A method for optimizing the control of the hot stamping motion curve based on a sliding mode controller

Abstract

The present invention discloses a hot stamping motion curve optimization control method based on a sliding mode controller. The present invention designs a hot stamping motion system by combining the hot stamping forming process, and proposes a smooth motion control scheme based on motion curve optimization, and establishes a quintic curve motion model; an improved particle swarm algorithm is used to optimize the impact-free motion curve, and a sliding mode controller is designed; simulation and experiments prove that under the quintic curve motion control scheme, the motion shock and vibration are effectively reduced. Compared with the traditional motion control scheme, the comprehensive motion accuracy is improved by 60%, and the comprehensive speed mutation is reduced by 50%, which effectively improves the reliability of the movable crossbeam movement during the hot stamping process. Therefore, the present invention can meet the requirements of motion accuracy and speed stability in the hot stamping motion process, and achieve a stable motion state in the hot stamping process and high-quality and high-efficiency production of products.

Description

Technical Field

[0001] The present invention belongs to the technical field of hot stamping, and in particular relates to a hot stamping motion curve optimization control method based on a sliding mode controller. Background Art

[0002] With the development of lightweight vehicles and new energy vehicles, hot stamping has become one of the most promising manufacturing technologies for lightweight vehicles. However, hydraulic presses experience multiple speed inflection points during production, leading to issues such as chattering, noise, and unstable forming speeds. Therefore, ensuring the stability of hydraulic presses is crucial for ensuring product quality in hot stamping production.

[0003] The design of flexible systems is a factor that affects high-quality and high-efficiency production, and optimal control has become an important research direction. Gao By establishing a multi-objective optimization scheme for stamping speed, etc., the control of stamping energy consumption and stability has been achieved to a certain extent. Chao designed a hierarchical controller, which achieved high fault-tolerant control of execution failures, external disturbances and model uncertainties, and achieved good accuracy and dynamic balance control effects.

[0004] In addition, the optimization of motion trajectory can provide a stable motion solution for the system. Varga The motion trajectory of the robot arm was optimized by considering the global constraints and a relatively stable motion state was obtained. Li The motion error curve was optimized and designed, and the forming time and quality were effectively improved. Kuo By comparing the motion curves, the best motion parameter combination is obtained, and the motion curves are optimized to obtain better forming time and quality.

[0005] Du The impact-free fastest descent curve was analyzed and optimized, and a fifth-order polynomial motion curve was found to be effective, significantly reducing the impact of the movable crossbar during its descent. For the subsequent stages of the stamping motion, impact and other issues remain key factors affecting forming quality, requiring further optimization of the entire stamping motion curve. Comprehensive analysis of motion curve optimization solutions has yielded promising results in this study, but widespread and effective application in hydraulic press motion schemes still requires extensive research. Summary of the Invention

[0006] In response to the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a hot stamping motion curve optimization control method based on a sliding mode controller, which solves the technical problems such as impact and vibration caused by sudden changes in speed during the movement of the movable crossbeam in the existing hot stamping production process.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A hot stamping motion curve optimization control method based on a sliding mode controller comprises the following steps:

[0009] S1. Modeling and analysis of hot stamping motion system:

[0010] S11. Design a hot stamping motion system, the system comprising:

[0011] The accumulator is used to charge energy when the system is running and release energy when the system pressure falls below the set pressure of the accumulator;

[0012] The pump group is used to supply oil to the system, and the oil circuit at the pump group outlet is connected to the accumulator;

[0013] Lower oil tank, used to store the hydraulic oil of the system and provide hydraulic oil to the upper oil tank;

[0014] Overflow valve 1 is used to stabilize the pressure at the outlet of the system pump group and plays a protective role. One end of the overflow valve is connected to the oil return line and the other end is connected to the lower oil tank;

[0015] The protection valve group is used to quickly return oil and relieve pressure when the system stops or fails. One end of the valve group is connected to the oil circuit and the other end is connected to the lower oil tank.

[0016] The plug-in valve group is used to adjust the oil volume at the oil supply end of the system pump group and to buffer the impact on the high-frequency response proportional servo valve;

[0017] High-frequency response cartridge valve group is used to accurately control the return oil flow rate and stabilize the speed of the hydraulic cylinder;

[0018] High-frequency proportional servo valve is used to precisely adjust the oil flow at the hydraulic cylinder's oil inlet to achieve precise control of the hydraulic cylinder's stroke;

[0019] Overflow valve 2 is used to protect the hydraulic cylinder oil inlet pipeline from overflow. One end of the valve is connected to the oil inlet pipeline, and the other end is directly connected to the lower oil tank.

[0020] Overflow valve 3 is used to protect the hydraulic cylinder oil return line from overflow. One end of the valve is connected to the oil return line and the other end is connected to the lower oil tank.

[0021] The data processing module is used to collect pressure and displacement signals, perform comprehensive processing on the collected pressure and displacement signals, make judgments, and feed back the valve group opening and closing control signals to control the displacement of the hydraulic cylinder;

[0022] Pressure sensor 1 is used to measure the pressure at the oil inlet of the hydraulic cylinder. One end of the pressure sensor is connected to the oil inlet line, and the other end is connected to the data processing module.

