A method and system for hybrid control of force and position of multi-machine collaborative stretching pad in servo stamping line

Abstract

This invention belongs to the field of servo stamping line control and discloses a hybrid control method and system for force and position of multi-machine cooperative stretching pads in servo stamping lines. It mainly addresses the rigid impact and pressure overshoot problems caused by direct force and position switching at the instant of stamping contact of the servo stretching pad. Through the outer loop admittance compliant trajectory reconstruction module, the reference trajectory is dynamically corrected according to the actual contact force, realizing a smooth pressure build-up transition from "rigid resistance to pressure" to "flexible compliance". In order to address the problems of four-cylinder synchronization misalignment and reduced tracking accuracy caused by strong mechanical coupling, unmodeled friction and strong nonlinearity of hydraulic system under multi-cylinder cooperative downward and off-center load conditions, the invention introduces an Actor-Critic reinforcement learning network based on global state awareness and a recursive RISE robust feedback linearization control architecture to achieve accurate feedforward compensation for complex coupled nonlinearities and strong integral suppression of unknown external disturbances.

Description

Technical Field

[0001] This invention relates to the field of servo stamping line control, specifically to a method and system for hybrid control of multi-machine collaborative stretching pad force and position in a servo stamping line. Background Technology

[0002] Servo stretching pads, with their high efficiency and flexible processing capabilities, are gradually replacing traditional stretching pads in modern high-end manufacturing. To ensure the forming quality of complex components, stretching pads must possess extremely high-precision motion control capabilities, especially in the pre-acceleration and pressure-building stages, posing challenges to the equipment's speed / position composite control and force-position hybrid control. For the pre-acceleration stage, the slider needs to accelerate downwards while maintaining a strictly absolute horizontal posture. However, unknown disturbances, unmodeled friction terms, multi-cylinder mechanical coupling, and off-center loading effects significantly reduce the system's position synchronization accuracy. Furthermore, the inherent strong nonlinearity of electro-hydraulic servo systems further affects the realization of high-precision tracking control.

[0003] In recent years, scholars have proposed nonlinear adaptive control, robust control, and model predictive control for hydraulic systems. Among these, adaptive robust control and adaptive RISE control have become current research hotspots due to their stability. However, although the aforementioned nonlinear problems can be effectively solved, issues such as unmodeled friction terms and unknown system disturbances will affect control accuracy. To address these problems, disturbance observation-based control methods, such as disturbance observers and state observers, have been widely used. However, in disturbance observation-based control methods, the unknown dynamics are concentrated as disturbances, which leads to a slower observation rate, a heavier observation burden, and transient control performance that does not meet expectations. Summary of the Invention

[0004] For the aforementioned multi-cylinder hydraulic system with unknown disturbances, this invention proposes a servo stamping line multi-machine collaborative stretching pad force and position hybrid control method and system.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a method for hybrid control of force and position of a multi-machine cooperative stretching pad in a servo stamping line, comprising the following steps: Step S1: Obtain the target reference trajectory and target loading force set by the system, and perform compliant yielding calculation based on the actual loading force to output the reconstructed reference trajectory; Step S2: Receive the reconstructed reference trajectory, and calculate the virtual control law through robust feedback linearization control RISE and ACtor-Critie reinforcement learning network to suppress multi-cylinder rigid coupling disturbances.

[0006] As a further technical solution, step S1 includes the following steps: S11. Define the second-order differential equation for the admittance of the i-th hydraulic cylinder:

[0007] In the formula, , , These are the parameters of the virtual mass, virtual damping, and virtual stiffness matrix, respectively. This represents the actual contact force between the piston and the lower die. The ideal contact force between the piston and the lower die; Compensation displacement, Compensation speed; Compensation acceleration; S12. Based on the compensated displacement, compensated velocity, and compensated acceleration, generate the reconstructed reference trajectory and its derivative:

[0008]

[0009]

[0010] In the formula, , , These are the original target reference displacement, velocity, and acceleration, respectively. , , These are the reconstructed reference displacement, velocity, and acceleration, respectively.

[0011] As a further technical solution, step S2 includes the following steps: S21. Define position tracking error With filter tracking error :

[0012]

[0013] In the formula, Let i be the actual displacement of the i-th asymmetric cylinder. Positive feedback gain; for The derivative; S22. Define auxiliary variables as follows:

[0014] In the formula Positive feedback gain; for The derivative of can be calculated as follows:

[0015] In the formula, This represents the unmodeled nonlinear friction term; This represents the unknown rigid coupling force transmitted by other cylinders. This is the actual contact force between the piston and the lower die. This represents an unknown disturbance in the system. This indicates the pressure caused by the hydraulic differential pressure inside the actuator cylinder; This indicates the load and piston mass; Indicates the gravity coefficient; S23. Define hydraulic equivalent acceleration tracking error :

[0016] In the formula, The hydraulic pressure provides acceleration to the piston: For virtual control laws; S24. Construct the first-level RISE feedback control term and calculate the virtual control law. :

[0017] In the formula: ; for The estimate; and It is a positive constant control gain; t represents the control time; S25. Define auxiliary variables as follows:

[0018] In the formula: It is a positive number; for The derivative; Calculation yields:

[0019] In the formula:

[0020]

[0021] Input for the angular velocity of the servo motor; This includes lumped hydraulic leakage and unmodeled dynamic disturbances; For the bulk modulus of oil, Indicates pump displacement; , These represent the areas of the rodless cavity and the rod cavity, respectively; , These represent the time-varying volumes of the rodless cavity and the rod cavity, respectively; S26. Construct the second-level RISE feedback control term, design the dynamic surface feedback linearization control law, and output the final servo motor angular velocity input command. :

[0022] In the formula,

[0023] and It is a positive constant control gain; t is the control time.

