Inertia identification compensation method and system for multi-degree-of-freedom forming robot

Abstract

The invention relates to a multi-degree-of-freedom forming robot inertia identification compensation method and system, and the method comprises the following steps: S1, building a multi-degree-of-freedom forming robot electromechanical coupling dynamic model, and representing the inertia force and Coriolis force in the electromechanical coupling dynamic model through equivalent mass and equivalent damping, the electromechanical coupling dynamic model determines the influence of inertia force and Coriolis force on the control precision; s2, a multi-degree-of-freedom forming robot inertia identification model is established, and the inertia identification model carries out real-time self-adaptive adjustment on adjustment parameters by using the change rate of an identification result; and S3, a self-adaptive PI control model of the multi-degree-of-freedom forming robot is established, and the self-adaptive PI control model determines the mapping relation between PI parameters and equivalent mass and equivalent damping. According to the method, the change rate of the identification result is used for carrying out real-time self-adaptive adjustment on the adjusting parameters, so that real-time accurate identification of the equivalent mass and the equivalent damping is realized, and the control precision of the multi-degree-of-freedom forming robot at a high speed can be remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of forming equipment technology, and more specifically, to a method and system for inertia identification and compensation of a multi-degree-of-freedom forming robot. Background Technology

[0002] Thin-walled, high-ribbed components are widely used in the aerospace field. To achieve high-precision and high-efficiency forming of these components, a multi-degree-of-freedom forming robot driven by a permanent magnet synchronous motor was developed. However, due to the robot's parallel mechanism and large inertia, the permanent magnet synchronous motor experiences time-varying inertial forces at high forming speeds. This significantly reduces the control accuracy of the multi-degree-of-freedom forming robot under traditional PI control methods, making it impossible to achieve high-precision and high-efficiency forming of thin-walled, high-ribbed components using conventional methods. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method and system for inertia identification and compensation of multi-degree-of-freedom forming robots, which can realize high-precision and high-efficiency forming of thin-walled, high-rib components.

[0004] The technical solution adopted by this invention to solve its technical problem is: to construct a method for inertia identification and compensation of a multi-degree-of-freedom forming robot, comprising the following steps: S1. Establish an electromechanical coupling dynamic model for a multi-degree-of-freedom forming robot. The inertial force and Coriolis force in the electromechanical coupling dynamic model are represented by equivalent mass and equivalent damping. The electromechanical coupling dynamic model determines the influence of inertial force and Coriolis force on control accuracy. S2. Establish an inertia identification model for a multi-degree-of-freedom forming robot. The inertia identification model uses the rate of change of the identification results to adaptively adjust the adjustment parameters in real time. S3. Establish an adaptive PI control model for a multi-degree-of-freedom forming robot. The adaptive PI control model determines the mapping relationship between PI parameters and equivalent mass and equivalent damping.

[0005] According to the above scheme, the multi-degree-of-freedom forming robot includes a machine tool, a parallel structure, a moving platform, an envelope mold, and a lower mold. The parallel structure includes six branches, each of which is composed of a permanent magnet synchronous motor, a reducer, a ball screw, a drive slider, and a connecting rod in sequence. The ends of the six connecting rods are connected to the moving platform through ball joints. The envelope mold is installed on the moving platform. During forming, the blank is placed on the lower mold. Driven by the six permanent magnet synchronous motors, the envelope mold can achieve multi-degree-of-freedom movement, thereby processing the blank into a thin-walled, high-rib component.

[0006] According to the above scheme, the method for establishing the kinematic equations of the multi-degree-of-freedom forming robot in step S1 includes the following steps: At the center of the driving slider plane Establish a coordinate system At the center of the envelope mold base surface Establish a coordinate system ; ~ These are the center points of the connections between the six links and the moving platform. ~ These are the center points of the connections between the six links and the drive slider; ~ They are ~ The initial position, It is the radius of the moving platform. yes arrive Distance between points; and They are ~ and ~ exist and The angle of the coordinate system; the length of the connecting rod is ,Right now ; Click The distance between the points is ,Right now The distance the drive slider moves is ,Right now ; and The coordinates of a point in its respective coordinate system are expressed by equation (1): (1) arrive The coordinate transformation matrix of the coordinate system is represented by equation (2): (2) The geometric constraint relationship of the multi-degree-of-freedom forming robot is expressed by equation (3): (3) 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): (4)

