Construction method for control system for high-speed electric spindle supported by six-pole active magnetic bearings

Abstract

Disclosed in the present invention is a construction method for a control system for a high-speed electric spindle supported by six-pole active magnetic bearings. The method comprises: constructing a transfer learning model by means of a marginal distribution distance between a source domain data set and a target domain data set, training same to obtain a predicted disturbance function, and building the predicted disturbance function in a transfer learning module; using an actual displacement as an input of the transfer learning module so as to obtain a predicted disturbance, and forming an optimized active disturbance rejection controller by using a tracking differentiator, a nonlinear state error feedback control law, a first compensation factor, a second compensation factor, the transfer learning module and an extended state observer jointly; and three optimized active disturbance rejection controllers being connected in series to the front end of a three-degree-of-freedom compound controlled object, and two optimized active disturbance rejection controllers being connected in series to the front end of a two-degree-of-freedom compound controlled object, so as to jointly form a control system. Using active disturbance rejection control based on transfer learning optimization to predict a disturbance and using the optimized extended state observers to perform estimation and compensation for the total system disturbance improve the control performance of the system.

Description

Construction method of high-speed electric spindle control system supported by six-pole active magnetic bearings Technical Field

[0001] The present invention belongs to the technical field of electrical and mechanical transmission equipment, and specifically relates to an auto-disturbance rejection decoupling control system for a high-speed electric spindle supported by a six-pole active magnetic bearing. The present invention is suitable for the decoupling control of a high-speed electric spindle supported by a six-pole active magnetic bearing with multivariable, nonlinear, and strong coupling. Background Art

[0002] The high-speed electric spindle supported by six-pole active magnetic bearings is a combination of two six-pole active radial magnetic bearings and a single-degree-of-freedom axial magnetic bearing. These bearings utilize magnetic field forces to suspend the rotor in space, eliminating any mechanical contact between the rotor and stator. These new high-performance bearings address the problems of traditional bearing-based spindles, such as thermal deformation, short lifespan, and insufficient seismic resistance. The radial magnetic bearings utilize a six-pole symmetrical stator structure. This symmetrical structure minimizes magnetic coupling between the two radial degrees of freedom, resulting in high load capacity and excellent performance. Radial control coils are wound around the magnetic poles of the radial magnetic bearings and driven by a three-phase AC inverter. When energized, radial control magnetic flux is generated, generating a levitation force and achieving stable radial levitation. Since the radial magnetic bearings are all driven by inverters, radial magnetic flux coupling is unavoidable, affecting the precise control of the electric spindle. Therefore, an efficient decoupling controller is required to achieve high-speed, high-precision, and stable operation of the magnetic bearings.

[0003] Currently, the main approaches to decoupling control of magnetically levitated electric spindles include the combined application of approximate linearized auto-disturbance rejection decoupling control, matrix converter control, inverse system decoupling control, and other intelligent algorithms. Approximately linearized auto-disturbance rejection decoupling control is a new decoupling control approach that considers the mutual coupling between the radial magnetic circuits of the radial magnetic bearings in a five-degree-of-freedom magnetically levitated electric spindle as an internal disturbance in the system. It uses an extended state observer to estimate and compensate for internal disturbances, achieving precise decoupling control and linearizing each degree of freedom of the magnetic bearings. However, the performance of conventional approximate linearized auto-disturbance rejection controllers depends on the selection of internal parameters. When the operating conditions of a high-speed electric spindle supported by a six-pole active magnetic bearing change, the auto-disturbance rejection controller cannot accurately compensate for the disturbance.

[0004] The construction method provided in the document "Construction Method of AC Magnetic Levitation Electric Spindle Controller" with Chinese Patent Publication No. CN103076740B uses a fuzzy neural network to select static experimental data for offline training of the inverse system of the control object. However, the fuzzy control method has low control accuracy and cannot meet the high-precision requirements of the electric spindle. The control system provided in the document "Least Squares Support Vector Machine Optimization Control System for Five-Degree-of-Freedom Magnetic Levitation Electric Spindle" with Chinese Patent Publication No. CN112532134A uses the tracking signal and differential signal of the displacement as training samples to predict and compensate for the disturbance of the electric spindle. However, the selection of parameters in the least squares support vector machine results in a slow solution speed and requires a large amount of training data for each run, which affects the control accuracy of the system.

[0005] Summary of the Invention

[0006] The purpose of the present invention is to provide a construction method for a high-speed electric spindle control system supported by a six-pole active magnetic bearing that can solve the problems existing in the existing high-speed electric spindle control supported by a five-degree-of-freedom six-pole active magnetic bearing, such as reliance on internal parameter selection, inaccurate compensation of disturbances, requirement of a large amount of training data for operation, slow solution speed, and poor control accuracy.

[0007] To achieve the above-mentioned purpose, the technical solution adopted by the construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing of the present invention is:

[0008] The high-speed electric spindle has first and second six-pole radial active magnetic bearings and an axial magnetic bearing, and is characterized by comprising the following steps:

[0009] Step 1): constructing a three-degree-of-freedom composite controlled object including a first sextupole radial active magnetic bearing and an axial magnetic bearing, and a two-degree-of-freedom composite controlled object including a second sextupole radial active magnetic bearing, wherein the inputs of the three-degree-of-freedom composite controlled object and the two-degree-of-freedom composite controlled object are four corresponding radial control current expected values ​​and one axial control current expected value;

[0010] Step 2): The high-speed electric spindle is operated under a rated load, and multiple sets of displacement signals and corresponding disturbance signals outputted by the high-speed electric spindle are collected to form a source domain data set. The load size is changed within the rated load range, and multiple sets of displacement signals of the high-speed electric spindle are collected again to form a target domain data set. The edge distribution distance between the source domain data set and the target domain data set is calculated, and a transfer learning model is constructed based on the edge distribution distance. The transfer learning model is trained to obtain a prediction disturbance function, and the prediction disturbance function is built into the transfer learning module (504).

