A permanent magnet synchronous motor control method based on improved linear superhelix

Abstract

The present invention relates to the field of motor control technology, and discloses a permanent magnet synchronous motor control method based on an improved linear superhelix, establishes a two-phase stationary coordinate system, obtains a stator current equation, establishes a permanent magnet synchronous motor mechanical motion equation, defines the permanent magnet synchronous motor system state variables, establishes an integral sliding mode surface, and constructs a reaching law speed controller, establishes an improved linear superhelix sliding film observer for estimating back electromotive force, and calculates the rotor speed and rotor position of the permanent magnet synchronous motor. The method is improved on the basis of a linear superhelix sliding mode observer. When the system error increases, the sliding mode gain can be adjusted with the system error, and accurate estimation of the motor speed can be achieved without using a low-pass filter; at the same time, the traditional speed controller is improved, and a new reaching law speed controller that can adaptively adjust the gain coefficient when the system error changes is installed, which reduces the system's jitter phenomenon and improves its anti-interference ability.

Description

Technical Field

[0001] The invention relates to the technical field of motor control, and in particular to a permanent magnet synchronous motor control method based on an improved linear superhelix. Background Art

[0002] In industrial applications, especially in areas with demanding dynamic performance and precision, the high efficiency and compactness of permanent magnet synchronous motors make them the first choice. Traditional permanent magnet synchronous motor control strategies rely on mechanical position sensors to obtain the precise position of the rotor, but this increases costs and system complexity and is easily affected by environmental factors, thereby reducing the reliability of the motor. Therefore, sensorless control technology came into being, which estimates the rotor position and speed by analyzing the internal electrical signals of the motor, avoiding the limitations of traditional sensors.

[0003] However, these sensorless technologies, especially the sliding mode observer method, despite their excellent performance in anti-interference and robustness, still have problems with high-frequency jitter and insufficient dynamic response, resulting in a large number of high-frequency signals in the observed back electromotive force. For this reason, a low-pass filter is used to filter out the high-frequency signals, but the addition of a low-pass filter will increase the complexity of the system and cause system phase delay. In the speed loop control, PI control is usually used. The speed estimated by this method has problems such as high overshoot, large steady-state error, and slow convergence. Summary of the invention

[0004] 1. Technical issues to be solved

[0005] In view of the deficiencies in the prior art, the present invention provides a permanent magnet synchronous motor control method based on an improved linear superhelix, which has the advantages of reducing the system's jitter phenomenon and improving its anti-interference ability, thereby solving the above-mentioned technical problems.

[0006] (II) Technical solution

[0007] To achieve the above object, the present invention provides the following technical solution: a permanent magnet synchronous motor control method based on improved linear superhelix, comprising the following steps:

[0008] S1. Establish a two-phase stationary coordinate system and obtain the stator current equation;

[0009] S2. Establish the mechanical motion equation of the permanent magnet synchronous motor;

[0010] S3. Define the permanent magnet synchronous motor system state variables;

[0011] S4, establishing an integral sliding surface and constructing a reaching law speed controller for calculating the current estimation value;

[0012] S5. Based on the traditional sliding mode observer and the linear superhelical algorithm, an improved linear superhelical sliding mode observer is established to estimate the back electromotive force;

[0013] S6, calculating the rotor speed and rotor position of the permanent magnet synchronous motor;

[0014] S7, input the calculated permanent magnet synchronous motor rotor speed into the reaching law speed controller of step S4 to complete the system closed loop.

[0015] As a preferred technical solution of the present invention, the stator current equation in step S1 is expressed as follows:

[0016]

[0017] Among them, i α and i β represent the stator current of α-axis and β-axis respectively, u α and u β represents the stator voltage of α-axis and β-axis respectively, R and L represent the stator resistance and stator inductance respectively, e α and e β are the back electromotive force of the α-axis and the β-axis respectively, represents the α-axis stator current i α The derivative with respect to time t, represents the β-axis stator current i β The derivative with respect to time t.