[0007] According to the above scheme, the method for establishing the mechanical dynamics model of the multi-degree-of-freedom forming robot in step S1 includes the following steps: 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 exerted by the connecting rod on the moving platform. It is the constraint force exerted by the moving platform on the envelope mold. It is the constraint force acting on the envelope mold. , and These are the forces driving the slider, the moving platform, and the enveloping mold, respectively. Decoupling is the driving force used to overcome gravity, forming force, Coriolis force, and inertial force, respectively expressed as: , , and Furthermore, the relationship between the above forces is expressed by equation (5): (5) In order to obtain The force balance equation and the moment balance equation are expressed by equation (6): (6) According to the above formula, in order to overcome the driving force of gravity... From equation (7), we obtain: (7) In order to obtain The force balance equation and the moment balance equation are expressed by equation (8): (8) According to the above formula, in order to overcome the driving force of the forming force We obtain the result from equation (9): (9) In order to obtain The force balance equation and the moment balance equation are expressed by equation (10): (10) in yes Point of action to point position vector, It is the angular velocity of the enveloping mold. Since the enveloping mold and the moving platform are connected together, the angular velocity of the moving platform is... ; According to the above formula, in order to overcome the driving force of the Coriolis force We obtain the following from equation (11): (11) In order to obtain The force balance equation and the moment balance equation are expressed by equation (12): (12) in and These are the linear acceleration and angular acceleration of the enveloping mold, respectively; since the enveloping mold and the moving platform are connected together, the linear acceleration and angular acceleration of the moving platform are also... , ; According to the above formula, in order to overcome the driving force of inertia... We obtain the following from equation (13): (13) According to equation (5), the overall driving force is represented by equation (14): (14) Combining equations (7), (9), (11), (13), and (14), we obtain the mechanical dynamics model of the multi-degree-of-freedom forming robot, which is represented by equation (15): (15) in, and These are the mass matrix and the Coriolis force matrix, respectively. , , .

[0008] According to the above scheme, the method for establishing the electrodynamic model of the multi-degree-of-freedom forming robot in step S1 includes the following steps: The voltage equation of the permanent magnet synchronous motor is expressed by equation (16): (16) in, It is Hadamaji. , , , , , , , , ; , , , and These are the d-axis current, q-axis current, d-axis voltage, q-axis voltage, and motor speed of the permanent magnet synchronous motor. and These are the motor resistance and the magnetic flux; and These are the inductances of the d and q axes, respectively; The equation of motion for the permanent magnet synchronous motor is expressed by equation (17): (17) in , , ; It is the moment of inertia of the motor. , and These are the motor's damping coefficient, electromagnetic torque, and load torque, respectively. Electromagnetic torque is expressed by equation (18): (18) in, .

[0009] According to the above scheme, the method for establishing the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot in step S1 includes the following steps: Since the permanent magnet synchronous motor and the drive slider are connected through a reducer and a ball screw, we get equation (19): (19) in, It is the rotation angle of the motor. It is the reduction ratio of the reducer and the ball screw; Combining equations (14), (18), and (19), we obtain the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot, which is represented by equation (20): (20) in, and These are the acceleration Jacobian matrix and the velocity Jacobian matrix, respectively. and These are equivalent mass and equivalent damping, respectively. , .

[0010] According to the above scheme, the method for establishing the inertia identification model of the multi-degree-of-freedom forming robot in step S2 includes: Based on equations (18) and (20), we obtain equation (21): (twenty one) in, It is the sampling time; It remains unchanged between two adjacent sampling periods, that is: (twenty two) Combining equations (21) and (22), we obtain equation (23): (twenty three) in, , , , ; Taking equation (23) as the reference model, the adjustable model is represented by equation (24): (twenty four) in, and They are and The estimated value; The output errors of the reference model and the adjustable model are represented by equation (25): (25) The objective function is expressed by equation (26): (26) Based on equations (23), (24), (25) and (26), equation (27) can be obtained using the gradient descent algorithm: (27) in, , and It involves adjusting parameters; According to equations (23), (24), (25), (26) and (27), the identification rates of equivalent mass and equivalent damping can be expressed by equation (28): (28) To achieve higher recognition accuracy, the parameters will be adjusted. Designed with adaptive parameters to adjust the dynamic response of the identification system in real time; when the system is in steady state... Increase the size to improve system response speed; when the system is in a transient state. Reduce to decrease system overshoot; When the system is in a transient state, the identification results can change rapidly, therefore... To characterize the system state and adjust it in real time The adaptive adjustment rate is expressed by equation (29): (29) in, .

[0011] According to the above scheme, the method for establishing the current loop PI control model in step S3 includes: With the feedforward decoupling method adopted in the current loop, the simplified voltage equation of the permanent magnet synchronous motor is expressed by equation (30): (30) The closed-loop transfer function of the current loop is expressed by equation (31): (31) in, and These are the current loop PI parameters; The current loop PI parameter setpoint is expressed by equation (32): (32) in, It is the current loop bandwidth; Combining equations (31) and (32), we can obtain the closed-loop transfer function of the current loop, expressed as follows: (33) By configuring an appropriate bandwidth, the current loop poles can be made negative, thus proving stability.

