Force and damping cooperative control method for heavy-load high-speed forming robot

Abstract

The invention relates to a force and damping cooperative control method for a heavy-load high-speed forming robot. The method comprises the following steps that S1, an elastic dynamic model considering connecting rod deformation and hydraulic rod damping of the heavy-load high-speed forming robot is established; s2, establishing a hydraulic system model which takes a proportional valve to control a hydraulic rod as a main body; and S3, a main power / damping system control method is determined, a PI force loop is adopted to achieve tracking compensation of force, and a PI damping loop is adopted to control damping of an air cylinder to achieve tracking compensation of damping. The control precision and stability of the heavy-load high-speed forming robot can be improved. The invention provides a new method for force damping cooperative control of the heavy-load high-speed forming robot, and the method has great application potential in industry.

Description

Technical Field

[0001] The present invention relates to the technical field of forming robot control, and more specifically, to a method for coordinated control of force and damping of a heavy-load high-speed forming robot. Background Art

[0002] With the development of industrial automation, heavy-load and high-speed forming robots are increasingly widely used in the manufacturing industry. Such robots usually need to complete high-precision force control and position control while moving at high speed. However, traditional control methods have the following problems under heavy-load and high-speed conditions: Insufficient dynamic response: When moving at high speed, the inertial force and external interference force of the robot system will cause the control accuracy to decrease. Conflict between force control and position control: Traditional control methods are difficult to achieve coordinated control of force and position during high-speed movement, resulting in unstable forming quality. Insufficient damping characteristics: When moving at high speed, the vibration and impact of the robot system are difficult to effectively suppress, affecting the system stability and service life. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for coordinated control of force and damping of a heavy-load high-speed forming robot, which can improve the control accuracy and stability of the heavy-load high-speed forming robot.

[0004] The technical solution adopted by the present invention to solve its technical problems is: constructing a method for coordinated control of force and damping of a heavy-load high-speed forming robot, including the following steps:

[0005] S1. Establish an elastic dynamics model considering the deformation of its connecting rod and the damping of the hydraulic rod;

[0006] S2. Establish a hydraulic system model with a proportional valve controlling the hydraulic rod as the main body;

[0007] S3. Determine the control method of the active force / damping system, which uses a PI force loop to achieve force tracking compensation and a PI damping loop to control the damping of the cylinder to achieve damping tracking compensation.

[0008] According to the above solution, the elastic dynamics model in step S1 is:

[0009]

[0010] In the formula, the deformation amount of the connecting rod along the rod direction is defined as The driving torque of the driving roller is defined as The load applied to the moving platform is defined as F p , F p = [f p1 , f p2 , f p3 , f p4 , f p5, f p6 ] T ; G R is the gravity force on the driving roller, G l1 and G l2 are the gravity forces on the upper and lower parts of the connecting rod respectively, G p is the gravity force on the moving platform; represents the constraint reaction force on the driving roller, the constraint reaction force on the upper spherical pair of the connecting rod, represents the constraint reaction force on the lower spherical pair of the connecting rod, represents the constraint reaction force on the middle spherical joint at S B suffered, and represent the elastic force and damping force of the connecting rod respectively; and represent the pose vectors of the upper and lower mass parts of the connecting rod respectively, is the damping force of the hydraulic rod, represents the pose vector of the centroid of the hydraulic rod, It can be calculated by the following formula, represents in the coordinate system S A midpoint A i relative to point C i position vector of, r p represents the position vector of the action point of the load force on the S B coordinate system; represents the position vector of the center of the lower spherical pair of the hydraulic rod in the coordinate system S B ; I R represents the inertia matrix of the driving roller, I l1 and I l2 represent the inertia matrices of the upper and lower mass parts of the connecting rod respectively, I p represents the inertia matrix of the driving roller, represents the coordinate system to the coordinate system S A coordinate transformation matrix of, represents the coordinate system to the coordinate system S A coordinate transformation matrix of,, represents the coordinate system to the coordinate system S A coordinate transformation matrix of, represents the coordinate system to the coordinate system S A coordinate transformation matrix of.