[0011] Step 3): using the actual radial or axial displacement as input to the transfer learning module (504), obtaining a predicted disturbance according to the predicted disturbance function, compensating the radial or axial control current expected value with a second compensation factor (506), and then adding the predicted disturbance to obtain a second control variable;

[0012] The second control variable and the actual radial or axial displacement are used as inputs of an extended state observer (502), and the extended state observer (502) outputs a tracking signal, a first-order differential signal of the tracking signal, and an observed disturbance;

[0013] After adding the predicted disturbance and the observed disturbance, the first control variable is obtained after compensation by a first compensation factor (505);

[0014] A tracking signal and a differential signal of a given radial or axial displacement are outputted by a tracking differentiator (501), the tracking signal outputted by the tracking differentiator (501) is subtracted from the tracking signal outputted by the extended state observer (502), and the differential signal outputted by the tracking differentiator (501) is subtracted from the first-order differential signal outputted by the extended state observer (502), and the two errors obtained are used as inputs of a nonlinear state error feedback control law (503), and the nonlinear state error feedback control law (503) outputs a feedback control variable;

[0015] The feedback control amount is subtracted from the first control amount to obtain a compensated control amount as the radial or axial control current expected value;

[0016] The tracking differentiator (501), the nonlinear state error feedback control law (503), the first compensation factor (505), the second compensation factor (506), the transfer learning module (504) and the extended state observer (502) together constitute an optimized active disturbance rejection controller;

[0017] Step 4): three of the optimized auto-disturbance rejection controllers are connected in series to the front end of the three-degree-of-freedom composite controlled object, and two of the optimized auto-disturbance rejection controllers are connected in series to the front end of the two-degree-of-freedom composite controlled object, together forming a high-speed electric spindle control system.

[0018] The advantages of the present invention after adopting the above technical solution are:

[0019] (1) The present invention adopts auto-disturbance rejection control based on transfer learning optimization, optimizes the performance of the extended state observer, predicts the disturbance of the electric spindle, and uses the optimized extended state observer to estimate and compensate for the total disturbance of the system, thereby achieving precise decoupling control of the radial degrees of freedom of the two six-pole radial active magnetic bearings in the high-speed electric spindle. This method can decouple a strongly coupled, nonlinear system with multiple inputs and multiple outputs under non-ideal conditions into a multi-input, multi-output, uncoupled linear system, thereby improving the system control performance.

[0020] (2) The present invention uses a transfer learning algorithm to obtain predicted disturbances. The displacement signal and disturbance signal collected from the anti-disturbance controller are used as the source domain dataset, reducing data requirements. After the load is replaced, the displacement signal and the corresponding disturbance signal are collected as the target domain dataset. A transfer learning model is constructed based on the edge distance distribution, and the source domain data is used to train and test the transfer learning model. Because transfer learning has already captured the characteristics of the source domain dataset, it avoids excessive selection of internal parameters and reduces the need for large amounts of training data. This improves the computational speed of the control system, making the system more rapid.

[0021] (3) In the process of predicting the output of disturbances, transfer learning uses training data to obtain data features, which can avoid overfitting and improve the convergence speed and control accuracy of the control system.

[0022] (4) The radial magnetic bearings in the high-speed electric spindle supported by the six-pole active magnetic bearings are equipped with two radial magnetic bearings and one axial magnetic bearing to achieve stable suspension of the five degrees of freedom of the electric spindle shaft. The radial and axial magnetic circuits are independent of each other, reducing coupling. The radial magnetic bearings are driven and controlled by a three-phase inverter. Five anti-disturbance control controllers are used to decouple the high-speed electric spindle. This method does not require a precise mathematical model and has the characteristics of small overshoot, fast response, and strong anti-interference ability, which can significantly improve the control accuracy of the electric spindle control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] FIG1 is a schematic structural diagram of a high-speed electric spindle supported by a six-pole active magnetic bearing;

[0024] FIG2 is a schematic diagram of the radial structure and magnetic circuit of the first six-pole radial active magnetic bearing in FIG1 ;

[0025] FIG3 is a schematic diagram of the axial structure and magnetic circuit of the first six-pole radial active magnetic bearing in FIG1 ;

[0026] FIG4 is an equivalent structural block diagram of a three-degree-of-freedom composite controlled object constructed based on the first six-pole active radial magnetic bearing and the axial magnetic bearing in FIG1 ;

[0027] FIG5 is an equivalent structural block diagram of a two-degree-of-freedom composite controlled object constructed based on the second six-pole active radial magnetic bearing in FIG1 ;

[0028] FIG6 is a block diagram of the structure of the high-speed electric spindle control system supported by the constructed six-pole active magnetic bearing;

[0029] FIG7 is a control structure block diagram of the first optimized active disturbance rejection controller in FIG6;

[0030] FIG8 is a flow chart of a construction method of the transfer learning module in FIG7 ;

[0031] FIG9 is a control structure block diagram of the traditional active disturbance rejection controller shown in FIG7 .

[0032] In the figure: 1. First six-pole radial active magnetic bearing; 2. Axial magnetic bearing; 3. Second six-pole radial active magnetic bearing; 4. High-speed spindle motor; 5. Rotating shaft; 6, 7, 8, 9. Radial displacement sensor; 10. Axial displacement sensor; 11. Auxiliary bearing; 12, 13. End caps; 14. Steel cylinder outer sleeve; 15. Steel cylinder inner sleeve; 16. High-speed spindle motor stator; 17. High-speed spindle motor rotor; 20. First optimized active disturbance rejection controller; 21. Second optimized active disturbance rejection controller; 22. Third optimized active disturbance rejection controller; 23. Fourth optimized active disturbance rejection controller; 24. Fifth optimized active disturbance rejection controller; 25. First displacement sensor; 26. Second displacement sensor; 27. Third displacement sensor; 28. Fourth displacement sensor; 29. ​​Fifth displacement sensor; 31. First inverse Clark transform; 32. Second inverse Clark transform; 33. First current tracking inverter; 34. Second current tracking inverter; 35. Axial power amplifier;

