principle of dead time compensation is as follows. Figure 3 As shown; please follow these steps:

[0093] Step 1: Measure the induced current of the motor in the ABC coordinate system, and obtain the αβ axis current through transformation; specifically:

[0094] Step 1.1, the three-phase induced current i of the permanent magnet synchronous motor a i b i c Sampling is performed, and the Clarke transform is applied to obtain the α-axis current i. α and β-axis current i β Then perform a Park transformation on it to obtain the d-axis current i. d and q-axis current i q For the d-axis current i d and q-axis current iq Perform PI control to obtain the d-axis voltage command value u. d and q-axis voltage command value u q Then, perform an inverse Park transform to obtain the α-axis voltage command value u. α and β-axis voltage command value u β .

[0095] Step 2: Using a nonlinear flux linkage observer in the αβ coordinate system as a position observation model, the actual rotor position estimate is obtained, thus forming a speed loop to achieve sensorless control of the permanent magnet synchronous motor, such as... Figure 2 As shown; specifically:

[0096] Step 2.1, establish the mathematical model of the surface-mounted permanent magnet synchronous motor in the αβ coordinate system, as shown in equation (1);

[0097]

[0098] Among them, L and R s These are the stator inductance and stator resistance, ω and θ, respectively. r These are the motor angular velocity and the rotor position angle, ψ. m For permanent magnet flux linkage, T e Where P is the electromagnetic torque and P is the number of poles of the motor.

[0099] Step 2.2, define the state variable x and the output y, as shown in equations (2) and (3);

[0100]

[0101] Differentiating equation (2) yields the relationship between equation (2) and equation (3), as shown in equation (4).

[0102]

[0103] Step 2.3, define the vector function η(x), as shown in equation (5);

[0104]

[0105] Combining equation (3), the norm of η(x) is shown in equation (6);

[0106]

[0107] Step 2.4, combining equations (4), (5), and (6), construct the nonlinear flux observer model, as shown in equation (7);

[0108]

[0109] in, and are the state variables and their derivatives, respectively, of the nonlinear flux observer, where γ is the observer gain and γ>0;

[0110] Step 2.5, transform equation (3) to obtain equation (8);

[0111]

[0112] Therefore, the sine and cosine components containing the estimated rotor position are obtained by the observer, as shown in equation (9);

[0113]

[0114] In the formula, To estimate the rotor position.

[0115] Step 2.6: After normalizing the sine and cosine components containing the estimated rotor position, the estimated rotor position is obtained through phase-locked loop calculation. and estimated rotational speed This forms a speed ring.

[0116] Step 3: Construct a q-axis voltage disturbance observer by measuring the phase voltage output of the inverter; specifically:

[0117] Step 3.1, establish the motor voltage equation in the dq coordinate system, as shown in equation (10);

[0118]

[0119] Among them, u dd =-ωLi q u qd =ω(Li d +K E ), K E It is the back potential constant.

[0120] When dead-time compensation is not applied, the command voltage u d and u q There will be a disturbance voltage, as shown in equation (11);

[0121]

[0122] After dead zone compensation is performed, equation (11) will change to equation (12);

[0123]

[0124] in, These are the d-axis and q-axis disturbance voltages, respectively. These are the dead zone compensation voltages for the d-axis and q-axis, respectively.

[0125] Step 3.2, since the q-axis disturbance voltage change is very small and can be ignored, its derivative is always zero, as shown in equation (13);

[0126]

[0127] Therefore, the state equation of the permanent magnet synchronous motor after adding the disturbance voltage The output equation y1 is shown in equation (14);

[0128]

[0129] Step 3.3, construct the q-axis perturbation observer as shown in Equation (15);

[0130]

[0131] in, G2 = -Lγ1γ2, where γ1 and γ2 are the observer poles.

[0132] Step 4: Using the output of the q-axis perturbation observer as the input to the dead time calculation module, obtain the estimated dead time value; specifically:

[0133] Step 4.1, in order to compensate for the dead zone, in the ABC coordinate system, the command voltage of the three phases ABC is increased by the dead zone compensation voltage, where the dead zone compensation voltage of phase a is shown in equation (16).

[0134]

[0135] In the formula, For phase A dead zone compensation voltage, T c For dead time, T s U is the sampling period time. dc Bus voltage.

[0136] Step 4.2, define the transformation matrix from the ABC coordinate system to the rotating coordinate system as shown in equation (17);

[0137]

[0138] Because the q-axis dead zone compensation voltage fluctuates periodically, the maximum q-axis dead zone compensation voltage... From equations (16) and (17), we can obtain the result as shown in equation (18);

[0139]

[0140] Its average value The result is obtained through integration, as shown in equation (19);

[0141]

[0142] Replace the maximum value with the average value, as shown in equation (20);

[0143]

[0144] Step 4.3, transform equation (20) to obtain the dead time T. c As shown in equation (21);

[0145]

[0146] Step 5: Based on the estimated dead time, calculate and obtain the dead time compensation voltage, and compensate the inverter output phase voltage to achieve sensorless dead time compensation for permanent magnet synchronous motors based on nonlinear flux linkage observers.