[0011] According to the above solution, in the step S2, the force balance equation of the hydraulic cylinder of the hydraulic system, the flow characteristic equation of the proportional valve, and the continuity equation of the hydraulic cylinder are as follows:

[0012]

[0013] In the formula, x v is the opening displacement x of the spool valve p is the piston rod displacement, and f dh is the output force of the hydraulic cylinder, m is the piston mass, B is the viscous damping coefficient, and P L is the load pressure, β e is the bulk modulus of the hydraulic fluid, q L is the input flow rate of the hydraulic cylinder.

[0014] According to the above solution, in the step S3, the input is the flow rate q L , and the output is the hydraulic pressure f dh , and the transfer function of the hydraulic cylinder is:

[0015]

[0016] Taking the speed of the hydraulic cylinder as the output, the transfer function of the hydraulic cylinder is expressed as:

[0017]

[0018] For the proportional valve, its input is the electrical signal u(s), and the output is the flow rate q L (s), and the transfer function of the proportional valve is expressed as:

[0019]

[0020] In the formula, K sv , w sv , ξ sv are the gain coefficient, natural frequency, and damping ratio of the proportional valve respectively.

[0021] According to the above solution, the transfer function of the damping ring is:

[0022]

[0023] In the formula, K pD , K iD respectively represent the proportional gain and integral gain of the damping ring;

[0024] The transfer function of the force ring is:

[0025]

[0026] In the formula, K pf , K ifThey respectively represent the proportional gain and integral gain of the force loop.

[0027] According to the above solution, in the step S3, a three-loop PID control of a permanent magnet synchronous motor (PWSM) is adopted, which includes a position loop, a speed loop, and a current loop.

[0028] According to the above solution, in the step S3, the transfer function of the current loop is:

[0029]

[0030] In the formula, K pq , K iq They respectively represent the proportional gain and integral gain of the current loop.

[0031] According to the above solution, in the step S3, the transfer function of the speed loop is:

[0032]

[0033] In the formula, K pw , K iw They respectively represent the proportional gain and integral gain of the speed loop.

[0034] According to the above solution, in the step S3, the transfer function of the position loop is,

[0035]

[0036] In the formula, R s is the stator resistance, J m is the moment of inertia of the motor rotor, T d is the external torque applied to the motor, p n is the number of pole pairs of the permanent magnet synchronous motor. L d is the inductance of the d-axis.

[0037] According to the above solution, the control system includes a motor controller and three hydraulic controllers;

[0038] The motor controller is a three-loop servo controller. The kinematic model of the motor controller receives the desired attitude and drives the servo motor to track the given attitude. The input-output relationship of the three-loop servo controller is:

[0039]

[0040] The three hydraulic controllers are all PI double-loop controllers. The hydraulic controllers obtain the desired force and the desired damping from the dynamic model and drive the hydraulic rod to track the desired force and damping. The input-output relationship of the hydraulic controller is:

[0041]

[0042] The final control model of the entire control system is as follows:

[0043]

[0044] Implementing the force and damping collaborative control method for the heavy-load high-speed forming robot of the present invention has the following beneficial effects:

[0045] 1. The present invention establishes an elastic dynamics model considering the deformation of its connecting rods and the damping of the hydraulic rods. Subsequently, a hydraulic system model with a proportional valve controlling the hydraulic rods as the main body is established, and three basic equations of the hydraulic system are derived. Finally, an active force / damping system control method is proposed, in which three PI force loops are used to achieve force tracking, and three PI damping loops are used to control the damping of the cylinders to achieve damping tracking. The present invention provides a new method for the force-damping collaborative control of heavy-load high-speed forming robots and has great application potential in industry.

