Double-fractional-order differential sliding mode positioning compound control method for permanent magnet synchronous motor

Abstract

The invention discloses a double-fractional-order differential sliding mode positioning compound control method for a permanent magnet synchronous motor, and relates to the field of permanent magnet synchronous motor control, and the method comprises the following steps: S1, designing a second-order hyperlocal model of the permanent magnet synchronous motor with a motor position signal as a controlled object, S2, constructing a double-fractional-order differential sliding mode surface, s3, constructing an expansion state observer in a feedforward channel; S4, completing a positioning controller of a double-fractional-order differential sliding mode in a feedback channel; and S5, completing the double-fractional-order differential sliding mode positioning composite control method based on the permanent magnet synchronous motor second-order hyperlocal model by combining the expansion state observer and the positioning controller. The method has the advantages that the problem of singularity possibly caused by an existing integer order differential sliding mode controller is solved, and the design flexibility of the controller is improved; and finally, a composite positioning control method is constructed in combination with an expansion state observer and a superhelix reaching law, and the phenomenon of motor buffeting in traditional sliding mode control is weakened.

Description

Technical Field

[0001] The invention relates to the field of permanent magnet synchronous motor control, and in particular to a double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor. Background Art

[0002] The efficient and high-precision positioning control performance of permanent magnet synchronous motors depends largely on the electrical parameters, mechanical parameters and load information of the motor. However, these parameters may change during actual operation. For example, the electrical parameters of the motor will change with the operating conditions and temperature changes, the mechanical parameters cannot be obtained by direct measurement, and the load torque needs to be measured by additional devices. Changes in these parameters may lead to a decrease in the performance of positioning control and even cause system instability.

[0003] Based on the above characteristics, in recent years, the research focus of domestic and foreign academic circles has gradually shifted to the development and application of a positioning control method based on a super-local model of a permanent magnet synchronous motor. A notable feature of this positioning control method is that it has a low degree of dependence on the accuracy of motor parameters. However, the positioning method currently has the following disadvantages: First, the existing control method is based on the first-order super-local model of the permanent magnet synchronous motor. The state quantity in the first-order super-local model of the permanent magnet synchronous motor is the motor speed signal, which cannot accurately reflect the position signal of the motor; second, the integer-order double differential sliding mode controller currently used is prone to singular phenomena and has low flexibility; third, the traditional sliding mode positioning control has a jitter problem on the sliding mode surface, which may have a negative impact on the stability and control accuracy of the system. In practical applications, the jitter phenomenon may cause fluctuations in the system response, affecting the positioning accuracy and stability. Based on the above reasons, the present invention designs a double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor. Summary of the invention

[0004] The purpose of the present invention is to solve the problems in the prior art and to propose a double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor.

[0005] A dual fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor comprises the following steps:

[0006] S1: Design a second-order hyperlocal model of a permanent magnet synchronous motor with the motor position signal as the controlled object;

[0007] S2: constructing a double fractional-order differential sliding surface based on the second-order hyperlocal model of the motor position in step S1;

[0008] S3: constructing an extended state observer in the feedforward channel based on the second-order hyperlocal model of the motor position in step S1;

[0009] S4: using the double fractional-order differential sliding mode surface constructed in step S4 in the feedback channel to complete the positioning controller of the double fractional-order differential sliding mode;

[0010] S5: Combine the extended state observer constructed in the feedforward channel in step S3 and the positioning controller constructed in the feedback channel in step S4 to complete the double fractional-order differential sliding mode positioning composite control method based on the second-order super-local model of permanent magnet synchronous motor.

[0011] In the above-mentioned dual fractional-order differential sliding mode positioning composite control method of the permanent magnet synchronous motor, in step S1, the position second-order super-local model of the permanent magnet synchronous motor is designed as follows:

[0012]

[0013] Where y is the position signal of the permanent magnet synchronous motor;

[0014] F is the total disturbance of the system;

[0015] a is a parameter without specific physical meaning;

[0016] u is the system control quantity.

