Multi-degree-of-freedom forming robot motor cross coupling effect identification and compensation method

Abstract

The invention relates to a motor cross coupling effect identification and compensation method for a multi-degree-of-freedom forming robot. The method comprises the following steps: S1, establishing a kinematics model, a mechanical dynamics model, a permanent magnet synchronous motor dynamics model considering the cross coupling effect and an electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot; s2, establishing a motor cross coupling angle identification model of the multi-degree-of-freedom forming robot in combination with an electromechanical coupling dynamic model; and S3, combining the electromechanical coupling dynamics model and the motor cross coupling angle identification model to establish a multi-degree-of-freedom forming robot dynamics feedback control model, wherein the multi-degree-of-freedom forming robot dynamics feedback control model comprises coupling field orientation control, load feedback control and dynamics feedback control. High-precision and high-efficiency forming of the thin-wall high-rib component is achieved, and the forming precision can be guaranteed on the premise that the forming speed is increased.

Description

Technical Field

[0001] This invention relates to the field of forming equipment technology, and more specifically, to a method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot. Background Technology

[0002] Thin-walled, high-ribbed components are critical parts widely used in the aerospace field. To achieve high-precision forming, a multi-degree-of-freedom forming robot driven by a permanent magnet synchronous motor (PMSM) was developed. However, to obtain greater output power, the PMSM operates under brief overload conditions, causing the d-axis and q-axis magnetic fields of the PMSM to interact and alter the motor's dynamic model, a phenomenon known as the cross-coupling effect. This cross-coupling effect severely impacts the control accuracy of the multi-degree-of-freedom forming robot under traditional force-feedforward control methods, making it impossible to achieve high-precision forming of thin-walled, high-ribbed components using conventional methods. To achieve high-precision and high-efficiency forming of thin-walled, high-ribbed components, it is necessary to maintain forming accuracy while increasing forming speed. However, due to the large inertia of the multi-degree-of-freedom forming robot, each PMSM experiences a time-varying inertial force during high-speed forming, resulting in a significant decrease in the robot's control accuracy under traditional force-feedforward control, thus affecting the forming accuracy of thin-walled, high-ribbed components. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot, which can ensure forming accuracy while improving forming speed.

[0004] The technical solution adopted by this invention to solve its technical problem is: to construct a method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot, comprising the following steps:

[0005] S1. Establish the kinematic model, mechanical dynamics model, permanent magnet synchronous motor dynamics model and electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot considering the cross-coupling effect;

[0006] S2. Establish a cross-coupling angle identification model for motors of a multi-degree-of-freedom forming robot by combining the electromechanical coupling dynamics model;

[0007] S3. A dynamic feedback control model for a multi-degree-of-freedom forming robot is established by combining the electromechanical coupling dynamic model and the motor cross-coupling angle identification model, including coupled magnetic field orientation control, load feedback control and dynamic feedback control.

[0008] According to the above scheme, the multi-degree-of-freedom forming robot includes a machine tool, a six-degree-of-freedom parallel mechanism, a moving platform, an upper mold, and a lower mold. The parallel mechanism adopts six independent transmission chains arranged symmetrically. The drive unit of each transmission chain consists of a permanent magnet synchronous motor, a reducer, a ball screw, a drive slider, and a connecting rod connected in series. The connecting rod at the end of each branch is connected to the moving platform through a spherical hinge mechanism. The upper mold for forming is fixedly installed on the moving platform. During the processing, the blank to be formed is positioned on the surface of the lower mold. The six motors drive the movement of each branch through coordinated control, driving the upper mold to achieve a complex six-degree-of-freedom spatial motion trajectory, thereby progressively forming the metal sheet into a thin-walled part with a reinforcing rib structure.

[0009] According to the above scheme, in step S1, the method for establishing the kinematic model of the multi-degree-of-freedom forming robot includes:

[0010] A1 to A6 are the connection points between the moving platform and the connecting rod, B1 to B6 are the center points of the driving slider in the initial position, and C1 to C6 are the center points of the driving slider during equipment movement; A and B are the center points of the upper mold and the moving platform, and coordinate systems S are established at these two points respectively. A S B ;r A r B These are the radius of the moving platform and |B. i B|; and They are A i (i = 1…6) and B i The polar angle of (i = 1…6); the length of the connecting rod is l, and the distance the slider moves is h. i The distance from point A to point B is H;

[0011] A i and C i In coordinate system S A S B The coordinates are represented by equation (1):

[0012]

[0013] S A To S B The coordinate transformation matrix is ​​represented by equation (2):

[0014]

[0015] The geometric constraint relationship of the multi-degree-of-freedom forming robot is expressed by equation (3):

[0016] A i C i =A i A+AB+BC i(i=1…6) (3)

[0017] Based on equations (1) to (3), the kinematic equations of the multi-degree-of-freedom forming robot are established, and are expressed by equation (4):

[0018] |R(α,β,γ)a i +T(0,0,-H)-b i |=l (i=1…6) (4).