[0012] According to the above scheme, the method for establishing the speed loop PI control model in step S3 includes: Based on adaptive damping to tune the speed loop PI parameters, assuming the permanent magnet synchronous motor starts under no-load conditions, its motion equation is expressed by equation (34): (34) Adaptive damping is expressed by the following formula: (35) in, It is the adaptive damping coefficient; Combining equations (34) and (35), we obtain the following equation: (36) Based on equation (36), we obtain the following equation: (37) The design rate is expressed by equation (38): (38) Combining equations (37) and (38), we obtain the following equation: (39) in, It is the speed loop bandwidth; The closed-loop transfer function of the velocity loop can be expressed by the following equation: (40) in, and These are the speed loop PI parameters; The design rate of the speed loop PI parameter can be expressed by equation (41): (41) Combining equations (40) and (41), we obtain the closed-loop transfer function of the velocity loop, which can be expressed by equation (42): (42)

[0013] The present invention also provides a system for inertia identification and compensation of a multi-degree-of-freedom forming robot, comprising: The electromechanical coupling dynamics model construction module is used to establish an electromechanical coupling dynamics model of a multi-degree-of-freedom forming robot. The inertial force and Coriolis force in the electromechanical coupling dynamics model are represented by equivalent mass and equivalent damping. The electromechanical coupling dynamics model determines the influence of inertial force and Coriolis force on control accuracy. The inertia identification model building module is used to build an inertia identification model for a multi-degree-of-freedom forming robot. The inertia identification model uses the rate of change of the identification results to adaptively adjust the adjustment parameters in real time. The adaptive PI control model building module is used to build an adaptive PI control model for a multi-degree-of-freedom forming robot. The adaptive PI control model determines the mapping relationship between PI parameters and equivalent mass and equivalent damping.

[0014] The multi-degree-of-freedom forming robot inertia identification and compensation method and system of the present invention have the following beneficial effects: 1. This invention establishes an electromechanical coupling dynamic model for a multi-degree-of-freedom forming robot, in which inertial force and Coriolis force are represented by equivalent mass and equivalent damping, and reveals the influence of inertial force and Coriolis force on control accuracy.

[0015] 2. This invention proposes an equivalent mass and equivalent damping identification method. This method uses the rate of change of the identification results to adaptively adjust the adjustment parameters in real time, thereby achieving real-time and accurate identification of equivalent mass and equivalent damping.

[0016] 3. Based on stability conditions, this invention reveals the mapping relationship between PI parameters and equivalent mass and equivalent damping. Then, it proposes an adaptive PI control method considering the large inertia of a multi-degree-of-freedom forming robot, which can significantly improve the control accuracy of multi-degree-of-freedom forming robots at high speeds. Attached Figure Description

[0017] 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 3This is a schematic diagram of the forces acting on a multi-degree-of-freedom forming robot; Figure 4 This is a diagram analyzing the driving forces of a multi-degree-of-freedom forming robot. Figure 5 This is an analysis chart of the identification results from the traditional parameter identification method; Figure 6 This is an analysis diagram of the identification results of the adaptive parameter identification method; Figure 7 This is a structural diagram of the current loop PI control method for a multi-degree-of-freedom forming robot; Figure 8 This is a structural diagram of the speed loop PI control method for a multi-degree-of-freedom forming robot; Figure 9 This is a structural diagram of the adaptive PI control method for multi-degree-of-freedom forming robots; Figure 10 This is a diagram of an experimental platform for an adaptive PI control method for a multi-degree-of-freedom forming robot. Figure 11 This is a performance analysis diagram of the adaptive PI control method for multi-degree-of-freedom forming robots; Figure 12 This is a performance comparison chart between adaptive PI control method and traditional PI control method; Figure 13 This is an analysis diagram of the identification results of the adaptive parameter identification method. Detailed Implementation

[0018] 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.

[0019] Example 1 The inertia identification and compensation method for a multi-degree-of-freedom forming robot of the present invention includes the following steps: S1. Establish an electromechanical coupling dynamic model for a multi-degree-of-freedom forming robot.