[0017] In the above-mentioned dual fractional-order differential sliding mode positioning composite control method for the permanent magnet synchronous motor, in step S2, the design of the dual fractional-order differential sliding mode surface proposed based on the position second-order super-local model of the permanent magnet synchronous motor is as follows:

[0018]

[0019] Among them: sliding surface parameters k1>0, k2>0, k3>0;

[0020] y r It is the position given signal of the permanent magnet synchronous motor;

[0021] y is the position signal of the permanent magnet synchronous motor;

[0022] e is the error between the actual position and the given position of the permanent magnet synchronous motor;

[0023] and are fractional differential operation symbols respectively; ε1 and ε2 are fractional differential operators and satisfy 0<ε1<1 and 0<ε2<1;

[0024] s DFDSMS is the double fractional differential sliding surface;

[0025] is the double fractional-order differential signal of the position error;

[0026] ∫edt is the integral signal of the position error;

[0027] is the differential signal of the position error.

[0028] In the above-mentioned double fractional-order differential sliding mode positioning composite control method for the permanent magnet synchronous motor, in step S2, in order to weaken the chattering, the following sliding mode superhelical approach rate is selected:

[0029]

[0030] Among them, the coefficients η1 and η2 of the superhelical approach rate satisfy η1>0,η1>0, and the sign function in the approach rate is defined as follows:

[0031]

[0032] In the above-mentioned dual fractional-order differential sliding mode positioning composite control method for the permanent magnet synchronous motor, in order to design an observer in the feedforward channel in step S3, the position second-order super-local model (1) of the permanent magnet synchronous motor is expressed in the form of a state equation as follows:

[0033]

[0034] Among them, x1 and x2 represent the two state quantities of the system, position and speed respectively;

[0035] x3 represents the total disturbance of the system;

[0036] is the extended state quantity of the system, that is, the differential of the total disturbance x3;

[0037] u is the system control quantity;

[0038] The extended state observer constructed according to the state equation is as follows:

[0039]

[0040] Where Z 21 is the estimated value of the system state x2;

[0041] Z 22 is the estimated value of the total disturbance x3 of the system;

[0042] The coefficients of the extended state observer are β1>0, β2>0;

[0043] is the estimated error of the system state x2.

[0044] In the above-mentioned double fractional-order differential sliding mode positioning composite control method for the permanent magnet synchronous motor, in step 4, based on equations (1), (2) and (3), the double fractional-order differential sliding mode controller constructed in the feedback channel is:

[0045]

[0046] Where k1>0, k2>0, k3>0;

[0047] y r It is the position given signal of the permanent magnet synchronous motor;

[0048] y is the position signal of the permanent magnet synchronous motor;

[0049] e is the error of the position signal of the permanent magnet synchronous motor;

[0050] and is the fractional differential operator symbol; ε1 and ε2 are fractional differential operators and satisfy 0<ε1<1 and 0<ε2<1;

[0051] s DFDSMS is the double fractional differential sliding surface;

[0052] is the double fractional-order differential signal of the error;

[0053] ∫edt is the integrated signal of the error; is the differential signal of the error;

[0054] F is the total disturbance of the system, which is an unknown signal in this controller.

[0055] In the above-mentioned double fractional-order differential sliding mode positioning composite control method for permanent magnet synchronous motor, according to step S5, in order to solve the problem that F in equation (7) is the total disturbance of the system and is an unknown signal in the controller, combined with the extended state observer (6) constructed in the feedforward channel, the proposed double fractional-order differential sliding mode positioning composite control method based on the second-order super-local model of permanent magnet synchronous motor is constructed as follows:

[0056]

[0057] Where k1>0, k2>0, k3>0;

[0058] y r It is the position given signal of the permanent magnet synchronous motor;

[0059] y is the position signal of the permanent magnet synchronous motor;

[0060] e is the error of the position signal of the permanent magnet synchronous motor;

[0061] and y is the symbol of fractional differential operation; 0<ε1<1; 0<ε2<1;

[0062] s DFDSMS is the double fractional differential sliding surface;

[0063] is the double fractional-order differential signal of the error;

[0064] ∫edt is the integrated signal of the error;

[0065] is the differential signal of the error;

[0066] According to formula (6), Z 22 is the estimated value of the total disturbance F of the system.