[0019] According to the above scheme, in step S1, the method for establishing the mechanical dynamics model of the multi-degree-of-freedom forming robot includes:

[0020] It is the driving force of the permanent magnet synchronous motor acting on the drive slider. It is the constraint force exerted by the machine tool on the drive slider. It is the constraint force exerted by the connecting rod on the driving slider. It is the constraint force F exerted by the connecting rod on the moving platform. W It is the constraint force acting on the envelope mold, m S g and m L g represents the gravity driving the slider and the connecting rod, respectively; m represents the gravity driving the slider and the connecting rod. P g is the weight of the moving platform and the upper mold;

[0021] The force balance equation for driving the slider is expressed by equation (5):

[0022]

[0023] in, It is the acceleration of the i-th slider;

[0024] The force and torque balance equations of the connecting rod are expressed by equation (6):

[0025]

[0026] in, It is the inertia matrix of the i-th link;

[0027] The force and torque balance equations for the moving platform and the upper mold are expressed by equation (7):

[0028]

[0029] Among them, I P It is the inertia matrix of the moving platform and the upper mold;

[0030] Multiply both sides of equation (5) We can obtain:

[0031]

[0032] Where, τ i (i = 1…6) is the driving force of the i-th driving slider;

[0033] Equation (6) is rewritten as:

[0034]

[0035] Multiplying both ends We can obtain:

[0036]

[0037] Combining equations (6), (8), and (10), we get:

[0038]

[0039] Combining equations (7) and (11), the driving force τ i (i=1…6) is expressed by equation (12):

[0040]

[0041] According to the above scheme, in step S1, the method for establishing the dynamic model of the permanent magnet synchronous motor considering the cross-coupling effect includes:

[0042] When considering the cross-coupling effect, the flux linkage equation of the permanent magnet synchronous motor is expressed by equation (13):

[0043]

[0044] Where, ψ d and ψ q These are the stator flux linkages along the dq axis and ψ. f It is a permanent magnet flux linkage, L d and L q These are the self-inductance of the dq axis and the i axis, respectively. d and i q These are the dq-axis stator currents, L dq and L qd These are the mutual inductances of the d and q axes, respectively.

[0045] Differentiating equation (13), we get:

[0046]

[0047] in,

[0048] The voltage equation for the permanent magnet synchronous motor is expressed by equation (15):

[0049]

[0050] Among them, u d and u q These are the dq-axis stator voltages, R s It is the stator resistance, ω e It is electric angular velocity;

[0051] The dq-axis inductance matrix in equation (15) satisfies the following conditions: (1) the diagonal elements of the inductance matrix are equal; (2) all elements of the inductance matrix are greater than 0; therefore, the dq-axis inductance matrix can be regarded as a positive semi-definite matrix; hence, there exists a cross-coupling angle θ. c The dq-axis inductance matrix can be converted to d... through coordinate transformation. n q n Axis-diagonal inductance matrix;

[0052] Using the coordinate transformation matrix, equation (15) can be transformed into:

[0053]

[0054] Among them, L dn_inc and L qn_inc d respectively n q n Shaft self-inductance increment, L dn and L qn d respectively n q n Shaft self-inductance, i dn and i qn d respectively n q n Shaft stator current, u dn and u qn d respectively n q n Shaft-stator voltage;

[0055] According to equation (16), the electromagnetic torque of the permanent magnet synchronous motor is expressed by equation (17):

[0056]

[0057] According to the above scheme, in step S1, the method for establishing the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot includes:

[0058] The voltage equations for the six permanent magnet synchronous motors considering the cross-coupling effect are expressed by equation (18):

[0059]

[0060] in, and These are the d values ​​of the i-th motor.n q n Shaft stator current, and These are the d values ​​of the i-th motor. n q n Shaft stator voltage, It is the stator resistance of the i-th motor. It is the mechanical angular velocity of the i-th motor. It is the permanent magnet flux linkage of the i-th motor. and These are the d values ​​of the i-th motor. n q n Shaft self-inductance increment, and These are the d values ​​of the i-th motor. n q n Shaft self-inductance, It is the cross-coupling angle of the i-th motor. It is the number of pole pairs of the i-th motor;

[0061] The mechanical equations of the six permanent magnet synchronous motors are expressed by equation (19):

[0062]

[0063] in, B = diag(B1…B6), It is the moment of inertia of the i-th motor. B is the electromagnetic torque of the i-th motor. i (i = 1…6) is the damping coefficient of the i-th motor. It is the load of the i-th motor;

[0064] The electromagnetic torque of the six motors considering the cross-coupling effect is expressed by equation (20):

[0065]

[0066] When using I dn When the =0 control strategy is applied, the electromagnetic torque of the six motors is represented by equation (21):

[0067]

[0068] Since the permanent magnet synchronous motor and the drive slider are connected by a reducer and a ball screw, we can conclude that:

[0069]

[0070] Where H = diag(h1…h6), τ = diag(τ1…τ6); It is the mechanical angle of the i-th motor, and N is the reduction ratio of the reducer and the ball screw;

[0071] Combining equations (17), (19), (20), and (22), the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot is represented by equation (23):

[0072]

[0073] According to the above scheme, the method for establishing the motor cross-coupling angle identification model of the multi-degree-of-freedom forming robot in step S2 includes:

[0074] To obtain the cross-coupling angle, a high-frequency voltage injection method was employed; a d-value was established. v q v The axis is the injection axis, which is related to d. n q n The included angle of the axes is θ n The speed difference is ω con =ω e -ω dv The high-frequency injection voltage is expressed by equation (24):

[0075]

[0076] Among them, U hf ω hf and These are high-frequency voltages u hf Amplitude, frequency, and phase;

[0077] By transforming the coordinates, equation (16) is transformed to d. v q v The axis is represented by equation (25):

[0078]

[0079] Among them, u dv u qv i dv and i qv They are d v q v Stator voltage and current of the shaft;

[0080] Combining equations (24) and (25), the high-frequency current response can be obtained, and expressed by equation (26):

[0081]

[0082] in, It is the phase of the response current;

[0083] According to (26), curve S1 can be established, which is represented by equation (27):

[0084]

[0085] Among them, I hf It is the amplitude of the response current;

[0086] Then, curve S2 is established, which is represented by equation (28):

[0087] S2=cos[2(ω e -ω dv )t] (28)

[0088] Cross-coupling angle θ c It can be obtained from S1 and S2.

[0089] According to the above scheme, in step S3, the coupled magnetic field orientation control method includes:

[0090] In the coupled magnetic field orientation control method, the Park transformation matrix is ​​represented by equation (29):

[0091]

[0092] in, It is the cross-coupling angle of the i-th motor;

[0093] The motor sector determination is achieved by equation (30):

[0094]

[0095] Among them Sec i It is the sector of the i-th motor;

[0096] The appropriate action time is calculated by formula (31):

[0097]

[0098] Among them, T s It is the carrier frequency, U dc It is the bus voltage. and These refer to the appropriate duration of action. According to the above scheme, in step S3, the load feedback control method includes:

[0099] In this control method, The motor load for the next control cycle can be obtained by measuring the torque sensor. Equation (32) represents:

[0100]

[0101] Among them, aP_nex ε P_nex ω P_nex , and They are a P ε P ω P , L i , and Predicted value for the next control cycle;

[0102] Compensation current It can be expressed by equation (33):

[0103]

[0104] According to the above scheme, the dynamic feedback control method in step S3 adopts a three-loop control. In the position loop, the dynamic feedback control method is based on the desired sliding position. Compared with the actual sliding position h i (i = 1…6), using a scaling parameter of Proportional controller for position error Adjustments are made; in the speed loop, based on the actual sliding speed. The proportional parameter is Integral parameters are Proportional-integral controller for speed error Adjustments are made; in the current loop, based on and The proportional parameter is Integral parameters are Proportional-integral controller for current error Adjustments were made;

[0105] Control Law T of a Multi-Degree-of-Freedom Forming Robot in Equation (34) represents:

[0106]

[0107] in,

[0108] The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot, as described in this invention, has the following beneficial effects:

[0109] 1. This invention elucidates the mechanism of the cross-coupling effect in permanent magnet synchronous motors and reveals the influence of this effect on motor control.

[0110] 2. This invention establishes a dynamic model of a permanent magnet synchronous motor that considers the cross-coupling effect, uses the cross-coupling angle to quantify the effect, and realizes online identification of the cross-coupling angle based on the high-frequency injection method.

[0111] 3. This invention proposes a coupled magnetic field orientation control method, which effectively solves the inductor matrix coupling problem caused by cross-coupling effect.

[0112] 4. This invention develops a dynamic feedback control method for multi-degree-of-freedom forming robots. This method significantly improves control performance under transient overload conditions. Attached Figure Description

[0113] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a schematic diagram of the configuration of a multi-degree-of-freedom forming robot; Figure 2 This is a simplified structural diagram of a multi-degree-of-freedom forming robot; Figure 3 This is a schematic diagram of the forces acting on a multi-degree-of-freedom forming robot; Figure 4 yes Axis diagram; Figure 5 This is a flowchart of the method for identifying the cross-coupling angle of a permanent magnet synchronous motor; Figure 6 This is a structural diagram of the dynamic feedback control method for multi-degree-of-freedom forming robots; Figure 7 This is a diagram of an experimental platform for a multi-degree-of-freedom forming robot control method; Figures 8(a) and 8(b) are schematic diagrams of the blank and the formed part; Figure 9 This is a force diagram of a multi-degree-of-freedom forming robot; Figures 10(a)-10(d) show the experimental results of cross-coupling angle identification for multi-degree-of-freedom forming robots; Figures 11(a)-11(c) are comparison diagrams of electromagnetic torque between the traditional control method and the proposed control method; Figures 12(a)-12(f) are comparison charts of the control performance of the traditional control method and the proposed control method. Detailed Implementation

[0126] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0127] like Figure 1-7 As shown, the method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to the present invention includes the following steps:

[0128] S1. Establish an electromechanical coupling dynamic model for a multi-degree-of-freedom forming robot.

