Motor control method and control system based on fractional order disturbance observer and fractional order auxiliary system

Abstract

The invention discloses a motor control method and system based on a fractional order disturbance observer and a fractional order auxiliary system, and the method comprises the steps: constructing a permanent magnet synchronous motor nonlinear system comprising time-varying disturbance and input saturation according to the physical characteristics of a permanent magnet synchronous motor; designing a fractional order interference observer to estimate time-varying interference; constructing a fractional order auxiliary system to process an input saturation problem in a permanent magnet synchronous motor nonlinear system; integrating the fractional order disturbance observer and the fractional order auxiliary system to obtain an actual fractional order controller; and controlling the permanent magnet synchronous motor through the obtained fractional order controller. A fractional order interference observer is synthesized to estimate time-varying interference, and a fractional order auxiliary system is used to process the input saturation problem in a permanent magnet synchronous motor nonlinear system, so that the estimation capability of the time-varying interference is enhanced, and the adverse effect of the input saturation on the system is effectively processed; and the closed-loop system stability and robustness of the permanent magnet synchronous motor nonlinear system are improved.

Description

Technical Field

[0001] The present invention relates to fractional-order control of a motor, and in particular to a motor control method and control system based on a fractional-order disturbance observer and a fractional-order auxiliary system. Background Art

[0002] With the accelerated transformation and upgrading of the manufacturing industry, permanent magnet synchronous motors (PMSMs) have been widely used in various key sectors, including home appliances, aviation, and new energy vehicles. However, PMSMs are complex systems characterized by nonlinearity, strong coupling, multiple variability, and parameter variability. Their control performance is not only limited by design and manufacturing process errors but is also susceptible to multiple factors, including external load variations and nonlinear constraints. Therefore, it is crucial to explore advanced PMSM control methods to improve their operating efficiency and ensure optimal performance under various operating conditions.

[0003] Because fractional-order calculus can describe memory processes and encapsulate more information, it can more accurately and reasonably represent dynamic processes. Results show that incorporating fractional-order calculus methods into controller design can effectively improve the tracking performance of permanent magnet synchronous motor systems. Although fractional-order methods have been studied for permanent magnet synchronous motor systems, in-depth research on fractional-order control is still insufficient. Therefore, further research on this issue is of great significance for further improving the control performance of permanent magnet synchronous motor systems.

[0004] It is well known that external loads can cause severe interference to permanent magnet synchronous motor systems, and in severe cases, can even disrupt the system's normal operation. Therefore, developing effective anti-interference methods is crucial for improving the control performance of permanent magnet synchronous motor systems. Previous research has achieved interference suppression in permanent magnet synchronous motor systems using disturbance observers, improving their operational performance. However, existing disturbance observer control methods for permanent magnet synchronous motor systems under interference conditions remain insufficiently stable.

[0005] In engineering practice, control inputs to permanent magnet synchronous motor systems are restricted for safety reasons. Without effective control input limits, when the required control input exceeds the rated input upper limit, it is difficult to effectively ensure the safety of the permanent magnet synchronous motor equipment. Therefore, the input saturation problem needs to be addressed. Summary of the Invention

[0006] Purpose of the invention: In view of the above shortcomings, the present invention provides a motor control method and control system based on a fractional-order disturbance observer and a fractional-order auxiliary system with better control effect.

[0007] Technical solution: To solve the above problems, the present invention adopts a motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system, comprising the following steps:

[0008] (1) Based on the physical characteristics of permanent magnet synchronous motors, a nonlinear system of permanent magnet synchronous motors including time-varying interference and input saturation is constructed;

[0009] (2) Design a fractional-order disturbance observer to estimate time-varying disturbances; construct a fractional-order auxiliary system to handle the input saturation problem in the nonlinear system of permanent magnet synchronous motors;

[0010] (3) The actual fractional-order controller is obtained by integrating the fractional-order disturbance observer and the fractional-order auxiliary system;

[0011] (4) The permanent magnet synchronous motor is controlled by the obtained fractional-order controller.