[0023] The charging valve is used to quickly supply hydraulic oil to the hydraulic cylinder to ensure stable speed; the upper oil tank is located at the top of the system and is used to store oil for the charging valve;

[0024] The displacement sensor is used to feedback the displacement signal of the hydraulic cylinder. It is installed inside the hydraulic cylinder and extends a signal line to connect to the data processing module;

[0025] Hydraulic cylinder, used as the actuator of the hot stamping motion system;

[0026] Pressure sensor 2 is used to measure the pressure at the oil outlet of the hydraulic cylinder. One end of the pressure sensor is connected to the oil return line, and the other end is connected to the data processing module.

[0027] S12. Modeling and analyzing the hot stamping motion system, and obtaining the open-loop transfer function when the hydraulic cylinder moves downward is as shown in the following formula (10): (10)

[0028] in, ;

[0029] S2. Use the improved particle swarm optimization algorithm to perform multi-constraint optimization on the motion curve of the hot stamping forming motion system, obtain the fifth-order polynomial motion displacement curve equation, and establish the fifth-order curve motion model;

[0030] S3. Design a sliding mode controller.

[0031] Preferably, in step S12, modeling and analyzing the hot stamping motion system includes the following steps:

[0032] S121. Assuming that the connecting pipes of the hot stamping forming motion system and the high-frequency response proportional servo valve are in ideal conditions, the internal and external leakage are laminar flows, and the load force is defined as the reaction force during forming. Elastic load, viscous load, and inertial force are ignored. The linearized flow equation of the high-frequency response proportional servo valve, the flow continuity equation of the hydraulic cylinder, and the force balance equation are obtained as shown in the following equations (1), (2), and (3), respectively:

[0033] (1)

[0034] (2)

[0035] (3)

[0036] in, is the load flow, ; is the spool displacement of the servo valve, ; is the flow coefficient, ; is the flow pressure coefficient, ; is the load pressure, ; is the effective working area of the piston in the rodless cavity of the hydraulic cylinder, ; is the effective displacement output of the piston rod, ; is the external leakage coefficient of the hydraulic cylinder, ; is the leakage coefficient of the hydraulic cylinder, ; is the rodless chamber pressure of the hydraulic cylinder, ; is the rod chamber pressure of the hydraulic cylinder, ; is the effective volume of the rodless chamber of the hydraulic cylinder, ; is the effective bulk elastic modulus, ; is the effective working area of the piston in the rod cavity of the hydraulic cylinder, ; is the total mass of the piston and slider, ; is the load spring stiffness, ; is the external load acting on the piston, ;

[0037] S122, according to equations (1), (2) and 3, the total output displacement of the valve-controlled asymmetric cylinder is obtained , specifically expressed as follows (4):

[0038] (4);

[0039] Since the energy loss caused by viscous friction in the system is negligible, Equation (4) is simplified to the following Equation (5):

[0040] (5)

[0041] in, is the natural frequency of the hydraulic cylinder; is the hydraulic damping ratio, which is generally 0.1 to 0.2;

[0042] S123. Based on formula (5), the transfer function of the output displacement of the hydraulic cylinder to the given output displacement of the high-frequency response proportional servo valve and the transfer function of the output displacement of the hydraulic cylinder to the given load force of the high-frequency response proportional servo valve are further obtained as shown in the following formulas (6) and (7):

[0043] (6)

[0044] (7);

[0045] S124, due to the current of the servo proportional amplifier With input voltage Approximately proportional, so the servo proportional amplifier gain K a The mathematical model is shown in the following formula (8):

[0046] (8);

[0047] Further establish the displacement sensor gain K f The mathematical model is shown in the following formula (9):

[0048] (9)

[0049] in, is the feedback current signal, V; is the displacement of the hydraulic cylinder piston, m; further, the open-loop transfer function of the system when the hydraulic cylinder moves downward is obtained.

[0050] Preferably, in step S2, the improved particle swarm algorithm is used to perform multi-constraint optimization on the motion curve of the hot stamping motion system to obtain a quintic polynomial motion displacement curve equation, and the specific steps are:

[0051] A21. The jerk of the motion trajectory is introduced as a constraint condition. According to the conditions and parameters set by the system, the matrix expressions of displacement, velocity, acceleration and jerk are obtained as shown in the following formula (11):

[0052] (11)

[0053] in, 、 、 、 、 are the initial motion displacement, velocity, acceleration, jerk and time of the movable beam, 、 、 、 、 are the displacement, velocity, acceleration, jerk and time when the movable beam stops moving. a 0. a 1. a 2. a 3. a 4 and a 5 is the polynomial coefficient;

[0054] A22. Analyze the motion state according to formula (11) and determine the optimization constraint equation group as shown in the following formula (12):

[0055] (12)

[0056] A23. The improved particle swarm algorithm is used to perform multi-constraint optimization on the motion curve of the hot stamping motion system, and the fifth-order polynomial motion displacement curve shown in formula (13) is obtained: (13).