[0129] 1. Structural Description of a Multi-Degree-of-Freedom Forming Robot

[0130] Figure 1 The multi-degree-of-freedom forming robot system on display mainly consists of the following components: a machine tool, a six-degree-of-freedom parallel mechanism, a moving platform, an upper mold, and a lower mold. The parallel mechanism employs six independent drive chains arranged symmetrically. The drive unit of each drive chain consists of a permanent magnet synchronous motor, a reducer, a ball screw, a drive slider, and connecting rods connected in series. The connecting rods at the ends of each chain are connected to the moving platform via a spherical hinge mechanism, and the upper mold for forming is fixedly mounted on the moving platform. During processing, the blank to be formed is positioned on the surface of the lower mold. The six motors drive the movement of each chain through coordinated control, causing the upper mold to achieve a complex six-degree-of-freedom spatial motion trajectory, thereby progressively forming the metal sheet into a thin-walled part with a reinforcing rib structure.

[0131] 2. Kinematic Model of Multi-DOF Forming Robot

[0132] Figure 2 A simplified structural diagram of a multi-degree-of-freedom forming robot is shown. A1–A6 are the connection points between the moving platform and the connecting rod, B1–B6 are the center points of the drive slider in the initial position, and C1–C6 are the center points of the drive slider during assembly movement. A and B are the center points of the upper mold and the moving platform, respectively, and coordinate systems S are established at these two points. A S B r A r B These are the radius of the moving platform and |B. i B|. and They are A i (i = 1…6) and B i The polar angles of (i = 1…6). The length of the connecting rod is l, and the distance the slider moves is h. i The distance from point A to point B is H.

[0133] A i and C i In coordinate system S A S BThe coordinates can be represented by equation (1):

[0134]

[0135] S A To S B The coordinate transformation matrix can be represented by equation (2):

[0136]

[0137] The geometric constraint relationship of a multi-degree-of-freedom forming robot can be expressed by equation (3):

[0138] A i C i =A i A+AB+BC i (i=1…6) (3)

[0139] Based on equations (1) to (3), the kinematic equations of the multi-degree-of-freedom forming robot can be established, and expressed by equation (4):

[0140] |R(α,β,γ)a i +T(0,0,-H)-b i |=l(i=1…6) (4)

[0141] 3. Mechanical Dynamics Model of a Multi-Degree-of-Freedom Forming Robot

[0142] Figure 3 A simplified force diagram of a multi-degree-of-freedom forming robot is shown. It is the driving force of the permanent magnet synchronous motor acting on the drive slider. It is the constraint force exerted by the machine tool on the drive slider. It is the constraint force exerted by the connecting rod on the driving slider. It is the constraint force F exerted by the connecting rod on the moving platform. W It is the constraint force acting on the envelope mold, m S g and m L g represents the gravity driving the slider and the connecting rod, respectively; m represents the gravity driving the slider and the connecting rod. P g is the weight of the moving platform and the upper mold.

[0143] The force balance equation for driving the slider can be expressed by equation (5):

[0144]

[0145] in, It is the acceleration of the i-th slider.

[0146] The force and torque balance equations of the connecting rod can be expressed by equation (6):

[0147]

[0148] in, It is the inertia matrix of the i-th link.

[0149] The force and torque balance equations for the moving platform and the upper mold can be expressed by equation (7):

[0150]

[0151] Among them, I P It is the inertia matrix of the moving platform and the upper mold.

[0152] Multiply both sides of equation (5) We can obtain:

[0153]

[0154] Where, τ i (i = 1…6) is the driving force of the i-th driving slider.

[0155] Equation (6) can be rewritten as:

[0156]

[0157] Multiplying both ends We can obtain:

[0158]

[0159] Combining equations (6), (8), and (10), we obtain:

[0160]

[0161] Combining equations (7) and (11), the driving force τ i (i=1…6) can be expressed by equation (12):

[0162]

[0163] 4. Dynamic model of permanent magnet synchronous motor considering cross-coupling effect

[0164] When considering the cross-coupling effect, the flux linkage equation of the permanent magnet synchronous motor can be expressed by equation (13):

[0165]

[0166] Where, ψ d and ψ q These are the stator flux linkages along the dq axis and ψ. f It is a permanent magnet flux linkage, L d and L q These are the self-inductance of the dq axis and the i axis, respectively.d and i q These are the dq-axis stator currents, L dq and L qd These are the mutual inductances along the d and q axes, respectively.