[0033] 101. First radial rotor; 102. First radial stator; 103. First radial control coil; 104. First radial stator pole; 105. Bias flux; 106. Control flux; 107. Radial air gap;

[0034] 201. Axial stator; 202. Axial rotor; 203. Axial control coil; 204. Axial stator magnetic pole; 210. Three-degree-of-freedom composite controlled object; 211. Two-degree-of-freedom composite controlled object;

[0035] 301. Second radial rotor; 302. Second radial rotor; 303. Second radial control coil;

[0036] 501. First tracking differentiator; 502. First extended state observer; 503. First nonlinear feedback control law; 504. Transfer learning module; 505. First compensation factor; 506. Second compensation factor. DETAILED DESCRIPTION

[0037] Referring to Figure 1, the basic structure of a six-pole magnetic bearing-supported electric spindle includes a rotating shaft 5, a high-speed spindle motor 4, a first six-pole radial active magnetic bearing 1, an axial magnetic bearing 2, a second six-pole radial active magnetic bearing 3, an outer steel cylinder sleeve 14, an inner steel cylinder sleeve 15, radial displacement sensors 6, 7, 8, and 9, an axial displacement sensor 10, an auxiliary bearing 11, and end caps 12 and 13. The high-speed spindle motor 4 includes a high-speed spindle motor stator 16 and a high-speed spindle motor rotor 17. The high-speed spindle motor rotor 17 is coaxially fixedly mounted on the rotating shaft 5, driving the rotating shaft 5 in rotation. To the left of the high-speed spindle motor 4 is the second six-pole radial active magnetic bearing 3, and to the right are the axial magnetic bearing 2 and the first six-pole radial active magnetic bearing 1. The first six-pole radial active magnetic bearing 1 and the second six-pole radial active magnetic bearing 3 are identical in structure. The high-speed spindle motor 4, the first six-pole radial active magnetic bearing 1, the second six-pole radial active magnetic bearing 3, and the axial magnetic bearing 2 are collectively encased in a steel cylinder. This cylinder consists of an outer steel cylinder sleeve 14 and an inner steel cylinder sleeve 15. Spiral channels for water cooling are provided between the outer steel cylinder sleeve 14 and the inner steel cylinder sleeve 15. An end cap 12 and 13 are fixedly connected to the left and right end faces of the outer steel cylinder sleeve 14 and the inner steel cylinder sleeve 15, respectively. Each end cap 12 and 13 is supported on the exterior of the rotating shaft 5 by an auxiliary bearing 11. The auxiliary bearing 11 is used to support the rotating shaft 5 when the magnetic bearing is shut down or in a faulty state. The rotating shaft 5 coaxially passes through the first six-pole radial active magnetic bearing 1, the axial magnetic bearing 2, the high-speed spindle motor 4, and the second six-pole radial active magnetic bearing 3.

[0038] The second six-pole radial active magnetic bearing 3 is located between the high-speed spindle motor 4 and the left end cap 13, with an axial distance between each of the two. A third radial displacement sensor 8 and a fourth radial displacement sensor 9 are mounted between the left end cap 13 and the second six-pole radial active magnetic bearing 3. These sensors are radially symmetrically mounted face-to-face to detect radial displacements of two degrees of freedom on the left side of the rotating shaft 5.

[0039] The axial magnetic bearing 2 consists of an axial rotor 201, an axial stator 202, and an axial control coil 203. The axial magnetic bearing 2 is located between the high-speed spindle motor 4 and the first six-pole radial active magnetic bearing 1. Axially, two annular limiting sleeves are positioned between the first six-pole radial active magnetic bearing 1 and the axial magnetic bearing 2, and between the axial magnetic bearing 2 and the high-speed spindle motor 4, respectively, to secure the axial positions of the three. The first six-pole radial active magnetic bearing 1 is located between the axial magnetic bearing 2 and the right end cap 12, with an axial distance between the axial magnetic bearing 2 and the right end cap 12. A first radial displacement sensor 6 and a second radial displacement sensor 7 are installed between the right end cap 12 and the first six-pole radial active magnetic bearing 1. These sensors are mounted face-to-face and symmetrically in the radial direction to detect the displacement of the two radial degrees of freedom on the right side of the rotating shaft 5. An axial displacement sensor 10 is mounted on the right end cap 12 to detect the displacement of the axial degrees of freedom of the rotating shaft 5.

[0040] The probes of the first, second, third and fourth radial displacement sensors 6, 7, 8, 9 and the axial displacement sensor 10 are all eddy current sensors.

[0041] Referring to the first six-pole radial active magnetic bearing 1 shown in Figures 2 and 3, it is composed of a first radial rotor 101, a first radial stator 102, and a first radial control coil 103. The first radial rotor 101 is cylindrical and coaxially fixedly sleeved on the outside of the rotating shaft 5, forming an integral part of the rotating shaft 5. The outer wall of the first radial stator 102 is fixedly connected to the inner wall of the steel cylinder inner sleeve 15. The first radial stator 102 is coaxially sleeved on the outside of the first radial rotor 101, and a radial air gap 107 is formed between the two. The first radial stator 102 is composed of a circular stator yoke and six convex first radial stator poles 104 evenly arranged along the circumference of the inner wall of the stator yoke. The side surface of the first radial stator poles 104 is a cylindrical surface. Each first radial stator pole 104 is wound with a first radial control coil 103 in the same direction. The first radial control coils 103 on two opposite poles are connected in series to form a phase, forming a three-phase coil. The three-phase coils are connected in a star shape, and a three-phase inverter is used to control the first radial control coils 103 to control the magnitude and direction of the suspension force.

[0042] The first radial control coil 103 provides bias flux 105 and control flux 106 for the first six-pole radial active magnetic bearing 1. The bias flux 105 circulates from one first radial stator pole 104, through the radial air gap 107, into the first radial rotor 101, then through the opposite radial air gap 107 to the opposite first radial stator pole 104, and finally through the stator yoke back to the starting first radial stator pole 104. The bias flux 105 circuit primarily functions to balance the weight of the rotor with the levitation force generated by the bias magnetomotive force. The control flux 106 circuit circulates from one first radial stator pole 104, through the radial air gap 107, into the first radial rotor 101, and then through the opposite radial air gap 107 to the opposite first radial stator pole 104. The interaction between the bias flux 105 and the control flux 106 generates a radial two-degree-of-freedom levitation force on the first radial rotor 101 of the first six-pole radial active magnetic bearing 1.