[0024] As a further technical solution, in step S24, Methods for determining the estimated quantity: S241. Define the lumped nonlinear dynamics of the system as:

[0025] S242. The generalized function approximation property based on neural networks is expressed as follows:

[0026] In the formula, For the unmodeled nonlinear friction term, The unknown rigid coupling force transmitted to other cylinders. Equivalent mass of the lower mold; The global state input vector contains the reconstructed trajectory of the multi-cylinder engine; It is a bounded activation function. For function reconstruction residual error, For ideal bounded weights; S243. Set the output estimate of the Actor network. for:

[0027] In the formula, These are the actual estimated weights of the Actor network; S244. The system's filtering tracking error As an evaluation reinforcement signal for the Critic network, an adaptive weight update law is designed:

[0028] In the formula, It is a positive definite diagonal learning rate matrix. This is a robust adaptive leakage factor.

[0029] Secondly, the present invention provides a multi-machine collaborative stretching pad force-position hybrid control system for a servo stamping line, comprising: The first module is configured to construct the outer loop admittance compliant trajectory reconstruction module, obtain the target reference trajectory and target loading force set by the system, perform compliant yielding calculation based on the actual loading force, and output the reconstructed reference trajectory; The second module is configured to receive the reconstructed reference trajectory and compute a virtual control law through a robust feedback linearization control RISE and an ACtor-Critie reinforcement learning network to suppress multi-cylinder rigid coupling disturbances.

[0030] As a further technical solution, the first module specifically includes: The definition module is configured to define the second-order differential equation of the admittance of the i-th hydraulic cylinder:

[0031] In the formula, , , These are the parameters of the virtual mass, virtual damping, and virtual stiffness matrix, respectively. This represents the actual contact force between the piston and the lower die. The ideal contact force between the piston and the lower die; Compensation displacement, Compensation speed; Compensation acceleration; The reconstruction module is configured to generate a reconstructed reference trajectory and its derivative based on the compensated displacement, compensated velocity, and compensated acceleration.

[0032]

[0033]

[0034] In the formula, , , These are the original target reference displacement, velocity, and acceleration, respectively. , , These are the reconstructed reference displacement, velocity, and acceleration, respectively.

[0035] As a further technical solution, the second module includes: The first definition module is configured to define the position tracking error. With filter tracking error :

[0036]

[0037] In the formula, This represents the actual displacement of the i-th hydraulic cylinder. Positive feedback gain; for The derivative; The second definition module is configured to define auxiliary variables. as follows:

[0038] In the formula, , Positive gain; for The derivative; calculation yields:

[0039] In the formula, This represents the unmodeled nonlinear friction term; This represents the unknown rigid coupling force transmitted by other cylinders. This is the actual contact force between the piston and the lower die. This represents an unknown disturbance in the system. This indicates the pressure caused by the hydraulic differential pressure inside the actuator cylinder; This indicates the load and piston mass; Indicates the gravity coefficient; The third definition module is configured to define the hydraulic equivalent acceleration tracking error. :

[0040] In the formula, The hydraulic pressure provides acceleration to the piston: For virtual control laws; The first building module is configured to construct the first-level RISE feedback control term and calculate the virtual control law. :

[0041]

[0042] In the formula: ; for The estimate; and It is a positive constant control gain; t represents the control time; The fourth definition module is configured to define auxiliary variables. as follows:

[0043] In the formula: It is a positive number; for The derivative; Calculation yields:

[0044] In the formula:

[0045]

[0046] Input for the angular velocity of the servo motor; This includes lumped hydraulic leakage and unmodeled dynamic disturbances; For the bulk modulus of oil, Indicates pump displacement; , These represent the areas of the rodless cavity and the rod cavity, respectively; , These represent the time-varying volumes of the rodless cavity and the rod cavity, respectively; The second building module is configured to construct the second-level RISE feedback control term, design the dynamic surface feedback linearization control law, and output the final servo motor angular velocity input command. :

[0047] In the formula, ; and It is a positive constant control gain; t is the control time.

[0048] As a further technical solution, the aforementioned The module for determining the estimated quantity includes: The first submodule is configured to define the system's lumped nonlinear dynamics as follows:

[0049] The second submodule is configured to use the generalized function approximation property based on neural networks, and is expressed as follows:

[0050] In the formula, For the unmodeled nonlinear friction term, The unknown rigid coupling force transmitted to other cylinders. Equivalent mass of the lower mold; The global state input vector contains the reconstructed trajectory of the four cylinders; It is a bounded activation function. For function reconstruction residual error, For ideal bounded weights; The third submodule is configured to set the output estimate of the Actor network. for:

[0051] In the formula, These are the actual estimated weights of the Actor network; The fourth submodule is configured to track the system's filtered error. As an evaluation reinforcement signal for the Critic network, an adaptive weight update law is designed:

[0052] In the formula, It is a positive definite diagonal learning rate matrix. This is a robust adaptive leakage factor.