[0057] Preferably, in step S3, the sliding mode controller is designed by the following steps:

[0058] First, according to the control strategy of the hot stamping motion system, the state space equation is constructed, and the system error function and sliding surface are defined. The expressions are shown in the following equations (14), (15), and (16):

[0059] (14)

[0060] (15)

[0061] (16)

[0062] in, x is the output displacement of the hydraulic cylinder; P 1 is the rodless chamber pressure of the hydraulic cylinder; e is the difference between the expected displacement and the actual displacement; is the expected displacement value; Switching function for sliding mode controller; 、 、 is the switching function coefficient;

[0063] Furthermore, combined with the constant velocity reaching law expressed in the following equation (17), the control rate can be obtained from equations (15) and (16): , which is expressed as the following formula (18):

[0064] (17)

[0065] (18)

[0066] Then, from equations (1), (2) and (3), we can derive the following equation (19):

[0067] (19)

[0068] Finally, combining equations (15), (16) and (17), we can get and , the specific expression is shown in the following formula (20):

[0069] (20).

[0070] According to equations (14)-(20), the Lyapunov function is defined as , and according to the judgment conditions , after transformation, we get ; Therefore, the function converges, and the above settings are reasonable and meet the control requirements.

[0071] The present invention has the following beneficial effects:

[0072] The present invention designs a hot stamping motion system by combining it with the hot stamping process, proposes a smooth motion control scheme based on motion curve optimization, and establishes a quintic curve motion model; uses an improved particle swarm algorithm to optimize the impact-free motion curve, and designs a sliding mode controller; through simulation and experiments, it is proved that the quintic curve motion control scheme effectively reduces motion shock and vibration. Compared with the traditional motion control scheme, the motion accuracy is improved by 60%, and the speed mutation is reduced by 50%, which effectively improves the reliability of the movable crossbeam movement during the hot stamping process. Therefore, the present invention can meet the requirements of motion accuracy and speed stability in the hot stamping motion process, achieve a stable motion state in the hot stamping process, and achieve high-quality and high-efficiency production of products. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0074] Figure 1 This is the traditional motion curve diagram of a high-speed hot stamping hydraulic press;

[0075] Figure 2 Schematic diagram of the structure of the hot stamping motion system designed in Example 1;

[0076] Figure 3 Transfer block diagram for high-frequency response proportional servo valve controlled hydraulic cylinder control system;

[0077] Figure 4 This is the schematic diagram of the simulation control system;

[0078] Figure 5 Displacement tracking error curves under traditional motion control scheme and quintic curve motion control scheme Figure 1 ;

[0079] Figure 6 The displacement and velocity curves under the traditional motion control scheme Figure 1 ;

[0080] Figure 7 The displacement and velocity curves under the quintic curve motion control scheme Figure 1 ;

[0081] Figure 8 Displacement tracking error curves under traditional motion control scheme and quintic curve motion control scheme Figure 2 ;

[0082] Figure 9 Displacement and velocity curves under traditional motion control scheme Figure 2 ;

[0083] Figure 10 The displacement and velocity curves under the quintic curve motion control scheme Figure 2 ;

[0084] Figure numerals: 1. Accumulator; 2. Pump group; 3. Lower oil tank; 4. Overflow valve 1; 5. Protection valve group; 6. Cartridge valve group; 7. High-frequency response cartridge valve group; 8. High-frequency response proportional servo valve; 9. Overflow valve 2; 10. Overflow valve 3; 11. Data processing module; 12. Pressure sensor 1; 13. Filling valve; 14. Upper oil tank; 15. Displacement sensor; 16. Hydraulic cylinder; 17. Pressure sensor 2. DETAILED DESCRIPTION

[0085] In the following description, specific details such as particular system structures and techniques are provided for purposes of illustration, not limitation, to facilitate a thorough understanding of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.

[0086] Example 1

[0087] Reference Figure 1 , a hot stamping motion curve optimization control method based on a sliding mode controller, comprising the following steps:

[0088] S1. Modeling and analysis of hot stamping motion system:

[0089] Reference Figure 1, is the traditional motion curve of the high-speed hot stamping hydraulic press. It can be seen that the overall motion process of the high-speed hot stamping hydraulic press is divided into five stages, namely, the fast descent stage from T1 to T2, the deceleration forming stage from T2 to T5, the pressure holding stage from T5 to T6, the mold opening stage from T6 to T7, the fast return stage from T7 to T8, and the deceleration slow return stage from T8 to T9. For the descending forming stage, the high-speed falling stage is relatively long, so a large impact and shaking phenomenon will occur at the deceleration turning point. The traditional solution adopts multi-point turning to reduce the speed of the turning change at point T2, but it still causes problems such as impact at the multi-point turning point. Therefore, in order to reduce the motion impact of fast descent and pressing during forming, the present invention first analyzes and designs the hot stamping forming motion system in the motion scheme.

