Linear slope temperature rising control method and system of vacuum welding furnace

By using a linear slope heating control method for vacuum welding furnaces, the dynamic target temperature is calculated in real time and closed-loop control is performed, which solves the problem of uneven heating rate in traditional PID control, achieves smooth heating and precise temperature control, and improves welding quality and equipment life.

CN122284733APending Publication Date: 2026-06-26CHENGLIAN KAIDA TECH CO LTD
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Patent Information

Application Number
CN202610454584.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-04-08
Publication Date
2026-06-26

AI Technical Summary

Technical Problem

Traditional PID control in vacuum welding furnaces results in a high initial heating rate followed by a low rate of change, causing thermal shock and affecting welding quality. Furthermore, it introduces control disturbances when switching between step-by-step target temperatures.

Method used

A linear slope heating control method is adopted to calculate the dynamic target temperature in real time and perform closed-loop control. By dynamically adjusting the integral zeroing trigger threshold and thermal inertia characteristic parameters, a smooth heating trajectory and a gradual zeroing operation of the integral term are achieved.

Benefits of technology

It achieves uniform linear heating throughout the entire process, reduces thermal shock, improves welding quality consistency, reduces frequent equipment operation, and extends equipment life.

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Abstract

This application provides a linear slope heating control method and system for a vacuum welding furnace, relating to the field of vacuum welding technology. The method includes the following steps: acquiring the initial temperature and preset heating slope of the current process segment, and calculating the dynamic target temperature in real time based on the running time of the current process segment and a refresh frequency matching the PID control cycle; the dynamic target temperature changes continuously and linearly with time, and the difference between two adjacent calculated dynamic target temperatures is a constant minimum value, making the trajectory of the dynamic target temperature a smooth straight line; the real-time calculated dynamic target temperature is output as a setpoint; the actual temperature value of the vacuum welding furnace is collected as a feedback value, and the dynamic target temperature and the actual temperature value are used as inputs to perform PID calculation to generate a control quantity, driving the actuator to perform closed-loop control of the furnace body temperature; the actual temperature tracks a continuously moving smooth target trajectory, rather than discrete step-like target points.
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Description

Technical Field

[0001] This invention belongs to the field of vacuum welding technology, specifically relating to a linear slope temperature rise control method and system for a vacuum welding furnace. Background Technology

[0002] In the field of temperature control for vacuum welding furnaces, traditional PID control typically uses a static target temperature as the setpoint. During the heating process, due to the cumulative integral action of the PID controller and the thermal inertia of the controlled object, the actual temperature exhibits a nonlinear characteristic of "rapid heating in the early stage and moderate heating in the later stage" as it approaches the target temperature; that is, the heating rate is high at the beginning and low at the end. This phenomenon of rapid heating in the early stage can easily cause thermal shock to products made of certain materials, leading to a decrease in welding quality or even product damage.

[0003] To address this issue, existing technologies attempt to approximate linear heating by setting multiple stepped target temperatures. However, the stepped target temperatures exhibit abrupt changes at switching points, and the actual temperature tracks discrete target points rather than a continuous trajectory. This makes it difficult to achieve true uniform heating and can easily introduce new control disturbances when switching target temperatures. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, a linear slope temperature rise control method and system for a vacuum welding furnace is provided.

[0005] In a first aspect, this application proposes a linear slope temperature rise control method for a vacuum welding furnace, comprising the following steps: The initial temperature and preset heating slope of the current process segment are obtained, and the dynamic target temperature is calculated in real time according to the running time of the current process segment and the refresh frequency is matched with the PID control cycle. The dynamic target temperature changes continuously and linearly with time, and the difference between two adjacent calculated dynamic target temperatures is a constant minimum value, so that the change trajectory of the dynamic target temperature is a smooth straight line. The dynamically calculated target temperature is output as the set value. The actual temperature value of the vacuum welding furnace is collected as a feedback value, and the dynamic target temperature and the actual temperature value are used as inputs to perform PID calculation to generate control quantity, which drives the actuator to perform closed-loop control of the furnace body temperature; wherein, the actual temperature tracks a continuously moving smooth target trajectory, rather than a discrete step-like target point.

[0006] According to the technical solution provided in this application, the closed-loop control process also includes the following steps: When the actual temperature tracks the smooth target trajectory to enter the preset static target temperature range, the integral zeroing trigger threshold is dynamically determined according to the preset heating slope, and multiple zeroing operations are performed on the integral term in the PID calculation to suppress the overshoot of the actual temperature when it reaches the static target temperature. The integral zeroing trigger threshold is positively correlated with the preset heating slope. The larger the preset heating slope, the larger the integral zeroing trigger threshold, and the earlier the zeroing operation is initiated.

[0007] According to the technical solution provided in this application, the step of dynamically determining the integral zeroing trigger threshold based on the preset heating slope includes the following steps: The thermal inertia characteristic parameters of the vacuum welding furnace under the current operating conditions are identified in real time, and the thermal inertia characteristic parameters are dynamically updated according to the tracking lag deviation of the actual temperature to the dynamic target temperature. Based on the preset heating slope of the current process section and the real-time identified thermal inertia characteristic parameters, the integral zeroing trigger threshold is dynamically calculated, so that the integral zeroing trigger threshold increases with the increase of the preset heating slope and also increases with the increase of the thermal inertia characteristic parameters. When the difference between the actual temperature and the static target temperature is less than or equal to the dynamically calculated integral zeroing trigger threshold, multiple progressive zeroing operations are performed on the integral term in the PID calculation. Specifically, this includes: performing a zeroing operation once; if the actual temperature is still on an upward trend within a preset time window and the difference between it and the static target temperature is still less than or equal to the integral zeroing trigger threshold, then performing the zeroing operation again, and so on, until the integral term is completely zeroed or the actual temperature enters the stable range of the static target temperature.

[0008] According to the technical solution provided in this application, the process of dynamically determining the threshold for triggering zeroing out points also includes the following steps: The preset heating slope of the current process section is monitored in real time, and the difference between the preset heating slope of the current control cycle and the previous control cycle is calculated. When the difference exceeds the preset slope change threshold, it is determined that the preset heating slope has changed. In response to changes in the preset heating slope, a threshold smoothing transition operation is performed, specifically including: Obtain the first integral zeroing trigger threshold before the slope change and the second integral zeroing trigger threshold after the slope change; A transition time length is determined, which is positively correlated with thermal inertia characteristic parameters; Within the specified transition time, the integral zeroing trigger threshold is calculated and updated periodically using linear interpolation, with each control cycle as the unit, so that the integral zeroing trigger threshold gradually changes from the first integral zeroing trigger threshold to the second integral zeroing trigger threshold.

[0009] According to the technical solution provided in this application, within the said transition time length, the following steps are also included: Adjust the identification update cycle of thermal inertia characteristic parameters and shorten the identification update cycle to a preset ratio of the identification update cycle under normal operating conditions in order to accelerate the convergence of the tracking lag deviation of the actual temperature to the dynamic target temperature after the slope change. After the transition time ends, the identification and update cycle of the thermal inertia characteristic parameters will be restored to the identification and update cycle under normal operating conditions.