[0053] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the aforementioned servo stamping line multi-machine collaborative stretching pad force-position hybrid control method.

[0054] Fourthly, the present invention provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, wherein, when the program instructions are executed by a computer, the computer executes the aforementioned servo stamping line multi-machine collaborative stretching pad force-position hybrid control method.

[0055] The beneficial effects of this invention are as follows: This invention addresses the rigid impact and pressure overshoot issues caused by direct force-position switching during the stamping contact of servo tension pads. It utilizes an outer-loop admittance compliant trajectory reconstruction module to dynamically correct the reference trajectory based on the actual contact force, achieving a smooth pressure transition from "rigid resistance" to "flexible compliance." Furthermore, it addresses the issues of four-cylinder synchronization misalignment and decreased tracking accuracy under multi-cylinder coordinated downward and off-center load conditions due to strong mechanical coupling, unmodeled friction, and strong nonlinearity of the hydraulic system. By introducing an Actor-Critic reinforcement learning network based on global state awareness and a recursive RISE robust feedback linearization control architecture, it achieves precise feedforward compensation for complex coupled nonlinearities and strong integral suppression of unknown external disturbances.

[0056] This invention significantly reduces pressure overshoot and convergence time during the pressure build-up stage of the stretching pad, and substantially improves the horizontal attitude synchronization accuracy and constant force holding stability of multi-cylinder presses under strong off-center load disturbances. It effectively avoids defects such as abnormal die wear, sheet metal cracking, and wrinkling caused by uneven force or dynamic tilting, directly improving the forming quality of large-tonnage complex stamped parts. It provides an effective solution for overcoming the bottleneck of the underlying core control technology of high-end multi-machine collaborative servo presses and achieving the domestic substitution of high-precision equipment. Attached Figure Description

[0057] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0058] Figure 1 This is a hardware system diagram corresponding to the method proposed in the embodiments of the present invention; Figure 2 These are comparison charts of the control results of a single hydraulic cylinder; where (a) is the displacement effect chart and (b) is the displacement error effect chart. Figure 3 This is a comparison chart of constant pressure error during the pressure build-up process; Figure 4 The following is a comparison chart of the control error results of the method proposed in this invention applied to the coordinated motion control of four hydraulic cylinders; (a) is the control error result of the first hydraulic cylinder; (b) is the control error result of the second hydraulic cylinder; (c) is the control error result of the third hydraulic cylinder; (d) is the control error result of the fourth hydraulic cylinder. Figure 5 The following is a comparison chart of the control error results of the traditional PID algorithm applied to the coordinated motion control of four hydraulic cylinders; (a) is the control error result of the first hydraulic cylinder; (b) is the control error result of the second hydraulic cylinder; (c) is the control error result of the third hydraulic cylinder; (d) is the control error result of the fourth hydraulic cylinder. The diagram exaggerates the spacing or dimensions between parts to show their positions; the diagram is for illustrative purposes only.

[0059] 1. Stamping controller; 2. Servo pad controller; 3. Stamping machine; 4. Hydraulic pump; 5. Stretch pad; 6. Energy accumulator; 7. Check valve; 8. Hydraulic check valve; 9. Position sensor; 10. Pressure sensor; 11. Speed ​​sensor; 12. Hydraulic sensor; 13. Oil tank; Detailed Implementation It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0060] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless otherwise expressly indicated by the invention, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. As described in the background section, existing technologies have shortcomings. To address these technical problems, this invention proposes a hybrid control method and system for multi-machine collaborative stretching pad force and position in a servo stamping line. Addressing the high dynamic and high precision requirements of the servo stamping line during the pre-acceleration phase, the proposed algorithm's Actor neural network not only approximates the unmodeled complex nonlinear friction in each single-cylinder hydraulic system but also compensates for the strong mechanical coupling and off-center load disturbances generated during the synchronous downward movement of the four cylinders. The Critic neural network, on the other hand, evaluates the collaborative control performance in real-time online by strengthening the signal. Based on the aforementioned Actor-Critic structure design, this invention combines a recursive RISE control method to realize the core control architecture of the system. Subsequently, Lyapunov stability theory is used to prove that this control method can guarantee the asymptotic stability of the system under reasonable assumptions. Finally, experiments verify that this method exhibits high precision and high stability characteristics in terms of performance.

[0061] Example 1 In a typical embodiment of the present invention, such as Figure 1 As shown, this embodiment provides a multi-machine collaborative stretching pad force and position hybrid control method for servo stamping lines; The servo stamping line multi-machine collaborative stretching pad force and position control system corresponding to this embodiment adopts a pump-controlled asymmetric hydraulic cylinder architecture. The model mainly consists of three functional units: a stamping machine simulation execution unit, a stretching pad servo hydraulic drive unit, and a multi-source state perception and control unit.