[0090] In order to effectively study the fast-drop and pressing motion process, the present invention extracts and improves the traditional hydraulic system and provides a hot stamping forming motion system. Figure 2The system includes: an accumulator 1, which is used to charge energy when the system is running and release energy when the system pressure is lower than the set pressure of the accumulator 1; a pump group 2, which is used to supply oil to the system, and the oil circuit at the outlet of the pump group 2 is connected to the accumulator 1; a lower oil tank 3, which is used to store the hydraulic oil of the system and provide hydraulic oil to the upper oil tank 14; a relief valve 4, which is used to stabilize the pressure at the outlet of the system pump group 2 and play a protective role, one end of which is connected to the return oil circuit and the other end is connected to the lower oil tank 3; a protection valve group 5, which is used to quickly return oil and relieve pressure when the system stops or fails, and one end of which is connected to The other end is connected to the lower oil tank 3; the cartridge valve group 6 is used to adjust the oil volume at the oil supply end of the system pump group 2, and has a buffering effect on the impact of the high-frequency response proportional servo valve 8; the high-frequency response cartridge valve group 7 is used to accurately control the return oil flow rate, and has the effect of stably adjusting the speed of the hydraulic cylinder 16; the high-frequency response proportional servo valve 8 is used to accurately adjust the oil replenishment flow at the oil inlet of the hydraulic cylinder 16, so as to achieve precise control of the stroke of the hydraulic cylinder 16; the overflow valve 9 is used to protect the oil inlet pipeline of the hydraulic cylinder 16 from overflow, and one end of it is connected to the oil inlet circuit, and the other end is connected to the oil inlet circuit. One end is connected to the lower oil tank 3; the overflow valve 3 10 is used to protect the return oil pipeline of the hydraulic cylinder 16 from overflow. One end of the overflow valve 10 is connected to the return oil line and the other end is connected to the lower oil tank 3; the data processing module 11 is used to collect pressure and displacement signals, perform comprehensive processing on the collected pressure and displacement signals and make judgments, and feedback output high-frequency response cartridge valve group 7 opening and closing control signals to control the displacement of the hydraulic cylinder 16; the pressure sensor 12 is used to measure the pressure at the oil inlet of the hydraulic cylinder 16. One end of the pressure sensor 12 is connected to the oil inlet line and the other end is connected to the data processing module. 11; a filling valve 13, used to quickly provide hydraulic oil to the hydraulic cylinder 16 to ensure stable speed; an upper oil tank 14, located at the top of the system, used to store oil for the filling valve 13; a displacement sensor 15, used to feed back the displacement signal of the hydraulic cylinder 16, which is installed inside the hydraulic cylinder 16, and extends a signal line to be connected to the data processing module; the hydraulic cylinder 16 is used as an actuator of the hot stamping forming motion system; a pressure sensor 17 is used to measure the pressure at the oil outlet of the hydraulic cylinder 16, one end of which is connected to the return oil circuit, and the other end is connected to the data processing module 11.

[0091] Here, the present invention uses a high-response proportional servo valve 8 to control the opening (closing) of the return oil line cartridge valve assembly 6, achieving precise flow control. The cartridge valve assembly 6 is installed at the oil inlet for rapid oil inflow, and the high-response proportional servo valve 8 is also installed for precise oil replenishment and speed control during the pressing process. Secondly, the built-in displacement sensor 15 and pressure sensor 1 12 and pressure sensor 2 17 directly feed signals back to the data processing module 11 for processing, achieving real-time and stable control of speed and pressure.

[0092] Based on the hot stamping motion system designed above, the dynamic characteristics of the hot stamping motion system when the movable crossbeam is rapidly lowered are analyzed. Specifically, according to the designed hot stamping motion system, the servo system block diagrams of the rapid lowering motion stage and the pressing stage are obtained, as shown in the figure. Figure 3 As shown. To facilitate the modeling and analysis of the system, it is assumed here that the hot stamping forming motion system connecting pipes and the high-frequency response proportional servo valve 8 are in an ideal state, and the internal and external leakage is laminar flow. In addition, the load force is defined as the reaction force during forming, ignoring elastic load, viscous load and inertia force, etc., and thus the linearized flow equation of the valve, the flow continuity equation of the hydraulic cylinder and the force balance equation can be obtained as shown in the following equations (1), (2) and (3) respectively:

[0093] (1)

[0094] (2)

[0095] (3)

[0096] in, is the load flow, ; is the spool displacement of the servo valve, ; is the flow coefficient, ; is the flow pressure coefficient, ; is the load pressure, ; is the effective working area of the piston in the rodless cavity of the hydraulic cylinder, ; is the effective displacement output of the piston rod, ; is the external leakage coefficient of the hydraulic cylinder, ; is the leakage coefficient of the hydraulic cylinder, ; is the rodless chamber pressure of the hydraulic cylinder, ; is the rod chamber pressure of the hydraulic cylinder, ; is the effective volume of the rodless chamber of the hydraulic cylinder, ; is the effective bulk elastic modulus, ; is the effective working area of the piston in the rod cavity of the hydraulic cylinder, ; is the total mass of the piston and slider, ; is the load spring stiffness, ; is the external load acting on the piston, .