[0020] 1. Kinematic Model Multi-degree-of-freedom forming robots, such as Figure 1 As shown, the robot includes a machine tool, a parallel structure, a moving platform, an envelope mold, and a lower mold. The parallel structure comprises six branches, each consisting of a permanent magnet synchronous motor, a reducer, a ball screw, a drive slider, and a connecting rod, respectively. The ends of the six connecting rods are connected to the moving platform via ball joints. The envelope mold is mounted on the moving platform. During forming, the blank is placed on the lower mold, and driven by the six permanent magnet synchronous motors, the envelope mold achieves multi-degree-of-freedom movement, thereby processing the blank into a thin-walled, high-rib structure.

[0021] A simplified structural diagram of a multi-degree-of-freedom forming robot is shown below. Figure 2 As shown, at the center of the driving slider plane Establish a coordinate system At the center of the envelope mold base surface Establish a coordinate system . ~ These are the center points of the connections between the six links and the moving platform. ~ These are the center points of the connections between the six links and the drive slider. ~ They are ~ The initial position, It is the radius of the moving platform. yes arrive Distance between points. and They are ~ and ~ exist and Angle in the coordinate system. Link length is... ,Right now . Click The distance between the points is ,Right now The distance the drive slider moves is... ,Right now .

[0022] and The coordinates of a point in its respective coordinate system can be represented by equation (1): (1) arrive The coordinate transformation matrix of the coordinate system can be represented by equation (2): (2) The geometric constraint relationship of a multi-degree-of-freedom forming robot can be expressed by equation (3): (3) 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): (4) 2. Mechanical dynamics model A simplified force diagram of a multi-degree-of-freedom forming robot is shown below. Figure 3 As 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 exerted by the connecting rod on the moving platform. It is the constraint force exerted by the moving platform on the envelope mold. It is the constraint force acting on the envelope mold. , and These are the forces acting on the driving slider, the moving platform, and the enveloping mold, respectively.

[0023] This can be decoupled into driving forces to overcome gravity, forming force, Coriolis force, and inertial force, which are respectively expressed as: , , and Furthermore, the relationship between the above forces can be expressed by equation (5): (5) In order to obtain The force balance equation and the moment balance equation can be expressed by equation (6): (6) According to the above formula, in order to overcome the driving force of gravity... It can be obtained from equation (7): (7) In order to obtain The force balance equation and the moment balance equation can be expressed by equation (8): (8) According to the above formula, in order to overcome the driving force of the forming force It can be obtained from equation (9): (9) In order to obtain The force balance equation and the moment balance equation can be expressed by equation (10): (10) in yes Point of action to point position vector, It is the angular velocity of the enveloping mold. Since the enveloping mold and the moving platform are connected together, the angular velocity of the moving platform is... .

[0024] According to the above formula, in order to overcome the driving force of the Coriolis force It can be obtained from equation (11): (11) In order to obtain The force balance equation and the moment balance equation can be expressed by equation (12): (12) in and These are the linear acceleration and angular acceleration of the enveloping mold, respectively. Since the enveloping mold and the moving platform are connected, the linear acceleration and angular acceleration of the moving platform are also... , .

[0025] According to the above formula, in order to overcome the driving force of inertia... It can be obtained from equation (13): (13) According to equation (5), the overall driving force can be expressed by equation (14): (14) Combining equations (7), (9), (11), (13), and (14), we can obtain the mechanical dynamics model of the multi-degree-of-freedom forming robot, which is represented by equation (15): (15) in, and These are the mass matrix and the Coriolis force matrix, respectively. , , .

[0026] 3. Electrodynamics Model The voltage equation of a permanent magnet synchronous motor can be expressed by equation (16): (16) in, It is Hadamaji. , , , , , , , , . , , , and These are the d-axis current, q-axis current, d-axis voltage, q-axis voltage, and motor speed of the permanent magnet synchronous motor. and These are the motor resistance and the magnetic flux, respectively. and These are the inductances of the d and q axes, respectively.

[0027] The equation of motion for a permanent magnet synchronous motor can be expressed by equation (17): (17) in , , . It is the moment of inertia of the motor. , and These are the motor's damping coefficient, electromagnetic torque, and load torque, respectively.

[0028] Electromagnetic torque can be expressed by equation (18): (18) in, .

[0029] 4. Electromechanical coupling dynamics model Since the permanent magnet synchronous motor and the drive slider are connected through a reducer and a ball screw, equation (19) can be obtained: (19) in, It is the rotation angle of the motor. It refers to the reduction ratio of the speed reducer and the ball screw.

[0030] Combining equations (14), (18), and (19), the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot can be represented by equation (20): (20) in, and These are the acceleration Jacobian matrix and the velocity Jacobian matrix, respectively. and These are equivalent mass and equivalent damping, respectively. , .

[0031] S2. Establish an inertia identification model for a multi-degree-of-freedom forming robot.