[0018] As a preferred technical solution of the present invention, the mechanical motion equation of the permanent magnet synchronous motor in step S2 is expressed as follows:

[0019]

[0020] Where J represents the moment of inertia, ω m represents the rotor angular velocity, P n represents the pole pair number, i q represents the q-axis current, T L represents the load torque, Ψ f Represents the flux linkage of a permanent magnet.

[0021] As a preferred technical solution of the present invention, the expression of the system state variable x1 in step S3 is as follows:

[0022] x1=ω ref -ω m

[0023] Among them, ω ref represents the rotor reference angular velocity, ω m Indicates the mechanical angular velocity of the rotor.

[0024] As a preferred technical solution of the present invention, the expression of the integral sliding surface in step S4 is as follows:

[0025]

[0026] Among them, s represents the sliding surface, x1 represents the system state variable, c represents the integral coefficient, represents the integral of the system state variable from 0 to t with respect to time t, and the expression of the reaching law speed controller in step S4 is as follows:

[0027]

[0028] in, represents the derivative of the sliding surface with respect to the system state, sign(*) represents the sign function, |*| represents the absolute value operation, |x| α represents the exponential operation of the absolute value of the system state with α as the exponent, ε|x| α represents the gain coefficient of the sign function sign(s), s represents the sliding surface, k represents the sliding mode gain coefficient, b represents the gain coefficient of the sign function sign(|s|-1), and lim represents the limit operation on the system state.

[0029] As a preferred technical solution of the present invention, the estimated value expression of the current in step S4 is as follows:

[0030]

[0031] Among them, i q represents the q-axis current as the current estimate, sign(*) represents the sign function, |*| represents the absolute value operation, |x| α represents the exponential operation of the absolute value of the system with α as the exponent, ε|x| α represents the gain coefficient of the sign function sign(s), s represents the sliding surface, k represents the sliding gain coefficient, b represents the gain coefficient of the sign function sign(|s|-1), c represents the integral coefficient, J represents the moment of inertia, T L represents the load torque, Ψ f Represents the flux linkage of a permanent magnet.

[0032] As a preferred technical solution of the present invention, the current error state equation is obtained through the traditional sliding mode observer and the stator current equation of the two-phase stationary coordinate system in step S1, and the improved linear super-helical sliding mode observer is constructed in combination with the linear super-helical algorithm. The current error state equation is expressed as follows:

[0033]

[0034] in, and represents the error of the stator current of the α-axis and β-axis in the two-phase stationary coordinate system, sign(*) represents the sign function, R and L are the stator resistance and stator inductance respectively, Indicates the α-axis stator current error The derivative with respect to time t, Indicates the β-axis stator current error The derivative with respect to time t, e α and e β Denote the back electromotive force of the α-axis and the β-axis respectively. The expression of the improved linear super-helical sliding mode observer in step S5 is as follows:

[0035]

[0036] Among them, x1 represents the system state variable, x2 represents the intermediate variable, k1, k2, k3, and k4 are four different sliding mode gain coefficients.

[0037] As a preferred technical solution of the present invention, the back electromotive force expression in step S5 is as follows:

[0038]

[0039] Among them, e α and e β are the back electromotive force of the α-axis and the β-axis respectively, and They respectively represent the errors of the stator currents of the α-axis and β-axis in the two-phase stationary coordinate system, and k1, k2, k3, and k4 are four different sliding mode gain coefficients.

[0040] As a preferred technical solution of the present invention, the permanent magnet synchronous motor rotor speed and rotor position expressions in step S6 are as follows:

[0041] Permanent magnet synchronous motor rotor speed:

[0042]

[0043] Rotor position:

[0044]

[0045] in, represents the rotor angular velocity, represents the estimated rotor position, Ψ f represents the permanent magnet flux, e α and e β denote the back electromotive force of the α-axis and the β-axis respectively, and arctan(*) denotes the inverse tangent trigonometric function.