[0097] The total output displacement of the valve-controlled asymmetric cylinder can be obtained from the above equations (1), (2) and (3): , specifically expressed as follows (4):

[0098] (4)

[0099] Since the energy loss caused by viscous friction in the system can be ignored, the above formula (4) can be simplified to the following formula (5):

[0100] (5)

[0101] in, is the natural frequency of the hydraulic cylinder; It is the hydraulic damping ratio, which is generally between 0.1 and 0.2.

[0102] According to formula (5), the transfer function of the output displacement of the hydraulic cylinder 16 to the given output displacement of the high-frequency response proportional servo valve and the transfer function of the output displacement of the hydraulic cylinder to the given load force of the high-frequency response proportional servo valve can be further obtained as shown in the following formulas (6) and (7):

[0103] (6)

[0104] (7)

[0105] In addition, due to the current of the servo proportional amplifier With input voltage Approximately proportional, servo proportional amplifier gain K a The mathematical model is shown in the following formula (8):

[0106] (8)

[0107] Further establish the displacement sensor gain K f The mathematical model is shown in the following formula (9):

[0108] (9)

[0109] in, is the feedback current signal, V; is the displacement of the hydraulic cylinder piston, m.

[0110] Therefore, through the above equations (1) to (9), the transmission block diagram of the high-frequency response proportional servo valve controlled hydraulic cylinder control system can be derived, as shown in Figure 3 shown.

[0111] From the transfer function block diagram of the high-frequency response proportional servo valve-controlled hydraulic cylinder control system, the open-loop transfer function of the system hydraulic cylinder when it moves downward can be obtained as shown in the following formula (10):

[0112] (10)

[0113] in, .

[0114] S2. Use the improved particle swarm optimization algorithm to perform multi-constraint optimization on the motion curve of the hot stamping forming motion system, obtain the fifth-order polynomial motion displacement curve equation, and establish the fifth-order curve motion model;

[0115] Motion trajectory optimization can effectively address the coupling issues of minimum motion time and minimum motion impact in manipulator and robot motion control strategies. Quintic curves offer excellent acceleration continuity, effectively reducing the impact of the moving crossbar during hot stamping.

[0116] Specifically, the method includes the following steps:

[0117] A21. To ensure that the acceleration is continuous and without sudden changes, the jerk of the motion trajectory is introduced as a constraint. Therefore, according to the system conditions, the matrix expressions of displacement, velocity, acceleration, and jerk are obtained as shown in the following equation (11):

[0118] (11)

[0119] in, 、 、 、 、 are the initial motion displacement, velocity, acceleration, jerk and time of the movable beam; 、 、 、 、 are the displacement, velocity, acceleration, jerk and time when the movable crossbeam stops moving; a 0. a 1. a 2. a 3. a 4 and a 5 is the polynomial coefficient.

[0120] A22. Analyze the motion state according to formula (11) and determine the optimization constraint equation group as shown in formula (12):

[0121] (12)

[0122] From the motion characteristics of the movable crossbeam, it can be seen that in order to achieve the design of a fast and impact-free motion curve, multiple constraints need to be set in the nonlinear system to ensure a reasonable solution to the coupling phenomenon of time and impact. Multi-objective optimization refers to finding the global optimal combination solution by harmonizing and optimizing between the target constraints. Here, the non-inferior equilibrium solution generated by multi-objective optimization is the Pareto optimal solution. According to the application of advanced optimization algorithms in the multi-objective robot motion trajectory optimization, the improved particle swarm algorithm is selected to perform multi-constraint optimization on the motion curve of the hot stamping forming motion system, and finally the fifth-order polynomial motion displacement curve equation is obtained as shown in Equation (13):

[0123] (13)

[0124] This completes the optimization of the impact-free motion curve.

[0125] S3. Design a sliding mode controller;

[0126] In order to deal with the nonlinear and uncertainty problems in the hot stamping motion system, the present invention designs a sliding mode controller with strong adaptability.

[0127] Specifically, first, according to the control strategy of the hot stamping motion system, the state space equation is constructed, and the expressions of the system error function and the sliding surface are defined as shown in the following equations (14), (15), and (16):

[0128] (14)

[0129] (15)

[0130] (16)

[0131] in, x is the output displacement of the hydraulic cylinder; P 1 is the rodless chamber pressure of the hydraulic cylinder; e is the difference between the expected displacement and the actual displacement; is the expected displacement value; Switching function for sliding mode controller; 、 、 is the switching function coefficient.

[0132] Furthermore, combined with the constant velocity reaching law expressed in Equation (17), the control rate can be obtained from Equations 15 and 16: , its expression is shown in formula (18):

[0133] (17)

[0134] (18)

[0135] Then, from the above equations (1), (2) and (3), we can derive the following equation (19):

[0136] (19)

[0137] Finally, combining equations (15), (16) and (17), we can get and , the specific expression is shown in the following formula (20):

[0138] (20).

[0139] According to the above formulas (1) to (20), we first define the Lyapunov function: , and according to the judgment conditions , after transformation, we get Therefore, the function converges, and the above settings are reasonable and meet the control requirements.