[0167] Differentiating equation (13), we get:

[0168]

[0169] in,

[0170] The voltage equation of a permanent magnet synchronous motor can be expressed by equation (15):

[0171]

[0172] Among them, u d and u q These are the dq-axis stator voltages, R s It is the stator resistance, ω e It is electric angular velocity.

[0173] The dq-axis inductance matrix in equation (15) satisfies the following conditions: (1) the diagonal elements of the inductance matrix are equal; (2) all elements of the inductance matrix are greater than 0. Therefore, the dq-axis inductance matrix can be considered as a positive semi-definite matrix. Hence, there exists a cross-coupling angle θ. c The dq-axis inductance matrix can be converted to d... through coordinate transformation. n q n Axial diagonal inductance matrix.

[0174] Using the coordinate transformation matrix, equation (15) can be transformed into:

[0175]

[0176] Among them, L dn_inc and L qn_inc d respectively n q n Shaft self-inductance increment, L dn and L qn d respectively n q n Shaft self-inductance, i dn and i qn d respectively n q n Shaft stator current, u dn and u qn d respectively n q n Shaft stator voltage.

[0177] According to equation (16), the electromagnetic torque of the permanent magnet synchronous motor can be expressed by equation (17):

[0178]

[0179] 5. Electromechanical Coupling Dynamics Model of a Multi-Degree-of-Freedom Forming Robot

[0180] According to equation (16), the voltage equations for the six permanent magnet synchronous motors considering the cross-coupling effect can be expressed by equation (18):

[0181]

[0182] in, and These are the d values ​​of the i-th motor. n q n Shaft stator current, and These are the d values ​​of the i-th motor. n q n Shaft stator voltage, It is the stator resistance of the i-th motor. It is the mechanical angular velocity of the i-th motor. It is the permanent magnet flux linkage of the i-th motor. and These are the d values ​​of the i-th motor. n q n Shaft self-inductance increment, and These are the d values ​​of the i-th motor. n q n Shaft self-inductance, It is the cross-coupling angle of the i-th motor. It is the number of pole pairs of the i-th motor.

[0183] The mechanical equations of the six permanent magnet synchronous motors can be expressed by equation (19):

[0184]

[0185] in, B = diag(B1…B6), It is the moment of inertia of the i-th motor. B is the electromagnetic torque of the i-th motor. i (i = 1…6) is the damping coefficient of the i-th motor. It is the load of the i-th motor.

[0186] The electromagnetic torque of the six motors considering the cross-coupling effect can be expressed by equation (20):

[0187]

[0188] When using I dn When the =0 control strategy is applied, the electromagnetic torque of the six motors can be expressed by equation (21):

[0189]

[0190] Since the permanent magnet synchronous motor and the drive slider are connected by a reducer and a ball screw, we can conclude that:

[0191]

[0192] Where H = diag(h1…h6), τ = diag(τ1…τ6). It is the mechanical angle of the i-th motor, and N is the reduction ratio of the reducer and the ball screw.

[0193] Combining equations (17), (19), (20), and (22), the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot can be represented by equation (23):

[0194]

[0195] S2 establishes a model for identifying the cross-coupling angle of motors in a multi-degree-of-freedom forming robot.

[0196] To obtain the cross-coupling angle, a high-frequency voltage injection method was employed. A d-axis was established. v q v The axis is the injection axis, which is related to d. n q n The included angle of the axes is θ n The speed difference is ω con =ω e -ω dv ,like Figure 4 As shown. The high-frequency injection voltage can be expressed by equation (24):

[0197]

[0198] Among them, U hf ω hf and These are high-frequency voltages u hf The amplitude, frequency, and phase.

[0199] By transforming the coordinates, equation (16) is transformed to d. v q v The axis can be represented by equation (25):

[0200]

[0201] Among them, u dv u qv i dv and i qv They are d v q v Stator voltage and current of the shaft.

[0202] Combining equations (24) and (25), the high-frequency current response can be obtained, and can be expressed by equation (26):

[0203]

[0204] in, It is the phase of the response current.

[0205] Based on (26), curve S1 can be established, which can be represented by equation (27):

[0206]

[0207] Among them, I hf It is the amplitude of the response current.

[0208] Then, curve S2 is established, which can be represented by equation (28):

[0209] S2=cos[2(ω e -ω dv )t] (28)

[0210] Cross-coupling angle θ c It can be obtained from S1 and S2.

[0211] S3 establishes a dynamic feedback control model for a multi-degree-of-freedom forming robot.

[0212] 1. Coupled Magnetic Field Orientation Control Method

[0213] In the coupled magnetic field orientation control method, the Park transformation matrix can be represented by equation (29):

[0214]

[0215] in, It is the cross-coupling angle of the i-th motor.

[0216] Motor sector determination can be achieved using equation (30):

[0217]

[0218] Among them Sec i It is the sector of the i-th motor.