[0010] According to the technical solution provided in this application, within the said transition time length, the following steps are also included: Real-time calculation of the tracking deviation between the current dynamic target temperature and the actual temperature, as well as the rate of change of the tracking deviation; When the tracking deviation is less than or equal to the integral zeroing trigger threshold in the current transition, and the rate of change of the tracking deviation is positive, the execution of the multiple progressive zeroing operations is paused. Obtain the first preset heating slope before the slope change and the second preset heating slope after the slope change, and calculate the slope ratio; The zeroing delay time is dynamically determined based on the product of the slope ratio and the thermal inertia characteristic parameter. During the zeroing delay period, the zeroing operation is paused; after the zeroing delay period ends, the determination of the integral zeroing trigger threshold is resumed, and the multiple progressive zeroing operations are allowed to be executed.

[0011] According to the technical solution provided in this application, the process of the multiple progressive zeroing operations further includes the following steps: Record the actual temperature value each time a zeroing operation is performed, as well as the trajectory of the actual temperature change after each zeroing operation. The suppression efficiency of a single zeroing operation is calculated based on the temperature change between two adjacent zeroing operations. The suppression efficiency is positively correlated with the decrease in the actual temperature rise rate after the zeroing operation. When the suppression efficiency of two consecutive zeroing operations is lower than the preset efficiency threshold, it is determined that the current integral zeroing trigger threshold is too high, and an adaptive threshold shrinkage operation is performed, which specifically includes: The current integral zeroing trigger threshold is gradually reduced by a preset step size until the suppression efficiency when the zeroing operation is performed again is restored to a level higher than the preset efficiency threshold. The shrinkage integral zeroing trigger threshold is used as the subsequent integral zeroing trigger threshold for the current process segment, and the correspondence between this threshold and the current thermal inertia characteristic parameter and the preset heating slope is recorded for subsequent threshold initialization under the same operating conditions.

[0012] According to the technical solution provided in this application, the following steps are also included within the zeroing delay time: Monitor the sign change of the rate of change; When the rate of change of the tracking deviation is detected to change from a positive value to a negative value, it is determined that the actual temperature has changed from lagging behind the dynamic target temperature to leading the dynamic target temperature. In response to the sign change, a zeroing delay truncation operation is performed, specifically including: Immediately interrupt the remaining countdown of the reset delay time; In the next control cycle after the interruption, the determination of the integral zeroing trigger threshold is immediately resumed, and the multiple progressive zeroing operations are allowed to be executed.

[0013] According to the technical solution provided in this application, after the zeroing delay time is interrupted, the following steps are also included: Record the actual duration from the start of the zeroing delay to the interruption time, as well as the tracking deviation value and the rate of change of the tracking deviation at the interruption time; The actual duration, the tracking deviation value at the time of interruption, and the rate of change of the tracking deviation are stored as a complete sample in the sample library; When a preset temperature rise rate change occurs again within the same process segment and a new zeroing delay time is entered, historical samples with a similar rate change are retrieved from the sample library. The current zeroing delay time is then corrected based on the actual duration in the historical samples. Specifically, this includes: If the tracking deviation value at the time of interruption in the retrieved historical samples is less than the preset deviation threshold, the current zeroing delay time will be shortened to a preset proportion of the current preset delay time. If the rate of change of tracking deviation at the time of interruption is still positive in the retrieved historical samples, the current zeroing delay time will be extended to a preset proportion of the current preset delay time. If no similar historical samples are found, the current preset delay time will remain unchanged.

[0014] Secondly, this application proposes a linear slope heating control system for a vacuum welding furnace, used to implement the method described above, including: The calculation module is configured to obtain the initial temperature and preset heating slope of the current process segment, and calculate the dynamic target temperature in real time according to the running time of the current process segment and at a refresh frequency that matches the PID control cycle; wherein the dynamic target temperature changes continuously and linearly with time, and the difference between two adjacent calculated dynamic target temperatures is a constant minimum value, so that the change trajectory of the dynamic target temperature is a smooth straight line. An output module, configured to output the dynamically calculated target temperature as a set value in real time; The control module is configured to collect the actual temperature value of the vacuum welding furnace as a feedback value, and use the dynamic target temperature and the actual temperature value as inputs to perform PID calculations to generate control quantities, driving the actuator to perform closed-loop control of the furnace body temperature; wherein, the actual temperature tracks a continuously moving smooth target trajectory, rather than discrete step-like target points.

[0015] Compared with existing technologies, the advantages of this application are as follows: By calculating the dynamic target temperature in real time with a refresh rate matching the PID control cycle, the dynamic target temperature changes continuously and linearly over time. The difference between two adjacent calculated dynamic target temperatures is a constant minimum value, thus forming a smooth straight target trajectory. Based on this, the real-time calculated dynamic target temperature is output as the setpoint, and the PID calculation is performed using the dynamic target temperature and the actual temperature as inputs. This ensures that the actual temperature tracks a continuously moving smooth target trajectory, rather than discrete, stepped target points. Therefore, this application effectively overcomes the nonlinearity problem of traditional PID control, which involves a rapid initial temperature rise followed by a gradual temperature rise in the later stages of heating. It achieves uniform linear heating from the initial temperature to the static target temperature throughout the entire heating process. The actual temperature consistently tracks a continuous and smooth target trajectory throughout the heating process, avoiding control disturbances caused by stepped target switching. This makes the heating process more uniform and stable, significantly reducing thermal shock to the welded products and improving the consistency of welding quality. Simultaneously, due to the continuity and smoothness of the target trajectory, the output change of the PID controller is also more gradual, reducing frequent actuator movements and extending the equipment's service life. Attached Figure Description

[0016] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 A flowchart illustrating the steps of the linear slope temperature rise control method for the vacuum welding furnace provided in this application. Detailed Implementation

[0017] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] Example 1 As mentioned in the background section, this application proposes a linear slope temperature rise control method for a vacuum welding furnace, such as... Figure 1 As shown, it includes the following steps: S1. Obtain the initial temperature and preset heating slope of the current process segment, and calculate the dynamic target temperature in real time according to the running time of the current process segment and the refresh frequency that matches the PID control cycle; wherein, the dynamic target temperature changes continuously and linearly with time, and the difference between two adjacent calculated dynamic target temperatures is a constant minimum value, so that the change trajectory of the dynamic target temperature is a smooth straight line. S2. Output the dynamically calculated target temperature as the set value; S3. Collect the actual temperature value of the vacuum welding furnace as the feedback value, and use the dynamic target temperature and the actual temperature value as input to perform PID calculation to generate control quantity, drive the actuator to perform closed-loop control of the furnace body temperature; wherein, the actual temperature tracks a continuously moving smooth target trajectory, rather than discrete step-like target points.

[0020] Specifically, in the control system of the vacuum welding furnace, the host computer is used to set process parameters, while the slave computer uses a Siemens S7-200 PLC as the controller and is programmed using STEP 7-MicroWIN SMART programming software. Process parameters are input by the operator through the host computer interface, including the preset heating slope K for each process segment, the static target temperature, and the total running time for each process segment. These parameters are sent to the PLC via a communication protocol and stored in the PLC's data storage area.