[0046] Compared with the prior art, the present invention provides a permanent magnet synchronous motor control method based on an improved linear superhelix, which has the following beneficial effects:

[0047] The present invention improves on the basis of a linear super-helical sliding mode observer. When the system error increases, the sliding mode gain can be adjusted along with the system error, and accurate estimation of the motor speed can be achieved without using a low-pass filter. At the same time, the traditional PI speed controller is improved, and a new reaching law speed controller is installed that can adaptively adjust the gain coefficient as the system error changes, thereby reducing the system's chattering phenomenon and improving its anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a schematic diagram of the control principle of the permanent magnet synchronous motor of the present invention;

[0049] Figure 2 It is a schematic diagram of the improved linear super-helical sliding mode observer of the present invention;

[0050] Figure 3 This is a schematic diagram of speed comparison of the permanent magnet synchronous motor of the present invention at zero load;

[0051] Figure 4 A schematic diagram showing a comparison of the rotation speeds of the permanent magnet synchronous motor of the present invention when the load is suddenly increased or decreased;

[0052] Figure 5 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] See also Figure 1-5 , a permanent magnet synchronous motor control method based on improved linear superhelix, comprising the following steps:

[0055] S1. Establish a two-phase stationary coordinate system and obtain the stator current equation, which is expressed as follows:

[0056]

[0057] Among them, i α and i β represent the stator current of α-axis and β-axis respectively, u α and u β represents the stator voltage of α-axis and β-axis respectively, R and L represent the stator resistance and stator inductance respectively, eα and e β are the back electromotive force of the α-axis and the β-axis respectively, represents the α-axis stator current i α The derivative with respect to time t, represents the β-axis stator current i β The derivative with respect to time t;

[0058] S2. Establish the mechanical motion equation of the permanent magnet synchronous motor, which is expressed as follows:

[0059]

[0060] Where J represents the moment of inertia, ω m represents the rotor angular velocity, P n represents the pole pair number, i q represents the q-axis current, T L represents the load torque, Ψ f represents the flux linkage of permanent magnet;

[0061] S3. Define the expression of the permanent magnet synchronous motor system state variable x1:

[0062] x1=ω ref -ω m

[0063] Among them, ω ref represents the rotor reference angular velocity, ω m represents the rotor angular velocity;

[0064] S4, establish an integral sliding surface, and construct a reaching law speed controller. In the permanent magnet synchronous motor system, a new reaching law speed controller is designed for the speed loop, and the sliding surface is designed as an integral sliding surface. Combining the mechanical motion equation of the permanent magnet synchronous motor described in step S2 and the new reaching law speed controller described in step S4, an estimated value of the shaft current can be obtained. The expression of the integral sliding surface in step S4 is as follows:

[0065]

[0066] Among them, s represents the sliding surface, x1 represents the system state variable, c represents the integral coefficient, represents the integral of the system state variable from 0 to t with respect to time t, and the expression of the reaching law speed controller in step S4 is as follows:

[0067]

[0068] in, represents the derivative of the sliding surface with respect to the system state, sign(*) represents the sign function, |*| represents the absolute value operation, |x| αrepresents the exponential operation of the absolute value of the system state with α as the exponent, ε|x| α represents the gain coefficient of the sign function sign(s), s represents the sliding surface, k represents the sliding gain coefficient, b represents the gain coefficient of the sign function sign(|s|-1), The limit value indicating the system state is set to 0, and the estimated value of the current is expressed as follows:

[0069]

[0070] Among them, i q represents the q-axis current as the current estimate, |*| represents the absolute value operation, |x| α represents the exponential operation of the absolute value of the system with α as the exponent, sign(*) represents the sign function, s represents the sliding surface, k represents the sliding gain coefficient, c represents the integral coefficient, J represents the moment of inertia, T L Indicates load torque;