[0062] Specifically, the stamping press simulation execution unit (active interference source) includes a stamping controller 1, a stamping press 3, and an oil tank 13. The stamping controller 1 employs basic PID closed-loop control logic to simulate the behavior of the actual stamping press's main controller, precisely controlling the downward displacement and speed trajectory of the upper die slide. The single-rod hydraulic cylinder model built on the upper hydraulic circuit of the stamping press 3 represents the main slide of the stamping press. It moves downward and makes mechanical contact with the lower stretching pad, providing significant dynamic impact and positional boundary constraints to the bottom stretching pad system. The oil tank 13 provides a normal pressure return and suction environment for the stamping press's hydraulic circuit.

[0063] Furthermore, the servo hydraulic drive unit for the stretch pad includes a servo pad controller 2, a hydraulic pump 4, a stretch pad 5, and an energy accumulator. 6. Check valve 7 and hydraulically controlled check valve 8; Servo Pad Controller 2: This is the core control algorithm module designed in this invention. It receives error signals from various sensors, processes them using the algorithm, and then outputs precise motor speed commands to the underlying hydraulic pump.

[0064] Hydraulic pump 4: As the underlying power source, its speed is controlled by servo pad controller 2. By adjusting the speed and direction of the hydraulic pump, real-time control of the flow and pressure of the lower hydraulic circuit is achieved.

[0065] Stretch pad 5: The physical equivalent model of a single cylinder in a four-cylinder multi-machine collaborative system is represented by an asymmetric hydraulic cylinder. The piston rod of the hydraulic cylinder supports upwards, bears the downward force of the press during the stamping contact stage, and achieves constant blank holder force output and compliant yielding under the drive of hydraulic pump 4.

[0066] The accumulator 6, check valve 7, and hydraulically controlled check valve 8 together form the oil replenishment and safety control circuit of the closed / semi-closed pump-controlled cylinder system. The accumulator 6 absorbs transient pressure pulsations in the system and provides energy buffering during the pressure build-up phase; the hydraulically controlled check valve 8, in conjunction with the check valve 7, achieves dynamic compensation and balance of unequal flow rates in the two chambers of the asymmetrical cylinder, preventing cavitation or overload in the system.

[0067] Furthermore, the multi-source state perception and control unit (information closed loop) includes a position sensor 9, a pressure sensor 10, a speed sensor 11, and a hydraulic sensor 12; the functions of each sensor are as follows: Position sensor 9: Real-time acquisition of the current absolute displacement of the piston rod of tension pad 5.

[0068] Pressure sensor 10 (contact force sensor): installed at the mechanical interaction node between the press 3 and the stretching pad 5, to monitor the actual physical contact force when the upper and lower dies are closed in real time.

[0069] Speed ​​sensor 11: Real-time acquisition of the movement speed of the piston rod of the stretch pad.

[0070] Hydraulic sensor 12: It is arranged in the rodless chamber and rod chamber pipeline of the hydraulic cylinder corresponding to the tension pad 5 to monitor the fluid pressure in the two chambers in real time.

[0071] The specific working principle of the servo stretching pad of the present invention is as follows: 1. Pre-acceleration phase The press 3 accelerates downward rapidly under the command of the press controller 1. At this time, the upper and lower dies have not yet made contact, and the servo pad controller 2 is in position control mode, controlling the hydraulic pump 4 to maintain the tension pad 5. The piston rod slowly accelerates downward under the command of the servo pad controller 2, at which time the contact force is 0.

[0072] 2. Pressure Building Phase The instant the press 3 strikes the stretching pad 5, the pressure sensor 10 detects an exponential surge in contact force. The hydraulic oil in the lower chamber of the stretching pad 5 is subjected to instantaneous and violent compression. Upon capturing this force signal, the servo pad controller 2 instantly switches from position control to force control, driving the hydraulic pump 4 to build up upward pressure.

[0073] 3. Constant pressure holding stage The press 3 continues to press down under high pressure to stretch and form the sheet metal. To ensure that the blank holder force is constant and does not overload, the stretching pad 5 moves down with the upper die and maintains constant pressure.

[0074] The method provided in this invention mainly targets the servo speed control of the underlying servo motor and hydraulic pump (i.e., the process in which the servo pad controller 2 in the figure simultaneously controls four hydraulic pumps 4). The purpose is to indirectly control the pressure and volume of the two chambers of the asymmetric hydraulic cylinder through extremely precise motor speed fine-tuning, thereby realizing the above-mentioned pre-acceleration, pressure building, and pressure holding processes to ensure the quality of the deep-drawn parts.

[0075] Specifically, in this embodiment Figure 1 The image only shows one set of equipment for the lower mold; in reality, controlling the lower mold typically involves multiple sets. Figure 1 The equipment shown in this embodiment is illustrated using four sets as an example. The dynamics of the inertial load of the electro-hydraulic position servo system proposed in this embodiment are as follows:

[0076] In the formula, This indicates the load and piston mass; the load mainly refers to the lower mold, and the piston refers to the piston corresponding to the asymmetric hydraulic cylinder after the stretching pad 5 is equivalent. This represents the displacement of piston i (i=1,2,3,4); since this invention is illustrated using four sets as an example, i=1,2,3,4; here, the downward direction of the piston is set as positive; Indicates the gravity coefficient; This represents the unmodeled nonlinear friction term; This represents the unknown rigid coupling force transmitted by other cylinders; specifically, if i=1, This refers to the coupling force exerted by the second, third, and fourth hydraulic cylinders on the first hydraulic cylinder. If i=2, It refers to the coupling force from the first, third, and fourth hydraulic cylinders to the second hydraulic cylinder; This represents the actual contact force between the piston and the lower die. This indicates an unknown disturbance in the system; This indicates the pressure caused by the hydraulic differential pressure inside the actuator cylinder, and its specific description is as follows:

[0077] In the formula , Let represent the areas of the rodless cavity and the rod cavity, respectively. , Let represent the pressure in the rodless cavity and the rod cavity. According to the fluid continuity equation, the dynamic differential equations of the pressure in the two cavities can be expressed as:

[0078]

[0079] In the formula: For the bulk modulus of oil, Indicates pump displacement. Indicates the pump speed. , These represent the modeling errors for rodless and rod-type cavities, respectively. , Let represent the time-varying volumes of the rodless cavity and the rod cavity, where:

[0080]

[0081] In the formula: This represents the initial volume of the rodless chamber in an asymmetric cylinder. The initial volume of the rod chamber in an asymmetric cylinder is represented by defining state variables. The system under study can be represented by the following state space:

[0082] In the formula: For the angular velocity of the servo motor, To account for lumped hydraulic leakage and unmodeled dynamic disturbances, the system characteristic nonlinear function is defined as follows:

[0083]

[0084] Assumption 1: Disturbance as well as Sufficiently smooth and bounded, satisfying:

[0085] in , , , The given positive constant is .

[0086] This embodiment provides a multi-machine collaborative stretching pad force and position hybrid control method for a servo stamping line. Its control architecture is designed for a four-cylinder asymmetric hydraulic system and mainly includes the following three cascaded control execution modules: (1) Outer loop admittance compliant trajectory reconstruction module S1. Construct an outer loop admittance compliant trajectory reconstruction module, which receives the target reference trajectory and target loading force set by the system, performs compliant yielding calculations based on the actual loading force, and outputs the reconstructed reference trajectory. The specific steps are as follows: S11. Define the second-order differential equation of the admittance of the i-th asymmetric cylinder (i=1,2,3,4):

[0087] in, , , These are the parameters of the virtual mass, virtual damping, and virtual stiffness matrix, respectively. This represents the actual contact force between the piston and the lower die. The ideal contact force between the piston and the lower die is given; the compensating displacement is obtained by solving this second-order differential equation. Compensation speed and compensation acceleration .

[0088] S12. Based on the compensated displacement, compensated velocity, and compensated acceleration, generate the reconstructed reference trajectory and its derivative:

[0089]

[0090]

[0091] In the formula, , , These are the original target reference displacement, velocity, and acceleration, respectively. , , These are the reconstructed reference displacement, velocity, and acceleration, respectively.

[0092] (2) Asymmetric cylinder dynamic surface feedback linearization control module S2. Construct a kinematic control module based on RISE and Actor-Critie observers, receive the reconstructed reference trajectory, and calculate the virtual control law through state feedback and reinforcement learning network to suppress multi-cylinder rigid coupling disturbances. The specific steps are as follows: S21. Define position tracking error With filter tracking error :

[0093]

[0094] In the formula, Let i be the actual displacement of the i-th asymmetric cylinder. Positive feedback gain; S22. Define auxiliary variables as follows:

[0095] In the formula It is a positive gain. Combining the above equation, we can obtain:

[0096] S23. Define hydraulic equivalent acceleration tracking error :

[0097] The hydraulic pressure provides the piston with acceleration; This is a virtual control law, which is calculated in step S24.

[0098] S24. Construct the first-level RISE feedback control term and calculate the virtual control law. :

[0099]

[0100] in for The estimator; where, and It is a positive constant control gain.

[0101] S241. Define the lumped nonlinear dynamics of the system as:

[0102] S242. Based on the generalized function approximation property of neural networks, the lumped nonlinear dynamics of the system are expressed as:

[0103] In the formula, The global state input vector contains the reconstructed trajectory of the four cylinders; It is a bounded activation function. For function reconstruction residual error, For ideal bounded weights; and ideal weights are bounded, i.e.

[0104] in It is a known positive matrix.

[0105] S243. Set the output estimate of the Actor network. for:

[0106] In the formula, These are the actual estimated weights of the Actor network; S244. The system's filtering tracking error As an evaluation reinforcement signal for the Critic network, an adaptive weight update law is designed:

[0107] In the formula, It is a positive definite diagonal learning rate matrix. A robust adaptive leakage factor; The error between the estimated weights and the ideal weights is defined as follows:

[0108] S25. Then define the auxiliary variables. as follows

[0109] In the formula Combining the above formula, we get:

[0110] S26. Combining the second-stage RISE feedback control term, design a dynamic surface feedback linearization control law to output the final servo motor angular velocity input command. :

[0111]

[0112] in and It is a positive constant control gain.

[0113] To comprehensively consider kinematic errors, hydraulic dynamic errors, neural network weight estimation errors, and the energy state of the RISE robust integral term, the following positive definite composite Lyapunov candidate function is constructed. as follows:

[0114] in: , As long as a sufficiently large nonlinear control gain is selected, Heng was established.