[0021] When the PLC runs, it first acquires the initial temperature of the current process segment. The initial temperature T0 is acquired as follows: if it is the first process segment, the current value of the temperature sensor PV_I is read at the start of the process segment as the initial temperature; if it is a subsequent process segment, the ending temperature of the previous process segment is recorded as the initial temperature of the current process segment. The temperature sensor uses a thermocouple or resistance temperature detector (RTD), and its signal is converted into a digital value by the analog input module and stored in the PLC's variable memory area.

[0022] Simultaneously, the PLC acquires the preset heating rate K for the current process segment. This K value is a known variable set by the host computer and stored in the PLC's retention register, in degrees Celsius per second. For example, if the process requires a heating rate of 2 degrees Celsius per second, then the K value is set to 2.0.

[0023] When the PLC executes PID control, its control cycle is set to 0.5 seconds. This cycle value matches the execution cycle of the PID instruction and can be achieved by setting a timer interrupt or a cyclic scan cycle. At the beginning of each control cycle, the PLC calculates the running time Tim of the current process segment. The running time is calculated as follows: a timer is started at the start of the process segment, and the timer accumulates time in milliseconds. At the beginning of each control cycle, the current value of the timer is read and converted into seconds as the Tim value.

[0024] According to the dynamic target temperature calculation formula T = K × Tim + T0, the PLC performs one floating-point multiplication and one floating-point addition operation in each control cycle to calculate the dynamic target temperature T value for the current cycle. Taking a specific value as an example, assuming the initial temperature T0 is 100 degrees Celsius, the temperature rise rate K is 2 degrees Celsius per second, and the current running time Tim is 10.5 seconds, then the calculated dynamic target temperature T = 2 × 10.5 + 100 = 121 degrees Celsius.

[0025] Since the PID control cycle is fixed at 0.5 seconds, the time interval between two consecutive calculations is also constant at 0.5 seconds. Therefore, the difference between two consecutive calculated dynamic target temperatures is always K × 0.5. When K is 2, the difference is 1 degree Celsius; when K is 0.5, the difference is 0.25 degrees Celsius. This difference remains constant throughout the entire process. Due to the small control cycle, this difference is also correspondingly minimal, causing the dynamic target temperature to appear as a smooth straight line at discrete sampling points, rather than a stepped jump. This characteristic is naturally achieved through the calculation properties of the formula itself, without the need for additional algorithm processing.

[0026] After calculating the dynamic target temperature T, the PLC writes this T value to the Setpoint_R input of the PID instruction. The Siemens S7-200 PLC's PID instruction includes multiple input / output parameters, with Setpoint_R being a real number used to receive the target setpoint. Traditionally, Setpoint_R remains constant at the static target temperature during process operation; however, in this method, a new T value is written to Setpoint_R each control cycle, updating it in real time.

[0027] The PID instruction simultaneously receives the actual temperature value PV_I from the temperature sensor. PV_I is the actual temperature converted by the analog input module, in degrees Celsius, consistent with the unit of Setpoint_R. Based on the deviation between Setpoint_R and PV_I, the PID instruction performs proportional-integral-derivative (PID) calculations to generate the control output. The control output is a real number between 0.0 and 1.0, representing the percentage of the output opening.

[0028] The PLC converts the control output into an analog signal, which is then output to the actuator via an analog output module. The actuator is a thyristor power regulator or a solid-state relay, which receives an analog signal of 4-20mA or 0-10V and adjusts the conduction angle or on / off ratio of the heating element according to the signal magnitude, thereby controlling the heating power. For example, when the output is 0.6, the power regulator outputs 60% of the power, and the heating element operates with a 60% duty cycle.

[0029] Through this process, the actual temperature PV_I tracks the dynamically updated target temperature T in real time during each control cycle. Since the value of T increases linearly over time, the tracking trajectory of PV_I is also a continuous and smooth curve, rather than tracking discrete, stepped target points.

[0030] The technical principle of this scheme is to replace the original static target temperature with a dynamic target temperature that increases linearly with the running time. This causes the setpoint of the PID controller to change in each control cycle, thereby guiding the actual temperature to rise along a preset slope trajectory. Because the change in the setpoint is continuous and smooth, the integral term of the PID controller will not accumulate too quickly as in static target control, thus avoiding the phenomenon of rapid temperature rise in the early stage.

[0031] The technical advantages of this solution are: it achieves uniform linear heating throughout the entire process, the actual temperature rises evenly throughout the heating process, the thermal shock to the welded products is significantly reduced, the PID output changes smoothly, the actuator operates smoothly, and the equipment life is extended.

[0032] In a preferred embodiment, the closed-loop control process further includes the following steps: When the actual temperature tracks the smooth target trajectory to enter the preset static target temperature range, the integral zeroing trigger threshold is dynamically determined according to the preset heating slope, and multiple zeroing operations are performed on the integral term in the PID calculation to suppress the overshoot of the actual temperature when it reaches the static target temperature. The integral zeroing trigger threshold is positively correlated with the preset heating slope. The larger the preset heating slope, the larger the integral zeroing trigger threshold, and the earlier the zeroing operation is initiated.

[0033] Specifically, during the linear temperature rise control process, the PLC calculates the dynamic target temperature T in each control cycle and writes it to the Setpoint_R instruction of the PID controller. When the dynamic target temperature T gradually approaches the static target temperature T_set set by the host computer, the system needs to initiate an integral zeroing operation to prevent overshoot.

[0034] First, the PLC needs to define the static target temperature proximity range. This range is set through the host computer parameters, for example, set to the range of 10 degrees Celsius below the static target temperature T_set. When the difference ΔT = T_set - PV_I between the actual temperature PV_I and the static target temperature T_set is less than or equal to 10 degrees Celsius, the system enters the static target temperature proximity range.

[0035] After entering the proximity range, the PLC dynamically determines the integral reset trigger threshold F1 according to the preset heating slope K. The integral reset trigger threshold is a temperature difference threshold used to determine when to start performing integral reset. The determination method uses a look-up table as follows: On the host computer parameter setting interface, the operator pre-sets a set of slope breakpoints K1, K2, K3 and the corresponding integral reset trigger thresholds M1, M2, M3, M4, and K1 < K2 < K3, M1 < M2 < M3 < M4 are satisfied. For example, set the slope breakpoints K1 = 1.0, K2 = 2.0, K3 = 3.0, and set the corresponding thresholds M1 = 2.0, M2 = 4.0, M3 = 6.0, M4 = 8.0. Among them, the unit of the M value is degrees Celsius, representing the temperature difference threshold for starting the reset operation. The larger the M value, the earlier the reset starts (the earlier the intervention) when the distance from the static target temperature is farther.

[0036] The PLC determines the threshold F1 according to the current preset heating slope K: when K ≤ K1, F1 = M1; when K1 < K ≤ K2, F1 = M2; when K2 < K ≤ K3, F1 = M3; when K > K3, F1 = M4. Through this method, the integral reset trigger threshold F1 is positively correlated with the preset heating slope K, that is, the larger the K value, the larger the F1 value, and the earlier the reset operation intervenes. The above values are only examples and are determined by experimental calibration according to the equipment characteristics in actual use.

