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

Abstract

The application discloses a motor control method and control system based on a fractional order disturbance observer and a fractional order auxiliary system, constructs a permanent magnet synchronous motor nonlinear system including time-varying disturbance and input saturation according to physical characteristics of the permanent magnet synchronous motor; designs a fractional order disturbance observer to estimate the time-varying disturbance; constructs a fractional order auxiliary system to process the input saturation problem in the permanent magnet synchronous motor nonlinear system; comprehensively obtains an actual fractional order controller from the fractional order disturbance observer and the fractional order auxiliary system; and controls the permanent magnet synchronous motor through the obtained fractional order controller. Through the comprehensive estimation of the time-varying disturbance by the fractional order disturbance observer and the processing of the input saturation problem in the permanent magnet synchronous motor nonlinear system by the fractional order auxiliary system, the estimation capability of the time-varying disturbance is enhanced, 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 application relates to fractional order control of a motor, in particular to a motor control method and system based on a fractional order disturbance observer and a fractional order auxiliary system. BACKGROUND

[0002] With the acceleration of the transformation and upgrading of manufacturing industry, permanent magnet synchronous motors have been widely used in household appliances, aviation, new energy vehicles and other key fields. However, permanent magnet synchronous motors are a kind of complex system with characteristics such as nonlinearity, strong coupling, variability and parameter variability. Their control performance is not only limited by design and manufacturing process errors, but also easily affected by external load changes and nonlinear constraints. Therefore, it is particularly important to explore advanced permanent magnet synchronous motor control methods to improve their operating efficiency and ensure their optimal performance under various operating conditions.

[0003] Because fractional calculus can describe memory processes and encapsulate more information, it can more accurately and reasonably represent dynamic processes. The results show that the introduction of fractional calculus method into the controller design can effectively improve the tracking performance of the permanent magnet synchronous motor system. Although there have been studies on fractional order methods for permanent magnet synchronous motor systems, the study of fractional order control is not deep enough. Therefore, further research on this problem is of great significance to further improve the control performance of the permanent magnet synchronous motor system.

[0004] As is known to all, external load will cause serious disturbance to the permanent magnet synchronous motor system, and even destroy the normal operation of the system in severe cases. Therefore, exploring effective anti-interference methods is crucial to improve the control performance of the permanent magnet synchronous motor system. Previous research work has achieved disturbance suppression of the permanent magnet synchronous motor system through disturbance observer, and improved the operation performance of the permanent magnet synchronous motor system. However, the stability of the existing disturbance observer for the control method of the permanent magnet synchronous motor system under disturbance conditions is still not enough.

[0005] In engineering practice, the control input of the permanent magnet synchronous motor system is limited from the safety point of view. If the control input is not effectively limited, it is difficult to effectively ensure the safety of the permanent magnet synchronous motor equipment when the required control input exceeds the upper limit of the rated input, so the input saturation problem needs to be solved. SUMMARY

[0006] The application aims to provide a motor control method and 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 motor control method based on fractional order disturbance observer and fractional order auxiliary system is adopted, comprising the following steps:

[0008] (1) According to the physical characteristics of permanent magnet synchronous motor, a nonlinear system of permanent magnet synchronous motor including time-varying disturbance and input saturation is constructed;

[0009] (2) Design a fractional order disturbance observer to estimate the time-varying disturbance; Construct a fractional order auxiliary system to deal with the input saturation problem in the nonlinear system of permanent magnet synchronous motor;

[0010] (3) Synthesize the fractional order disturbance observer and the fractional order auxiliary system to obtain the actual fractional order controller;

[0011] (4) Control the permanent magnet synchronous motor through the obtained fractional order controller.

[0012] Further, the step (1) includes a nonlinear system of permanent magnet synchronous motor with time-varying disturbance and input saturation:

[0013]

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

[0015] Further, the saturation function is written as:

[0016]

[0017] Wherein, is the upper limit of the saturation function , and is the lower limit of the saturation function .

[0018] Further, the fractional disturbance observer is:

[0019]

[0020] wherein, , and are auxiliary vectors of the fractional disturbance observer, is a fractional order integral of is a fractional order integral of with respect to variable is a fractional order integral of with respect to variable is a fractional order, is a derivative of auxiliary vector is an estimation of disturbance , and are designed normal numbers, is a hyperbolic tangent function. Further, the auxiliary vectors of the fractional disturbance observer are calculated by:

[0021] .

[0022] .