[0115] right Differentiation yields:

[0116] By Young's theorem, we can obtain:

[0117] As can be seen from the definition, There is a boundary, so:

[0118] in Define the positive definite convergence constant. ,but:

[0119]

[0120] This proves that all states and tracking errors in the system are semi-globally uniformly eventually bounded (SGUUB), and the steady-state error is strictly limited to... The tight layout ensures the system's ultra-high precision tracking performance.

[0121] The experimental verification process of the method proposed in this invention is as follows: In this invention, the effectiveness of the proposed controller was demonstrated experimentally. The trajectory tracked by the controller is as follows: Figure 2 As shown in (a), the curve encompasses motion processes including variable acceleration, uniform speed, and horizontal stability, covering the entire actual processing procedure. Specific experimental details are as follows: (1) Experiment 1 Figure 2 The results of single hydraulic cylinder control are compared, where (a) is the displacement effect diagram and (b) is the displacement error effect diagram. Depend on Figure 2 As can be seen from the single-cylinder basic trajectory tracking response curve, in the combined tracking process of speed and position, the method proposed in this invention exhibits superior performance that comprehensively surpasses traditional PID algorithms in both transient response speed and steady-state tracking accuracy. Especially... Figure 2In the horizontal position holding (position maintenance) stage shown in (a), the traditional PID algorithm, lacking an understanding of the time-varying volume and frictional nonlinearity of the asymmetric hydraulic cylinder, relies solely on error feedback for adjustment, resulting in significant micro-amplitude oscillations and position drift during the steady-state phase. In contrast, the proposed algorithm exhibits extremely high static stiffness and disturbance resistance stability during the horizontal position holding stage, fully demonstrating the effectiveness of the proposed underlying controller in handling strong electromechanical-hydraulic nonlinear coupling.

[0122] (2) Experiment 2 like Figure 3 As shown, in the dynamic pressure build-up phase at the moment of impact contact, the proposed control algorithm exhibits significantly superior transient response and steady-state tracking performance compared to traditional PID controllers. Traditional PID algorithms, lacking feedforward understanding of the physical characteristics of asymmetric hydraulic cylinders, rely solely on simple error feedback for lag adjustment, resulting in slow response to sudden high-flow-rate pressure build-up demands and a high risk of pressure overshoot and oscillation. In contrast, the proposed algorithm not only significantly shortens the pressure build-up convergence time but also greatly suppresses the steady-state pressure error.

[0123] (3) Experiment 3 Table 1. Statistics of average / maximum error in the coordinated motion of four hydraulic cylinders.

[0124] Figure 4 This is a diagram showing the four-cylinder tracking error under the control algorithm proposed in this invention. Figure 5 This refers to the tracking error of the four-cylinder system under the PID control algorithm; for example... Figure 4 As shown in the synchronization error evolution curve and the quantitative indicators in Table 1, for the four-cylinder coordinated control of the servo stretching pad under complex off-center load conditions, traditional methods are prone to severe motion asynchrony between cylinders when facing strong mechanical coupling of the stamping slider and asymmetric off-center load impact, leading to dynamic tilting of the stretching pad. The proposed method demonstrates excellent horizontal plane attitude stabilization capability, and its synchronization accuracy and disturbance rejection robustness comprehensively surpass traditional control strategies.

[0125] Example 2 Based on the servo stamping line multi-machine cooperative stretching pad force-position hybrid control method disclosed in the embodiments, this embodiment provides a servo stamping line multi-machine cooperative stretching pad force-position hybrid control system, including: The first module is configured to construct the outer loop admittance compliant trajectory reconstruction module, obtain the target reference trajectory and target loading force set by the system, perform compliant yielding calculation based on the actual loading force, and output the reconstructed reference trajectory; The second module is configured to receive the reconstructed reference trajectory and compute a virtual control law through a robust feedback linearization control RISE and an ACtor-Critie reinforcement learning network to suppress multi-cylinder rigid coupling disturbances.

[0126] As a further technical solution, the first module specifically includes: The definition module is configured to define the second-order differential equation of the admittance of the i-th hydraulic cylinder:

[0127] in, , , These are the parameters of the virtual mass, virtual damping, and virtual stiffness matrix, respectively. This represents the actual contact force between the piston and the lower die. The ideal contact force between the piston and the lower die; Compensation displacement, Compensation speed; Compensation acceleration; The reconstruction module is configured to generate a reconstructed reference trajectory and its derivative based on the compensated displacement, compensated velocity, and compensated acceleration.

[0128]

[0129]

[0130] In the formula, , , These are the original target reference displacement, velocity, and acceleration, respectively. , , These are the reconstructed reference displacement, velocity, and acceleration, respectively.

[0131] As a further technical solution, the second module includes: The first definition module is configured to define the position tracking error. With filter tracking error :

[0132]

[0133] In the formula, This represents the actual displacement of the i-th hydraulic cylinder. Positive feedback gain; The second definition module is configured to define auxiliary variables. as follows:

[0134] In the formula , It is a positive gain; calculations show that:

[0135] in, and It is a positive constant control gain; The third definition module is configured to define the hydraulic equivalent acceleration tracking error. :

[0136] The virtual control law obtained through calculation; The first building module is configured to construct the first-level RISE feedback control term and calculate the virtual control law. :

[0137]

[0138] in for The estimate; The fourth definition module is configured to define auxiliary variables. as follows:

[0139] Calculation yields:

[0140] The second building module is configured to construct the second-level RISE feedback control term, design the dynamic surface feedback linearization control law, and output the final servo motor angular velocity input command. :

[0141]

[0142] in and It is a positive constant control gain.

