Permanent Magnet Synchronous Motor Rotor Position and Speed Estimation Method Based on an Enhanced Observer

Abstract

The present invention discloses a method for estimating the rotor position and speed of a permanent magnet synchronous motor by using an enhanced observer, which specifically includes the following steps: Step 1, construct the state equation of the permanent magnet synchronous motor; Step 2, construct an enhanced extended state observer based on the state equation obtained in Step 1 to estimate the extended back electromotive force; Step 3, estimate the rotor position and speed of the permanent magnet synchronous motor through a phase-locked loop by using the extended back electromotive force obtained in Step 2. This solves the problem that the existing extended state observer cannot estimate the rapidly changing extended back electromotive force, resulting in a serious lag of the estimated rotor position behind the actual rotor position, and even causing the system to diverge.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor control, and relates to a method for estimating the rotor position and speed of a permanent magnet synchronous motor with an enhanced observer. Background Technique

[0002] Permanent magnet synchronous motors have many advantages such as high efficiency, high power density, and wide speed regulation range, and have been widely used in household appliances, rail transit, industrial manufacturing, aerospace and other fields. Accurate rotor position and speed are crucial for a high-quality permanent magnet synchronous motor drive system. Usually, mechanical sensors are installed to detect the rotor position and speed. However, installing mechanical sensors not only increases the cost of the permanent magnet synchronous motor drive system, but also reduces the reliability of the system. Therefore, accurate rotor position and speed estimation is an important way to improve the reliability of the permanent magnet synchronous motor drive system and reduce the cost of the permanent magnet synchronous motor drive system.

[0003] The extended state observer observes the total disturbance of the system as an extended state variable of the system, and does not depend on the accurate mathematical model of the controlled object. Using the extended state observer to estimate the rotor position and speed has anti-disturbance characteristics. However, the extended state observer has a low-pass filtering characteristic. When the motor operates in the high-speed region, the extended back electromotive force is a high-frequency disturbance, and the phase lag of the extended back electromotive force estimated by the extended state observer is serious, resulting in a serious lag of the estimated rotor position behind the actual rotor position, and even causing the system to diverge. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for estimating the rotor position and speed of a permanent magnet synchronous motor with an enhanced observer, which solves the problem that the existing extended state observer cannot estimate the rapidly changing extended back electromotive force, resulting in a serious lag of the estimated rotor position behind the actual rotor position, and even causing the system to diverge.

[0005] The technical solution adopted by the present invention is a method for estimating the rotor position and speed of a permanent magnet synchronous motor with an enhanced observer, which specifically includes the following steps:

[0006] Step 1, construct the state equation of the permanent magnet synchronous motor;

[0007] Step 2, construct an enhanced extended state observer based on the state equation obtained in Step 1 to estimate the extended back electromotive force;

[0008] Step 3, estimate the rotor position and speed of the permanent magnet synchronous motor through the extended back electromotive force obtained in Step 2 by using a phase-locked loop.

[0009] The characteristics of the present invention also lie in:

[0010] The specific process of Step 1 is as follows:

[0011] Atαβ The voltage equation of a permanent magnet synchronous motor in a two-phase stationary coordinate system is shown in the following formula (1):

[0012] (1);

[0013] Wherein, u α and u β are the components of the stator voltage on the α axis and β axis respectively, i α and i β are the components of the stator current on the α axis and β axis respectively, p is the differential operator, R s is the stator resistance, and are the components of the extended back electromotive force on the α axis and β axis respectively, L d is the d axis inductance, L q is the q axis inductance, i d is the component of the stator current on the d axis, is the permanent magnet flux linkage, ω r is the actual rotor speed, θ r is the actual rotor position;

[0014] The differential of the stator current obtained from formula (1) is shown in the following formula (2):

[0015] (2);

[0016] Formula (2) is written in the form of a state equation as shown in the following formula (3):

[0017] (3);

[0018] Wherein, x 1 = i α i β T , b 0 = 1 / L q , u ​= u α u β T , f =- i α i β T R s / L q , d = e α e β T ;

[0019] Expand the d in Equation (3) into new state variables as shown in the following Equation (4):

[0020] (4);