[0043] Referring to Figure 1 , the second six-pole radial active magnetic bearing 3 consists of a second radial stator 302, a second radial rotor 301, and a second radial control coil 303. Its structure and assembly are identical to those of the first radial stator 102, first radial rotor 101, and first radial control coil 103. The first radial air gap 107 between the first radial stator 102 and the first radial rotor 101 is the same size as the second radial air gap between the second radial stator 302 and the second radial rotor 301: both are 0.5 mm. Similarly, the bias flux and control flux of the second six-pole radial active magnetic bearing interact to generate a radial two-degree-of-freedom suspension force on the second radial rotor 301 of the second six-pole radial active magnetic bearing 3.

[0044] The axial magnetic bearing 2 consists of an axial stator 201, an axial rotor 202, and an axial control coil 203. The axial rotor 202 is cylindrical and coaxially fixedly sleeved around the rotating shaft 5, forming an integral part of the rotating shaft 5. The axial control coil 203 is wound around the left and right magnetic poles of the axial stator 202. A bipolar DC power amplifier generates axial control magnetic flux and axial bias magnetic flux. The interaction between the axial control magnetic flux and the axial bias magnetic flux generates an axial suspension force on the axial rotor 202 of the axial magnetic bearing 2.

[0045] The first radial stator 102, first radial rotor 101, second radial stator 302, second radial rotor 301, axial stator 202, and axial rotor 201 are all constructed from laminated silicon steel sheets. The first radial control coil 103, second radial control coil 303, and axial control coil 203 are all made from 0.67 mm diameter insulated copper wire. The auxiliary bearing 11 utilizes a self-aligning ball bearing.

[0046] As shown in FIG4 , based on the first six-pole radial active magnetic bearing 1 and the axial magnetic bearing 2, a three-degree-of-freedom composite controlled object 210 including the first six-pole radial active magnetic bearing 1 and the axial magnetic axis 2 is constructed. The three-degree-of-freedom composite controlled object 210 is composed of a first Clark inverse transform 31, a first current tracking inverter 33, a first six-pole radial active magnetic bearing 1, and an axial power amplifier 35 and an axial magnetic bearing 2 connected in series. The input of the three-degree-of-freedom composite controlled object 210 is the first radial control current expected value i ax * , the second radial control current expected value i ay * and the expected value of the axial control current i az * The output of the three-DOF composite controlled object 210 is the actual radial displacement x a 、y a and the actual axial displacement z a Among them, the first radial control current expected value i ax * and the second radial control current expected value i ay * After the first Clark inverse transformation 31, the current i is obtained au * 、i av * and i aw * , current i au * 、i av * and i aw * The radial control current i is outputted by the first current tracking inverter 33. au 、i av and i aw The radial control current i au 、i av 、i aw Control the first radial control coil 103 in the first six-pole radial active magnetic bearing 1, and the first six-pole radial active magnetic bearing 1 generates an actual radial displacement x a 、y a The first and second radial displacement sensors 6 and 7 respectively detect the actual radial displacement x a 、y a . Expected value of axial control current i az * After passing through the axial power amplifier 35, the axial control current i is output az , axial control current i azControl the axial control coil 203 in the axial magnetic bearing 2, and the axial magnetic bearing 2 generates an actual axial displacement z a , the axial displacement sensor 10 detects the actual axial displacement z a , which is constructed into a three-degree-of-freedom composite controlled object 210 including a first six-pole radial active magnetic bearing 1 and an axial magnetic bearing 2.

[0047] As shown in FIG5 , based on the second sextupole radial active magnetic bearing 3, a two-degree-of-freedom composite controlled object 211 including the second sextupole radial active magnetic bearing 3 is constructed. The second Clark inverse transform 32, the second current tracking inverter 34, and the second sextupole radial active magnetic bearing 3 connected in series together constitute the two-degree-of-freedom composite controlled object 211. The input of the two-degree-of-freedom composite controlled object 211 is the third and fourth radial control current expected values ​​i bx * 、i by * The output of the two-DOF composite controlled object 211 is the actual radial displacement x b 、y b Among them, the third and fourth radial control current expected values ​​i bx * 、i by * The second Clark inverse transform 32 is inputted together, and the second Clark inverse transform 32 outputs the current i bu * 、i bv * and i bw * , current i bu * 、i bv * and i bw * The radial control current i is outputted by the second current tracking inverter 34. bu 、i bv 、i bw To the second six-pole radial active magnetic bearing 3, the second radial control coil 302 therein is controlled, and the second six-pole radial active magnetic bearing 3 outputs the actual radial displacement x b 、y b , is constructed into a two-degree-of-freedom composite controlled object 211 including a second six-pole radial active magnetic bearing 3. The third and fourth radial displacement sensors 8 and 9 detect the actual radial displacement x b 、y b .

[0048] As shown in Figure 6, because the five degrees of freedom of the high-speed electric spindle supported by the six-pole active magnetic bearing shown in Figure 1 need to be controlled, five optimized ADRC controllers are used to form the control system, each controlling one of the five degrees of freedom. These five optimized ADRC controllers are the first, second, third, fourth, and fifth optimized ADRC controllers 20, 21, 22, 23, and 24. These five optimized ADRC controllers differ only in their input and output signals; their internal structures are identical.