[0147] Step 5.1, let the output of the q-axis perturbation observer in step 3 be... Equal to the q-axis average dead zone compensation voltage in step 4 Obtain the estimated dead time As shown in equation (22);

[0148]

[0149] Step 5.2, substitute equation (22) into equation (16) to obtain the estimated dead zone compensation voltage of phase A, as shown in equation (22-1);

[0150]

[0151] Similarly, the estimated dead zone compensation voltages for phases B and C are shown in equations (23) and (24).

[0152]

[0153] Step 5.3: Apply the estimated dead-zone compensation voltage of phases ABC to the three-phase output voltage of the inverter to achieve dead-zone compensation.

[0154] When a permanent magnet synchronous motor (PMSM) operates in the high-speed range and the inverter dead time is relatively small, the sensorless drive system is less affected by the inverter dead time. However, when the motor operates in the low-speed range, the dead time significantly impacts the sensorless control performance. To improve the sensorless control performance of PMSMs used as airborne pump loads in aviation, this invention proposes a PMSM dead time compensation method based on a nonlinear flux linkage observer. This method aims to improve the motor's control performance after sudden load changes during high-speed operation and its sensorless control performance during low-speed operation.

[0155] The overall control structure of the present invention is as follows: Figure 1As shown, the estimated rotational speed and estimated rotor position are calculated using a nonlinear flux observer, forming a sensorless control closed-loop structure. By correcting the command voltage, dead zone compensation is achieved. Figure 4 and Figure 5 The graphs show the speed waveforms at a given speed of 8000 rpm, with and without this method. Both graphs show an initial load of 0.5 Nm, which abruptly increases to 2 Nm at 1 second. It is clear from the graphs that after dead-zone compensation, the time required for the speed fluctuation caused by the sudden load change to recover to a steady-state value is significantly reduced. Furthermore, compared to the waveform without dead-zone compensation, the waveform fluctuation of the estimated speed after dead-zone compensation is also improved, and it is closer to the actual speed. Figure 6 to Figure 9 Given a rotational speed of 200 rpm, the load increases over time, reaching its maximum at 0.35 s, with a maximum value of 2.5 Nm. The comparison in the graph shows that using this method yields a better actual rotor position waveform compared to the unused method, as the actual rotor position curve is closer to a straight line. Furthermore, there is a certain delay between the estimated rotor position and the actual rotor position in the graph, which is due to calculation delay. Delay compensation is added to eliminate this delay.

[0156] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein. The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Within the spirit and principles of the present invention, any person skilled in the art may use the disclosed technical content to make changes or modifications to create equivalent embodiments applicable to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention, any modifications, equivalent substitutions, improvements, etc., should be included within the protection scope of the present invention.