[0021] Wherein, x 2= d = e α e β T 。

[0022] The specific process of Step 2 is as follows:

[0023] Step 2.1, construct an enhanced extended state observer through the state equation obtained in Step 1 to estimate the extended back electromotive force;

[0024] Step 2.2, design the nonlinear function h ;

[0025] Step 2.3, design the fast disturbance tracker g。

[0026] The specific process of Step 2.1 is as follows:

[0027] Construct an enhanced extended state observer through Equation (4) as shown in the following Equation (5):

[0028] (5);

[0029] Wherein, is 's estimated value, is 's estimated value, is​​​​ The estimated value of is The estimated value of is α Axis extended back electromotive force e α The estimated value of is β Axis extended back electromotive force e β The estimated value of is The estimated value of Is the estimated value The difference from the measured value of , , β 1. β 2 is an adjustable parameter, h is a non - linear function, g is a fast disturbance tracker.

[0030] The specific process of step 2.2 is as follows:

[0031] Design the non - linear function in the enhanced extended state observer h as shown in the following formula (6):

[0032] (6);

[0033] Where, when estimating α Axis extended back electromotive force at that time, is .

[0034] The specific process of step 2.3 is as follows:

[0035] Implant the fast disturbance tracker in the extended state observer g , the designed fast disturbance tracker g is shown in the following formula (7):

[0036] (7);

[0037] Where, is the estimated rotor speed; is the width of the center frequency; is an adjustable parameter, The value of mainly affects the amplitude at the center frequency; is an adjustable parameter and is negative, The value of mainly affects the dynamic response of the fast disturbance tracker g ;

[0038] Adjustable parameter The adjustment method is as shown in formula (8) below:

[0039] (8);

[0040] Wherein, is the given rotational speed.

[0041] The specific process of step 3 is as follows:

[0042] The estimated extended back electromotive force obtained from formula (5) 、 Calculate the rotor position error signal as shown in formula (9) below:

[0043] (9);

[0044] Wherein, θ e is the estimated rotor position, is the rotor position error signal;

[0045] The rotor position error signal is adjusted by a PI regulator to obtain the estimated rotational speed as shown in formula (10) below:

[0046] (10);

[0047] Wherein, is the proportional gain, is the integral gain, is the estimated rotational speed;

[0048] Integrate the estimated rotational speed ω e to obtain the estimated rotor position as shown in formula (11) below:

[0049] (11).

[0050] The beneficial effect of the present invention is that, compared with the traditional method for estimating the rotor position and rotational speed using an extended state observer, the method for estimating the rotor position and rotational speed of a permanent magnet synchronous motor using an enhanced extended state observer proposed by the present invention, through the fast disturbance tracker g , can accurately estimate the rotor position and rotational speed even when the motor is running at high speed, and the designed fast disturbance tracker g can improve the robustness of the estimated extended back electromotive force to the center frequency and improve the dynamic performance of the fast disturbance tracker for estimating the extended back electromotive force by designing adjustable parameters and . At the same time, the designed nonlinear function h has a robust effect on large errors. When the error is large, the nonlinear functionh It decreases, avoiding the oscillation and large overshoot of the estimated extended back electromotive force. It solves the problem that the extended state observer cannot estimate the rapidly changing extended back electromotive force, resulting in a serious lag of the estimated rotor position behind the actual rotor position, and even causing the system to diverge. Description of the Drawings

[0051] Figure 1 is the vector control system block diagram adopted by the rotor position and speed estimation method of the permanent magnet synchronous motor with an enhanced observer of the present invention;

[0052] Figures 2(a) to 2(b) are the block diagrams of the enhanced extended state observer adopted in the rotor position and speed estimation method of the permanent magnet synchronous motor with an enhanced observer of the present invention;

[0053] Figure 3 is the block diagram of the phase-locked loop structure adopted in the rotor position and speed estimation method of the permanent magnet synchronous motor with an enhanced observer of the present invention;

[0054] Figure 4 is the simulation result diagram of the rotor speed estimated by using the traditional extended state observer;

[0055] Figure 5 is the simulation diagram of the rotor speed estimated by using the rotor position and speed estimation method of the permanent magnet synchronous motor with an enhanced observer of the present invention. Detailed Embodiment