[0049] The first and second radial displacement sensors 6 and 7 collect the actual radial displacement x of the three-degree-of-freedom composite controlled object 210. a 、y a , actual radial displacement x a 、y a The axial displacement sensor 10 collects the actual axial displacement z of the three-degree-of-freedom composite controlled object 210. a , actual axial displacement z a Input to the third optimized ADRC 22. At the same time, the corresponding given radial displacement x a * The first optimized active disturbance rejection controller 20 is input to the actual radial displacement x a and given radial displacement x a * Processing, outputting the first radial control current expected value i ax * to the three-DOF composite controlled object 210. Similarly, the corresponding given radial displacement y a * The second optimized active disturbance rejection controller 21 outputs the second radial control current expected value i ay * to the three-degree-of-freedom composite controlled object 210; the given axial displacement z a * The input is sent to the third optimized active disturbance rejection controller 22, and the third optimized active disturbance rejection controller 22 outputs the expected value of the axial control current i az * To the three-degree-of-freedom composite controlled object 210. Thus, the first radial control current expected value i ax * , the second radial control current expected value i ay * and the expected value of the axial control current i az * Together they serve as inputs to the three-DOF composite controlled object 210 .

[0050] The third and fourth radial displacement sensors 8 and 9 collect the actual radial displacement x of the two-degree-of-freedom composite controlled object 211. b 、y b , actual radial displacement x b 、y b They are input into the corresponding fourth optimized ADRC controller 23 and the fifth optimized ADRC controller 24 respectively, and the corresponding given radial displacement x b * The input is sent to the fourth optimized active disturbance rejection controller 23, which responds to the input actual radial displacement x b and given radial displacement x b * Processing, outputting the third radial control current expected value i bx * To the two-DOF composite controlled object 211. The corresponding given radial displacement y b * The fifth optimized active disturbance rejection controller 24 outputs the fourth radial control current expected value i by * To the two-degree-of-freedom composite controlled object 211. The third radial control current expected value i bx * and the fourth radial control current expected value i by * Together they serve as the input of the two-DOF composite controlled object 211 .

[0051] As shown in FIG7 , the construction process of the optimized ADRC controller is described in detail below by taking the first optimized ADRC controller 20 as an example:

[0052] The first optimized active disturbance rejection controller 20 is composed of a tracking differentiator 501 , a nonlinear state error feedback control law 503 , a first compensation factor 505 , a second compensation factor 506 , a transfer learning module 504 and an extended state observer 502 .

[0053] Given radial displacement x a * The tracking differentiator 501 outputs the given radial displacement x a * The tracking signal v a1x and given radial displacement x a * The differential signal v a2x The mathematical model of the tracking differentiator 501 is:

[0054] Where: sat is a nonlinear function, and the expression is: in T is the fast tracking factor, ranging from [0,1]. The value of T determines the system tracking performance; ε is the integration step size; h is the system sampling period; For a given displacement The value at time k; ν a1x (k) and ν a1x (k+1) are given radial displacement tracking signals v a1x The value at time k and k+1; ν a2x (k) and ν a2x (k+1) are given radial displacement differential signals v a2x The values ​​at time k and k+1.

[0055] Actual radial displacement x a The tracking signal z is outputted by the extended state observer 502 a1x , tracking signal z a1x The first-order differential signal z a2x and the observed disturbance z of the system a3x .

[0056] The tracking signal v output by the tracking differentiator 501 is a1x The tracking signal z output by the extended state observer 502 a1x Subtract and get the first system state error e a1x =v a1x -z a1x The differential signal v output by the tracking differentiator 501 a2x and the first-order differential signal z output by the extended state observer 502 a2x The second system state error e is obtained by subtraction a2x =v a2x -z a2x The two system state errors e a1x and e a2x Together they serve as the input of the nonlinear state error feedback control law 503, which outputs the feedback control quantity u a0x The model of the nonlinear state error feedback control law is: a0x =k1fal(e a1x ,α4,δ2)+k2fal(e a2x ,α5,δ2),

[0057] Where: k1, k2, α4, α5 and δ2 are the adjustable parameters of the nonlinear feedback control law. Generally, α4 is 0.5; α5 is 0.25; the range of k1 and k2 is [0,100], the range of δ2 is [0,1], and the nonlinear function Where e is a natural constant, α is a constant between 0 and 1, and δ is a custom constant that affects the filtering effect.

[0058] Feedback control quantity u a0x After compensation by the first compensation factor 505, the compensated control quantity u is obtained ax :

[0059] Where: 1 / d is the first compensation factor; f ax is the predicted disturbance output by the transfer learning module 504. Considering comprehensive factors, the value range of d is [10, 200].

[0060] The control quantity u after compensation ax It is also used as the input of the second compensation factor 506. The second compensation factor is d. After the compensation of the second compensation factor 506, the compensated control amount du is obtained. ax , and then the control quantity du ax and the predicted disturbance f ax Add together to get the second control quantity (f ax +du ax ), the second control amount after addition (f ax +du ax ) is used as the second input of the extended state observer 502. The discrete mathematical model of the extended state observer 502 is:

[0061] Where: fal is a nonlinear function, and its expression is: Where e is a natural constant, α is a constant between 0 and 1, and δ is a custom constant that affects the filtering effect; α1, α2, α3, β1, β2, β3, and δ1 are the 502 adjustable parameters of the extended state observer; z a1x (k+1), z a2x (k+1) and z a3x (k+1) are z a1x 、z a2x and z a3x The value at time k+1; h is the sampling period; e a1x is the first system state error; e a2x is the second system state error; x a (k) is the actual radial (axial) displacement at time k, u ax (k) is the controlled variable u after compensation at time k ax ;f ax (k) is the predicted disturbance f output by the transfer learning module (504) at time k ax, α1 is usually taken as 0.75, α2 is taken as 0.5, α3 is taken as 0.25, δ1 is taken as 5 to 10 times of the sampling period, and β1, β2, and β3 should be continuously adjusted according to the tracking effect required by the system.

[0062] The actual radial displacement x collected by the first radial displacement sensor 6 a As the first input of the extended state observer 502, the second control variable (f ax +du ax ) is used as the second input of the extended state observer 502, which outputs the actual radial displacement x a The tracking signal z a1x , tracking signal z a1x The first-order differential signal z a2x and the observed disturbance z of the system a3x .