[0032] Based on equations (18) and (20), we can obtain equation (21): (twenty one) in, That is the sampling time.

[0033] Since the electrical time constant is much smaller than the mechanical time constant, it can be considered that... It remains unchanged between two adjacent sampling periods, that is: (twenty two) Combining equations (21) and (22), we obtain equation (23): (twenty three) in, , , , .

[0034] Taking equation (23) as the reference model, the adjustable model is represented by equation (24): (twenty four) in, and They are and The estimated value.

[0035] The output errors of the reference model and the adjustable model can be expressed by equation (25): (25) The objective function is expressed by equation (26): (26) Based on equations (23), (24), (25) and (26), equation (27) can be obtained using the gradient descent algorithm: (27) in, , and It's about adjusting the parameters.

[0036] According to equations (23), (24), (25), (26) and (27), the identification rates of equivalent mass and equivalent damping can be expressed by equation (28): (28) To achieve higher recognition accuracy, the parameters will be adjusted. The system is designed with adaptive parameters to adjust the dynamic response of the identification system in real time. When the system is in a steady state... Increase the size to improve system response speed. When the system is in a transient state, Reduce to decrease system overshoot.

[0037] When the system is in a transient state, the identification results can change rapidly, therefore... To characterize the system state and adjust it in real time The adaptive adjustment rate is expressed by equation (29): (29) in, .

[0038] S3. Establish an adaptive PI control model for a multi-degree-of-freedom forming robot.

[0039] 1. Current loop PI control model Because the voltage equation of a permanent magnet synchronous motor contains nonlinear terms, it is not conducive to tuning the PI parameters of the current loop. Therefore, a feedforward decoupling method is adopted in the current loop, such as... Figure 7 As shown. Based on this, the simplified voltage equation of the permanent magnet synchronous motor can be expressed by equation (30): (30) The closed-loop transfer function of the current loop can be expressed by equation (31): (31) in, and These are the PI parameters of the current loop.

[0040] To obtain a better dynamic response of the current loop, the current loop PI parameter setpoint can be expressed by equation (32): (32) in, It is the current loop bandwidth.

[0041] Combining equations (31) and (32), we can obtain the closed-loop transfer function of the current loop, expressed as follows: (33) By configuring an appropriate bandwidth, the current loop poles can be made negative, thus proving stability.

[0042] 2. Speed ​​loop PI control model To achieve better dynamic performance by configuring the speed loop PI parameters, the speed loop PI parameters are tuned based on adaptive damping, such as... Figure 8 As shown. Assuming the permanent magnet synchronous motor starts under no-load conditions, its equation of motion can be expressed by equation (34): (34) Adaptive damping can be expressed by the following formula: (35) in, It is the adaptive damping coefficient.

[0043] Combining equations (34) and (35), we obtain the following equation: (36) Based on equation (36), the following equation can be obtained: (37) The design rate can be expressed by equation (38): (38) Combining equations (37) and (38), we obtain the following equation: (39) in, It is the speed loop bandwidth.

[0044] The closed-loop transfer function of the velocity loop can be expressed by the following equation: (40) in, and It is the speed loop PI parameter.

[0045] The design rate of the speed loop PI parameter can be expressed by equation (41): (41) Combining equations (40) and (41), the closed-loop transfer function of the velocity loop can be obtained, which can be expressed by equation (42): (42) 3. Adaptive PI control model Based on the above analysis, this invention proposes an adaptive PI control method, the control structure of which is as follows: Figure 9 As shown. A three-loop PI control scheme is used. The current loop PI parameters are tuned using equation (32), the speed loop PI parameters are tuned using equation (41), the equivalent mass and equivalent damping parameter identification methods are implemented using equations (28) and (29), the electromechanical coupling dynamic model is established using equation (20), and the current loop feedforward decoupling method is implemented using... Figure 7 Achieved through adaptive damping of the velocity loop. Figure 8 accomplish.

[0046] 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 envelope mold in Table 2, the solution of the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot can be obtained, such as... Figure 4 As shown, the driving force curve exhibits periodicity. The inertial force ranges from approximately 1300 to 2700 N, the Coriolis force from approximately -590 to 120 N, and the gravitational force from approximately 120 to 230 N. The inertial force exhibits the largest range and amplitude of variation, thus having the greatest impact on control accuracy. Based on the method provided by this invention and the permanent magnet synchronous motor parameters in Table 3, a method for identifying the equivalent mass and equivalent damping parameters of a multi-degree-of-freedom forming robot can be implemented. Based on the implementation of the above method, an adaptive PI control method can be implemented according to the method provided by this invention.

