Improved sliding mode observation method suitable for PMSM non-inductive control system

Abstract

An improved sliding mode observation method suitable for a PMSM non-inductive control system comprises the following steps: constructing a voltage equation under a static coordinate system based on a motor mathematical model under the static coordinate system, and further rewriting the voltage equation into a stator current equation; designing a sliding-mode observer to obtain an observed value of stator current under a static coordinate system, and taking the deviation between the observed value and an actual value as the input of a designed segmented continuous function; multiplying the output of the piecewise continuous function by the sliding mode gain to obtain an equivalent back electromotive force, and extracting the rotor position and the rotating speed from the back electromotive force by using an arc tangent method; a sliding-mode observer adopting a segmented continuous function is introduced into a PMSM vector control method to replace the effect of a position sensor, the rotating speed is obtained through phase voltage and phase current, and closed-loop control is achieved. According to the method, the characteristic that the switching function has derivative continuity in the time domain is ensured, the goal of smooth switching process is realized, and the switching function can be simplified, so that the method has the characteristics of simple operation and flexible change.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet synchronous motor control methods, and specifically relates to an improved sliding mode observer suitable for a PMSM sensorless control system, which is mainly used to quickly and accurately obtain the rotor position of the permanent magnet synchronous motor, accurately predict the speed of the permanent magnet synchronous motor without a speed sensor, realize intelligent monitoring and control of the motor speed, and ensure the safety and reliability of the motor operation. Background Art

[0002] In the control of permanent magnet synchronous motors, traditional methods are based on sensors. Although the presence of sensors ensures the accuracy of feedback information, there are also the following disadvantages: adding sensors will increase costs; to ensure system stability, sensors have requirements for installation environment and space, which will restrict the application scenarios of motors; sensors need to be calibrated before being put into use, making system debugging more complicated and increasing the steps before being put into use. The emergence of sensorless control technology has overcome these disadvantages, but the current accuracy cannot reach the level of sensored control. How to improve the accuracy of sensorless control so that it can gradually replace sensored control in most application scenarios is a hot topic of current research. The core of sensorless control is the rotor position estimation algorithm, and the sliding mode observer method is an estimation method with simple adjustment and high robustness. The sliding surface and switching function are the key to adjustment. In terms of the change of the switching function, the traditional sign function (sgn) is simple and easy to implement, but due to its discontinuity at the switching point, it often causes the chattering problem of the sliding mode controller, affecting the stability and control accuracy of the system. To reduce jitter, researchers have proposed using continuous functions such as the hyperbolic tangent function (tanh) to replace the sign function. However, although the hyperbolic tangent function can reduce jitter, its calculation introduces exponential operations, which is relatively complex. Especially in embedded systems, it increases the computational burden of the microcontroller (MCU). Especially in real-time control systems, it affects the response speed and control effect of the system. Therefore, how to effectively reduce jitter while reducing the burden on the microcontroller is an important research direction in current sensorless control.

[0003] The existing sensorless control method of permanent magnet synchronous motor based on sliding film observer has the following disadvantages: 1) The switching function of the traditional sliding mode observer has the characteristic of derivative discontinuity in the time domain, and the switching process will change significantly, resulting in the jitter phenomenon in the traditional sliding mode observation, affecting the control accuracy and stability of the system; 2) The existing optimized switching function includes complex functions such as hyperbolic tangent. Although it ensures the continuity of the derivative in the time domain and makes the switching process smooth, it involves advanced operations including exponential operations, which has high requirements for the microcontroller (MCU) with limited resources in embedded devices. Summary of the invention

[0004] In order to overcome the shortcomings of the existing technology, the present invention provides a sliding mode observation method based on a piecewise continuous switching function suitable for a permanent magnet synchronous motor (PMSM) sensorless control system, which not only ensures that the switching function has the characteristics of derivative continuity in the time domain and achieves the goal of a smooth switching process, but also simplifies the switching function so that it has the characteristics of simple calculation and flexible change.

[0005] The technical solution adopted by the present invention to solve its technical problem is:

[0006] An improved sliding mode observation method suitable for PMSM sensorless control system includes the following steps:

[0007] Step 1: Based on the mathematical model of the motor in the stationary coordinate system, construct the voltage equation in the stationary coordinate system, and further rewrite it into the stator current equation;

[0008] Step 2: Design a sliding mode observer SMO to obtain the observed value of the stator current in the stationary coordinate system, and the deviation between the observed value and the actual value is used as the input of the designed piecewise continuous function F(x);

[0009] Step 3: Multiply the output of the piecewise continuous function by the sliding mode gain to obtain the equivalent back electromotive force, and use the inverse tangent method to extract the rotor position and speed from the back electromotive force;

[0010] Step 4: Introduce the sliding mode observer using piecewise continuous function into the PMSM vector control method to replace the role of the position sensor, obtain the speed through the phase voltage and phase current, and realize closed-loop control.