[0063] The actual radial displacement x a , source domain dataset D s And the target domain dataset D t As input to the transfer learning module 504, the transfer learning module 504 outputs the predicted disturbance f of the system ax , the predicted disturbance f ax The observed disturbance z output by the extended state observer 502 a3x Add them together and get the sum of disturbances (z a3x +f ax ) is used as the input of the first compensation factor 505, and the first control amount is obtained after the first compensation factor 505 acts The feedback control quantity u output by the nonlinear state error feedback control law 503 is a0x With the first control quantity Make the difference and get the control quantity u after compensation ax , the controlled quantity u after compensation ax That is the expected value of radial control current i ax * ,u ax =i ax * , as the output of the first optimized active disturbance rejection controller 20.

[0064] The construction methods of the second, third, fourth and fifth optimized ADRC controllers 20, 21, 22, 23 and 24 are exactly the same as that of the first optimized ADRC controller 20. They output corresponding control current expected values ​​for different given radial or axial displacements. Therefore, the other four optimized ADRC controllers are not described in detail.

[0065] 7 , 8 and 9 , the method for constructing the transfer learning module 504 is as follows:

[0066] Step S1: Dataset Collection

[0067] The high-speed electric spindle supported by the six-pole active magnetic bearing shown in Figure 1 is connected to a traditional active disturbance rejection controller. The traditional active disturbance rejection controller is a controller that can detect the disturbance signal of the electric spindle, such as the support vector machine optimized active disturbance rejection controller in Figure 9 (using the active disturbance rejection controller with patent publication number CN112532134A), or other controllers that detect the disturbance signal of the electric spindle, including a tracking differentiator 501, a nonlinear state error feedback control law 503, a first compensation factor 505, a second compensation factor 506, an extended state observer 502 and a least squares support vector machine module. Compared with the first optimized active disturbance rejection controller 20 of the present invention shown in Figure 7, only the predicted disturbance output module is different, and the functions and effects of the remaining parts are the same.

[0068] Under the control of the traditional support vector machine optimized active disturbance rejection controller shown in Figure 9, the high-speed electric spindle supported by the six-pole active magnetic bearing shown in Figure 1 is operated under the rated load, and multiple sets of displacement signals x are collected from the output. i and its corresponding disturbance signal y i , for the displacement signal x i and the disturbance signal y i Perform preprocessing to form the source domain dataset D s ={(x1,y1),...,(x n ,y n )}, the present invention collects n groups of displacement signals x i And disturbance signal, n is the number of source domain data samples, 1≤i≤n. Change the load size within the rated load range, and then collect multiple sets of high-speed electric spindle displacement signals z j , and the displacement signal z j Perform preprocessing to form the target domain data D t ={z1,...,z m}, 1≤j≤m, m is the collected displacement signal z j The number is also the number of target domain data samples.

[0069] Step S2: Edge distribution distance calculation

[0070] The key to transfer learning is to quantify the data difference between the source domain and the target domain to ensure the effectiveness of transfer learning. s With the target domain dataset D t Mapped to the reproducing kernel Hilbert space, the maximum mean discrepancy (MMD) is used to represent the edge distribution distance D between the source domain and the target domain. H . Source domain dataset Ds With the target domain dataset D t The marginal distribution distance D H Calculated by the following formula:

[0071] Where: H represents the reproducing kernel Hilbert space, x i is the displacement signal in the source domain data set; z j is the displacement signal in the target domain dataset; n is the number of samples in the source domain dataset; m is the number of samples in the target domain dataset; θ(x i ),θ(z j ) are the mapping functions θ(x) of the displacement signals in the source domain dataset and the target domain dataset in the reproducing kernel Hilbert space, and the initial function of the mapping function θ(x) is defined as the softmax function. The disturbance signal y in the source domain dataset is i The mapping function can be used to transform the original data in the reproducing kernel Hilbert space, so the disturbance signal y in the source domain data set is i for:

[0072] e is a natural constant.

[0073] Step S3: Based on the edge distribution distance D H Build a transfer learning model:

[0074] Where: f(y i ) represents the transfer learning model; argmin represents minimizing the objective function; L is the loss function that measures the accuracy of the source domain dataset, where L selects the cross entropy loss function. λ is a correction coefficient, which is selected in the range of [0, 1], and the best value in the present invention is 0.5.

[0075] Step S4: Train the transfer learning model f(y i )

[0076] Step S4.1: To train the transfer learning model, call the deep learning toolbox in the MATLAB software environment. s Sampling the ω group, ω≤n, and taking half of the ω group as the training sample set The other half is used as the test sample set Considering the training accuracy and training time, the value range of ω is [100,600]. i As a transfer learning model f(y i ) input, disturbance signal y i As a transfer learning model f(y i ) output.

[0077] Step S4.2: Use the training module to train the ω / 2 group of training sample sets D train Training. Take the ω / 2 group of training samples as the transfer learning model f(y i ) input and output signals, and output ω / 2 group mapping function through software fitting Map the displacement signals in the ω / 2 group of training samples to the reproducing kernel Hilbert space, and respectively map the ω / 2 group of mapping functions Substitute the marginal distribution distance The calculation formula is used to obtain the marginal distribution distance of ω / 2 groups.

[0078] Step S4.3: Distribute the edge distances of the ω / 2 groups separately Substitute into the transfer learning model f(y i ), we get ω / 2 groups of transfer learning models f(y i ), that is, Select the mapping function θ corresponding to the minimum value among the corresponding values ​​of the ω / 2 group transfer learning model min (x), the mapping function θ min (x) is the predicted disturbance function f ax (x), training is completed.

[0079] Step S5: Test the predicted disturbance function f ax (x)

[0080] The test sample set D test The displacement signal [x test1 ,x test2 ,...,x testω / 2 ] Input to the trained prediction perturbation function f ax (x), we can get the predicted perturbation output set D out =[y out1 ,y out2 ,…,y outω / 2 ].