[0012] Furthermore, the step (1) includes a permanent magnet synchronous motor nonlinear system with time-varying interference and input saturation as follows:

[0013]

[0014] in, is the rotor physical angle, is the mechanical angular velocity of the motor, For time, is the moment of inertia, is the number of poles of the permanent magnet synchronous motor, is the flux linkage of the permanent magnet, is the damping coefficient, is the torque component of the external load, i.e. the disturbance, is the current component in the q-axis coordinate system, is the current component in the d-axis coordinate system, is the inductance in the q-axis coordinate system, is the inductance in the d-axis coordinate system, is the voltage component in the q-axis coordinate system, is the resistance, is a saturation function.

[0015] Furthermore, the saturation function Written as:

[0016]

[0017] in, is a saturation function The upper bound of is a saturation function The lower bound.

[0018] Furthermore, the fractional-order interference observer is:

[0019]

[0020] in, 、 and is the auxiliary vector of the fractional-order disturbance observer, The fractional order is For variables The fractional integral of The fractional order is For variables The fractional integral of is the fractional order, For the auxiliary vector Seek the derivative, For interference Estimates, 、 and is a designed normal number, is the hyperbolic tangent function.

[0021] Furthermore, the auxiliary vector of the fractional-order interference observer The calculation formula is:

[0022] .

[0023] Furthermore, the fractional-order auxiliary system is:

[0024]

[0025] in, 、 and is the variation of the fractional-order auxiliary system; ,and Respectively for 、 and Derivative; 、 、 、 、 and is the designed constant; The fractional order is Fractional integral of ; 、 and The intermediate variables are defined as 、 and ; is the desired reference signal; and is the output of the first-order filter; 、 and is a designed positive constant; .

[0026] Furthermore, the fractional-order controller is:

[0027]

[0028] in, is a designed normal number, For Find the derivative.

[0029] The present invention also adopts a control system using the motor control method based on the fractional-order disturbance observer and the fractional-order auxiliary system, comprising:

[0030] A model building module is used to build a nonlinear system of a permanent magnet synchronous motor including time-varying disturbances and input saturation based on the physical characteristics of the permanent magnet synchronous motor;

[0031] The fractional-order interference observer module is used to design a fractional-order interference observer to estimate time-varying interference;

[0032] Fractional-order auxiliary system module, used for fractional-order auxiliary system to deal with input saturation problem in permanent magnet synchronous motor nonlinear system;

[0033] The fractional-order controller establishment module is used to integrate the fractional-order disturbance observer and the fractional-order auxiliary system to obtain the actual fractional-order controller;

[0034] A controller module is used to control the permanent magnet synchronous motor through the obtained fractional-order controller.

[0035] The present invention also adopts a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0036] The present invention also adopts a computer-readable storage medium having a computer program stored thereon, and the computer program implements the steps of the above method when executed by a processor.

[0037] Beneficial effects: Compared with the existing technology, the significant advantage of the present invention is that it estimates the time-varying interference through a comprehensive fractional-order interference observer and a fractional-order auxiliary system to deal with the input saturation problem in the nonlinear system of the permanent magnet synchronous motor, thereby enhancing the estimation capability of the time-varying interference, effectively dealing with the adverse effects of input saturation on the system, and improving the closed-loop system stability and robustness of the nonlinear system of the permanent magnet synchronous motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the flow of the fractional-order control method of the present invention.

[0039] Figure 2 This is a diagram showing the signal tracking control effect in the present invention.

[0040] Figure 3 This is a diagram showing the effect of time-varying interference estimation in the present invention. DETAILED DESCRIPTION

[0041] like Figure 1 As shown, a motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system in this embodiment includes the following steps:

[0042] Step 1: Based on the physical characteristics of the permanent magnet synchronous motor, a nonlinear system of the permanent magnet synchronous motor including time-varying disturbance and input saturation is constructed as follows:

[0043] (1.1)

[0044] in, is the rotor physical angle, is the moment of inertia, is the damping coefficient, is the mechanical angular velocity of the motor, is the number of poles of the permanent magnet synchronous motor, is the flux linkage of the permanent magnet, is the torque component of the external load, 、 and They are the voltage component, current component and inductance in the dq axis coordinate system respectively, , is the resistance. In addition, is a saturation function and can be written as

[0045] (1.2)

[0046] in, and Saturation function According to the physical characteristics of permanent magnet synchronous motor, the error between its actual control input and saturation control input is always bounded, so , Is a positive number.