[0071] S5. According to the traditional sliding mode observer and the linear superhelical algorithm, an improved linear superhelical sliding mode observer is established to estimate the back electromotive force. The current error state equation is obtained through the traditional sliding mode observer and the stator current equation of the two-phase stationary coordinate system in step S1. The improved linear superhelical sliding mode observer is constructed in combination with the linear superhelical algorithm. The expression of the traditional sliding mode observer is as follows:

[0072]

[0073] in, and The current estimation values ​​of the A-axis and β-axis stator currents, and the current error state equation expressions are as follows:

[0074]

[0075] in, and represents the error of the stator current of the α-axis and β-axis in the two-phase stationary coordinate system, sign(*) represents the sign function, R and L are the stator resistance and stator inductance respectively, Indicates the α-axis stator current error The derivative with respect to time t, Indicates the β-axis stator current error The derivative with respect to time t, e α and e β They represent the back electromotive force of the α-axis and the β-axis respectively, where the expression of the linear superhelical algorithm is as follows:

[0076]

[0077] The expression of the improved linear super-helical sliding mode observer in step S5 is as follows:

[0078]

[0079] Among them, x1 represents the system state variable, k1, k2, k3, and k4 are four different sliding mode gain coefficients;

[0080] S6. Calculate the rotor speed and rotor position of the permanent magnet synchronous motor from the estimated back electromotive force using the inverse tangent function. The formula is as follows: Permanent magnet synchronous motor rotor speed:

[0081]

[0082] Rotor position:

[0083]

[0084] in, represents the estimated rotor angular velocity, represents the estimated rotor position, e α and e β denote the back electromotive force of the α-axis and the β-axis respectively, arctan(*) denotes the inverse tangent trigonometric function;

[0085] S7, input the calculated permanent magnet synchronous motor rotor speed into the reaching law speed controller of step S4 to complete the system closed loop.

[0086] according to Figure 1 The control block diagram shown in the figure is used to build a physical platform for experimental verification. The parameters of the permanent magnet synchronous motor are as follows: rated power 750W, rated speed 3000r / (min), rated torque 2.4N·m, pole pair number 4, permanent magnet flux linkage 0.11Wb, stator resistance 0.901Ω, and inductance 6.552mH. Figure 3 This is the experimental result of the motor accelerating from 0 to 1300r / min when it is unloaded. Figure 4 The speed test results are as follows: the motor accelerates from 0 to 1300r / (min) when it is unloaded, and when the speed stabilizes at 1300r / (min), a 2N·m load is suddenly added or reduced. Figure 3 It can be seen that the speed estimation of the method of the present invention is greatly improved compared with the traditional method, and there is almost no overshoot. Figure 4 It can be seen that after loading 2N·m or unloading 2N·m, the speed of the method of the present invention quickly recovers to the given speed after decreasing or increasing. The experimental results show that the method of the present invention estimates the speed accurately and has strong dynamic robustness, which proves the effectiveness of the present invention.

[0087] The present invention provides a permanent magnet synchronous motor control method based on an improved linear superhelix. The control method is improved on the basis of a linear superhelix sliding mode observer. When a system error increases, the sliding mode gain can be adjusted along with the system error, so that accurate estimation of the motor speed can be achieved without using a low-pass filter. At the same time, a traditional PI speed controller is improved, and a new reaching law speed controller that can adaptively adjust the gain coefficient as the system error changes is installed, thereby reducing the system's chattering phenomenon and improving its anti-interference ability.