[0047] For parameter identification methods Figure 5 This is an analysis chart of the identification results using a traditional parameter identification method, with a step load added at 2 seconds. It is evident that rapidly time-varying loads significantly impact identification accuracy. (Parameters) This has a significant impact on the identification of dynamic responses. When At that time, the overshoot time of the equivalent quality identification result is approximately 60%, and the rise time is approximately 0.02 s. At that time, the overshoot time of the equivalent quality identification result was approximately 40%, and the rise time was approximately 0.03 s. At that time, the overshoot time of the equivalent mass identification results was approximately 18%, and the rise time was approximately 0.06 s. The equivalent damping identification results also exhibited the same pattern. In summary, as the parameters... With the increase of [something], the recognition response speed is faster and the overshoot is larger. Figure 6 The identification errors of equivalent mass and equivalent damping under adaptive adjustment parameters are presented. It can be seen that the overshoot time of the equivalent mass identification result is approximately 14%, and the rise time is approximately 0.018 s. Figure 5 Compared to the identification results shown, the identification results achieved a better dynamic response.

[0048] For adaptive PI control methods, in such cases... Figure 10 The experimental platform shown was used for experiments at different rotational speeds. Figure 11 The control errors of slider 1 are compared under the traditional PI control method and the proposed control method at forming speeds of 20 r / min, 30 r / min, and 60 r / min. It can be seen that the control error curve varies along a sinusoidal pattern. At a forming speed of 20 r / min, the error range of the traditional PI control method is approximately -50 to 50. The error range of the adaptive PI control method is approximately -45 to 45. At a forming speed of 30 r / min, the error range of the traditional PI control method is approximately -80 to 80. The error range of the adaptive PI control method is approximately -60 to 60. At a forming speed of 60 r / min, the error range of the traditional PI control method is approximately -150 to 130. The error range of the adaptive PI control method is -85 to 90. . Figure 12The root mean square (RMS) values ​​of the control errors of the traditional PI method and the adaptive PI method at low, medium, and high speeds are presented. It can be seen that the effectiveness of the proposed method becomes increasingly apparent with increasing forming speed. This is because acceleration increases with speed, leading to increased inertial and Coriolis forces. At low speeds, the control error is reduced by 17.23% compared to the traditional PI control method. At medium speeds, the control error is reduced by 26.67% compared to the traditional PI control method. At high speeds, the control error is reduced by 34.62% compared to the traditional PI control method. Figure 13 The parameter identification results are shown for forming speeds of 20 r / min, 30 r / min, and 60 r / min. It can be seen that the curves of the identification results change periodically with time. This is because the pose of the multi-degree-of-freedom forming robot also changes periodically. At different forming speeds, the amplitude of the identification results is basically the same. This is because forming speed does not affect the equivalent mass and equivalent damping. However, as the forming speed increases, the parameters adaptively adjust... This will decrease. Therefore, the fluctuation of the parameter identification results decreases as the forming speed increases.

[0049] Table 1 Structural parameters of multi-degree-of-freedom forming robot

[0050] Table 2 Desired pose of the envelope mold

[0051] Table 3. Parameters of Permanent Magnet Synchronous Motor

[0052] Example 2 The present invention also provides a system for inertia identification and compensation of a multi-degree-of-freedom forming robot, comprising: The electromechanical coupling dynamics model construction module is used to establish an electromechanical coupling dynamics model of a multi-degree-of-freedom forming robot. The inertial force and Coriolis force in the electromechanical coupling dynamics model are represented by equivalent mass and equivalent damping. The electromechanical coupling dynamics model determines the influence of inertial force and Coriolis force on control accuracy. The inertia identification model building module is used to build an inertia identification model for a multi-degree-of-freedom forming robot. The inertia identification model uses the rate of change of the identification results to adaptively adjust the adjustment parameters in real time. The adaptive PI control model building module is used to build an adaptive PI control model for a multi-degree-of-freedom forming robot. The adaptive PI control model determines the mapping relationship between PI parameters and equivalent mass and equivalent damping.

[0053] 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 inertia identification and compensation of a multi-degree-of-freedom forming robot, characterized in that, Includes the following steps: S1. Establish an electromechanical coupling dynamic model for a multi-degree-of-freedom forming robot. The inertial force and Coriolis force in the electromechanical coupling dynamic model are represented by equivalent mass and equivalent damping. The electromechanical coupling dynamic model determines the influence of inertial force and Coriolis force on control accuracy. S2. Establish an inertia identification model for a multi-degree-of-freedom forming robot. The inertia identification model uses the rate of change of the identification results to adaptively adjust the adjustment parameters in real time. S3. Establish an adaptive PI control model for a multi-degree-of-freedom forming robot. The adaptive PI control model determines the mapping relationship between PI parameters and equivalent mass and equivalent damping.