[0067] The advantages are:

[0068] 1. Compared with the existing positioning method which is constructed based on the first-order super-local model of the permanent magnet synchronous motor, the state quantity in the first-order super-local model of the permanent magnet synchronous motor is the motor speed signal, which cannot accurately reflect the motor position signal. The present invention proposes to use the second-order super-local model of the permanent magnet synchronous motor as the construction basis of the controller, and directly use the motor position signal in the second-order super-local model as the controlled quantity, so as to achieve higher control accuracy.

[0069] 2. Compared with the currently used integer-order double differential sliding mode controller, which is prone to singular phenomena and has low flexibility, the present invention constructs a double fractional-order differential sliding mode surface based on the second-order super-local model, and constructs a double fractional-order differential sliding mode positioning control method for a permanent magnet synchronous motor based on the new sliding surface in the system feedback channel. This control method not only solves the problem of singularity, but also improves the design flexibility of the controller.

[0070] 3. The present invention combines the extended state observer and the superhelical reaching law to weaken the vibration problem caused by traditional sliding mode control, and finally completes the construction of a double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor.

[0071] In summary, the control method proposed in the present invention improves the positioning of the permanent magnet synchronous motor more accurately and with smaller errors compared with the existing control methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 This is a schematic diagram of the framework of a double fractional-order differential sliding mode positioning composite control method for a second-order super-local model of a permanent magnet synchronous motor proposed in the present invention.

[0073] FIG2 is an output response diagram of the permanent magnet synchronous motor position under the existing permanent magnet synchronous motor double differential sliding mode positioning control method when the given position signal is 5 rad under the condition of light load, where Figure 2a For the overall picture, Figure 2b Enlarge the image for details.

[0074] Figure 3 is an output response diagram of the permanent magnet synchronous motor position under a double fractional-order differential sliding mode positioning composite control method based on a second-order super-local model of the permanent magnet synchronous motor proposed in the present invention when the given position signal is 5 rad under a small load condition, wherein Figure a is an overall diagram and Figure b is an enlarged diagram of the details.

[0075] FIG4 is an output response diagram of the permanent magnet synchronous motor position under the existing permanent magnet synchronous motor double differential sliding mode positioning control method when the given position signal is 5 rad under heavy load, wherein FIGa is an overall diagram and FIGb is an enlarged diagram of the details.

[0076] Figure 5 is an output response diagram of the permanent magnet synchronous motor position under a double fractional-order differential sliding mode positioning composite control method based on a second-order super-local model of the permanent magnet synchronous motor proposed in the present invention when the given position signal is 5 rad under heavy load conditions, wherein Figure a is an overall diagram and Figure b is an enlarged diagram of the details.

[0077] FIG6 is an output response diagram of the permanent magnet synchronous motor position under the existing permanent magnet synchronous motor double differential sliding mode positioning control method when the initial given position signal is 5 rad and is changed to 8 rad at the 5th second, wherein FIGa is an overall diagram and FIGb is an enlarged diagram of the details.

[0078] FIG7 is an output response diagram of the position of a permanent magnet synchronous motor under a double fractional-order differential sliding mode positioning composite control method based on a second-order super-local model of a permanent magnet synchronous motor proposed in the present invention, when the initial given position signal is 5 rad and is changed to 8 rad in the 5th second, wherein FIGa is an overall diagram and FIGb is an enlarged diagram of the details. DETAILED DESCRIPTION

[0079] Reference Figure 1 -7, the second-order hyperlocal model of the permanent magnet synchronous motor is:

[0080]

[0081] Where y is the position signal of the permanent magnet synchronous motor, F is the total disturbance of the system; a is a parameter without specific physical meaning; and u is the system control quantity.