[0056] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0057] For the rotor position and speed estimation method of the permanent magnet synchronous motor with an enhanced observer of the present invention, the vector control system block diagram adopted therein is as Figure 1 shown, and it is specifically implemented according to the following steps:

[0058] Step 1, construct the state equation of the permanent magnet synchronous motor, specifically:

[0059] In αβ the voltage equation of the permanent magnet synchronous motor in the two-phase stationary coordinate system is as shown in the following formula (1):

[0060] (1);

[0061] Among them, u α , u β are respectively the components of the stator voltage on the α axis and the β axis, i α , i β are respectively the stator currents on theα The axis and β the components of the axis, p are differential operators, R s is the stator resistance, 、 are the components of the extended back electromotive force in α the axis and β the axis, L d is d the axis inductance, L q is q the axis inductance, i d is the component of the stator current in d the axis, is the permanent magnet flux linkage, ω r is the actual rotor speed, θ r is the actual rotor position.

[0062] The differential of the stator current is obtained by formula (1) as shown in formula (2) below:

[0063] (2);

[0064] Formula (2) is written in the form of a state equation as shown in formula (3) below:

[0065] (3);

[0066] Among them, x 1 = i α i β T , b 0 = 1 / L q , u = u α u β T , f = - i α i β T R s / L q , d = e α e ​​​β T 。

[0067] Expand the d in Equation (3) into new state variables as shown in Equation (4) below:

[0068] (4);

[0069] where x 2 = d = e α e β T 。

[0070] Step 2. Construct an enhanced extended state observer based on the state equation obtained in Step 1 to estimate the extended back electromotive force as shown in Figures 2(a) and 2(b). Figure 2(a) shows the axis extended back electromotive force; Figure 2(b) shows the axis extended back electromotive force; specifically:

[0071] Step 2.1. Construct an enhanced extended state observer based on the state equation obtained in Step 1 to estimate the extended back electromotive force;

[0072] Construct an enhanced extended state observer through Equation (4) as shown in Equation (5) below:

[0073] (5);

[0074] where is the estimated value of , is the estimated value of , is the estimated value of , is the estimated value of , is the estimated value of the α axis extended back electromotive force e α , is the estimated value of the β axis extended back electromotive force e β , is the estimated value of , is the difference between the estimated value and the measured value , , , β 1, β 2 are adjustable parameters, h ​​is a non - linear function, g is a fast disturbance tracker.

[0075] Step 2.2, design the non - linear function in the enhanced extended state observer h ;

[0076] The non - linear function in the enhanced extended state observer h determines the rapidity of the enhanced extended state observer in estimating the disturbance. The non - linear function h should have the characteristics of small error and large gain, and large error and small gain. Design the non - linear function in the enhanced extended state observer h as shown in the following formula (6):

[0077] (6);

[0078] where, when estimating the α axis extended back - electromotive force at that time is ; when estimating the β axis extended back - electromotive force at that time is , τ is an adjustable parameter. A smaller τ value results in a faster dynamic response, but too small a τ value will cause system oscillation. On the contrary, the larger the τ value, the smaller the overshoot, but the slower the dynamic performance. Take τ = 0.6.

[0079] Step 2.3, design the fast disturbance tracker in the enhanced extended state observer g ;

[0080] The traditional extended state observer has a low - pass filtering characteristic. When the motor operates in the high - speed region, the extended back - electromotive force is a high - frequency disturbance. The phase lag of the extended back - electromotive force estimated by the traditional extended state observer is serious, resulting in a serious lag of the estimated rotor position behind the actual rotor position, and even causing the system to diverge. Implant a fast disturbance tracker g in the extended state observer. The designed fast disturbance tracker g is shown in the following formula (7):

[0081] (7);

[0082] where, is the estimated rotor speed; is the width of the center frequency. Take ; is an adjustable parameter, The value mainly affects the amplitude at the center frequency; is an adjustable parameter and is negative, The value of g mainly affects the dynamic response of the fast interference tracker The larger the absolute value of , the better the dynamic performance, but too large a causes the estimated fast disturbance phase to be misaligned. Take

[0083] Adjustable parameter The adjustment method is shown in the following formula (8):

[0084] (8);

[0085] Where, is the given rotational speed.