[0143] As a further technical solution, the aforementioned The module for determining the estimated quantity includes: The first submodule is configured to define the system's lumped nonlinear dynamics as follows:

[0144] The second submodule is configured to use the generalized function approximation property based on neural networks, and is expressed as follows:

[0145] In the formula, For the unmodeled nonlinear friction term, The unknown rigid coupling force transmitted to other cylinders. Equivalent mass of the lower mold; The global state input vector contains the reconstructed trajectory of the four cylinders; It is a bounded activation function. For function reconstruction residual error, For ideal bounded weights; The third submodule is configured to set the output estimate of the Actor network. for:

[0146] In the formula, These are the actual estimated weights of the Actor network; The fourth submodule is configured to track the system's filtered error. As an evaluation reinforcement signal for the Critic network, an adaptive weight update law is designed:

[0147] In the formula, It is a positive definite diagonal learning rate matrix. This is a robust adaptive leakage factor.

[0148] This embodiment addresses the rigid impact and pressure overshoot issues caused by direct force-position switching during the stamping contact of servo tension pads. It utilizes an outer-loop admittance compliant trajectory reconstruction module to dynamically correct the reference trajectory based on the actual contact force, achieving a smooth pressure transition from "rigid resistance" to "flexible compliance." Furthermore, it addresses the issues of four-cylinder synchronization misalignment and decreased tracking accuracy under multi-cylinder coordinated downward and off-center load conditions, caused by strong mechanical coupling, unmodeled friction, and strong nonlinearity of the hydraulic system. This is achieved by introducing an Actor-Critic reinforcement learning network based on global state awareness and a recursive RISE robust feedback linearization control architecture, enabling precise feedforward compensation for complex coupled nonlinearities and strong integral suppression of unknown external disturbances.

[0149] Example 3 This embodiment provides a computer-readable storage medium storing a computer program thereon, which, when executed, implements the servo stamping line multi-machine collaborative stretching pad force-position hybrid control method described in Embodiment 1.

[0150] Example 4 This embodiment provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, wherein when the program instructions are executed by a computer, the computer executes the servo stamping line multi-machine collaborative stretching pad force-position hybrid control method described in Embodiment 1.

[0151] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0152] In the embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between devices or units through some interfaces, and may be electrical, mechanical, or other forms.

[0153] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0154] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0155] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0156] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for hybrid control of force and position of multi-machine collaborative stretching pad in a servo stamping line, characterized in that, Includes the following steps: Step S1: Obtain the target reference trajectory and target loading force set by the system, and perform compliant yielding calculation based on the actual loading force to output the reconstructed reference trajectory; Step S2: Receive the reconstructed reference trajectory, and calculate the virtual control law through robust feedback linearization control RISE and Actor-Critie reinforcement learning network to suppress multi-cylinder rigid coupling disturbances; Step S1 includes the following steps: S11. Define the second-order differential equation for the admittance of the i-th hydraulic cylinder: In the formula, , , These are the parameters of the virtual mass, virtual damping, and virtual stiffness matrix, respectively. This represents the actual contact force between the piston and the lower die. The ideal contact force between the piston and the lower die; Compensation displacement, Compensation speed; Compensation acceleration; S12. Based on the compensated displacement, compensated velocity, and compensated acceleration, generate the reconstructed reference trajectory and its derivative: In the formula, , , These are the original target reference displacement, velocity, and acceleration, respectively. , , These are the reconstructed reference displacement, velocity, and acceleration, respectively. Step S2 includes the following steps: S21. Define position tracking error With filter tracking error : In the formula, Let i be the actual displacement of the i-th asymmetric cylinder. Positive feedback gain; for The derivative; S22. Define auxiliary variables as follows: In the formula Positive feedback gain; for The derivative of can be calculated as follows: In the formula, This represents the unmodeled nonlinear friction term; This represents the unknown rigid coupling force transmitted by other cylinders. This is the actual contact force between the piston and the lower die. This represents an unknown disturbance in the system. This indicates the pressure caused by the hydraulic differential pressure inside the actuator cylinder; This indicates the load and piston mass; Indicates the gravity coefficient; S23. Define hydraulic equivalent acceleration tracking error : In the formula, The hydraulic pressure provides acceleration to the piston: For virtual control laws; S24. Construct the first-level RISE feedback control term and calculate the virtual control law. : In the formula: ; for The estimate; and It is a positive constant control gain; t represents the control time; S25. Define auxiliary variables as follows: In the formula: It is a positive number; for The derivative; Calculation yields: In the formula: Input for the angular velocity of the servo motor; This includes lumped hydraulic leakage and unmodeled dynamic disturbances; For the bulk modulus of oil, Indicates pump displacement; , These represent the areas of the rodless cavity and the rod cavity, respectively; , These represent the time-varying volumes of the rodless cavity and the rod cavity, respectively; S26. Construct a second-stage RISE feedback control term, design a dynamic surface feedback linearization control law, and output the final servo motor angular velocity input. : In the formula, ; and It is a positive constant control gain; t is the control time.