2. The inertia identification and compensation method for 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 parallel structure, a moving platform, an envelope mold, and a lower mold. The parallel structure comprises six branches, each consisting of a permanent magnet synchronous motor, a reducer, a ball screw, a drive slider, and a connecting rod. The ends of the six connecting rods are connected to the moving platform via ball joints. The envelope mold is mounted on the moving platform. During forming, the blank is placed on the lower mold, and driven by the six permanent magnet synchronous motors, the envelope mold achieves multi-degree-of-freedom movement, thereby processing the blank into a thin-walled, high-rib component.

3. The inertia identification and compensation method for a multi-degree-of-freedom forming robot according to claim 1, characterized in that, In step S1, the method for establishing the kinematic equations of a multi-degree-of-freedom forming robot includes the following steps: At the center of the driving slider plane Establish a coordinate system At the center of the envelope mold base surface Establish a coordinate system ; ~ These are the center points of the connections between the six links and the moving platform. ~ These are the center points of the connections between the six links and the drive slider; ~ They are ~ The initial position, It is the radius of the moving platform. yes arrive Distance between points; and They are ~ and ~ exist and The angle of the coordinate system; the length of the connecting rod is ,Right now ; Click The distance between the points is ,Right now The distance the drive slider moves is ,Right now ; and The coordinates of a point in its respective coordinate system are expressed by equation (1): (1) arrive The coordinate transformation matrix of the coordinate system is represented by equation (2): (2) The geometric constraint relationship of the multi-degree-of-freedom forming robot is expressed by equation (3): (3) 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): (4)。 4. The inertia identification and compensation method for a multi-degree-of-freedom forming robot according to claim 1, characterized in that, In step S1, the method for establishing the mechanical dynamics model of a multi-degree-of-freedom forming robot includes the following steps: 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 exerted by the connecting rod on the moving platform. It is the constraint force exerted by the moving platform on the envelope mold. It is the constraint force acting on the envelope mold. , and These are the forces driving the slider, the moving platform, and the enveloping mold, respectively. Decoupling is the driving force used to overcome gravity, forming force, Coriolis force, and inertial force, respectively expressed as: , , and Furthermore, the relationship between the above forces is expressed by equation (5): (5) In order to obtain The force balance equation and the moment balance equation are expressed by equation (6): (6) According to the above formula, in order to overcome the driving force of gravity We obtain the following from equation (7): (7) In order to obtain The force balance equation and the moment balance equation are expressed by equation (8): (8) According to the above formula, in order to overcome the driving force of the forming force We obtain the result from equation (9): (9) In order to obtain The force balance equation and the moment balance equation are expressed by equation (10): (10) in yes Point of action to point position vector, It is the angular velocity of the enveloping mold. Since the enveloping mold and the moving platform are connected together, the angular velocity of the moving platform is... ; According to the above formula, in order to overcome the driving force of the Coriolis force We obtain the following from equation (11): (11) In order to obtain The force balance equation and the moment balance equation are expressed by equation (12): (12) in and These are the linear acceleration and angular acceleration of the enveloping mold, respectively; since the enveloping mold and the moving platform are connected together, the linear acceleration and angular acceleration of the moving platform are also... , ; According to the above formula, in order to overcome the driving force of inertia... We obtain the following from equation (13): (13) According to equation (5), the overall driving force is represented by equation (14): (14) Combining equations (7), (9), (11), (13), and (14), we obtain the mechanical dynamics model of the multi-degree-of-freedom forming robot, which is represented by equation (15): (15) in, and These are the mass matrix and the Coriolis force matrix, respectively. , , .

5. The inertia identification and compensation method for a multi-degree-of-freedom forming robot according to claim 1, characterized in that, In step S1, the method for establishing the electrodynamic model of a multi-degree-of-freedom forming robot includes the following steps: The voltage equation of the permanent magnet synchronous motor is expressed by equation (16): (16) in, It is Hadamaji. , , , , , , , , ; , , , and These are the d-axis current, q-axis current, d-axis voltage, q-axis voltage, and motor speed of the permanent magnet synchronous motor. and These are the motor resistance and the magnetic flux; and These are the inductances of the d and q axes, respectively; The equation of motion for the permanent magnet synchronous motor is expressed by equation (17): (17) in , , ; It is the moment of inertia of the motor. , and These are the motor's damping coefficient, electromagnetic torque, and load torque, respectively. Electromagnetic torque is expressed by equation (18): (18) in, .