[0046] 2. Through the force-damping collaborative control method of the heavy-load high-speed forming robot of the present invention, the low-frequency vibration of the 3RSS / S PKM is reduced by 49.5%, the high-frequency vibration is reduced by 83.8%, and the tooth profile error of the formed bevel gear is reduced by 37%, significantly improving the control accuracy and stability of the system. Description of the Drawings

[0047] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0048] Figure 1 is the basic structure schematic diagram of the 3RSS / S PKM;

[0049] Figure 2 is the dynamic model diagram of the 3RSS / S PKM;

[0050] Figure 3 is the dynamic model diagram of the hydraulic system;

[0051] Figure 4 is the block diagram of the PI force and damping dual-loop control of the hydraulic system;

[0052] Figure 5 is the transfer function of the dual-loop PI force and damping control of the hydraulic system;

[0053] Figure 6 is the three-loop PID control diagram of the PWSM;

[0054] Figure 7 is the schematic diagram of the force and damping collaborative control model of the heavy-load high-speed forming robot;

[0055] Figure 8 Figure 3RSS-S is a schematic diagram of force / attitude detection of PKM;

[0056] Figure 9 Figure 3 shows the spectral diagrams in three directions under the experimental results;

[0057] Figure 10 Figure 4 shows the low-frequency and high-frequency error diagrams in three directions under the experimental results;

[0058] Figure 11 Figure 5 shows the tooth profile error diagram of the formed bevel gear. Specific Embodiments

[0059] In order to have a clearer understanding of the technical features, objectives, and effects of the present invention, the specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0060] The method for collaborative control of force and damping of a heavy-duty high-speed forming machine of the present invention includes the following design process steps:

[0061] S1. Taking the developed 3RSS / S PKM as an example, an elastic dynamics model considering the deformation of its connecting rods and the damping of the hydraulic cylinders is established;

[0062] S2. Establish a hydraulic system model with a proportional valve controlling the hydraulic cylinders as the main body, and derive three basic equations of the hydraulic system;

[0063] S3. Propose a control method for the active force / damping system of PKM, in which three PI force loops are used to achieve force tracking compensation, and three PI damping loops are used to control the damping of the cylinders to achieve damping tracking compensation.

[0064] Combined with the above steps, the following will be described in detail.

[0065] S1. Taking the developed 3RSS / S PKM as an example, an elastic dynamics model considering the deformation of its connecting rods and the damping of the hydraulic cylinders is established;

[0066] The elastic dynamics model of 3RSS / S PKM considering the hydraulic cylinders is as shown in Figure 2 . As can be seen from the figure, the connecting rod is equivalent to two identical mass blocks, which are connected by a spring and a damper, and the hydraulic cylinder is equivalent to a damper. The deformation of the connecting rod along the rod direction is defined as The driving torque of the driving roller is defined as The load applied to the moving platform is defined as F p , which can be expressed as F p = [f p1 , f p2 , f p3 , f p4 , f p5,f p6 T . According to the Newton-Euler method, the dynamic model of 3RSS / S PKM can be expressed as,

[0067]

[0068] where, G R is the gravity force acting on the driving roller, G l1 and G l2 are the gravity forces acting on the upper and lower parts of the connecting rod respectively, and G p is the gravity force acting on the moving platform. represents the constraint reaction force acting on the driving roller, and it can be expressed as The constraint reaction force acting on the upper spherical pair of the connecting rod, and it can be expressed as represents the constraint reaction force acting on the lower spherical pair of the connecting rod, and it can be expressed as represents the constraint reaction force acting on the middle spherical joint at S B , and it can be expressed as and represent the elastic force and damping force of the connecting rod respectively. and represent the pose vectors of the upper and lower mass parts of the connecting rod respectively, and they can be expressed as, and is the damping force of the hydraulic rod, represents the pose vector of the centroid of the hydraulic rod, and it can be calculated by the following formula, represents the position vector of point A A at the midpoint of the coordinate system S i relative to point C i , and it can be expressed as r p represents the position vector of the action point of the load force on the coordinate system S B . represents the position vector of the center of the lower spherical pair of the hydraulic rod in the coordinate system S B . I R represents the inertia matrix of the driving roller, I l1 and I l2 represent the inertia matrices of the upper and lower mass parts of the connecting rod respectively, and I p represents the inertia matrix of the driving roller, represents the coordinate transformation matrix from the coordinate system to the coordinate system S A , represents the coordinate transformation matrix from the coordinate system to the coordinate system S A , and it can be expressed as, represents the coordinate transformation matrix from the coordinate system to the coordinate system S​A The coordinate transformation matrix representing the coordinate system to the coordinate system S A The coordinate transformation matrix.