Claims

1. A method for dead-zone compensation of permanent magnet synchronous motors based on a nonlinear flux linkage observer, characterized in that, The specific steps are as follows: Step 1: Measure the induced current of the motor in the ABC coordinate system and obtain the αβ axis current through Clark transformation; Step 2: Using a nonlinear flux linkage observer in the αβ coordinate system as a position observation model to obtain the actual rotor position estimate, forming a speed loop to achieve sensorless control of the permanent magnet synchronous motor. Step 3: Construct a q-axis voltage disturbance observer by measuring the phase voltage output of the inverter; Step 4: Use the output of the q-axis perturbation observer as the input to the dead time calculation module to obtain the dead time estimate; Step 5: Calculate and obtain the dead time compensation voltage based on the dead time estimate, and compensate the inverter output phase voltage. Step 1 is as follows: Step 1.1, the three-phase induced current i of the permanent magnet synchronous motor a i b i c Sampling is performed, and the Clarke transform is applied to obtain the α-axis current i. α and β-axis current i β Then perform a Park transformation on it to obtain the d-axis current i. d and q-axis current i q For the d-axis current i d and q-axis current i q Perform PI control to obtain the d-axis voltage command value u. d and q-axis voltage command value u q Then, perform an inverse Park transform to obtain the α-axis voltage command value u. α and β-axis voltage command value u β ; Step 3 specifically involves: Step 3.1, establish the motor voltage equation in the dq coordinate system, as shown in equation (10); （10）； in, , K E It is the back potential constant; When dead-time compensation is not applied, the command voltage u d and u q There will be a disturbance voltage, as shown in equation (11); （11）； After dead zone compensation is performed, equation (11) will change to equation (12). （12）； in, , These are the d-axis and q-axis disturbance voltages, respectively. , These are the dead zone compensation voltages for the d-axis and q-axis, respectively. Step 3.2, since the q-axis disturbance voltage change is very small and can be ignored, its derivative is always zero, as shown in equation (13); （13）； Therefore, the state equation of the permanent magnet synchronous motor after adding the disturbance voltage and output equation As shown in equation (14); （14）； Step 3.3, construct the q-axis perturbation observer as shown in equation (15); （15）； in, , , and The observer poles; Step 4 specifically involves: Step 4.1, in order to compensate for the dead zone, in the ABC coordinate system, the command voltage of the three phases ABC is increased by the dead zone compensation voltage, where the dead zone compensation voltage of phase A is shown in equation (16). （16）； In the formula, For phase A dead zone compensation voltage, T c For dead time, T s U is the sampling period time. dc Bus voltage; Step 4.2, define the transformation matrix from the ABC coordinate system to the rotating coordinate system as shown in equation (17); （17）； Because the q-axis dead zone compensation voltage fluctuates periodically, the maximum q-axis dead zone compensation voltage... From equations (16) and (17), we can obtain the result as shown in equation (18); （18）； Its average value The result is obtained through integration, as shown in equation (19); （19）； Replace the maximum value with the average value, as shown in equation (20); （20）； Step 4.3, transform equation (20) to obtain the dead time T. c As shown in equation (21); （21）； L and R s These are the stator inductance and stator resistance, ω and θ, respectively. r These are the motor angular velocity and the rotor position angle, respectively.

2. The method as described in claim 1, characterized in that, Step 2 is as follows: Step 2.1, establish the mathematical model of the surface-mounted permanent magnet synchronous motor in the αβ coordinate system, as shown in equation (1); （1）； Among them, Ψ m For permanent magnet flux linkage, T e Where P is the electromagnetic torque and P is the number of poles of the motor; Step 2.2, define the state variable x and the output y, as shown in equations (2) and (3); （2）； （3）； Differentiating equation (2) yields the relationship between equation (2) and equation (3), as shown in equation (4); （4）； Step 2.3, define the vector function η(x), as shown in equation (5); （5）； Combining equation (3), the norm of η(x) is shown in equation (6); （6）； Step 2.4, combining equations (4), (5), and (6), construct the nonlinear flux observer model, as shown in equation (7); （7）； in, and Let be the state variables and their derivatives, respectively, of the nonlinear flux observer. For observer gain and >0; Step 2.5, transform equation (3) to obtain equation (8); （8）； The sine and cosine components containing the estimated rotor position are obtained from the observer, as shown in Equation (9); （9）； In the formula, To estimate the rotor position; Step 2.6: After normalizing the sine and cosine components containing the estimated rotor position, the estimated rotor position is obtained through phase-locked loop calculation. and estimated rotational speed This forms a speed ring.

3. The method as described in claim 1, characterized in that, Step 5 specifically involves: Step 5.1, let the output of the q-axis perturbation observer in step 3 be... Equal to the q-axis average dead zone compensation voltage in step 4 The estimated dead time is obtained. As shown in equation (22); （22）； Step 5.2, substitute equation (22) into equation (16) to obtain the estimated dead zone compensation voltage of phase A, as shown in equation (22-1); （22-1）； Similarly, the estimated dead zone compensation voltages for phases BC are shown in equations (23) and (24); （23）； （24）； Step 5.3: Apply the estimated dead-zone compensation voltage of phases ABC to the three-phase output voltage of the inverter to achieve dead-zone compensation.

4. The method as described in claim 1, characterized in that, Before step 1, the motor control system should have the functions of sampling at least two phase currents and bus voltage.

5. The method as described in claim 1, characterized in that, After completing step 5, the feasibility of the method is verified through simulation modeling or experiments. The experimental verification method includes high-speed and low-speed operating conditions.

6. The method as described in claim 5, characterized in that, The above-mentioned high-speed operating condition verification method is as follows: when the given speed is 8000 rpm, the initial load is 0.5 Nm, and the load suddenly changes to 2 Nm at 1 s. After the dead zone is compensated, the time required for the speed fluctuation caused by the sudden load change to recover to the steady state value is significantly reduced. In addition, compared with the waveform without dead zone compensation, the waveform fluctuation of the estimated speed after dead zone compensation is also improved and is closer to the actual speed.

7. The method as described in claim 6, characterized in that, The specific verification method for low-speed operation is as follows: given a speed of 200 rpm, the load increases with time and reaches its maximum at 0.35 s, with a maximum value of 2.5 Nm.

Images