6. The inertia identification and compensation method for a multi-degree-of-freedom forming robot according to claim 1, characterized in that, In step S1, the method for establishing the electromechanical coupling dynamics model of a multi-degree-of-freedom forming robot includes the following steps: Since the permanent magnet synchronous motor and the drive slider are connected through a reducer and a ball screw, we get equation (19): (19) in, It is the rotation angle of the motor. It is the reduction ratio of the speed reducer and the ball screw; Combining equations (14), (18), and (19), we obtain the electromechanical coupling dynamics model of the multi-degree-of-freedom forming robot, which is represented by equation (20): (20) in, and These are the acceleration Jacobian matrix and the velocity Jacobian matrix, respectively. and These are equivalent mass and equivalent damping, respectively; , .

7. The inertia identification and compensation method for a multi-degree-of-freedom forming robot according to claim 6, characterized in that, In step S2, the method for establishing the inertia identification model of a multi-degree-of-freedom forming robot includes: Based on equations (18) and (20), we obtain equation (21): (21) in, It is the sampling time; It remains unchanged between two adjacent sampling periods, that is: (22) Combining equations (21) and (22), we obtain equation (23): (23) in, , , , ; Taking equation (23) as the reference model, the adjustable model is represented by equation (24): (24) in, and They are and The estimated value; The output errors of the reference model and the adjustable model are represented by equation (25): (25) The objective function is expressed by equation (26): (26) Based on equations (23), (24), (25) and (26), equation (27) can be obtained using the gradient descent algorithm: (27) in, , and It involves adjusting parameters; According to equations (23), (24), (25), (26) and (27), the identification rates of equivalent mass and equivalent damping can be expressed by equation (28): (28) To achieve higher recognition accuracy, the parameters will be adjusted. Designed with adaptive parameters to adjust the dynamic response of the identification system in real time; when the system is in steady state... Increase the size to improve system response speed; when the system is in a transient state. Reduce to decrease system overshoot; When the system is in a transient state, the identification results can change rapidly, therefore... To characterize the system state and adjust it in real time The adaptive adjustment rate is expressed by equation (29): (29) in, .

8. The inertia identification and compensation method for a multi-degree-of-freedom forming robot according to claim 7, characterized in that, In step S3, the method for establishing the current loop PI control model includes: With the feedforward decoupling method adopted in the current loop, the simplified voltage equation of the permanent magnet synchronous motor is expressed by equation (30): (30) The closed-loop transfer function of the current loop is expressed by equation (31): (31) in, and These are the current loop PI parameters; The current loop PI parameter setpoint is expressed by equation (32): (32) in, It is the current loop bandwidth; Combining equations (31) and (32), we can obtain the closed-loop transfer function of the current loop, expressed as follows: (33) By configuring an appropriate bandwidth, the current loop poles can be made negative, thus proving stability.

9. The inertia identification and compensation method for a multi-degree-of-freedom forming robot according to claim 8, characterized in that, In step S3, the method for establishing the speed loop PI control model includes: Based on adaptive damping to tune the speed loop PI parameters, assuming the permanent magnet synchronous motor starts under no-load conditions, its motion equation is expressed by equation (34): (34) Adaptive damping is expressed by the following formula: (35) in, It is the adaptive damping coefficient; Combining equations (34) and (35), we obtain the following equation: (36) Based on equation (36), we obtain the following equation: (37) The design rate is expressed by equation (38): (38) Combining equations (37) and (38), we obtain the following equation: (39) in, It is the speed loop bandwidth; The closed-loop transfer function of the velocity loop can be expressed by the following equation: (40) in, and These are the speed loop PI parameters; The design rate of the speed loop PI parameter can be expressed by equation (41): (41) Combining equations (40) and (41), we obtain the closed-loop transfer function of the velocity loop, which can be expressed by equation (42): (42)。 10. A system for inertia identification and compensation of a multi-degree-of-freedom forming robot, characterized in that, include: The electromechanical coupling dynamics model construction module is used to establish an electromechanical coupling dynamics model of a multi-degree-of-freedom forming robot. The inertial force and Coriolis force in the electromechanical coupling dynamics model are represented by equivalent mass and equivalent damping. The electromechanical coupling dynamics model determines the influence of inertial force and Coriolis force on control accuracy. The inertia identification model building module is used to build an inertia identification model for a multi-degree-of-freedom forming robot. The inertia identification model uses the rate of change of the identification results to adaptively adjust the adjustment parameters in real time. The adaptive PI control model building module is used to build an adaptive PI control model for a multi-degree-of-freedom forming robot. The adaptive PI control model determines the mapping relationship between PI parameters and equivalent mass and equivalent damping.

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