[0037] After determining F1, the PLC calculates ΔT = T_set - PV_I in real time, that is, the difference between the actual temperature and the static target temperature. When ΔT is less than or equal to F1, the PLC starts to perform the integral reset operation. The specific implementation method of the integral reset operation is: the PLC forcibly sets the cumulative value of the integral term inside the PID instruction to zero through the program. In the Siemens S7-200 PLC, the integral term of the PID instruction is stored in a specific data area, and the integral reset can be achieved by writing a floating-point number 0.0 to this storage address through the MOV_R instruction.

[0038] The integral zeroing operation in this method is performed multiple times, rather than a single zeroing. Specifically, the implementation is as follows: when the actual temperature PV_I first enters the vicinity of the static target temperature T_set, i.e., when PV_I ≥ T_set - F1, the first integral zeroing is performed. After zeroing, the system continues to run, and when the actual temperature PV_I successively reaches a preset node closer to T_set, the integral zeroing operation is performed again. For example, let T_set = 200°C, and the preset nodes be 199.0°C, 199.5°C, and 200.0°C. That is, when PV_I successively passes through these temperature values, an integral zeroing operation is performed once for each of them. These node values ​​are preset by the host computer and can be adjusted according to actual debugging results, aiming to suppress overshoot when the actual temperature reaches T_set.

[0039] The physical significance of multiple zeroing operations lies in the fact that, during the process of approaching the static target temperature, a single zeroing operation may not completely eliminate the residual effect of the integral term. Multiple zeroing operations can achieve a "braking" effect, gradually weakening the integral action and allowing the system to smoothly reach the target temperature. The number of zeroing operations and the node positions can be adjusted according to the heating slope and thermal inertia. When the slope is greater or the thermal inertia is greater, the node settings can be more dense.

[0040] The technical principle behind this solution is as follows: In linear temperature rise control, the integral term of the PID controller continuously accumulates during the temperature rise process. When approaching the static target temperature, the output of the integral term dominates, making it difficult for the system to decelerate, thus causing overshoot. By performing integral zeroing in advance and multiple times after entering the target proximity range, the integral effect can be effectively weakened. This is equivalent to "applying the brakes" in advance when approaching the target and performing multiple "pumping brakes" during the process to achieve a smooth stop.

[0041] The technical advantages of this solution are: it effectively suppresses overshoot when reaching the static target temperature in linear temperature rise control, enabling the actual temperature to be accurately stabilized near the static target temperature. Simultaneously, the integral zero-trigger threshold is positively correlated with the temperature rise slope, allowing the control system to adapt to overshoot suppression requirements at different temperature rise rates; the greater the slope, the earlier the intervention, ensuring temperature control accuracy under various operating conditions.

[0042] In a preferred embodiment, dynamically determining the integral zeroing trigger threshold based on the preset heating slope includes the following steps: The thermal inertia characteristic parameters of the vacuum welding furnace under the current operating conditions are identified in real time, and the thermal inertia characteristic parameters are dynamically updated according to the tracking lag deviation of the actual temperature to the dynamic target temperature. Based on the preset heating slope of the current process section and the real-time identified thermal inertia characteristic parameters, the integral zeroing trigger threshold is dynamically calculated, so that the integral zeroing trigger threshold increases with the increase of the preset heating slope and also increases with the increase of the thermal inertia characteristic parameters. When the difference between the actual temperature and the static target temperature is less than or equal to the dynamically calculated integral zeroing trigger threshold, multiple progressive zeroing operations are performed on the integral term in the PID calculation. Specifically, this includes: performing a zeroing operation once; if the actual temperature is still on an upward trend within a preset time window and the difference between it and the static target temperature is still less than or equal to the integral zeroing trigger threshold, then performing the zeroing operation again, and so on, until the integral term is completely zeroed or the actual temperature enters the stable range of the static target temperature.

[0043] Specifically, this method first requires real-time identification of the thermal inertia characteristic parameters of the vacuum welding furnace under the current operating conditions. The thermal inertia characteristic parameter θ characterizes the furnace body's response speed to changes in heating power, and its identification process is as follows: In each PID control cycle, the PLC calculates the tracking lag deviation E = T - PV_I between the dynamic target temperature T and the actual temperature PV_I. When E is positive, it indicates that the actual temperature lags behind the dynamic target temperature; the larger the E value, the more severe the lag. The PLC stores the E value in a circular queue of length N, where N can be, for example, 10 or 20.

[0044] Every 10 control cycles, the PLC performs a statistical analysis on the E values ​​in the queue, calculating the average value E_avg and its trend. Based on the ratio of E_avg to the current heating slope K, the thermal inertia characteristic parameter θ = α × (E_avg / K) is calculated, where α is an empirical coefficient determined through experimental calibration. For example, when K = 2.0, if E_avg is 1.2 and α is 1.0, then θ = 0.6. The larger the θ value, the greater the thermal inertia and the more sluggish the system response. This identification process is continuously performed in each process segment, allowing θ to be updated in real time as operating conditions change.

[0045] After obtaining the thermal inertia characteristic parameter θ, the PLC dynamically calculates the integral zero-trigger threshold F1 based on the preset heating slope K of the current process section and the value of θ. The calculation method uses a two-dimensional lookup table, and the specific implementation is as follows: On the host computer parameter setting interface, the operator pre-calibrates a set of two-dimensional mapping tables through experiments. The rows of the mapping table correspond to different temperature rise slope K intervals, and the columns correspond to different thermal inertia characteristic parameter θ intervals. The values ​​in the table are the optimal integral zero-trigger thresholds for that operating condition. For example, for operating conditions where K is between 1.0 and 2.0 and θ is between 0.3 and 0.6, the optimal threshold is calibrated to be 5.0 degrees Celsius; for operating conditions where K is between 2.0 and 3.0 and θ is between 0.6 and 0.9, the optimal threshold is calibrated to be 3.0 degrees Celsius. This mapping table is stored in the PLC's retention register.

[0046] In each control cycle, the PLC looks up the value in the mapping table based on the current K and θ values. First, it determines the row interval containing the K value, then the column interval containing the θ value, and extracts the corresponding threshold as F1. If K or θ falls on the boundary, linear interpolation is used to calculate the accurate F1 value. In this way, F1 increases with both K and θ. For example, the larger K is, the greater the kinetic energy of the system as it approaches the target, requiring earlier intervention, thus resulting in a larger F1 value; similarly, the larger θ is, the more delayed the system's response, again requiring earlier intervention, and therefore also resulting in a larger F1 value.

[0047] After determining the integral zeroing trigger threshold F1, the PLC calculates ΔT = T_set - PV_I in real time. When ΔT is less than or equal to F1, the PLC performs multiple progressive zeroing operations. This operation differs from the multiple zeroing operations described earlier; the number of zeroing operations and the timing are not predetermined but dynamically determined based on the temperature response after zeroing.

[0048] The specific procedure for multiple gradual zeroing operations is as follows: The first step is to perform the first zeroing. The PLC forces the stored value of the integral term in the PID instruction to zero and records the actual temperature value PV_1 at the time of zeroing.

[0049] The second step is to start a time window timer, with the timing duration set to 5 PID control cycles, or 2.5 seconds.

[0050] The third step involves calculating the difference between the current actual temperature PV_current and the temperature PV_1 at the time of zeroing for each control cycle within the time window, to determine whether the actual temperature is still on an upward trend. The criteria for determining an upward trend are: the difference between PV_current for three consecutive control cycles is positive, and the ratio of the difference d3 in the third cycle to the difference d1 in the first cycle is greater than a preset threshold, for example, d3 / d1 > 0.5.