[0140] Example 2

[0141] The design scheme in Example 1 is verified through simulation and experiments.

[0142] (1) Verify the design scheme in Example 1 through AMEsim and Simulink joint simulation;

[0143] Specifically, according to the test bench component parameters, a simulation model of the hot stamping forming motion system with the parameters shown in Table 1 is established in AMEsim. At the same time, through the joint simulation interface, a control system is established in Simulink, and a schematic diagram of the design simulation control system is established, as shown in Figure 1. Figure 4 As shown. Based on the control model of the sliding mode controller in Equations (18) and (20), the controller's S-Function was established, and a control group of the traditional motion scheme was set in the model. Simulation tests were performed by combining software. Based on the performance of the hydraulic components in the experiment, the parameters of the state equation in the controller were obtained as shown in Table 2.

[0144] Table 1. Main hydraulic components and parameters of the hot stamping motion system simulation model

[0145]

[0146] Table 2. Basic parameters

[0147]

[0148] (2) Analysis of simulation results

[0149] like Figure 5As shown, the displacement tracking error curves under the quintic curve motion control scheme and the traditional motion control scheme Figure 1 .

[0150] Depend on Figure 5 The results show that compared with the traditional motion control scheme, the displacement tracking effect of the quintic curve motion control scheme is better, the error throughout the process is kept within ±0.05, and the final error is only 0.001mm. Although the traditional motion control scheme can achieve stable displacement motion tracking, the motion error is larger than that of the quintic curve motion control scheme, and there are multiple large drop points during the motion process, with the final error reaching 0.1mm. Therefore, simulation analysis verifies that the improved quintic curve motion control scheme can meet the design requirements for model motion error, and the displacement control accuracy of the quintic curve motion control scheme is improved by 0.099mm compared to the traditional motion control scheme.

[0151] like Figure 6 and Figure 7 As shown, they are the displacement and velocity curves under the traditional motion control scheme. Figure 1 and five Displacement and velocity curves under subcurve motion control scheme Figure 1 .

[0152] Depend on Figure 6 The results show that despite the multi-point turning point optimization of the motion curve under the traditional motion control solution, significant speed jumps still occurred at 3.8s, 5.8s, 7s, and 9s. The maximum speed jump reached 42.1mm / s, which could cause vibration of the movable beam at this point during movement, pipe impact, and movable beam imbalance.

[0153] Depend on Figure 7 The results show that, compared to traditional motion control schemes, the quintic curve motion control scheme achieves the desired impact-free motion speed after 1.8 seconds. At the end of the steady-state motion after 9 seconds, oscillation remains within 0.1 mm / s, effectively meeting the design stability requirements. Therefore, the sliding mode (adaptive) controller and optimized quintic curve motion model designed in this invention effectively eliminate the displacement error and impact vibration generated by the movable crossbeam during rapid descent. Simulation analysis validates the system rationality of the quintic curve motion control scheme, completing the establishment of a stable variable speed, high-precision, and low-impact system.

[0154] (2) Verify the design scheme in Example 1 through experiments;

[0155] (1) A test bench for hydroforming equipment was built:

[0156] Table 3. Main hydraulic components and their parameters

[0157]

[0158] To implement the practical application of the quintic curve motion control model, the present invention built a hydroforming equipment test bench. Its main hydraulic components and related parameters are shown in Table 3. The industrial computer serves as the main control computer, collects signals through analog and digital signal acquisition cards, and uses the Simulink real-time platform to complete signal processing and control signal output.

[0159] Based on this, the hot stamping motion system, motion curve, and controller were experimentally verified by tracking and controlling the master cylinder's displacement. Secondly, multiple pressure and displacement sensors were installed in the test bench to monitor the system's operating status and improve the control scheme in real time. Finally, a control group for the traditional motion control scheme was established to verify the feasibility and applicability of the quintic curve motion control scheme.

[0160] (2) Experimental data analysis

[0161] In the embodiment of the present invention, two control schemes are used to match the motion model for verification. Figures 8 to 10 shown.

[0162] Figure 8 Displacement tracking error curves under traditional motion control scheme and quintic curve motion control scheme Figure 2 ,Depend on Figure 8 The results show that the error of the quintic curve motion control scheme fluctuates around 0, but remains within 0.1mm. The error eventually decreases, reaching a termination error of only 0.01mm. The traditional motion control scheme showed an overall decreasing error trend in the experiment, but the stability of the stage after 4 seconds in the simulation was poor, with a termination error of 0.694mm. These data indicate that the quintic curve motion scheme improves the overall displacement tracking accuracy by 60% compared to the traditional motion scheme.

[0163] Figure 9 、 Figure 10 They are the displacement and velocity curves under the traditional motion control scheme Figure 2 and five Displacement and velocity curves under subcurve motion control scheme Figure 2 .

[0164] Depend on Figure 9 and Figure 10The results show that after 6 seconds, the movement speed of both control schemes decreases significantly, and there are certain speed fluctuations. However, compared with the traditional motion scheme, the movement speed of the quintic curve motion control scheme decreases steadily, with no speed mutations at 5.8 seconds, 7 seconds, and 9 seconds.