[0047] Step 2: To suppress the time-varying disturbance in the nonlinear system of the permanent magnet synchronous motor, a fractional-order disturbance observer is designed as follows:

[0048] (1.3)

[0049] in, 、 and is the auxiliary vector of the fractional-order disturbance observer, and the fractional-order order is ,function is the hyperbolic tangent function, For interference Estimates, 、 and is a designed normal number, and The fractional orders are and For variables The fractional integral of .

[0050] According to formula (1.3), we can get

[0051] (1.4)

[0052] Then, formula (1.4) can be written as

[0053] (1.5)

[0054] Select Lyapunov function for

[0055] (1.6)

[0056] Combined with the above analysis, it can be described as

[0057] (1.7)

[0058] Therefore, based on formula (1.7), we can get is bounded. Since the function is bounded. According to the design form of the disturbance observer (1.3), we can get the disturbance observer and Bounded, where Is a positive number.

[0059] Step 3: To deal with the input saturation problem in the nonlinear permanent magnet synchronous motor system, the fractional-order auxiliary system is designed as

[0060] (1.8)

[0061] in, 、 and It is a change in the auxiliary system. 、 、 、 and is a design constant. In addition, 、 and They are defined as 、 and , is the desired reference signal, the variable and is the output of the first-order filter, parameter 、 、 is a designed normal number, , The fractional order is The fractional integral of is the hyperbolic tangent function.

[0062] Step 4: Based on the designed fractional-order disturbance observer (1.3) and fractional-order auxiliary system (1.8), design the fractional-order control method. , then Then, based on equations (1.1) and (1.8), we have

[0063] (1.9)

[0064] Among them, the variable , is a fractional-order virtual control law and can be designed as

[0065] (1.10)

[0066] in, is a design constant.

[0067] To handle complex variables , giving a first-order filter of the form

[0068] (1.11)

[0069] in, is the output of the first-order filter, parameter is a constant. and Respectively and Then, according to And (1.11), we can get

[0070] (1.12)

[0071] in, is a continuous function. Under given initial conditions, the function In a tight concentration. Therefore, there is , where the parameters is a constant.

[0072] Then, choose the Lyapunov function for

[0073] (1.13)

[0074] Combining equations (1.9), (1.10), (1.11), (1.12) and (1.13), we have

[0075] (1.14)

[0076] Among them, the variable 、 and This will be dealt with in the following analysis.

[0077] according to , then Then, based on equations (1.1), (1.8) and , we can get

[0078] (1.15)

[0079] Among them, the variable , is a fractional-order virtual control law, which can be designed as

[0080] (1.16)

[0081] in, is a designed normal number.

[0082] To handle complex variables , giving the following first-order filter

[0083] (1.17)

[0084] in, is the output of the first-order filter, parameter is a constant. and Respectively and Then, according to And (1.17), we can get

[0085] (1.18)

[0086] in, is a continuous function. Under given initial conditions, the function In a tight concentration. Therefore, there is ,parameter is a constant.

[0087] Then, choose the Lyapunov function for

[0088] (1.19)

[0089] Combining equations (1.3), (1.8), (1.15), (1.18) and (1.19), we have

[0090] (1.20)

[0091] Among them, the variable This will be dealt with in the following analysis.

[0092] According to formula (1.1), formula (1.8) and , then

[0093] (1.21)

[0094] Then, the fractional order controller Designed for

[0095] (1.22)

[0096] in, is a designed normal number.

[0097] Then, choose the Lyapunov function for

[0098] (1.23)

[0099] Combining equations (1.21), (1.22) and (1.23), we have

[0100] (1.24)

[0101] The above analysis gives the design steps of the controller, and the effectiveness of the fractional-order controller will be proved next.