[0023] Further, the fractional auxiliary system is:

[0024]

[0025] wherein, , and are variables of the fractional auxiliary system; , and are derivatives of , and respectively; , , , , and are designed constants; is a fractional order integral with fractional order , , and are intermediate variables defined as , and respectively;​​ is a desired reference signal; and is an output of a first-order filter; , and is a design normal number; .

[0026] Further, the fractional order controller is:

[0027]

[0028] wherein, is a design normal number, is a derivative of .

[0029] The application also adopts a control system applying the motor control method based on the fractional order disturbance observer and the fractional order auxiliary system, comprising:

[0030] a model establishing module, configured to construct a permanent magnet synchronous motor nonlinear system including time-varying disturbance and input saturation according to physical characteristics of the permanent magnet synchronous motor;

[0031] a fractional order disturbance observer module, configured to design a fractional order disturbance observer to estimate the time-varying disturbance;

[0032] a fractional order auxiliary system module, configured to a fractional order auxiliary system to process the input saturation problem in the permanent magnet synchronous motor nonlinear system;

[0033] a fractional order controller establishing module, configured to obtain an actual fractional order controller by synthesizing the fractional order disturbance observer and the fractional order auxiliary system;

[0034] a controller module, configured to control the permanent magnet synchronous motor through the obtained fractional order controller.

[0035] The application also adopts a computer device, comprising 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 application also adopts a computer readable storage medium, which stores a computer program, wherein the computer program is executed by a processor to implement the steps of the above method.

[0037] Beneficial effects: relative to the prior art, the significant advantages of the present application are that the time-varying disturbance is estimated by the comprehensive fractional order disturbance observer, and the fractional order auxiliary system is used to process the input saturation problem in the permanent magnet synchronous motor nonlinear system, the estimation ability of the time-varying disturbance is enhanced, the adverse effects of input saturation on the system are effectively processed, and the closed-loop system stability and robustness of the permanent magnet synchronous motor nonlinear system are improved. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 The flowchart of the fractional order control method of the present application.

[0039] Figure 2 The signal tracking control effect diagram in the present application.

[0040] Figure 3 The time-varying disturbance estimation effect diagram in the present application. DETAILED DESCRIPTION

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

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

[0043] (1.1)

[0044] wherein, 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 of the permanent magnet, is the torque component of the external load, , and are the voltage component, current component and inductance in the d-q axis coordinate system, , is the resistance. In addition, is a saturation function, and can be written as

[0045] (1.2)

[0046] wherein, and are saturation functions The upper and lower bounds. Based on the physical characteristics of permanent magnet synchronous motors, the error between the actual control input and the saturation control input is always bounded, therefore... , It is a positive number.

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

[0048] (1.3)

[0049] in, , and Here is the auxiliary vector for the fractional-order disturbance observer, with the fractional order being... ,function It is the hyperbolic tangent function. For interference The estimate, , and For the design of positive constants, and The fractional orders are respectively and For variables Fractional integrals.

[0050] According to equation (1.3), we can obtain

[0051] (1.4)

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

[0053] (1.5)

[0054] Choose Lyapunov function for

[0055] (1.6)

[0056] Based on the above analysis, it can be described as follows:

[0057] (1.7)

[0058] Therefore, based on equation (1.7), we can obtain It is bounded. Because the function It is bounded. Based on the design form of the interference observer (1.3), the interference observer can be obtained. and Bounded, in which It is a positive number.

[0059] Step 3: To handle the input saturation problem in the nonlinear PMSM system, a fractional-order auxiliary system is designed as

[0060] (1.8)

[0061] where, , and are the variables of the auxiliary system, , , , and are the designed constants. In addition, , and are defined as , and , is the desired reference signal, and the variables and are the outputs of the first-order filters, with the parameters , , being the designed normal numbers, , is the fractional-order integral with the fractional order is the hyperbolic tangent function.

[0062] Step 4: Based on the designed fractional-order disturbance observer (1.3) and the fractional-order auxiliary system (1.8), the fractional-order control method is designed. First, according to , we have . Then, based on equation (1.1) and equation (1.8), we have

[0063] (1.9)

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

[0065] (1.10)

[0066] where is the designed constant.

[0067] To handle the complex variable , a first-order filter is given as follows

[0068] (1.11) ​

[0069] where is the output of the first-order filter, and the parameter is a constant. and respectively represent and the initial values of and formula (1.11), we can get

[0070] (1.12)

[0071] where is a continuous function, and the function is compact under the given initial condition. Therefore, we have where the parameter is a constant.

[0072] Then, we select the Lyapunov function as

[0073] (1.13)

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

[0075] (1.14)

[0076] where the variables , and will be processed in the following analysis.