[0081] For the test sample set Take out all the disturbance signals and form a disturbance signal sample set [y test1 ,y test2 ,...,y testω / 2 ], calculate the disturbance signal sample set [y test1 ,y test2 ,...,y testω / 2 ] and the predicted perturbation output set D out =[y out1 ,y out2 ,…,y outω / 2]’s mean square error:

[0082] Among them, y outp ,y testp Denote the predicted output set D out And the test sample set D test The pth disturbance signal in , 0 <p<ω / 2。

[0083] The mean square error threshold γ is set according to the actual accuracy requirement. The range of γ set by this invention is [10 -5 ,10 -3 ]. Compare the mean square error Δ with the set error threshold γ. If the mean square error Δ is less than the error threshold γ, it is considered that the prediction disturbance function f obtained in step S4.3 is correct. ax (x) meets the requirements; on the contrary, if the mean square error δ is greater than or equal to the error threshold γ, it is necessary to readjust the correction coefficient λ, and then reconstruct the transfer learning model f(y based on the adjusted new correction coefficient λ i ), repeat steps S3-S5, that is, it is necessary to rebuild the transfer learning model f(y based on the adjusted new correction coefficient λ i ), and train the newly constructed transfer learning model f(y i ) and test until the mean square error is less than γ, then the prediction disturbance function f that meets the requirements is obtained ax (x).

[0084] Step S6: Constructing an optimized ADRC controller

[0085] See Figure 7, the predicted disturbance function f that meets the requirements after the test is ax (x) is built into the transfer learning module 504 and connected to the first optimized ADRC 20. The transfer learning module 504 reduces the burden of the extended state observer 502 and improves the stability of the overall control system.

[0086] Real-time displacement signal of high-speed electric spindle supported by six-pole active magnetic bearings a As the input signal of the transfer learning module 504, the transfer learning module 504 outputs the predicted disturbance f ax =f ax (x). The predicted disturbance f ax The du output by the second compensation factor 506 ax Adding, the second control quantity (f ax +du ax ) as the second input of the extended state observer 502. The predicted disturbance f ax The observed disturbance z output by the extended state observer 502 a3x Add together to get the disturbance (fax +z a3x ), disturbance (f ax +z a3x ) is compensated by the first compensation factor 505 to obtain the first control amount The feedback control quantity u output by the nonlinear state error feedback control law 503 is a0x With the first control quantity Make the difference and get the control amount after compensation The current radially controls the current desired value, thus forming an optimized active disturbance rejection controller.

[0087] The second, third, fourth, and fifth optimized ADRC controllers 21, 22, 23, and 24 are each connected to a transfer learning module to predict disturbances. The method is similar to that of the first optimized ADRC controller 20, so this will not be repeated here. This results in five identical optimized ADRC controllers 20, 21, 22, 23, and 24. Three of the optimized ADRC controllers 20, 21, and 22 are connected in series to the front end of the three-DOF composite controlled object 210, and two of the optimized ADRC controllers 23 and 24 are connected in series to the front end of the two-DOF composite controlled object 211, collectively forming a high-speed electric spindle control system.

[0088] As described above, a high-speed electric spindle supported by hexapolar active magnetic bearings uses a three-phase inverter to drive and control the first and second hexapolar radial active magnetic bearings 1 and 3, respectively, and a bipolar power amplifier to drive the axial magnetic bearing 2, thereby achieving stable suspension of the electric spindle's five degrees of freedom. Because the radial magnetic bearings are driven and controlled by a three-phase AC inverter, coupling exists between the radial magnetic circuits, affecting the high-precision control of the electric spindle's rotational axis. Five active disturbance rejection controllers are used to decouple the high-speed electric spindle supported by the hexapolar active magnetic bearings. This system, which does not require a precise mathematical model, exhibits minimal overshoot, fast response, and strong anti-interference capabilities, significantly improving the control accuracy of the electric spindle system. A transfer learning algorithm is used to obtain predicted disturbances. The displacement and disturbance signals of the electric spindle rotor under rated load are collected as a source domain dataset. The displacement and disturbance signals are then collected after the load is changed as a target domain dataset. A transfer learning model is constructed based on the edge distance distribution, and the model is trained and tested using the source data. Since transfer learning has obtained the features from the data set, it reduces the need for large amounts of data, improves the calculation speed of the control system, and makes the system more rapid. The trained transfer learning module is connected to the ADRC, and the source domain data set D is used. s , target domain dataset D t The real-time displacement signal of the high-speed electric spindle supported by the six-pole active magnetic bearing is used as the input signal of the trained transfer learning model, and the predicted disturbance is used as the output of the transfer learning module to realize the operation of the control system.

Claims

1. A construction method of a high-speed electric spindle control system supported by a six-pole active magnetic bearing, wherein the high-speed electric spindle has a first and a second six-pole radial active magnetic bearing and an axial magnetic bearing, characterized in that The following steps are involved: Step 1): constructing a three-degree-of-freedom composite controlled object including a first six-pole radial active magnetic bearing and an axial magnetic bearing, and a two-degree-of-freedom composite controlled object including a second six-pole radial active magnetic bearing, wherein the inputs of the three-degree-of-freedom composite controlled object and the two-degree-of-freedom composite controlled object are four corresponding radial control current expected values ​​and one axial control current expected value; Step 2): The high-speed electric spindle is operated under rated load, and multiple groups of displacement signals and corresponding disturbance signals outputted by the high-speed electric spindle are collected to form a source domain data set. The load size is changed within the rated load range, and multiple groups of displacement signals of the high-speed electric spindle are collected to form a target domain data set. Calculating the marginal distribution distance between the source domain data set and the target domain data set, constructing a transfer learning model based on the marginal distribution distance, training the transfer learning model to obtain a prediction perturbation function, and embedding the prediction perturbation function into a transfer learning module (504); Step 3): using the actual radial or axial displacement as the input of the transfer learning module (504), obtaining the predicted disturbance according to the predicted disturbance function, and compensating the radial or axial control current expected value with the second compensation factor (506), and then adding the predicted disturbance to obtain the second control amount; The second control variable and the actual radial or axial displacement are used as inputs of an extended state observer (502), and the extended state observer (502) outputs a tracking signal, a first-order differential signal of the tracking signal, and an observed disturbance; After adding the predicted disturbance to the observed disturbance, the first control amount is obtained after compensation by a first compensation factor (505); A tracking signal and a differential signal of a given radial or axial displacement are outputted through a tracking differentiator (501), the tracking signal outputted by the tracking differentiator (501) is subtracted from the tracking signal outputted by an extended state observer (502), and the differential signal outputted by the tracking differentiator (501) is subtracted from the first-order differential signal outputted by the extended state observer (502), and the two errors obtained are used together as inputs of a nonlinear state error feedback control law (503), and the nonlinear state error feedback control law (503) outputs a feedback control amount; The feedback control amount is subtracted from the first control amount to obtain a compensated control amount as the radial or axial control current expected value; The tracking differentiator (501), the nonlinear state error feedback control law (503), the first compensation factor (505), the second compensation factor (506), the transfer learning module (504) and the extended state observer (502) together constitute an optimized active disturbance rejection controller; Step 4): three of the optimized anti-disturbance controllers are connected in series to the front end of the three-degree-of-freedom composite controlled object, and two of the optimized anti-disturbance controllers are connected in series to the front end of the two-degree-of-freedom composite controlled object, together forming a high-speed electric main Axis control system.