[0219] The appropriate action time can be calculated using equation (31):

[0220]

[0221] Among them, T s It is the carrier frequency, U dc It is the bus voltage. and These refer to the appropriate application time.

[0222] 2. Load feedback control method

[0223] In this control method, The forming force F can be measured by a torque sensor and calculated according to equation (12). w Since the electrical time constant is much smaller than the mechanical time constant, it can be assumed that the forming force remains unchanged in adjacent control cycles. According to equations (12) and (22), the motor load for the next control cycle can be obtained. Equation (32) represents:

[0224]

[0225] Among them, a P_nex ε P_nex ω P_nex , and They are a P ε P ω P , L i , and Predicted value for the next control cycle.

[0226] According to equation (21), the compensation current It can be expressed by equation (33):

[0227]

[0228] 3. Dynamic feedback control method

[0229] This control method employs a three-loop control mechanism, such as... Figure 6 As shown. In the position loop, according to the desired sliding position. Compared with the actual sliding position h i (i = 1…6), using a scaling parameter of Proportional controller for position error Adjustments are made. In the speed loop, based on the actual sliding speed... The proportional parameter is Integral parameters are Proportional-integral controller for speed error Adjustments are made. In the current loop, based on... and The proportional parameter is Integral parameters are Proportional-integral controller for current error Adjustments were made.

[0230] In summary, the control law T of a multi-degree-of-freedom forming robot in It can be expressed by equation (34):

[0231]

[0232] in,

[0233] According to the method provided by this invention, the structural parameters of the multi-degree-of-freedom forming robot in Table 1, and the desired trajectory of the upper mold in Table 2, the solutions to the kinematics and electromechanical coupling dynamics models of the multi-degree-of-freedom forming robot can be obtained. According to the method provided by this invention, the motor parameters of the permanent magnet synchronous motor in Table 3, and the identification method parameters in Table 4, a method for identifying the motor cross-coupling angle of the multi-degree-of-freedom forming robot can be implemented. Based on the implementation of the above methods, according to the method provided by this invention and the control method parameters in Table 5, a dynamic feedback control method can be implemented. Figure 7 The experimental platform shown was used for comparative experiments. During the experiments, the processed blanks and formed parts are shown in Figures 8(a) and 8(b), and the forces acting on the multi-degree-of-freedom forming robot are as follows. Figure 9 As shown.

[0234] For parameter identification methods Figures 10(a)-10(d) The experimental results of online cross-coupling angle identification under different forming loads are presented. It can be seen that the cross-coupling angle identification results are 0.8°, 4.6°, and 9.7° under forming loads of 1500kN, 4000kN, and 8000kN, respectively. As the load torque of the permanent magnet synchronous motor increases, the cross-coupling effect becomes more significant; therefore, the cross-coupling angle increases with the increase of the forming load.

[0235] Figures 11(a)-11(c)The electromagnetic torque characteristics of a permanent magnet synchronous motor (PMSM) under forming loads of 1500 kN, 4000 kN, and 8000 kN using different control methods are demonstrated. Experimental results show that when using the conventional control method, the maximum local fluctuation amplitude under the three loads is approximately 20 N·m, 80 N·m, and 200 N·m, respectively; while when using the control method proposed in this invention, the corresponding amplitudes are only 7 N·m, 20 N·m, and 35 N·m. The cross-coupling effect leads to uneven electromagnetic torque, therefore the torque fluctuation amplitude of the conventional control method increases significantly with increasing forming load. The control method proposed in this invention, due to the integration of an online cross-coupling angle identification subsystem for the PMSM, ultimately yields a smoother electromagnetic torque curve.

[0236] Figures 12(a)-12(f) illustrate the variance reduction effect of the driven slider motion error under different forming loads when using the conventional control method and the method proposed in this invention. It can be seen that the advantages of the proposed method become increasingly significant as the forming load increases. This is because the cross-coupling effect becomes more pronounced when the forming load increases, and the cross-coupling angle also increases accordingly. Experimental data show that under low load conditions, the variance of the driven slider motion error is reduced by approximately 150% compared to the conventional control method; under medium load conditions, the variance reduction reaches 300%; and under high load conditions, the variance reduction effect is even more significant, reaching 800%.

[0237] Table 1 Structural parameters of the multi-degree-of-freedom forming robot

[0238]

[0239] Table 2 shows the desired mold pose.