[0011] Furthermore, in step 1, the voltage in the stationary coordinate system is as shown in formula (1):

[0012]

[0013] Where, R is the stator resistance, L is the s is the stator inductance, i α 、i β is the stator current, u α 、u β is the stator voltage, E α 、E β To expand the back EMF;

[0014] The current in the stationary coordinate system is shown in formula (2):

[0015]

[0016] The extended back electromotive force is shown in formula (3):

[0017]

[0018] where ω e Electrical angular velocity, ψ f For magnetic link.

[0019] In step 2, the observation current designed in the stationary coordinate system is shown in formula (4):

[0020]

[0021] The difference between formula (4) and formula (2) gives formula (5):

[0022]

[0023] in is the observed value of stator current, is the difference between the observed value and the actual value of the stator current, v α , v β is the designed sliding mode control law, which is shown in formula (6):

[0024]

[0025] Where K is the sliding mode gain, and F(x) replaces the sign function sgn(x), as shown in formula (7):

[0026]

[0027] T1 and T2 are segmentation points, satisfying 0≤T1≤T2. To satisfy the conditions of continuity of the junction point value and derivative, we can get

[0028] After using a piecewise continuous quadratic switching function instead of the sign function, when the absolute value of the current error is greater than T2, the output of the switching function is consistent with the output of the sign function. When the absolute value of the current error is less than T1, the output of the switching function is a linear function. When the absolute value of the current error is between T1 and T2, the output of the switching function is a quadratic function, which has the same derivative at T1 and T2, so that the output of the piecewise function will not change suddenly and can transition smoothly.

[0029] In step 3, when the observer state variable reaches the sliding surface When , the equivalent back electromotive force is as shown in formula (8):

[0030]

[0031] Combining formula (3), we get formula (9):

[0032]

[0033] In step 4, the sensorless vector control process based on the piecewise continuous function sliding mode observer is as follows: the timer triggers the analog-to-digital converter (ADC) to sample the phase current, and the phase current is transformed by Clark to obtain the two-phase stationary coordinate system current i α 、i β , and then converted into the synchronous rotating coordinate system dq axis current i through Park coordinate transformation d 、i q , and the deviation from the speed loop output is used as the input of the current loop PI controller; the timer triggers the ADC sampling to obtain the phase voltage, and the phase voltage is transformed by Clark to obtain the two-phase stationary coordinate system current u α 、u β ;change i α 、i β 、u α 、u β As the input signal of the sliding mode observer, the speed signal is output, and the deviation from the expected speed is used as the input of the speed loop PI controller to form the speed loop feedback and realize the sensorless closed-loop control of the permanent magnet synchronous motor.

[0034] The beneficial effects of the present invention are mainly manifested in: 1) A piecewise continuous function is designed, which has the characteristic of piecewise point derivative continuity, which significantly alleviates the high-frequency jitter problem existing in the sensorless control of permanent magnet synchronous motors using traditional sliding film observers, and achieves a smooth control effect; 2) Different from complex functions such as hyperbolic tangent that involve advanced operations, the piecewise quadratic continuous function designed by the present invention only involves basic operations of addition, subtraction, multiplication and division. For embedded systems and control systems with high real-time requirements, it has lower occupancy and higher efficiency, and has broad prospects in industrial control applications with high real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of the improved sliding mode observation method suitable for PMSM sensorless control system.

[0036] Figure 2 This is the structural block diagram of the sliding mode observer based on piecewise continuous quadratic switching function.

[0037] Figure 3 It is the rotor speed obtained by the sliding film observer within 0-0.1s when the switching function is sgn(x) under continuous system conditions.

[0038] Figure 4 It is the rotor speed obtained by the sliding film observer within 0-0.1s when the switching function is F(x) under continuous system conditions.

[0039] Figure 5 It is the rotor speed obtained by the sliding film observer within 0-0.1s when the switching function is tanh(x) under discrete system conditions.

[0040] Figure 6 It is the rotor speed obtained by the sliding film observer within 0-0.1s when the switching function is F(x) under discrete system conditions. DETAILED DESCRIPTION

[0041] The present invention will be further described below in conjunction with the accompanying drawings.