[0086] Step 3, estimate the rotor position and rotational speed of the permanent magnet synchronous motor from the extended back electromotive force obtained in Step 2 through the phase-locked loop as shown in Figure 3 Specifically:

[0087] The estimated extended back electromotive force obtained from formula (5) , Calculate the rotor position error signal as shown in the following formula (9):

[0088] (9);

[0089] Where, θ e is the estimated rotor position, is the rotor position error signal.

[0090] The rotor position error signal is adjusted through a PI regulator to obtain the estimated rotational speed as shown in the following formula (10):

[0091] (10);

[0092] Where, is the proportional gain, is the integral gain, is the estimated rotational speed.

[0093] Integrate the estimated rotational speed ω e to obtain the estimated rotor position as shown in the following formula (11):

[0094] (11);

[0095] The vector control system block diagram adopted by the rotor position and speed estimation method of the permanent magnet synchronous motor with an enhanced observer is as follows Figure 1 shown. The system consists of three PI regulators to form a double-loop control of the speed loop and the current loop. The output of the speed loop PI regulator serves as the input of the maximum torque per ampere control (MTPA). The current command output by MTPA 、 serves as the input of the current loop PI regulator, and the output of the current regulator controls the power electronic converter.

[0096] The stator current of the permanent magnet synchronous motor in the three-phase stationary coordinate system is detected by a current Hall sensor i a 、 i b 、 i c ; The detected three-phase stator currents i a 、 i b 、 i c are transformed through abc / αβ to the current values in the two-phase stationary coordinate system i α 、 i β ; i α 、 i β are transformed through αβ / dq to the current values in the two-phase synchronous rotating coordinate system i d 、 i q ; The two-phase voltages u α 、 u β and the two-phase currents i α 、 i β in the two-phase stationary coordinate system are used as the inputs of the enhanced extended state observer shown in Figures 2(a) and 2(b). The outputs of the enhanced extended state observer are the estimated extended back electromotive forces 、 ; The estimated extended back electromotive forces 、 pass through the phase-locked loop shown in Figure 3 to obtain the estimated rotor position θ e and speed ω e ; The given speed of the speed loop The rotational speed estimated by the phase-locked loop ω e Take the difference, and after passing through the rotational speed loop PI controller, output the given value of electromagnetic torque Then, obtain the given excitation current from the maximum torque per ampere (MTPA) And the given torque current ; The given excitation current And the feedback current i d Take the difference, and after passing through the current loop PI controller, output d Axis voltage The given excitation current And the feedback current i q Take the difference, and after passing through the current loop PI controller, output q Axis voltage ; , After passing through dq / αβ Transformation to obtain the two-phase voltages in the two-phase stationary coordinate system u α , u β , and then through SVPWM modulation to control the three-phase inverter, and finally drive the permanent magnet synchronous motor to work.

[0097] Figure 4 is the simulation diagram of the rotor speed estimated by using the traditional extended state observer;

[0098] Figure 5 is the simulation diagram of the rotor speed estimated by using the method of the present invention.

[0099] Figure 4 and Figure 5 The parameters of the permanent magnet synchronous motor used in the simulation are shown in Table 1. Figure 4 and Figure 5 In the simulation results, the rotational speed is set as follows: from 0 s to 0.2 s, the motor accelerates from 0 rpm to 500 pm; from 0.2 s to 0.5 s, the motor runs at 500 rpm, and the rated load is suddenly applied at 0.3 s; from 0.5 s to 0.7 s, the motor accelerates from 500 rpm to 1000 rpm; from 0.7 s to 0.8 s, the motor runs at 1000 rpm.

[0100] Compare Figure 4 and Figure 5It can be found that: during the process of the motor accelerating from 500 rpm to 1000 rpm, the rotor speed estimated by the traditional extended state observer cannot track the set speed as the speed increases, resulting in system divergence, while the rotor speed estimated by the present invention can accurately track the set speed. The above simulation results show that the present invention can effectively solve the problem that the speed and rotor position estimated by the existing extended state observer cannot accurately track the actual speed and rotor position, and even lead to system divergence.