[0069] S2 establishes a hydraulic system model with a proportional valve controlling the hydraulic rod as the main body, and derives three basic equations of the hydraulic system;

[0070] As Figure 3 shown, the hydraulic drive system consists of a hydraulic cylinder, a proportional valve, and hydraulic pipes. A1 and A2 are the areas on both sides of the piston. The area ratio of the asymmetric piston is A2 / A1 = n1. When n1 = 1, the hydraulic cylinder is a symmetric hydraulic cylinder. P1 and P2 are the pressures in the rodless chamber and the rod chamber respectively, q1 and q2 are the flows in the rod chamber and the rodless chamber respectively, x p is the displacement of the piston rod, x v is the opening displacement of the spool valve, P s and P r are the oil supply pressure and the oil return pressure of the pump respectively. The piston velocity v can be obtained by calculating v = q1 / A1 = q2 / A2. By considering the area ratio n1 of the asymmetric piston, the flow relationship between the rod chamber and the rodless chamber can be expressed as q2 / q1 = n1. The force balance equation of the piston can be expressed as:

[0071]

[0072] In the formula, f dh is the output force of the hydraulic cylinder, m is the mass of the piston, and B is the viscous damping coefficient. When the piston is in a steady state, Equation (2) can be simplified to A1(P1 - nP2) = f dh0 , where f dh0 is the steady-state load force acting on the piston.

[0073] Therefore, the load pressure can be defined as:

[0074] P L = P1 - nP2 (5)

[0075] The flows q1 and q2 in the rod chamber and the rodless chamber can be expressed as,

[0076]

[0077] In the formula, C d is the flow coefficient, generally taken between 0.6 and 1, w is the area gradient of the spool valve, and ρ is the density of the medium. The load flow q L can be expressed as,

[0078]

[0079] The flow gain coefficient of the valve can be obtained from differential equation (5).

[0080]

[0081] Meanwhile, the flow-pressure coefficient of the valve can be obtained as:

[0082]

[0083] Therefore, the flow equation of the proportional valve can be uniformly expressed as

[0084] q L =K q x v -K c P L (10)

[0085] For the hydraulic cylinder, it is assumed that the pressure in the chamber is the same everywhere, there is no saturated cavitation phenomenon, and the temperature and density remain constant. In addition, it is assumed that the piston is at a certain position such that these volumes are equal - i.e., V 10 =V 20 =V0, V 10 and V 20 are the initial volumes of the rod chamber and the non-rod chamber respectively. Under these assumptions, the continuity equation for each piston chamber can be written as:

[0086]

[0087] where C ic is the internal leakage coefficient of the hydraulic cylinder, C ec is the external leakage coefficient of the hydraulic cylinder, and β e is the bulk modulus of the hydraulic fluid. Substituting Equation (3) into Equation (9), and expressing the pressures P1 and P2 in the non-rod chamber and the rod chamber with the load pressure P L respectively, the general form of the continuity equation for the valve-controlled asymmetric hydraulic cylinder can be obtained as:

[0088]

[0089] After performing Laplace transforms on Equations (2), (8), and (10), the three basic equations of the hydraulic system can be obtained:

[0090]

[0091] The above equation is the basic equation of the hydraulic system, which consists of the force balance equation of the hydraulic cylinder, the flow characteristic equation of the proportional valve, and the continuity equation of the hydraulic cylinder. This equation serves as the basis for deriving the transfer function of the control loop.

[0092] S3 proposes an active force / damping system control method for PKM, in which three PI force loops are adopted to achieve force tracking, and three PI damping loops are used to control the damping of the cylinder to achieve damping tracking.