[0088] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A permanent magnet synchronous motor control method based on improved linear superhelix, characterized in that: The following steps are involved: S1. Establish a two-phase stationary coordinate system and obtain the stator current equation; S2. Establish the mechanical motion equation of the permanent magnet synchronous motor; S3. Define the permanent magnet synchronous motor system state variables; S4, establishing an integral sliding surface and constructing a reaching law speed controller for calculating the current estimation value; S5. Based on the traditional sliding mode observer and the linear super-helical algorithm, an improved linear super-helical sliding mode observer is established to estimate the back electromotive force; Through the traditional sliding mode observer and the stator current equation of the two-phase stationary coordinate system in step S1, the current error state equation is obtained, and combined with the linear super-helical algorithm, the construction of the improved linear super-helical sliding mode observer is completed. The current error state equation is expressed as follows: ； in, and Indicates the two-phase stationary coordinate system Axis and The error of the shaft stator current, represents the symbolic function, and are the stator resistance and stator inductance respectively, express Axis stator current error About Time The derivative of express Axis stator current error About Time The derivative of and Respectively Axis and The back electromotive force of the shaft, the expression of the improved linear super-helical sliding mode observer in step S5 is as follows: ； in, represents the system state variable, represents the intermediate variable, , , , There are four different sliding mode gain coefficients respectively; The back electromotive force expression in step S5 is as follows: ； in, and Respectively Axis and The back EMF of the shaft, and Represent the two-phase stationary coordinate system Axis and The error of the shaft stator current, , , , There are four different sliding mode gain coefficients respectively; S6, calculating the rotor speed and rotor position of the permanent magnet synchronous motor; The permanent magnet synchronous motor rotor speed and rotor position expressions in step S6 are as follows: Permanent magnet synchronous motor rotor speed: ； Rotor position: ； in, represents the estimated rotor angular velocity, represents the estimated rotor position, represents the permanent magnet flux, and Respectively Axis and The back EMF of the shaft, represents the inverse tangent trigonometric function; S7, input the calculated permanent magnet synchronous motor rotor speed into the reaching law speed controller of step S4 to complete the system closed loop.

2. The method for controlling a permanent magnet synchronous motor based on an improved linear superhelix according to claim 1, characterized in that: The expression of the stator current equation in step S1 is as follows: ； in, and Respectively Axis and The stator current of the shaft, and Respectively Axis and The stator voltage of the shaft, and are the stator resistance and stator inductance respectively, and Respectively Axis and The back EMF of the shaft, express Shaft stator current About Time The derivative of express Shaft stator current About Time The derivative of .

3. The method for controlling a permanent magnet synchronous motor based on an improved linear superhelix according to claim 1, characterized in that: The mechanical motion equation of the permanent magnet synchronous motor in step S2 is expressed as follows: ； in, represents the moment of inertia, represents the rotor mechanical angular velocity, represents the pole pair number, express Shaft current, represents the load torque, Represents the flux linkage of a permanent magnet.

4. The method for controlling a permanent magnet synchronous motor based on an improved linear superhelix according to claim 3 is characterized in that: The system state variables in step S3 The expression is as follows: ； in, represents the rotor reference angular velocity, Indicates the mechanical angular velocity of the rotor.

5. The method for controlling a permanent magnet synchronous motor based on an improved linear superhelix according to claim 1, characterized in that: The expression of the integral sliding surface in step S4 is as follows: ； in, represents the sliding surface, represents the system state variable, represents the integral coefficient, Indicates that the system state variables are arrive About time The integral of , the expression of the reaching law speed controller in step S4 is as follows: ； in, represents the derivative of the sliding surface with respect to the system state, represents the symbolic function, represents the absolute value operation, Indicates that the absolute value of the system state is is the exponential operation of the exponent, The gain factor, represents the sliding surface, represents the sliding mode gain coefficient, Represents a symbolic function The gain factor, Represents a limit operation on the system state.

6. The method for controlling a permanent magnet synchronous motor based on an improved linear superhelix according to claim 5, characterized in that: The estimated value expression of the current in step S4 is as follows: ； in, express The shaft current, as an estimate of the current, represents the symbolic function, represents the absolute value operation, Indicates that the absolute value of the system is is the exponential operation of the exponent, The gain factor, represents the sliding surface, represents the sliding mode gain coefficient, Represents a symbolic function The gain factor, represents the integral coefficient, represents the moment of inertia, represents the load torque, represents the permanent magnet flux, Represents the number of pole pairs.

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