[0042] Figure 1 The flowchart of the improved sliding mode observation method suitable for PMSM sensorless control system is shown in the figure. The process of the entire improved sliding mode observation method includes: (1) Based on the mathematical model of the motor in the stationary coordinate system, the voltage equation in the stationary coordinate system is constructed, and then further rewritten into the stator current equation; (2) The SMO is designed to obtain the observed value of the stator current in the stationary coordinate system, and the deviation between the observed value and the actual value is used as the input of the designed piecewise continuous function F(x); (3) The output of the piecewise continuous function is multiplied by the sliding mode gain to obtain the equivalent back electromotive force, and the inverse tangent method is used to extract the rotor position and speed from the back electromotive force; (4) The sliding mode observer using the piecewise continuous function is introduced into the PMSM vector control method to replace the role of the position sensor, and the speed is obtained through the phase voltage and phase current to achieve closed-loop control.

[0043] An improved sliding mode observation method suitable for PMSM sensorless control system includes the following steps:

[0044] Step 1: Based on the motor mathematical model in the stationary coordinate system, construct the voltage equation in the stationary coordinate system, and further rewrite it into the stator current equation. The process is as follows:

[0045] The motor controlled in this embodiment is a three-phase permanent magnet synchronous motor with a surface mount structure, a stator resistance of 2.875 ohms, a stator inductance of 8.5e-3 Henry, a flux linkage of 0.175 Weber, a moment of inertia of 1e-3, a damping coefficient of 0, a pole pair number of 2, and a set speed of 1500 rpm;

[0046] The voltage in the stationary coordinate system is shown in formula (1):

[0047]

[0048] Where, R is the stator resistance, L is the s is the stator inductance, i α 、i β is the stator current, u α 、u β is the stator voltage, E α 、E β To expand the back EMF;

[0049] The current in the stationary coordinate system is shown in formula (2):

[0050]

[0051] The extended back electromotive force is shown in formula (3):

[0052]

[0053] where ω e Electrical angular velocity, ψ f is the magnetic link;

[0054] Step 2: Design SMO to obtain the observed value of the stator current in the stationary coordinate system. The deviation between the observed value and the actual value is used as the input of the designed piecewise continuous function F(x). The process is as follows:

[0055] The observation current designed in the stationary coordinate system is shown in formula (4):

[0056]

[0057] Subtracting formula (4) from formula (2), we get formula (5):

[0058]

[0059] in is the observed value of stator current, is the difference between the observed value and the actual value of the stator current, v α , v β is the designed sliding mode control law, which is shown in formula (6):

[0060]

[0061] Where K is the sliding mode gain, which is set to 200, and F(x) replaces the sign function sgn(x), as shown in formula (7):

[0062]

[0063] T1 and T2 are segmentation points, satisfying 0≤T1≤T2. Taking T1=0.6 and T2=1.7 as an example, since the conditions of junction point value and derivative continuity need to be met, we can get

[0064] Therefore

[0065] Step 3: Multiply the output of the piecewise continuous function by the sliding mode gain to obtain the equivalent back electromotive force, and use the inverse tangent method to extract the rotor position and speed from the back electromotive force. The process is as follows:

[0066] When the observer state variable reaches the sliding surface When , the equivalent back electromotive force is as shown in formula (8):

[0067]

[0068] Combining formula (3), we can get formula (9):

[0069]

[0070] Step 4: Introduce the sliding mode observer using piecewise continuous function into the PMSM vector control method to replace the role of the position sensor, obtain the speed through the phase voltage and phase current, and realize closed-loop control. The process is as follows:

[0071] Through MATLAB / SIMULINK experiments, it was found that under the same motor model, load and expected speed:

[0072] In continuous systems, such as Figure 3 and Figure 4 As shown in the figure, compared with the traditional synovial film observer, the designed optimized synovial film observer can significantly reduce the chattering frequency in sensorless vector control.

[0073] In discrete systems, such as Figure 5 and Figure 6 As shown in the figure, compared with the sliding mode observer using hyperbolic tangent function, the designed optimized sliding mode observer can achieve a similar control effect in sensorless vector control.

[0074] As shown in Table 1, this paper compares the operation speed of different switching functions in STM32F103C8T6. The input variable of the function is 5*sin(x), x is a positive integer that changes from 1 to 1000, and the time obtained is the time for 1000 operations of each function. It can be seen that the running time of the sign function is the shortest, and the running time of the hyperbolic tangent function is the longest. The designed piecewise continuous function only increases by 7.5% compared with the sign function and decreases by 54.3% compared with the hyperbolic tangent function.