[0093] For a hydraulic cylinder, its input is the flow rate q L , and the output is the hydraulic pressure f dh , and its transfer function can be derived through Equation (11):

[0094]

[0095] Similarly, if the speed of the hydraulic cylinder is taken as the output, its transfer function can be expressed as

[0096]

[0097] For a proportional valve, its input is the electrical signal u(s), and the output is the flow rate q L (s), and its transfer function can be expressed as:

[0098]

[0099] In the formula, K sv , w sv , ξ sv are the gain coefficient, natural frequency, and damping ratio of the proportional valve, respectively.

[0100] In order to achieve real-time control and compensation of force and damping, a PKM active force / damping cooperative control method is proposed, which uses a PI force control loop to achieve force tracking and a PI damping control loop to control the damping of the cylinder to achieve damping tracking. Figure 4 It is the block diagram of the PI force and damping dual-loop control for the hydraulic system.

[0101] Figure 5 It is the transfer function of the dual-loop PI force and damping control for the hydraulic system. From the figure, the transfer function of the damping loop can be obtained as

[0102]

[0103] In the formula, K pD , K iD represent the proportional gain and integral gain of the damping loop, respectively. Similarly, the transfer function of the force loop is

[0104]

[0105] In the formula, K pf , K if represent the proportional gain and integral gain of the force loop, respectively.

[0106] The 3RSS / S PKM is controlled by a permanent magnet synchronous motor (PWSM). Figure 6 The three-loop PID control diagram of the PWSM is given. The three loops are the position loop, the speed loop, and the current loop.

[0107] For the current loop, its transfer function is:[[]]END]]

[0108]

[0109] In the formula, K pq , K iq respectively represent the proportional gain and integral gain of the current loop.

[0110] For the speed loop, its transfer function is:[[]]END]]

[0111]

[0112] In the formula, K pw , K iw respectively represent the proportional gain and integral gain of the speed loop.

[0113] Similarly, for the position loop, its transfer function is

[0114]

[0115] In the formula, R s is the stator resistance, J m is the moment of inertia of the motor rotor, T d is the external torque applied to the motor. p n is the number of pole pairs of the permanent magnet synchronous motor. L d is the inductance of the d-axis.

[0116] Based on the above analysis, the active force / damping collaborative control system is as Figure 7 shown. It can be seen that the control system consists of 1 motor controller and 3 hydraulic controllers. The motor controller is a three-loop servo controller. It receives the desired attitude from the kinematic model and drives the servo motor to track the given attitude. According to the above discussion, the input-output relationship can be written as:[[]]END]]

[0117]

[0118] The three hydraulic controllers are all PI double-loop controllers. They obtain the desired force and the desired damping from the dynamic model and drive the hydraulic rod to track the desired force and damping. Thus, their input-output relationship can be written as:[[]]END]]

[0119]

[0120] In summary, the final control model of the entire control system is

[0121]

[0122] The present invention also provides a specific embodiment as follows:

[0123] First, taking 3RSS / S PKM (a type of parallel robot) as an example, its structural schematic diagram is as Figure 1 shown. The pose of the moving platform can be obtained through the following formula,

[0124]

[0125] In the formula, l i represents the direction vector of the i-th link, l represents the length of the link, represents the deformation amount of the i-th link along the rod direction. represents the coordinate transformation matrix from coordinate system S B to coordinate system S A . and respectively represent the position vectors of the centers of the spherical joints and lower spherical joints on the link in coordinate systems S A and S B .

[0126] On this basis, an elastic dynamics model (Equation 1) of 3RSS / S PKM is established. Subsequently, a hydraulic system model with a proportional valve controlling the hydraulic rod as the main body is established, and three basic equations of the hydraulic system are derived: the force balance equation of the hydraulic cylinder: describing the relationship between the output force of the hydraulic cylinder and the piston movement; the flow characteristic equation of the proportional valve: describing the relationship between the flow of the proportional valve and the input of the electrical signal; the continuity equation of the hydraulic cylinder: describing the relationship between the liquid flow in the hydraulic cylinder and the pressure change. Through these equations, the transfer function of the hydraulic system can be derived, providing a basis for subsequent control design.