[0077] According to we have . Then, based on formula (1.1), formula (1.8) and we can get

[0078] (1.15)

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

[0080] (1.16)

[0081] where is a designed positive constant.

[0082] In order to process the complex variable , we give the following first-order filter

[0083] (1.17)

[0084] where is the output of the first-order filter, and the parameter is a constant. and denote the initial values of and respectively. Then, according to and equation (1.17), we have

[0085] (1.18)

[0086] where is a continuous function, and the function is compact in given initial conditions. Therefore, we have , and the parameter is a constant.

[0087] Then, the Lyapunov function is chosen as

[0088] (1.19)

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

[0090] (1.20)

[0091] where the variable will be processed in the following analysis.

[0092] According to equation (1.1), equation (1.8) and , we have

[0093] (1.21)

[0094] Then, the fractional-order controller is designed as

[0095] (1.22)

[0096] where is a positive constant.

[0097] Then, the Lyapunov function is chosen as

[0098] (1.23)

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

[0100] (1.24)

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

[0102] For the closed-loop control system, the following total Lyapunov function is selected

[0103] (1.25)

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

[0105] (1.26)

[0106] According to equation (1.26), if the variables and , the closed-loop system is semi-global and eventually uniformly bounded. Therefore, the design parameters must satisfy , , , , , , , and . At the same time, the variable satisfies and , where is the minimum value.

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

Claims

1. A motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system, characterized by, The method comprises the following steps: (1) constructing a nonlinear system of a permanent magnet synchronous motor including time-varying disturbance and input saturation according to physical characteristics of the permanent magnet synchronous motor; (2) designing a fractional order disturbance observer to estimate the time-varying disturbance; and constructing a fractional order auxiliary system to deal with the input saturation problem in the nonlinear system of the permanent magnet synchronous motor; (3) synthesizing the fractional order disturbance observer and the fractional order auxiliary system to obtain an actual fractional order controller; (4) controlling the permanent magnet synchronous motor by using the obtained fractional order controller. The nonlinear system of the permanent magnet synchronous motor including time-varying disturbance and input saturation in the step (1) is as follows: ； wherein, is the rotor physical angle, is the mechanical angular velocity of the motor, is the time, is the moment of inertia, is the number of poles of the permanent magnet synchronous motor, is the flux of the permanent magnet, is the damping coefficient, is the torque component of the external load, i.e. 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 the saturation function; The fractional order disturbance observer is as follows: ； in, , and This is the auxiliary vector for the fractional-order disturbance observer. For fractional order, the order is For variables fractional integrals, For fractional order, the order is For variables fractional integrals, For fractional order, For auxiliary vectors Differentiate, For interference The estimate, , and For the design of positive constants, It is the hyperbolic tangent function; The fractional order auxiliary system is as follows: ； wherein , and are variables of the fractional order auxiliary system; , and are derivatives of , and ; , , , , and are design constants; is a fractional order integral with the fractional order ; , and are intermediate variables defined as , and ; is the desired reference signal; and are outputs of the first order filters; , and are design normal numbers; .

2. The motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system according to claim 1, characterized by, The saturation function is written as: ； wherein is an upper bound of the saturation function , is a lower bound of the saturation function .

3. The motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system according to claim 2, characterized by, Auxiliary vector of the fractional-order disturbance observer The calculation formula is: 。 4. The motor control method based on a fractional-order disturbance observer and a fractional-order auxiliary system according to claim 3, characterized by, The fractional order controller is as follows: ； wherein is a normal number of design, is a derivative of derivative.

5. A control system employing the motor control method based on the fractional-order disturbance observer and the fractional-order auxiliary system according to claim 1, characterized by, The method comprises the following steps: a model establishing module, configured to construct a nonlinear system of a permanent magnet synchronous motor including time-varying disturbance and input saturation according to physical characteristics of the permanent magnet synchronous motor; a fractional order disturbance observer module, configured to design a fractional order disturbance observer to estimate the time-varying disturbance; a fractional order auxiliary system module, configured to construct a fractional order auxiliary system to deal with the input saturation problem in the nonlinear system of the permanent magnet synchronous motor; a fractional order controller establishing module, configured to synthesize the fractional order disturbance observer and the fractional order auxiliary system to obtain an actual fractional order controller; a controller module, configured to control the permanent magnet synchronous motor by using the obtained fractional order controller.

6. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the method in any one of claims 1 to 4.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the method in any one of claims 1 to 4.

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