[0075] It can be seen that the SIMULINK results show that the present invention can significantly reduce the chattering phenomenon of the sliding mode observer in the sensorless control of the permanent magnet synchronous motor. The MCU test results show that the present invention greatly reduces the amount of calculation when the control effect is close to the hyperbolic tangent function, and has important application significance in embedded systems with limited resources.

[0076] Table 1 is the running speed test data of STM32F103C8T6 (1000 calculations).

[0077]

[0078] Table 1

[0079] The contents described in the embodiments of this specification are merely enumerations of implementation forms of the inventive concept and are for illustrative purposes only. The protection scope of the present invention should not be considered to be limited to the specific forms described in this embodiment, and the protection scope of the present invention also extends to equivalent technical means that can be thought of by ordinary technicians in this field based on the inventive concept.

Claims

1. An improved sliding mode observation method suitable for PMSM sensorless control system, characterized in that: The method comprises the following steps: Step 1: Based on the mathematical model of the motor in the stationary coordinate system, construct the voltage equation in the stationary coordinate system, and further rewrite it into the stator current equation; Step 2: Design a sliding mode observer SMO to obtain the observed value of the stator current in the stationary coordinate system, and the deviation between the observed value and the actual value is used as the input of the designed piecewise continuous function F(x); Step 3: Multiply the output of the piecewise continuous function by the sliding mode gain to obtain the equivalent back electromotive force, and use the inverse tangent method to extract the rotor position and speed from the back electromotive force; Step 4: Introduce the sliding mode observer using piecewise continuous function into the PMSM vector control method to replace the role of the position sensor, obtain the speed through the phase voltage and phase current, and realize closed-loop control.

2. The improved sliding mode observation method suitable for PMSM sensorless control system according to claim 1, characterized in that: In step 1, the voltage in the stationary coordinate system is as shown in formula (1): Where, R is the stator resistance, L is the s is the stator inductance, i α 、i β is the stator current, u α 、u β is the stator voltage, E α 、E β To expand the back EMF; The current in the stationary coordinate system is shown in formula (2): The extended back electromotive force is shown in formula (3): where ω e Electrical angular velocity, ψ f For magnetic link.

3. An improved sliding mode observation method suitable for PMSM sensorless control system as claimed in claim 2, characterized in that: In step 2, the observation current designed in the stationary coordinate system is shown in formula (4): The difference between formula (4) and formula (2) gives formula (5): in is the observed value of stator current, is the difference between the observed value and the actual value of the stator current, v α , v β is the designed sliding mode control law, which is shown in formula (6): Where K is the sliding mode gain, and F(x) replaces the sign function sgn(x), as shown in formula (7): T1 and T2 are segmentation points, satisfying 0≤T1≤T2. To satisfy the conditions of continuity of the junction point value and derivative, we can get After using a piecewise continuous quadratic switching function instead of the sign function, when the absolute value of the current error is greater than T2, the output of the switching function is consistent with the output of the sign function. When the absolute value of the current error is less than T1, the output of the switching function is a linear function. When the absolute value of the current error is between T1 and T2, the output of the switching function is a quadratic function, which has the same derivative at T1 and T2, so that the output of the piecewise function will not change suddenly and can transition smoothly.

4. The improved sliding mode observation method applicable to the PMSM sensorless control system as claimed in claim 3, characterized in that: In step 3, when the observer state variable reaches the sliding surface When , the equivalent back electromotive force is as shown in formula (8): Combining formula (3), we get formula (9):

5. An improved sliding mode observation method applicable to a PMSM sensorless control system as claimed in any one of claims 1 to 4, characterized in that: In step 4, the sensorless vector control process based on the piecewise continuous function sliding mode observer is as follows: the timer triggers the analog-to-digital converter to sample and obtain the phase current, and the phase current is transformed by Clark to obtain the two-phase stationary coordinate system current i α 、i β , and then converted into the synchronous rotating coordinate system dq axis current i through Park coordinate transformation d 、i q , and the deviation from the speed loop output is used as the input of the current loop PI controller; the timer triggers the ADC sampling to obtain the phase voltage, and the phase voltage is transformed by Clark to obtain the two-phase stationary coordinate system current u α 、u β ;change i α 、i β 、u α 、u β As the input signal of the sliding mode observer, the speed signal is output, and the deviation from the expected speed is used as the input of the speed loop PI controller to form the speed loop feedback and realize the sensorless closed-loop control of the permanent magnet synchronous motor.

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