[0165] also, Figure 9 and Figure 10 The results also show that the maximum velocity mutation under the traditional motion control scheme is as high as 47.46 mm / s, while the velocity mutation under the quintic curve motion control scheme is only 15.59 mm / s, improving the overall relative stability by 50%. Furthermore, when the traditional motion control scheme is applied, there are mutation peaks during speed transitions compared to the simulation data, increasing the risk of jitter causing the movable beam to deviate. Therefore, the quintic curve motion control scheme can effectively improve the nonlinear impact vibration of the movable beam during the motion of the traditional motion control scheme and improve the displacement motion accuracy.

[0166] (3) System applicability analysis

[0167] Simulation and experimental verification demonstrate that, compared to traditional motion control solutions, the combination of a quintic polynomial motion curve model and a sliding mode controller improves the speed fluctuation problem inherent in traditional approaches. This motion model effectively eliminates the impact and vibration issues associated with sudden speed fluctuations during the movement of the movable crossbar. Furthermore, the excellent application performance of high-precision nonlinear hot stamping motion system control, coupled with a high-response proportional servo valve, has been demonstrated. Finally, the system, using the industrial computer Simulink Realtime platform, lays the foundation for the production application of more advanced control solutions, optimization algorithms, and controllers.

[0168] In summary, in order to solve the problems such as the impact of the movable crossbeam movement during the hot stamping production process, the present invention proposes a smooth motion control scheme based on motion curve optimization, establishes a quintic curve motion model, designs a sliding mode controller, and finally proves through simulation and experiments that the quintic curve motion control scheme effectively reduces motion shock and vibration. Compared with the traditional motion control scheme, the motion accuracy is improved by 60%, and the speed mutation is reduced by 50%, which effectively improves the reliability of the movable crossbeam movement during the hot stamping process. Therefore, the present invention can meet the requirements of motion accuracy and speed stability in the hot stamping motion process, and after subsequent research, it can achieve fast and high-quality applications with different process requirements, promoting the development of hot stamping forming.

[0169] The present invention is not limited to the above-mentioned specific implementation methods. Various changes made by ordinary technicians in this field based on the above-mentioned concept without creative work are all within the scope of protection of the present invention.

Claims

1. A hot stamping motion curve optimization control method based on a sliding mode controller, characterized in that: The following steps are involved: S1. Modeling and analysis of hot stamping motion system: S11. Design a hot stamping motion system, the system comprising: The accumulator is used to charge energy when the system is running and release energy when the system pressure falls below the set pressure of the accumulator; The pump group is used to supply oil to the system, and the oil circuit at the pump group outlet is connected to the accumulator; Lower oil tank, used to store the hydraulic oil of the system and provide hydraulic oil to the upper oil tank; Overflow valve 1 is used to stabilize the pressure at the outlet of the system pump group and plays a protective role. One end of the overflow valve is connected to the oil return line and the other end is connected to the lower oil tank; The protection valve group is used to quickly return oil and relieve pressure when the system stops or fails. One end of the valve group is connected to the oil circuit and the other end is connected to the lower oil tank. The plug-in valve group is used to adjust the oil volume at the oil supply end of the system pump group and to buffer the impact on the high-frequency response proportional servo valve; High-frequency response cartridge valve group is used to accurately control the return oil flow rate and stabilize the speed of the hydraulic cylinder; High-frequency proportional servo valve is used to precisely adjust the oil flow at the hydraulic cylinder's oil inlet to achieve precise control of the hydraulic cylinder's stroke; Overflow valve 2 is used to protect the hydraulic cylinder oil inlet pipeline from overflow. One end of the valve is connected to the oil inlet pipeline, and the other end is connected to the lower oil tank. Overflow valve 3 is used to protect the hydraulic cylinder oil return line from overflow. One end of the valve is connected to the oil return line and the other end is connected to the lower oil tank. The data processing module is used to collect pressure and displacement signals, perform comprehensive processing on the collected pressure and displacement signals, make judgments, and output high-frequency response cartridge valve group opening and closing control signals to control the displacement of the hydraulic cylinder; Pressure sensor 1 is used to measure the pressure at the oil inlet of the hydraulic cylinder. One end of the pressure sensor is connected to the oil inlet line, and the other end is connected to the data processing module. Filling valve, used to quickly supply hydraulic oil to the hydraulic cylinder to ensure stable speed; The upper oil tank, located at the top of the system, is used to store oil for the filling valve; The displacement sensor is used to feedback the displacement signal of the hydraulic cylinder. It is installed inside the hydraulic cylinder and extends a signal line to connect to the data processing module; Hydraulic cylinder, used as the actuator of the hot stamping motion system; Pressure sensor 2 is used to measure the pressure at the oil outlet of the hydraulic cylinder. One end of the pressure sensor is connected to the oil return line, and the other end is connected to the data processing module. S12. Modeling and analyzing the hot stamping motion system, and obtaining the open-loop transfer function when the hydraulic cylinder moves downward is as shown in the following formula (10): (10) in, ; S2. Use the improved particle swarm optimization algorithm to perform multi-constraint optimization on the motion curve of the hot stamping forming motion system, obtain the fifth-order polynomial motion displacement curve equation, and establish the fifth-order curve motion model; S3. Design a sliding mode controller; In step S12, modeling and analyzing the hot stamping motion system is performed, including the following steps: S121. Assuming that the connecting pipes of the hot stamping forming motion system and the high-frequency response proportional servo valve are in ideal conditions, the internal and external leakage are laminar flows, and the load force is defined as the reaction force during forming. Elastic load, viscous load, and inertial force are ignored. The linearized flow equation of the high-frequency response proportional servo valve, the flow continuity equation of the hydraulic cylinder, and the force balance equation are obtained as shown in the following equations (1), (2), and (3), respectively: （1） （2） （3） in, is the load flow, ; is the spool displacement of the servo valve, ; is the flow coefficient, ; is the flow pressure coefficient, ; is the load pressure, ; is the effective working area of the piston in the rodless cavity of the hydraulic cylinder, ; is the effective displacement output of the piston rod, ; is the external leakage coefficient of the hydraulic cylinder, ; is the leakage coefficient of the hydraulic cylinder, ; is the rodless chamber pressure of the hydraulic cylinder, ; is the rod chamber pressure of the hydraulic cylinder, ; is the effective volume of the rodless chamber of the hydraulic cylinder, ; is the effective bulk elastic modulus, ; is the effective working area of the piston in the rod cavity of the hydraulic cylinder, ; is the total mass of the piston and slider, ; is the load spring stiffness, ; is the external load acting on the piston, ; S122, according to equations (1), (2) and (3), the total output displacement of the valve-controlled asymmetric cylinder is obtained , specifically expressed as follows (4): （4）； in, B p is the damping coefficient, K ce is the total flow coefficient; Since the energy loss caused by viscous friction in the system is negligible, Equation (4) is simplified to the following Equation (5): （5） in, is the natural frequency of the hydraulic cylinder; is the hydraulic damping ratio, ranging from 0.1 to 0.2; S123. Based on formula (5), the transfer function of the output displacement of the hydraulic cylinder to the given output displacement of the high-frequency response proportional servo valve and the transfer function of the output displacement of the hydraulic cylinder to the given load force of the high-frequency response proportional servo valve are further obtained as shown in the following formulas (6) and (7): （6） （7）； S124, due to the current of the servo proportional amplifier With input voltage Approximately proportional, so the servo proportional amplifier gain K a The mathematical model is shown in the following formula (8): （8）； Further establish the displacement sensor gain K f The mathematical model is shown in the following formula (9): （9） in, is the feedback current signal, V; is the displacement of the hydraulic cylinder piston, m; further, the open-loop transfer function of the system when the hydraulic cylinder moves downward is obtained.