[0051] Fourth, at the end of the time window, determine two conditions: first, whether the actual temperature is still on an upward trend; second, whether ΔT is still less than or equal to F1. If both conditions are met, perform a second zeroing operation, setting the integral term to zero again, and record the temperature PV_2 at the zeroing moment.

[0052] Fifth, repeat the above steps, restarting the time window after each zeroing operation to monitor the temperature response and determine whether to perform the next zeroing. This process continues until either of the following conditions is met: the absolute value of the integral term is less than the preset lower limit threshold for integration after three consecutive zeroing operations (e.g., less than 1% of the maximum output), indicating that the integral effect is negligible; or the actual temperature enters the stable range of the static target temperature, i.e., the absolute deviation between PV_I and T_set is less than 0.5 degrees Celsius and remains so for 5 consecutive control cycles.

[0053] The essence of this gradual zeroing mechanism is zeroing on demand. Taking a specific scenario as an example, suppose that after a certain zeroing, the actual rate of temperature rise within the time window decreases significantly, from 0.8 degrees Celsius per second before zeroing to 0.2 degrees Celsius per second, and the upward trend stops before the end of the window, then no further zeroing will be performed. Conversely, if the temperature continues to rise at a relatively rapid rate after zeroing, indicating that the integral residue or thermal inertia is still large, then zeroing will be performed again until the temperature rise is effectively suppressed.

[0054] The technical principle of this scheme lies in: by identifying thermal inertia characteristic parameters in real time, the integral zeroing trigger threshold can simultaneously reflect process requirements (temperature rise rate) and equipment physical characteristics (thermal inertia), achieving precise adaptation. Through multiple progressive zeroing operations, the number and timing of zeroing operations are coupled with the actual temperature response, forming a closed-loop regulation. Compared with traditional single zeroing, progressive zeroing can determine whether to continue zeroing based on the effect of the previous zeroing, ensuring overshoot suppression while avoiding excessive weakening of the integral effect.

[0055] The technical advantages of this scheme are as follows: the integral zeroing trigger threshold can adapt to different heating rates and equipment thermal inertia, ensuring that the zeroing intervention timing is always optimal. Multiple progressive zeroing operations can dynamically determine the number of zeroing operations based on the actual temperature response to zeroing, matching the degree of weakening of the integral effect with actual needs. This effectively suppresses overshoot and avoids slow heating or steady-state fluctuations caused by excessive zeroing. Simultaneously, by recording the correspondence between the threshold and operating conditions, a basis is provided for subsequent threshold initialization under the same operating conditions, enabling the control system to possess self-learning and self-optimization capabilities.

[0056] In a preferred embodiment, the process of dynamically determining the integral zeroing trigger threshold further includes the following steps: The preset heating slope of the current process section is monitored in real time, and the difference between the preset heating slope of the current control cycle and the previous control cycle is calculated. When the difference exceeds the preset slope change threshold, it is determined that the preset heating slope has changed. In response to changes in the preset heating slope, a threshold smoothing transition operation is performed, specifically including: Obtain the first integral zeroing trigger threshold before the slope change and the second integral zeroing trigger threshold after the slope change; A transition time length is determined, which is positively correlated with thermal inertia characteristic parameters; Within the specified transition time, the integral zeroing trigger threshold is calculated and updated periodically using linear interpolation, with each control cycle as the unit, so that the integral zeroing trigger threshold gradually changes from the first integral zeroing trigger threshold to the second integral zeroing trigger threshold.

[0057] Specifically, in the actual operation of a vacuum welding furnace, a complete welding process typically includes multiple heating stages, each with a different preset heating slope. For example, the first stage heats from 100 degrees Celsius to 200 degrees Celsius at a slope of 1 degree Celsius per second, and the second stage heats from 200 degrees Celsius to 300 degrees Celsius at a slope of 3 degrees Celsius per second. When switching between stages, the preset heating slope K will change abruptly. If the integral zeroing trigger threshold F1 also changes abruptly at this time, it will cause a sudden change in the control quantity, resulting in fluctuations in the furnace temperature.

[0058] To address this issue, the PLC performs slope change detection in each PID control cycle. The specific implementation is as follows: The PLC sets two variables in its data storage area: K_current stores the preset temperature rise slope for the current control cycle, and K_previous stores the preset temperature rise slope for the previous control cycle. At the beginning of each control cycle, the PLC reads the preset temperature rise slope K_current for the current process segment and compares it with K_previous. The difference ΔK is calculated as: ΔK = K_current - the absolute value of K_previous. The PLC presets a slope change threshold ΔK_th, for example, set to 0.1 degrees Celsius per second. When the absolute value of ΔK is greater than ΔK_th, it is determined that the preset temperature rise slope has changed.

[0059] When a slope change is detected, the PLC first obtains the first integral zeroing trigger threshold F1_old before the slope change and the second integral zeroing trigger threshold F1_new after the slope change. F1_old is calculated as follows: in the last control cycle before the slope change, the PLC calculates it using a two-dimensional lookup table based on the then-current preset heating slope K_old and thermal inertia characteristic parameter θ_old. F1_new is calculated as follows: in the first control cycle after the slope change, the PLC calculates it using the same two-dimensional lookup table based on the new preset heating slope K_new and the current thermal inertia characteristic parameter θ_current. These two thresholds are stored in the variables F1_old and F1_new, respectively, in the PLC program.

[0060] After obtaining F1_old and F1_new, the PLC determines the transition time length T_trans. The determination of the transition time length is positively correlated with the thermal inertia characteristic parameter θ. In specific implementation, the PLC presets a basic transition time T_base, for example, 5 seconds, and then corrects the basic transition time according to the thermal inertia characteristic parameter θ. The correction formula is T_trans = T_base × (1 + β × θ), where β is an empirical coefficient, for example, a value of 2.0. When θ is small, for example, θ = 0.2, T_trans = 5 × (1 + 2.0 × 0.2) = 7 seconds; when θ is large, for example, θ = 1.0, T_trans = 5 × (1 + 2.0 × 1.0) = 15 seconds. The physical significance of this design is that the greater the thermal inertia of the device, the more delayed the temperature response during slope switching, requiring a longer transition time for smooth adjustment to avoid control disturbances.

[0061] After determining the transition time length T_trans, the PLC calculates and updates the integral zero-trigger threshold cycle by cycle using linear interpolation, with the PID control cycle as the unit. The specific implementation is as follows: Let N be the number of control cycles contained within the transition time length T_trans, where N = T_trans / T_pid, and T_pid is the PID control cycle, for example, 0.5 seconds, then N = 15 seconds / 0.5 seconds = 30 cycles. In each control cycle i (i ranges from 0 to N-1), the PLC calculates the integral zero-trigger threshold F1_i = F1_old + (F1_new - F1_old) × (i / N) using the linear interpolation formula. When i = 0, F1_0 = F1_old; when i = N-1, F1_{N-1} = F1_new. During the transition period, the PLC uses the calculated F1_i as the current integral zero-trigger threshold in each control cycle for subsequent integral zero-trigger judgments.