[0082] In a dual fractional-order differential sliding mode positioning composite control method based on a second-order super-local model of a motor constructed by the present invention, a new dual fractional-order differential sliding mode surface is constructed in combination with the second-order super-local model (1):

[0083]

[0084] Where k1>0, k2>0, k3>0; y r is the position given signal of the permanent magnet synchronous motor; y is the position signal of the permanent magnet synchronous motor; e is the error of the position signal of the permanent magnet synchronous motor; and is the symbol of fractional differential operation; 0<ε1<1; 0<ε2<1; s DFDSMS is the double fractional differential sliding surface; is the double fractional-order differential signal of the error; ∫edt is the integral signal of the error; is the differential signal of the error.

[0085] Based on the new fractional-order sliding surface (2), the controller constructed in the feedback channel is:

[0086]

[0087] Where k1>0, k2>0, k3>0; y r is the position given signal of the permanent magnet synchronous motor; y is the position signal of the permanent magnet synchronous motor; e is the error of the position signal of the permanent magnet synchronous motor; and is the symbol of fractional differential operation; 0<ε1<1; 0<ε2<1; s DFDSMS is the double fractional differential sliding surface; is the double fractional-order differential signal of the error; ∫edt is the integral signal of the error; is the differential signal of the error.

[0088] According to the second-order super-local model of permanent magnet synchronous motor, an extended state observer is constructed as follows:

[0089]

[0090] Where Z 21 is the estimated value of the system state x2; Z 22 is the estimated value of the total disturbance x3 of the system; the observer parameters β1>0, β2>0; is the estimated error of the system state x2.

[0091] Finally, by combining the extended state observer (4) constructed in the feedforward channel and the controller (3) constructed in the feedback channel, a double fractional-order differential sliding mode positioning composite control method based on the second-order super-local model of the permanent magnet synchronous motor is constructed as follows:

[0092]

[0093] In order to verify the effectiveness of the method proposed in the present invention, the control effects of the traditional double differential sliding mode positioning control method (method 2) of the existing permanent magnet synchronous motor and the double fractional-order differential sliding mode positioning composite control method (method 1) based on the second-order super-local model of the permanent magnet synchronous motor established in the present invention were simulated and compared in Matlab / Simulink.

[0094] Method 1: The key parameters of the dual fractional-order differential sliding mode positioning composite control method based on the second-order hyperlocal model are set as follows:

[0095] a=20, k1=0.1, k2=200, k3=0.1, eta1=1, eta2=10, β1=100, β2=10000,

[0096] ε1=0.05,ε1=0.1

[0097] Method 2: Traditional double differential sliding mode positioning control method of existing permanent magnet synchronous motor.

[0098] The traditional double differential sliding surface design is:

[0099]

[0100] The sliding surface parameters k1>0, k2>0, k3>0; s DDSMS It is the traditional double differential sliding surface.

[0101] The sliding mode reaching law adopted is as follows:

[0102]

[0103] Where η>0, the symbolic function is defined as follows:

[0104]

[0105] The conventional double differential sliding mode positioning control method (method 2) of the existing permanent magnet synchronous motor and its settings are as follows:

[0106]

[0107] Combined with the extended state observer (4), the traditional double differential sliding mode positioning control method of the permanent magnet synchronous motor can be obtained as follows:

[0108]

[0109] The parameters of the conventional double differential sliding mode positioning control method of the existing permanent magnet synchronous motor are set as follows:

[0110] a=20,k1=0.1,k2=200,k3=0.1,η=1,β1=100,β2=10000,the control effects of the existing control method and the control method proposed by the present invention are shown in Figures 2 to 7. It can be seen from Figures 2 to 7 that the positioning of the permanent magnet synchronous motor under the new composite controller proposed by the present invention is more accurate when carrying a small load or a large load.

[0111] It is known from common technical knowledge that the present invention can be implemented by other embodiments that do not deviate from its spirit or essential features. Therefore, the above disclosed embodiments are only illustrative in all respects and are not exclusive. All changes within the scope of the present invention or within the scope equivalent to the present invention are included in the present invention.