2. The hot stamping motion curve optimization control method based on sliding mode controller according to claim 1, characterized in that: In step S2, the improved particle swarm optimization algorithm is used to perform multi-constraint optimization on the motion curve of the hot stamping motion system to obtain a fifth-order polynomial motion displacement curve equation. The specific steps are: A21. The jerk of the motion trajectory is introduced as a constraint condition. According to the conditions and parameters set by the system, the matrix expressions of displacement, velocity, acceleration and jerk are obtained as shown in the following formula (11): （11） in, 、 、 、 、 are the initial motion displacement, velocity, acceleration, jerk and time of the movable beam, 、 、 、 、 are the displacement, velocity, acceleration, jerk and time when the movable beam stops moving. a 0. a 1. a 2. a 3. a 4 and a 5 is the polynomial coefficient; A22. Analyze the motion state according to formula (11) and determine the optimization constraint equation group as shown in the following formula (12): （12） A23. The improved particle swarm algorithm is used to perform multi-constraint optimization on the motion curve of the hot stamping motion system, and the fifth-order polynomial motion displacement curve shown in formula (13) is obtained: （13）。 3. The hot stamping motion curve optimization control method based on sliding mode controller according to claim 1 is characterized in that: The specific steps of designing the sliding mode controller are as follows: First, according to the control strategy of the hot stamping motion system, the state space equation is constructed, and the system error function and sliding surface are defined. The expressions are shown in the following equations (14), (15), and (16): （14） （15） （16） in, x is the output displacement of the hydraulic cylinder; P 1 is the pressure of the rodless chamber of the hydraulic cylinder; e is the difference between the expected displacement and the actual displacement; is the expected displacement value; Switching function for sliding mode controller; 、 、 is the switching function coefficient; Furthermore, combined with the constant velocity approaching law expressed in the following equation (17), the control rate can be obtained from equations (15) and (16): , which is expressed as the following formula (18): （17） （18） Then, from equations (1), (2) and (3), we can derive the following equation (19): （19） ； Finally, combining equations (15), (16) and (17), we can get and , the specific expression is shown in the following formula (20): （20）； According to equations (14)-(20), the Lyapunov function is defined as , and according to the judgment conditions , after transformation, we get ; Therefore, the function converges, and the above settings are reasonable and meet the control requirements.

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