[0101] Table 1 Parameters of the permanent magnet synchronous motor

[0102]

Claims

1. A method for estimating the rotor position and speed of a permanent magnet synchronous motor using an enhanced observer, characterized in that: Specifically, it includes the following steps: Step 1, construct the state equation of the permanent magnet synchronous motor; The specific process of Step 1 is as follows: In αβ The voltage equation of a permanent magnet synchronous motor in a two-phase static coordinate system is as shown in the following formula (1): （1）； Among them, u α and u β are the components of the stator voltage on the α axis and the β axis respectively, i α and i β are the components of the stator current on the α axis and the β axis respectively, p is the differential operator, R s is the stator resistance, and are the components of the extended back electromotive force on the α axis and the β axis respectively, L d is the d axis inductance, L q is the q axis inductance, i d is the component of the stator current on the d axis, is the permanent magnet flux linkage, ω r is the actual rotor speed, θ r is the actual rotor position; The differential of the stator current is obtained through Formula (1) as shown in the following Formula (2): （2）； Formula (2) is written in the form of a state equation as shown in the following Formula (3): （3）； Among them, x 1 = i α i β T , b 0 = 1 / L q , u = u α u β T , f = - i α i β T R s / L q , d = e α e β T ;​​​​ Expand the d in Equation (3) into new state variables as shown in Equation (4) below: （4） ； Among them, x 2 = d = e α e β T ;​ Step 2, construct an enhanced extended state observer based on the state equation obtained in Step 1 to estimate the extended back electromotive force; The specific process of Step 2 is as follows: Step 2.1, construct an enhanced extended state observer based on the state equation obtained in Step 1 to estimate the extended back electromotive force; The specific process of Step 2.1 is as follows: Construct an enhanced extended state observer through Formula (4) as shown in the following Formula (5): （5）； wherein, is 's estimated value, is 's estimated value, is 's estimated value, is 's estimated value, is α axis extended back electromotive force e α 's estimated value, is β axis extended back electromotive force e β 's estimated value, is 's estimated value, is the estimated value and the measured value 's difference, , , β 1, β 2 are adjustable parameters, h is a non-linear function, g is a fast disturbance tracker; Step 2.2, design the non-linear function in the enhanced extended state observer h ; Step 2.3, design the fast disturbance tracker in the enhanced extended state observer g ; Step 3, estimate the rotor position and speed of the permanent magnet synchronous motor through the extended back electromotive force obtained in Step 2 by using a phase-locked loop.

2. The method for estimating the rotor position and speed of a permanent magnet synchronous motor with an enhanced observer according to claim 1, characterized in that: The specific process of Step 2.2 is as follows: Nonlinear function in the designed enhanced extended state observer h As shown in the following formula (6): （6）； Among them, when estimating α axis extended back electromotive force time, is .

3. The method for estimating the rotor position and speed of a permanent magnet synchronous motor with an enhanced observer according to claim 2, wherein: The specific process of Step 2.3 is as follows: Implanting a fast disturbance tracker in the extended state observer g , the designed fast disturbance tracker g is shown in the following formula (7): （7）； Among them, is the estimated rotor speed; is the width of the center frequency; is an adjustable parameter, and the value of mainly affects the amplitude at the center frequency; is an adjustable parameter and is negative, and the value of mainly affects the dynamic response of the fast interference tracker g ; Adjustable parameter The adjustment method is shown in the following formula (8): （8） Among them, is the given rotational speed.

4. The method for estimating the rotor position and speed of a permanent magnet synchronous motor with an enhanced observer according to claim 3, characterized in that: The specific process of Step 3 is as follows: Estimated extended back electromotive force obtained from Equation (5) , The rotor position error signal is calculated as shown in Equation (9) below: （9）； Among them, θ e is the estimated rotor position, is the rotor position error signal; Rotor position error signal The estimated speed is adjusted by a PI regulator as shown in the following formula (10): （10）； Among them, is the proportional gain, is the integral gain, is the estimated rotational speed; The estimated rotational speed ω e Integrating gives the estimated rotor position as shown in the following formula (11): （11）。

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