[0127] Finally, a force and damping co-control method for a heavy-duty high-speed forming machine is proposed. The control system consists of 1 motor controller and 3 hydraulic controllers. The motor controller adopts a three-loop PID control (position loop, speed loop, current loop) to control the movement of the permanent magnet synchronous motor (PWSM). The hydraulic controller adopts a PI dual-loop control. Among them, the force control adopts three PI (proportional-integral) force control loops to achieve precise tracking of the output force of the hydraulic cylinder, and the damping control adopts three PI damping control loops to control the damping characteristics of the hydraulic cylinder to achieve precise tracking of the damping of the hydraulic system. Through the coordinated work of the motor controller and the hydraulic controller, precise control of 3RSS / S PKM is achieved.

[0128] Verify the effectiveness of the proposed coordinated control method of force and damping for heavy-load high-speed forming machines through experiments. The experiments were carried out by machining bevel gears to make the 3RSS / SPKM operate under heavy-load (200kN) and high-speed (4m / s) conditions, and the vibration error signals of the moving platform were measured by a laser rangefinder and an angular displacement sensor. The schematic diagram of the experimental detection is as shown in Figure 8 as follows. The experimental results ( Figure 9 , 10 , 11) show that: under different experimental conditions, peak values appear in the angular error curves in the three directions in the frequency ranges of 0Hz and 100 - 200Hz. It can be seen that in the case of no hydraulic pressure and no damping, that is, when the proposed method is not adopted, the low-frequency and high-frequency errors are higher than those when the hydraulic pressure and damping are set to 9.2 (the coordinated control method of force and damping for heavy-load high-speed forming machines is adopted). In the alpha direction, the low-frequency error decreases from 0.74mrad to 0.4mrad, a decrease of 46%, and the high-frequency error decreases from 0.063mrad to 0.023mrad, a decrease of 63.5%. In the beta direction, the low-frequency error decreases from 0.75mrad to 0.4mrad, a decrease of 46.7%, and the high-frequency error decreases from 0.075mrad to 0.025mrad, a decrease of 66.7%. In the gamma direction, the low-frequency error decreases from 1.9mrad to 0.96mrad, a decrease of 49.5%, and the high-frequency error decreases from 0.74mrad to 0.12mrad, a decrease of 83.8%. At the same time, it can be observed that when the damping is 0 and there is no hydraulic pressure, the error range of the formed bevel gear is about -39 - 54um; when the damping is 9.2 and there is hydraulic pressure, the error range is about -26 - 34um. This shows that compared with the case where the method is not applied, after adopting the proposed coordinated control method of force and damping for heavy-load high-speed forming machines, the error of the formed gear is reduced by nearly 37%. These results further verify the effectiveness and feasibility of the proposed method.

[0129] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the present invention and the claims. These all belong to the protection scope of the present invention.

Claims

1. A method for collaborative control of force and damping of an overloaded high-speed forming machine, characterized in that, It includes the following steps: S1. Establish an elastic dynamic model considering the deformation of its connecting rod and the damping of the hydraulic rod; S2. Establish a hydraulic system model with a proportional valve controlling the hydraulic rod as the main body; S3. Determine the control method of the active force / damping system, which adopts a PI force loop to achieve force tracking compensation and a PI damping loop to control the damping of the cylinder to achieve damping tracking compensation.