Claims

1. A double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor, characterized in that: The following steps are involved: S1: Design a second-order hyperlocal model of a permanent magnet synchronous motor with the motor position signal as the controlled object; S2: constructing a double fractional-order differential sliding surface based on the second-order hyperlocal model; S3: constructing an extended state observer in a feedforward channel based on the second-order hyperlocal model; S4: using the double fractional-order differential sliding mode surface in a feedback channel to complete a positioning controller of the double fractional-order differential sliding mode; S5: Combining the extended state observer and the positioning controller constructed in the feedforward channel to complete the double fractional-order differential sliding mode positioning composite control method based on the second-order super-local model of the permanent magnet synchronous motor.

2. The double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor according to claim 1, characterized in that: In step S1, the position second-order hyperlocal model of the permanent magnet synchronous motor is designed as follows: Where y is the position signal of the permanent magnet synchronous motor; F is the total disturbance of the system; a is a parameter without specific physical meaning; u is the system control quantity.

3. The double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor according to claim 1, characterized in that: In step S2, the design of the double fractional-order differential sliding surface proposed based on the position second-order hyperlocal model of the permanent magnet synchronous motor is as follows: Among them: sliding surface parameters k1>0, k2>0, k3>0; y r It is the position given signal of the permanent magnet synchronous motor; y is the position signal of the permanent magnet synchronous motor; e is the error between the actual position and the given position of the permanent magnet synchronous motor; and are fractional differential operation symbols respectively; ε1 and ε2 are fractional differential operators and satisfy 0<ε1<1 and 0<ε2<1; s DFDSMS is the double fractional differential sliding surface; is the double fractional-order differential signal of the position error; ∫edt is the integral signal of the position error; is the differential signal of the position error.

4. The double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor according to claim 1, characterized in that: In step S2, in order to reduce chattering, the following sliding mode superhelix approach rate is selected: Among them, the coefficients η1 and η2 of the superhelical approach rate satisfy η1>0,η1>0, and the sign function in the approach rate is defined as follows:

5. The double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor according to claim 2, characterized in that: In order to design the observer in the feedforward channel in step S3, the position second-order super-local model (1) of the permanent magnet synchronous motor is expressed in the form of a state equation as follows: Among them, x1 and x2 represent the two state quantities of the system, position and speed respectively; x3 represents the total disturbance of the system; is the extended state quantity of the system, that is, the differential of the total disturbance x3; u is the system control quantity; The extended state observer constructed according to the state equation is as follows: Where Z 21 is the estimated value of the system state x2; Z 22 is the estimated value of the total disturbance x3 of the system; The coefficients of the extended state observer are β1>0, β2>0; is the estimated error of the system state x2.

6. The double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor according to claim 4, characterized in that: In step 4, based on equations (1), (2) and (3), the double fractional-order differential sliding mode controller constructed in the feedback channel is: Where k1>0, k2>0, k3>0; y r It is the position given signal of the permanent magnet synchronous motor; y is the position signal of the permanent magnet synchronous motor; e is the error of the position signal of the permanent magnet synchronous motor; and is the fractional differential operator symbol; ε1 and ε2 are fractional differential operators and satisfy 0<ε1<1 and 0<ε2<1; s DFDSMS is the double fractional differential sliding surface; is the double fractional-order differential signal of the error; ∫edt is the integrated signal of the error; is the differential signal of the error; F is the total disturbance of the system, which is an unknown signal in this controller.

7. The double fractional-order differential sliding mode positioning composite control method for a permanent magnet synchronous motor according to claim 6, characterized in that: According to step S5, in order to solve the problem that F in equation (7) is the total disturbance of the system and is an unknown signal in the controller, combined with the extended state observer (6) constructed in the feedforward channel, the proposed double fractional-order differential sliding mode positioning composite control method based on the second-order super-local model of permanent magnet synchronous motor is constructed as follows: Where k1>0, k2>0, k3>0; y r It is the position given signal of the permanent magnet synchronous motor; y is the position signal of the permanent magnet synchronous motor; e is the error of the position signal of the permanent magnet synchronous motor; and y is the symbol of fractional differential operation; 0<ε1<1; 0<ε2<1; s DFDSMS is the double fractional differential sliding surface; is the double fractional-order differential signal of the error; ∫edt is the integrated signal of the error; is the differential signal of the error; According to formula (6), Z 22 is the estimated value of the total disturbance F of the system.

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