2. The construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing according to claim 1 is characterized by: In step 2), the edge distribution distance H represents the reproducing kernel Hilbert space, x i 、z j are the displacement signals in the source domain dataset and the target domain dataset respectively; n and m are the number of samples in the source domain dataset and the target domain dataset respectively; 1≤i≤n, 1≤j≤m; θ(x i ),θ(z j ) are the mapping functions θ(x) of the displacement signals in the source domain dataset and the target domain dataset in the reproducing kernel Hilbert space, respectively. The initial function of the mapping function θ(x) is the softmax function. Then the disturbance signal in the source domain dataset is 3. The construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing according to claim 2 is characterized by: The transfer learning model described argmin means to minimize the objective function; λ is the correction coefficient, which is in the range of [0, 1].

4. The construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing according to claim 3 is characterized by: First, sample ω groups from the source domain dataset, ω≤n, and use half of the ω groups as training sample sets and the other half as test sample sets; then use the ω / 2 training sample sets as the transfer learning model f(y i ) input and output signals, output ω / 2 groups of mapping functions, map the displacement signals in the ω / 2 groups of training samples to the reproducing kernel Hilbert space, and substitute the ω / 2 groups of mapping functions into the marginal distribution distance D H Calculate and get the edge distribution distance D of ω / 2 groups Hi ; Finally, the ω / 2 groups of marginal distribution distances are substituted into the transfer learning model f(y i ), and obtain ω / 2 groups of transfer learning models f(y i ), select the mapping function corresponding to the minimum value among the corresponding values, and this mapping function is the trained prediction disturbance function.

5. The construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing according to claim 4 is characterized by: The displacement signal in the test sample set is input into the trained prediction disturbance function to obtain the predicted disturbance output set; all the disturbance signals in the test sample set are taken out to form a disturbance signal sample set, the mean square error between the disturbance signal sample set and the predicted disturbance output set is calculated, and the mean square error is compared with the set error threshold. If the mean square error is less than the error threshold, the trained prediction disturbance function meets the requirements; otherwise, the transfer learning model f(y i ) and then reconstruct the transfer learning model f(y i ).

6. The construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing according to claim 1 is characterized by: In step 3), the mathematical model of the tracking differentiator (501) is: Nonlinear functions T is the fast tracking factor, ε is the integration step size; h is the sampling period; For a given displacement The value at time k; ν a1x (k) and ν a1x (k+1) are given displacement tracking signals v a1x The value at time k and k+1; ν a2x (k) and ν a2x (k+1) are given displacement differential signals v a2x The values ​​at time k and k+1.

7. The construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing according to claim 6 is characterized by: In step 3), the feedback control amount u a0x =k1fal(e a1x ,α4,δ2)+k2fal(e a2x ,α5,δ2), k1, k2, α4, α5 and δ2 are the adjustable parameters of the nonlinear feedback control law, α4 is 0.5; α5 is 0.25; the range of k1 and k2 is [0,100], and the range of δ2 is [0,1], e is a natural constant, α is a constant between 0 and 1, and δ is a custom constant that affects the filtering effect; e a1x =v a1x -z a1x ;e a2x =v a2x -z a2x ; z a1x 、z a2x They are respectively the tracking signal and the first-order differential signal output by the extended state observer (502).

8. The construction method of the high-speed electric spindle control system supported by the six-pole active magnetic bearing according to claim 7 is characterized by: In step 3), the discrete mathematical model of the extended state observer (502) is: α1, α2, α3, β1, β2, β3 and δ1 are adjustable parameters; z a1x (k+1), z a2x (k+1) and z a3x (k+1) are z a1x 、z a2x and the observed disturbance z a3x The value at time k+1; x a (k) is the actual displacement at time k, u ax (k) is the compensated control quantity u at time k ax ;f ax (k) is the predicted disturbance f output by the transfer learning module (504) at time k ax .

9. The method for constructing a high-speed electric spindle control system supported by a six-pole active magnetic bearing according to claim 1, characterized in that: In step 3), the control amount after compensation is u a0x is the feedback control quantity, 1 / d is the first compensation factor, and its value is [10, 200]; z a3x is the observed disturbance output by the extended state observer (502); ax To predict disturbances.

10. The method for constructing a high-speed electric spindle control system supported by a six-pole active magnetic bearing according to claim 1, characterized in that: In step 1), the three-degree-of-freedom composite controlled object is composed of the first Clark inverse transform, the first current tracking inverter, the first six-pole radial active magnetic bearing, the axial power amplifier, and the axial magnetic bearing connected in series in sequence; the two-degree-of-freedom composite controlled object is composed of the second Clark inverse transform, the second current tracking inverter, and the second six-pole radial active magnetic bearing connected in series in sequence.

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