[0062] Taking specific values ​​as an example, assuming F1_old = 8.0 degrees Celsius, F1_new = 3.0 degrees Celsius, transition time T_trans = 10 seconds, and control cycle T_pid = 0.5 seconds, then N = 20. In the first control cycle i = 0, F1 = 8.0 degrees Celsius; in the 5th control cycle i = 4, F1 = 8.0 + (3.0 - 8.0) × (4 / 20) = 8.0 - 1.0 = 7.0 degrees Celsius; in the 10th control cycle i = 9, F1 = 8.0 + (3.0 - 8.0) × (9 / 20) = 8.0 - 2.25 = 5.75 degrees Celsius; in the 20th control cycle i = 19, F1 = 8.0 + (3.0 - 8.0) × (19 / 20) = 8.0 - 4.75 = 3.25 degrees Celsius, which is close to F1_new.

[0063] When the transition time ends, i.e., when i reaches N, the PLC stops linear interpolation updates and directly uses F1_new as the subsequent integral zeroing trigger threshold. At this point, the threshold has completely transitioned to the new value, and the control process smoothly switches to threshold control for the new process segment.

[0064] The technical principle of this solution is as follows: when the preset heating slope changes, the integral zeroing trigger threshold jumps from the old value to the new value, causing a sudden change in the PID control quantity, resulting in fluctuations in the furnace temperature rise. By setting a transition time length and updating the threshold linearly by interpolation cycle by cycle within this time, the change in the threshold is made smooth and gradual rather than abrupt, thus avoiding control disturbances. The transition time length is positively correlated with the thermal inertia characteristic parameter, allowing equipment with greater thermal inertia to obtain a longer transition time, ensuring that the threshold change matches the equipment response speed.

[0065] The technical advantages of this solution are: it eliminates the threshold jump caused by the integral zeroing triggered by the process segment switching, making the threshold change process smooth and controllable, avoiding abrupt changes in control quantity and fluctuations in furnace temperature rise, and improving the control stability and welding quality consistency under multi-stage heating process.

[0066] In a preferred embodiment, within the transition time length, the following step is further included: Adjust the identification update cycle of thermal inertia characteristic parameters and shorten the identification update cycle to a preset ratio of the identification update cycle under normal operating conditions in order to accelerate the convergence of the tracking lag deviation of the actual temperature to the dynamic target temperature after the slope change. After the transition time ends, the identification and update cycle of the thermal inertia characteristic parameters will be restored to the identification and update cycle under normal operating conditions.

[0067] Specifically, during the transition time, the furnace's temperature response characteristics are dynamically adjusted due to changes in the preset heating slope. At this time, the original thermal inertia characteristic parameter θ may not accurately reflect the thermal inertia under the new operating condition. If updated according to the identification update cycle under normal operating conditions, the identification results may lag, affecting the accuracy of the integral zeroing trigger threshold during the transition period.

[0068] To address this issue, the PLC adjusts the identification and update cycle of the thermal inertia characteristic parameters within the transition time. Under normal operating conditions, the PLC performs the identification and update of the thermal inertia characteristic parameters every 10 PID control cycles, meaning the identification and update cycle is 10 control cycles, equivalent to 5 seconds. This cycle value is preset by the host computer and can be adjusted according to the equipment characteristics.

[0069] Once the transition period begins, the PLC shortens the identification and update cycle to a preset ratio under normal operating conditions. This preset ratio is set by the host computer, for example, to one-half or one-quarter. Taking one-half as an example, the PLC shortens the identification and update cycle from 10 control cycles to 5 control cycles, meaning that the thermal inertia characteristic parameters are identified and updated once every 2.5 seconds. In specific implementation, the PLC sets a counter Update_Cnt in the program. Under normal operating conditions, the counter is reset to zero every 10 control cycles, triggering an identification and update. During the transition period, the PLC modifies the integral zeroing trigger threshold of the counter to 5, thus doubling the identification and update frequency.

[0070] The specific algorithm for identification and updating is the same as described previously: In each identification and updating cycle, the PLC calculates the tracking lag deviation E = T - PV_I between the dynamic target temperature T and the actual temperature PV_I, stores the E value in a circular queue of length N, calculates the average value E_avg of the E value, and calculates the thermal inertia characteristic parameter θ = α × (E_avg / K) based on the ratio of E_avg to the current heating slope K. Because the identification and updating cycle is shortened, the update frequency of the θ value is increased, enabling a faster reflection of the actual temperature tracking lag after slope changes.

[0071] After the transition time ends, the PLC restores the identification and update cycle of the thermal inertia characteristic parameters to the identification and update cycle under normal operating conditions, that is, from 5 control cycles to 10 control cycles. The restoration operation is achieved by resetting the counter's integral reset trigger threshold to 10.

[0072] The technical principle behind this scheme is as follows: During the transition period after the slope switch, the furnace's temperature response characteristics are not yet stable, and the original thermal inertia parameters have become invalid. If the thermal inertia parameters are updated at the normal frequency, the parameter convergence speed is slow, which may lead to inaccurate calculation of the integral zeroing trigger threshold. By increasing the identification and update frequency, the thermal inertia parameters can quickly converge to the true value under the new operating conditions, thereby ensuring that the parameters on which the threshold smooth transition is based are accurate and timely.

[0073] The technical advantages of this scheme are: it accelerates the convergence speed of thermal inertia characteristic parameters after slope change, makes the calculation of the integral zeroing trigger threshold more accurate, ensures that the thermal inertia parameters used in the threshold smooth transition process always reflect the current operating conditions, and improves the control accuracy and stability during the transition period.

[0074] In a preferred embodiment, within the transition time length, the following step is further included: Real-time calculation of the tracking deviation between the current dynamic target temperature and the actual temperature, as well as the rate of change of the tracking deviation; When the tracking deviation is less than or equal to the integral zeroing trigger threshold in the current transition, and the rate of change of the tracking deviation is positive, the execution of the multiple progressive zeroing operations is paused. Obtain the first preset heating slope before the slope change and the second preset heating slope after the slope change, and calculate the slope ratio; The zeroing delay time is dynamically determined based on the product of the slope ratio and the thermal inertia characteristic parameter. During the zeroing delay period, the zeroing operation is paused; after the zeroing delay period ends, the determination of the integral zeroing trigger threshold is resumed, and the multiple progressive zeroing operations are allowed to be executed.

[0075] Specifically, during the transition time, as the integral zeroing trigger threshold is smoothly transitioning from the old value to the new value, immediately performing the integral zeroing operation according to the new threshold may lead to a mismatch in the timing of zeroing. Specifically, when switching from a high slope to a low slope, the actual temperature may still be catching up with the dynamic target temperature with a significant lag. If zeroing is allowed immediately at this time, the integral effect will weaken prematurely, reducing heating efficiency. When switching from a low slope to a high slope, the actual temperature may already be close to the dynamic target temperature. If zeroing is allowed immediately after the new threshold widens, incomplete zeroing of the integral term may lead to overshoot.

[0076] To address this issue, the PLC introduces a zeroing delay mechanism within the transition time. First, in each control cycle, the PLC calculates in real-time the tracking deviation E = T - PV_I between the current dynamic target temperature and the actual temperature, as well as the rate of change of the tracking deviation dE / dt. The rate of change of the tracking deviation is calculated using a differential method: Let the tracking deviation of the previous control cycle be E_previous, and the tracking deviation of the current cycle be E_current, then dE / dt = (E_current - E_previous) / T_pid, where T_pid is the PID control cycle.