2. The servo stamping line multi-machine collaborative stretching pad force and position hybrid control method as described in claim 1, characterized in that, In step S24, Methods for determining the estimated quantity: S241. Define the lumped nonlinear dynamics of the system as: S242. The generalized function approximation property based on neural networks is expressed as follows: In the formula, For the unmodeled nonlinear friction term, The unknown rigid coupling force transmitted to other cylinders. Equivalent mass of the lower mold; The global state input vector contains the reconstructed trajectory of the four cylinders; It is a bounded activation function. For function reconstruction residual error, For ideal bounded weights; S243. Set the output estimate of the Actor network. for: In the formula, These are the actual estimated weights of the Actor network; S244. The system's filtering tracking error As an evaluation reinforcement signal for the Critic network, an adaptive weight update law is designed: In the formula, It is a positive definite diagonal learning rate matrix. This is a robust adaptive leakage factor.

3. A servo stamping line multi-machine collaborative stretching pad force-position hybrid control system, characterized in that, include: The first module is configured to construct the outer loop admittance compliant trajectory reconstruction module, obtain the target reference trajectory and target loading force set by the system, perform compliant yielding calculation based on the actual loading force, and output the reconstructed reference trajectory; The second module is configured to receive the reconstructed reference trajectory and compute a virtual control law through a robust feedback linearization control RISE and an ACtor-Critie reinforcement learning network to suppress multi-cylinder rigid coupling disturbances. The first module specifically includes: The definition module is configured to define the second-order differential equation of the admittance of the i-th hydraulic cylinder: In the formula, , , These are the parameters of the virtual mass, virtual damping, and virtual stiffness matrix, respectively. This represents the actual contact force between the piston and the lower die. The ideal contact force between the piston and the lower die; Compensation displacement, Compensation speed; Compensation acceleration; The reconstruction module is configured to generate a reconstructed reference trajectory and its derivative based on the compensated displacement, compensated velocity, and compensated acceleration. In the formula, , , These are the original target reference displacement, velocity, and acceleration, respectively. , , These are the reconstructed reference displacement, velocity, and acceleration, respectively. The second module includes: The first definition module is configured to define the position tracking error. With filter tracking error : In the formula, This represents the actual displacement of the i-th hydraulic cylinder. Positive feedback gain; for The derivative; The second definition module is configured to define auxiliary variables. as follows: In the formula, , Positive gain; for The derivative; calculation yields: In the formula, This represents the unmodeled nonlinear friction term; This represents the unknown rigid coupling force transmitted by other cylinders. This is the actual contact force between the piston and the lower die. This represents an unknown disturbance in the system. This indicates the pressure caused by the hydraulic differential pressure inside the actuator cylinder; This indicates the load and piston mass; Indicates the gravity coefficient; The third definition module is configured to define the hydraulic equivalent acceleration tracking error. : In the formula, The hydraulic pressure provides acceleration to the piston: For virtual control laws; The first building module is configured to construct the first-level RISE feedback control term and calculate the virtual control law. : In the formula: ; for The estimate; and It is a positive constant control gain; t represents the control time; The fourth definition module is configured to define auxiliary variables. as follows: In the formula: It is a positive number; for The derivative; Calculation yields: In the formula: Input for the angular velocity of the servo motor; This includes lumped hydraulic leakage and unmodeled dynamic disturbances; For the bulk modulus of oil, Indicates pump displacement; , These represent the areas of the rodless cavity and the rod cavity, respectively; , These represent the time-varying volumes of the rodless cavity and the rod cavity, respectively; The second building module is configured to construct the second-level RISE feedback control term, design the dynamic surface feedback linearization control law, and output the final servo motor angular velocity input command. : In the formula, ; and It is a positive constant control gain; t is the control time.

4. The servo stamping line multi-machine collaborative stretching pad force and position hybrid control system as described in claim 3, characterized in that, The module for determining the estimated quantity includes: The first submodule is configured to define the system's lumped nonlinear dynamics as follows: The second submodule is configured to use the generalized function approximation property based on neural networks, and is expressed as follows: In the formula, For the unmodeled nonlinear friction term, The unknown rigid coupling force transmitted to other cylinders. Equivalent mass of the lower mold; The global state input vector contains the reconstructed trajectory of the four cylinders; It is a bounded activation function. For function reconstruction residual error, For ideal bounded weights; The third submodule is configured to set the output estimate of the Actor network. for: In the formula, These are the actual estimated weights of the Actor network; The fourth submodule is configured to track the system's filtered error. As an evaluation reinforcement signal for the Critic network, an adaptive weight update law is designed: In the formula, It is a positive definite diagonal learning rate matrix. This is a robust adaptive leakage factor.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the servo stamping line multi-machine collaborative stretching pad force-position hybrid control method according to any one of claims 1-2.

6. A computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, characterized in that, When the program instructions are executed by the computer, the computer performs the servo stamping line multi-machine collaborative stretching pad force and position hybrid control method according to any one of claims 1-2.

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