[0102] For closed-loop control systems, choose the following general Lyapunov function for

[0103] (1.25)

[0104] Combining equations (1.21), (1.22) and (1.23), we have

[0105] (1.26)

[0106] According to formula (1.26), if the variable and , then the closed-loop system is semi-global and ultimately uniformly bounded. Therefore, the design parameters must satisfy 、 、 、 、 、 、 、 and At the same time, the variable satisfy and ,in is the minimum value.

[0107] Step 5: Figure 2 and Figure 3 As shown in the figure, the effective control of the permanent magnet synchronous motor nonlinear system is realized according to the designed fractional-order control method.

Claims

1. A motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system, characterized in that: The following steps are involved: (1) Based on the physical characteristics of permanent magnet synchronous motors, a nonlinear system of permanent magnet synchronous motors including time-varying interference and input saturation is constructed; (2) Design a fractional-order disturbance observer to estimate time-varying disturbances; construct a fractional-order auxiliary system to handle the input saturation problem in the nonlinear system of permanent magnet synchronous motors; (3) The actual fractional-order controller is obtained by integrating the fractional-order disturbance observer and the fractional-order auxiliary system; (4) The permanent magnet synchronous motor is controlled by the obtained fractional-order controller.

2. The motor control method based on fractional-order disturbance observer and fractional-order auxiliary system according to claim 1, characterized in that: The step (1) includes a permanent magnet synchronous motor nonlinear system with time-varying disturbance and input saturation as follows: ； in, is the rotor physical angle, is the mechanical angular velocity of the motor, For time, is the moment of inertia, is the number of poles of the permanent magnet synchronous motor, is the flux linkage of the permanent magnet, is the damping coefficient, is the torque component of the external load, i.e. the disturbance, is the current component in the q-axis coordinate system, is the current component in the d-axis coordinate system, is the inductance in the q-axis coordinate system, is the inductance in the d-axis coordinate system, is the voltage component in the q-axis coordinate system, is the resistance, is a saturation function.

3. The motor control method based on fractional-order disturbance observer and fractional-order auxiliary system according to claim 2, characterized in that: The saturation function Written as: ； in, is a saturation function The upper bound of is a saturation function The lower bound.

4. The motor control method based on fractional-order disturbance observer and fractional-order auxiliary system according to claim 2, characterized in that: The fractional-order disturbance observer is: ； in, 、 and is the auxiliary vector of the fractional-order disturbance observer, The fractional order is For variables The fractional integral of The fractional order is For variables The fractional integral of is the fractional order, For the auxiliary vector Seek the derivative, For interference Estimates, 、 and is a designed normal number, is the hyperbolic tangent function.

5. The motor control method based on fractional-order disturbance observer and fractional-order auxiliary system according to claim 4, characterized in that: The auxiliary vector of the fractional-order disturbance observer The calculation formula is: 。 6. The motor control method based on fractional-order disturbance observer and fractional-order auxiliary system according to claim 4, characterized in that: The fractional-order auxiliary system is: ； in, 、 and is the variation of the fractional-order auxiliary system; 、 and Respectively for 、 and Derivative; 、 、 、 、 and is the designed constant; The fractional order is Fractional integral of ; 、 and The intermediate variables are defined as 、 and ; is the desired reference signal; and is the output of the first-order filter; 、 and is a designed positive constant; .

7. The motor control method based on fractional-order disturbance observer and fractional-order auxiliary system according to claim 6, characterized in that: The fractional-order controller is: ； in, is a designed normal number, For Find the derivative.

8. A control system using the motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system according to claim 1, characterized in that: include: A model building module is used to build a nonlinear system of a permanent magnet synchronous motor including time-varying disturbances and input saturation based on the physical characteristics of the permanent magnet synchronous motor; The fractional-order interference observer module is used to design a fractional-order interference observer to estimate time-varying interference; Fractional-order auxiliary system module, used for fractional-order auxiliary system to deal with input saturation problem in permanent magnet synchronous motor nonlinear system; The fractional-order controller establishment module is used to integrate the fractional-order disturbance observer and the fractional-order auxiliary system to obtain the actual fractional-order controller; A controller module is used to control the permanent magnet synchronous motor through the obtained fractional-order controller.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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