2. The collaborative control method of force and damping for the heavy-load high-speed forming machine according to claim 1, characterized in that The elastic dynamic model in the step S1 is as follows: In the formula, the deformation of the connecting rod along the rod direction is defined as The driving torque of the driving roller is defined as The load applied to the moving platform is defined as F p , F p =[f p1 , f p2 , f p3 , f p4 , f p5 , f p6 T ; G R is the gravity of the driving roller, G l1 and G l2 are the gravities of the upper and lower parts of the connecting rod respectively, G p is the gravity of the moving platform; represents the constraint reaction force of the driving roller, the constraint reaction force of the spherical pair on the connecting rod, represents the constraint reaction force of the lower spherical pair of the connecting rod, represents the constraint reaction force of the middle spherical joint at S B suffered, and represent the elastic force and damping force of the connecting rod respectively; and represent the pose vectors of the upper and lower mass parts of the connecting rod respectively, is the damping force of the hydraulic rod, represents the pose vector of the centroid of the hydraulic rod, It can be calculated by the following formula, represents the position vector of point A A at the midpoint of the coordinate system S i relative to point C i ; r p represents the position vector of the acting point of the load force on the S B coordinate system; represents the position vector of the center of the lower spherical pair of the hydraulic rod in the coordinate system S B ; I R represents the inertia matrix of the driving roller, I l1 and I l2 represent the inertia matrices of the upper and lower mass parts of the connecting rod respectively, I p represents the inertia matrix of the driving roller, represents the coordinate system to the coordinate system S A coordinate transformation matrix, represents the coordinate system to the coordinate system S A coordinate transformation matrix, ​Represents the coordinate system to the coordinate system S A coordinate transformation matrix Represents the coordinate system to the coordinate system S A coordinate transformation matrix 3. The collaborative control method of force and damping for the heavy-load high-speed forming machine according to claim 2, characterized in that, In the step S2, the force balance equation of the hydraulic cylinder of the hydraulic system, the flow characteristic equation of the proportional valve, and the continuity equation of the hydraulic cylinder are as follows: where x v is the opening displacement x of the spool valve p is the piston rod displacement, f dh is the output force of the hydraulic cylinder, m is the mass of the piston, B is the viscous damping coefficient, P L is the load pressure, β e is the bulk modulus of the hydraulic fluid, q L is the input flow rate of the hydraulic cylinder.

4. The collaborative control method of force and damping for a heavy-load high-speed forming machine according to claim 3, wherein, In the step S3, the input is the flow rate q L , and the output is the hydraulic pressure f dh . The transfer function of the hydraulic cylinder is as follows: Taking the speed of the hydraulic cylinder as the output, the transfer function of the hydraulic cylinder is expressed as: For a proportional valve, its input is the electrical signal u(s), and its output is the flow rate q L (s). The transfer function of the proportional valve is expressed as: where K sv , w sv , ξ sv are the gain coefficient, natural frequency, and damping ratio of the proportional valve, respectively.

5. The collaborative control method for force and damping of a heavy-duty high-speed forming machine according to claim 4, characterized in that In the step S3, the transfer function of the damping loop is: where K pD and K iD respectively represent the proportional gain and integral gain of the damping ring; The transfer function of the force loop is: where K pf and K if represent the proportional gain and integral gain of the force loop, respectively.

6. The collaborative control method of force and damping for a heavy-load high-speed forming machine according to claim 5, characterized in that In the step S3, a permanent magnet synchronous motor (PWSM) three-loop PID control is adopted, which includes a position loop, a speed loop, and a current loop.

7. The collaborative control method of force and damping for the heavy-load high-speed forming machine according to claim 6, characterized in that, In the step S3, the transfer function of the current loop is: where K pq and K iq respectively represent the proportional gain and integral gain of the current loop.

8. The collaborative control method for force and damping of a heavy-duty high-speed forming machine according to claim 6, characterized in that In the step S3, the transfer function of the speed loop is: where K pw and K iw represent the proportional gain and integral gain of the speed loop respectively.

9. The collaborative control method of force and damping for the heavy-load high-speed forming machine according to claim 6, characterized in that, In the step S3, the transfer function of the position loop is: where R s is the stator resistance, J m is the moment of inertia of the motor rotor, T d is the external torque applied to the motor, p n is the number of pole pairs of the permanent magnet synchronous motor. L d is the inductance of the d-axis.

10. The collaborative control method of force and damping for a heavy-duty high-speed forming machine according to claim 6, characterized in that In the step S3, the control system includes a motor controller and three hydraulic controllers; The motor controller is a three-loop servo controller. In the kinematic model of the motor controller, it receives the desired attitude and drives the servo motor to track the given attitude. The input-output relationship of the three-loop servo controller is as follows: All three hydraulic controllers are PI double-loop controllers. The hydraulic controllers obtain the desired force from the dynamic model and the desired damping and drive the hydraulic rod to track the desired force and damping. The input-output relationship of the hydraulic controller is as follows: The final control model of the entire control system is:

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