[0077] The PLC simultaneously monitors the integral zeroing trigger threshold F1_current during the current transition. When the tracking deviation E is less than or equal to F1_current, and the rate of change of the tracking deviation dE / dt is positive, the PLC determines that the system is currently in a state requiring delayed zeroing. A positive dE / dt value means that the tracking deviation is increasing, i.e., the lag between the actual temperature and the dynamic target temperature is intensifying. At this time, the system is in the process of catching up with the dynamic target temperature, and it is not advisable to immediately perform zeroing.

[0078] When the above conditions are met, the PLC pauses the execution of multiple progressive zeroing operations. The pause is achieved by setting a pause flag, Pause_Flag, in the program logic. When Pause_Flag is TRUE, the relevant program segments for zeroing judgment and execution are skipped.

[0079] While pausing and resetting, the PLC acquires the first preset heating slope K_old before the slope change and the second preset heating slope K_new after the slope change. These two values ​​have already been recorded during slope change detection and stored in the variables K_old and K_new. The PLC calculates the slope ratio R = K_new / K_old. When K_new is greater than K_old, R is greater than 1; when K_new is less than K_old, R is less than 1.

[0080] The PLC dynamically determines the zeroing delay time T_delay based on the product of the slope ratio R and the current thermal inertia characteristic parameter θ. Specifically, the PLC presets a base delay time T_delay_base, for example, 2 seconds, and then corrects it based on the product of R and θ. The correction formula is T_delay = T_delay_base × (R × θ). When R × θ is large, the delay time is extended; when R × θ is small, the delay time is shortened. For example, assuming T_delay_base = 2 seconds, R = 3.0, and θ = 0.5, then R × θ = 1.5, and T_delay = 3 seconds; if R = 0.5 and θ = 0.8, then R × θ = 0.4, and T_delay = 0.8 seconds. The physical meaning of this design is that the more drastic the slope change (the further R deviates from 1) or the greater the thermal inertia, the longer the system needs to adapt to the new target trajectory; conversely, the delay time is shortened accordingly.

[0081] After determining the zeroing delay time T_delay, the PLC starts a delay timer Delay_Timer with a timing duration set to T_delay. During the delay timer's timeout period, the PLC maintains a paused zeroing operation state, that is, Pause_Flag remains TRUE, and multiple progressive zeroing operations are always skipped.

[0082] When the delay timer expires, the PLC sets Pause_Flag to FALSE, resumes the judgment of the integral zeroing trigger threshold, and allows multiple progressive zeroing operations to be performed. At this time, the integral zeroing trigger threshold has gradually approached F1_new through the smooth transition mechanism, and the tracking relationship between the actual temperature and the dynamic target temperature has stabilized after the delay time buffer, making the judgment of the zeroing timing more accurate.

[0083] The technical principle of this scheme is as follows: During the transition period after slope switching, the tracking relationship between the actual temperature and the dynamic target temperature is mismatched. Immediately performing zeroing according to the new threshold at this time would lead to control inaccuracy. By introducing a dynamic delay time related to the slope ratio and thermal inertia, the zeroing operation is paused during the delay time, allowing the system sufficient time for the actual temperature to synchronize with the new dynamic target trajectory. Zeroing judgment is resumed after the delay time ends, ensuring that the zeroing timing matches the dynamic characteristics of the new process segment.

[0084] The technical effect of this solution is that it solves the problem of mismatch between the zeroing timing after slope switching and the dynamic characteristics of the new process segment, avoids overshoot suppression failure or heating interruption caused by executing zeroing too early or too late, enables the control system to smoothly transition to the new process segment, and ensures the temperature control accuracy under multi-stage heating process.

[0085] In a preferred embodiment, the process of the multiple progressive zeroing operations further includes the following steps: Record the actual temperature value each time a zeroing operation is performed, as well as the trajectory of the actual temperature change after each zeroing operation. The suppression efficiency of a single zeroing operation is calculated based on the temperature change between two adjacent zeroing operations. The suppression efficiency is positively correlated with the decrease in the actual temperature rise rate after the zeroing operation. When the suppression efficiency of two consecutive zeroing operations is lower than the preset efficiency threshold, it is determined that the current integral zeroing trigger threshold is too high, and an adaptive threshold shrinkage operation is performed, which specifically includes: The current integral zeroing trigger threshold is gradually reduced by a preset step size until the suppression efficiency when the zeroing operation is performed again is restored to a level higher than the preset efficiency threshold. The shrinkage integral zeroing trigger threshold is used as the subsequent integral zeroing trigger threshold for the current process segment, and the correspondence between this threshold and the current thermal inertia characteristic parameter and the preset heating slope is recorded for subsequent threshold initialization under the same operating conditions.

[0086] Specifically, during multiple progressive zeroing operations, the integral zeroing trigger threshold F1 is calculated using a two-dimensional lookup table method based on the preset heating slope K and thermal inertia characteristic parameter θ. However, due to factors such as equipment aging, load changes, or vacuum fluctuations, the pre-calibrated mapping table may deviate from the actual operating conditions, resulting in an excessively large F1. When F1 is too large, the zeroing operation intervenes too early, and the rate of decrease in the actual temperature rise after each zeroing is small, i.e., the suppression efficiency is insufficient, requiring multiple zeroing operations to effectively suppress overshoot.

[0087] To address this issue, the PLC records relevant data and calculates the suppression efficiency each time a zeroing operation is performed. The specific implementation method is as follows: During multiple progressive zeroing operations, the PLC sets a zeroing counter, Clear_Cnt, to record the number of zeroing operations performed within the current process segment. Each time a zeroing operation is performed, the PLC records the actual temperature value PV_clear at that moment and stores it in the array PV_clear_array[Clear_Cnt]. Simultaneously, the PLC records the actual temperature change trajectory after each zeroing operation. The recording method is as follows: within a preset time window after the zeroing operation, for example, 5 PID control cycles, the actual temperature value is recorded every other cycle, forming a temperature sequence. The length of this time window is consistent with the time window used to determine whether to zero again.

[0088] After each zeroing operation, the PLC calculates the suppression efficiency of that zeroing operation. The suppression efficiency is calculated as follows: First, the actual temperature rise rate (Rate_before) before the zeroing operation is calculated by linearly fitting the actual temperature values ​​of the previous five control cycles, expressed in degrees Celsius per second. Then, the actual temperature rise rate (Rate_after) after the zeroing operation is calculated by linearly fitting the temperature sequence recorded within the time window after the zeroing operation. The suppression efficiency η is defined as (Rate_before - Rate_after) / Rate_before, which is the ratio of the decrease in the rise rate after the zeroing operation to the rise rate before the zeroing operation. When η is positive, it indicates that the zeroing operation has a suppressive effect; the larger η is, the more significant the suppression effect.

[0089] When the suppression efficiency of two consecutive zeroing operations is lower than the preset efficiency threshold η_th, the PLC determines that the current integral zeroing trigger threshold F1 is too high. The efficiency threshold η_th is preset by the host computer. For example, setting it to 0.3 means that when the suppression efficiency of two zeroing operations is lower than 30%, the threshold is considered too high and needs to be reduced. The condition of two consecutive judgments is to avoid misjudgment caused by a single abnormal fluctuation.