[0240] symbol numerical values unit α 1.5·cos(2πwt) deg β 1.5·sin(2πwt) deg γ 0 deg

[0241] Table 3. Motor parameters of permanent magnet synchronous motor

[0242] symbol <![CDATA[R s ]]> <![CDATA[L d ]]> <![CDATA[L q ]]> <![CDATA[ψ mg ]]> <![CDATA[J m ]]> B <![CDATA[P n ]]> numerical values 16.8 1.29 3.12 0.572 0.064 0.002 4 unit mΩ mH mH Wb <![CDATA[kg·m 2 ]]>

[0243] Table 4 Cross-coupling angle identification parameters

[0244]

[0245] Table 5 Dynamic Feedback Control Parameters

[0246]

[0247] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot, characterized in that, Includes the following steps: S1. Establish the kinematic model, mechanical dynamics model, permanent magnet synchronous motor dynamics model and electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot considering the cross-coupling effect; S2. Establish a cross-coupling angle identification model for motors of a multi-degree-of-freedom forming robot by combining the electromechanical coupling dynamics model; S3. A dynamic feedback control model for a multi-degree-of-freedom forming robot is established by combining the electromechanical coupling dynamic model and the motor cross-coupling angle identification model, including coupled magnetic field orientation control, load feedback control and dynamic feedback control.

2. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 1, characterized in that, The multi-degree-of-freedom forming robot includes a machine tool, a six-degree-of-freedom parallel mechanism, a moving platform, an upper mold, and a lower mold. The parallel mechanism adopts six independent transmission chains arranged symmetrically. The drive unit of each transmission chain consists of a permanent magnet synchronous motor, a reducer, a ball screw, a drive slider, and a connecting rod connected in series. The connecting rod at the end of each branch is connected to the moving platform through a spherical hinge mechanism. The upper mold for forming is fixedly installed on the moving platform. During the processing, the blank to be formed is positioned on the surface of the lower mold. The six motors drive the movement of each branch through coordinated control, driving the upper mold to achieve a complex six-degree-of-freedom spatial motion trajectory, thereby progressively forming the metal sheet into a thin-walled part with a reinforcing rib structure.

3. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 2, characterized in that, In step S1, the method for establishing the kinematic model of the multi-degree-of-freedom forming robot includes: A1 to A6 are the connection points between the moving platform and the connecting rod, B1 to B6 are the center points of the driving slider in the initial position, and C1 to C6 are the center points of the driving slider during equipment movement; A and B are the center points of the upper mold and the moving platform, and coordinate systems S are established at these two points respectively. A S B ;r A r B These are the radius of the moving platform and |B. i B|; and They are A i (i = 1…6) and B i The polar angle of (i = 1…6); the length of the connecting rod is l, and the distance the slider moves is h. i The distance from point A to point B is H; A i and C i In coordinate system S A S B The coordinates are represented by equation (1): S A To S B The coordinate transformation matrix is ​​represented by equation (2): The geometric constraint relationship of the multi-degree-of-freedom forming robot is expressed by equation (3): A i C i =A i A+AB+BC i (i=1…6) (3) Based on equations (1) to (3), the kinematic equations of the multi-degree-of-freedom forming robot are established, and are expressed by equation (4): |R(α,β,γ)a i +T(0,0,-H)-b i |=l(i=1…6) (4).

4. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 3, characterized in that, In step S1, the method for establishing the mechanical dynamics model of the multi-degree-of-freedom forming robot includes: It is the driving force of the permanent magnet synchronous motor acting on the drive slider. It is the constraint force exerted by the machine tool on the drive slider. It is the constraint force exerted by the connecting rod on the driving slider. It is the constraint force F exerted by the connecting rod on the moving platform. W It is the constraint force acting on the envelope mold, m S g and m L g represents the gravity driving the slider and the connecting rod, respectively; m represents the gravity driving the slider and the connecting rod. P g is the weight of the moving platform and the upper mold; The force balance equation for driving the slider is expressed by equation (5): in, It is the acceleration of the i-th slider; The force and torque balance equations of the connecting rod are expressed by equation (6): in, It is the inertia matrix of the i-th link; The force and torque balance equations for the moving platform and the upper mold are expressed by equation (7): Among them, I P It is the inertia matrix of the moving platform and the upper mold; Multiply both sides of equation (5) We can obtain: Where, τ i (i = 1…6) is the driving force of the i-th driving slider; Equation (6) is rewritten as: Multiplying both ends We can obtain: Combining equations (6), (8), and (10), we get: Combining equations (7) and (11), the driving force τ i (i=1…6) is expressed by equation (12):

5. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 4, characterized in that, In step S1, the method for establishing the dynamic model of the permanent magnet synchronous motor considering the cross-coupling effect includes: When considering the cross-coupling effect, the flux linkage equation of the permanent magnet synchronous motor is expressed by equation (13): Where, ψ d and ψ q These are the stator flux linkages along the dq axis and ψ. f It is a permanent magnet flux linkage, L d and L q These are the self-inductance of the dq axis and the i axis, respectively. d and i q These are the dq-axis stator currents, L dq and L qd These are the mutual inductances of the d and q axes, respectively. Differentiating equation (13), we get: in, The voltage equation for the permanent magnet synchronous motor is expressed by equation (15): Among them, u d and u q These are the dq-axis stator voltages, R s It is the stator resistance, ω e It is electric angular velocity; The dq-axis inductance matrix in equation (15) satisfies the following conditions: (1) the diagonal elements of the inductance matrix are equal; (2) all elements of the inductance matrix are greater than 0; therefore, the dq-axis inductance matrix can be regarded as a positive semi-definite matrix; hence, there exists a cross-coupling angle θ. c The dq-axis inductance matrix can be converted to d... through coordinate transformation. n q n Axis-diagonal inductance matrix; Using the coordinate transformation matrix, equation (15) can be transformed into: Among them, L dn_inc and L qn_inc d respectively n q n Shaft self-inductance increment, L dn and L qn d respectively n q n Shaft self-inductance, i dn and i qn d respectively n q n Shaft stator current, u dn and u qn d respectively n q n Shaft-stator voltage; According to equation (16), the electromagnetic torque of the permanent magnet synchronous motor is expressed by equation (17):

6. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 5, characterized in that, In step S1, the method for establishing the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot includes: The voltage equations for the six permanent magnet synchronous motors considering the cross-coupling effect are expressed by equation (18): in, and These are the d values ​​of the i-th motor. n q n Shaft stator current, and These are the d values ​​of the i-th motor. n q n Shaft stator voltage, It is the stator resistance of the i-th motor. It is the mechanical angular velocity of the i-th motor. It is the permanent magnet flux linkage of the i-th motor. and These are the d values ​​of the i-th motor. n q n Shaft self-inductance increment, and These are the d values ​​of the i-th motor. n q n Shaft self-inductance, It is the cross-coupling angle of the i-th motor. It is the number of pole pairs of the i-th motor; The mechanical equations of the six permanent magnet synchronous motors are expressed by equation (19): in, B = diag(B1…B6), It is the moment of inertia of the i-th motor. B is the electromagnetic torque of the i-th motor. i (i = 1…6) is the damping coefficient of the i-th motor. It is the load of the i-th motor; The electromagnetic torque of the six motors considering the cross-coupling effect is expressed by equation (20): When using I dn When the =0 control strategy is applied, the electromagnetic torque of the six motors is represented by equation (21): Since the permanent magnet synchronous motor and the drive slider are connected by a reducer and a ball screw, we can conclude that: Where H = diag(h1…h6), τ = diag(τ1…τ6); It is the mechanical angle of the i-th motor, and N is the reduction ratio of the reducer and the ball screw; Combining equations (17), (19), (20), and (22), the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot is represented by equation (23):

7. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 1, characterized in that, In step S2, the method for establishing the motor cross-coupling angle identification model of the multi-degree-of-freedom forming robot includes: To obtain the cross-coupling angle, a high-frequency voltage injection method was employed; a d-value was established. v q v The axis is the injection axis, which is related to d. n q n The included angle of the axes is θ n The speed difference is ω con =ω e -ω dv The high-frequency injection voltage is expressed by equation (24): Among them, U hf ω hf and These are high-frequency voltages u hf Amplitude, frequency, and phase; By transforming the coordinates, equation (16) is transformed to d. v q v The axis is represented by equation (25): Among them, u dv u qv i dv and i qv They are d v q v Stator voltage and current of the shaft; Combining equations (24) and (25), the high-frequency current response can be obtained, and expressed by equation (26): in, It is the phase of the response current; According to (26), curve S1 can be established, which is represented by equation (27): Among them, I hf It is the amplitude of the response current; Then, curve S2 is established, which is represented by equation (28): S2=cos[2(ω e -oh dv )t] (28) Cross-coupling angle θ c It can be obtained from S1 and S2.

8. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 1, characterized in that, In step S3, the coupled magnetic field orientation control method includes: In the coupled magnetic field orientation control method, the Park transformation matrix is ​​represented by equation (29): in, It is the cross-coupling angle of the i-th motor; The motor sector determination is achieved by equation (30): Among them Sec i It is the sector of the i-th motor; The appropriate action time is calculated by formula (31): Among them, T s It is the carrier frequency, U dc It is the bus voltage. and These refer to the appropriate application time.

9. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot according to claim 1, characterized in that, In step S3, the load feedback control method includes: In this control method, The motor load for the next control cycle can be obtained by measuring the torque sensor. Equation (32) represents: Among them, a P_nex ε P_nex ω P_nex , and They are a P ε P ω P , L i , and Predicted value for the next control cycle; Compensation current It can be expressed by equation (33):

10. The method for identifying and compensating for the cross-coupling effect of motors in a multi-degree-of-freedom forming robot as described in claim 1, characterized in that, The dynamic feedback control method in step S3 employs a three-loop control. In the position loop, the control is based on the desired sliding position. Compared with the actual sliding position h i (i = 1…6), using a scaling parameter of Proportional controller for position error Adjustments are made; in the speed loop, based on the actual sliding speed. The proportional parameter is Integral parameters are Proportional-integral controller for speed error Adjustments are made; in the current loop, based on and The proportional parameter is Integral parameters are Proportional-integral controller for current error Adjustments were made; Control Law T of a Multi-Degree-of-Freedom Forming Robot in Equation (34) represents: in,

Images