[0090] In response to this determination, the PLC performs a threshold-adaptive shrinkage operation. The specific implementation method is as follows: First, the PLC gradually decreases the current integral zeroing trigger threshold F1 according to a preset step size Step. The step size Step is preset by the host computer, for example, set to 0.5 degrees Celsius. The decrease operation is implemented by F1_new = F1_current-Step. After decreasing the threshold, the PLC continues to perform multiple progressive zeroing operations and continues to calculate the suppression efficiency under the new threshold.

[0091] The PLC continuously executes the above-described successive reduction operation, monitoring the suppression efficiency of subsequent zeroing operations after each reduction. When the suppression efficiency of a subsequent zeroing operation recovers to above the preset efficiency threshold η_th at a threshold after a certain reduction, the contraction operation stops. At this point, the current contracted integral zeroing trigger threshold F1_adjusted is used as the subsequent integral zeroing trigger threshold for the current process segment.

[0092] After determining the threshold after contraction, the PLC records the correspondence between this threshold and the current thermal inertia characteristic parameter θ and the preset heating slope K. The recording method is as follows: K, θ, and F1_adjusted are stored as a triple in the PLC's retainable memory. This storage area uses a first-in, first-out queue structure, storing a maximum of the most recent 10 sets of data to avoid unlimited expansion of the storage space.

[0093] This correspondence is used for threshold initialization under subsequent identical operating conditions. Specifically, when the same preset heating slope K and similar thermal inertia characteristic parameters θ reappear in subsequent process stages, the PLC, when calculating the integral zeroing trigger threshold, preferentially uses the F1_adjusted value from the stored triplet as the initial threshold, rather than directly using the value obtained by the two-dimensional lookup table method. This avoids the need for a contraction process each time, allowing the system to quickly adapt to known operating conditions.

[0094] The technical principle of this scheme is as follows: by calculating the suppression efficiency of each zeroing operation in real time, it determines whether the current threshold is too large. When the suppression efficiency is continuously low, it indicates that the threshold is set too high, the zeroing intervention is too early, or the strength is insufficient. By successively reducing the threshold and monitoring the recovery of the suppression efficiency, a closed-loop self-optimization of the threshold is achieved. At the same time, the correspondence between the optimized threshold and the operating conditions is stored, enabling the system to have memory and learning capabilities, and the optimized threshold can be directly reused when encountering the same operating conditions in the future.

[0095] The technical advantages of this scheme are: it enables the integral zeroing trigger threshold to be adaptively corrected based on the actual control effect, overcoming the problem of deviation between the pre-calibrated mapping table and the real-time operating conditions. By successively shrinking to approach the optimal threshold, the accuracy of overshoot suppression is improved. Simultaneously, by recording and reusing the optimized threshold, the control system possesses self-learning and self-optimization capabilities, reducing the time spent on repeated adjustments and improving process efficiency.

[0096] In a preferred embodiment, the zeroing delay time further includes the following steps: Monitor the sign change of the rate of change; When the rate of change of the tracking deviation is detected to change from a positive value to a negative value, it is determined that the actual temperature has changed from lagging behind the dynamic target temperature to leading the dynamic target temperature. In response to the sign change, a zeroing delay truncation operation is performed, specifically including: Immediately interrupt the remaining countdown of the reset delay time; In the next control cycle after the interruption, the determination of the integral zeroing trigger threshold is immediately resumed, and the multiple progressive zeroing operations are allowed to be executed.

[0097] Specifically, during the zeroing delay time, the PLC pauses multiple progressive zeroing operations, waiting for the actual temperature to synchronize with the new dynamic target trajectory. However, in some cases, the actual temperature may have already synchronized before the zeroing delay time ends, or even become ahead of the dynamic target temperature. In this case, continuing to wait for the remaining delay time would miss the optimal zeroing opportunity, potentially leading to insufficient overshoot suppression.

[0098] To solve this problem, the PLC continuously monitors and tracks the sign of the rate of change of the deviation during the zeroing delay time, and immediately truncates the delay time when the sign changes from positive to negative. The specific implementation method is as follows: During the zeroing delay time, the PLC calculates the rate of change of the tracking deviation, dE / dt, in each control cycle and records its sign. The PLC sets a variable `Sign_prev` in the program to store the sign of the rate of change from the previous control cycle; and a variable `Sign_curr` to store the sign of the rate of change for the current control cycle. The sign is determined as follows: when dE / dt is greater than 0, the sign is positive; when dE / dt is less than 0, the sign is negative; and when dE / dt equals 0, the sign remains unchanged from the previous cycle.

[0099] The PLC compares Sign_curr and Sign_prev in each control cycle. When Sign_prev is detected to be positive and Sign_curr to be negative, the rate of change of the tracking deviation changes from positive to negative. This sign change has a clear physical meaning: tracking deviation E = T - PV_I. When dE / dt changes from positive to negative, it indicates that the difference between the actual temperature and the dynamic target temperature has changed from gradually widening to gradually narrowing, meaning the actual temperature has changed from lagging behind the dynamic target temperature to leading the dynamic target temperature. At this point, the system has completed its adaptation to the new operating condition, and there is no need to continue waiting for the delay time.

[0100] In response to this sign change, the PLC immediately executes a zero-delay time truncation operation. The specific implementation steps are as follows: The first step is for the PLC to call the system timer interrupt function to immediately stop the started Delay_Timer and clear its current value. Interrupting the remaining countdown means that it will no longer wait for the originally scheduled clearing delay time to end.

[0101] The second step is that in the next PID control cycle after the truncation operation, the PLC immediately resumes the judgment of the integral zeroing trigger threshold and allows multiple progressive zeroing operations to be performed. Specifically, the pause flag Pause_Flag is set to FALSE, causing the program flow to jump to the logic branch for zeroing judgment and execution.

[0102] Taking a specific scenario as an example, assume the calculated zeroing delay time T_delay is 5 seconds. When the delay timer reaches 3 seconds, the PLC detects that the rate of change of the tracking deviation has changed from positive to negative. At this point, the actual temperature has changed from lagging to leading. The PLC immediately interrupts the remaining 2 seconds of the delay timer and resumes the zeroing judgment in the next control cycle. Since the actual temperature is now leading, immediately performing integral zeroing can promptly suppress any potential overshoot.

[0103] The technical principle of this scheme is as follows: the zeroing delay time is a fixed duration predetermined based on the slope ratio and thermal inertia characteristic parameters. However, the synchronization time between the actual temperature and the target trajectory is affected by various factors and may be shorter or longer than this fixed duration. By monitoring the sign change of the tracking deviation rate in real time, it is possible to accurately determine whether the system has completed synchronization. When the sign changes from positive to negative, it indicates that the actual temperature has changed from lagging to leading, which is a clear sign that the system has completed adaptation. At this point, immediately resuming the zeroing judgment allows the integral zeroing to intervene at the most appropriate time.

[0104] The technical advantages of this solution are: it solves the problem of delayed zeroing timing that may be caused by a fixed zeroing delay time, enabling the zeroing operation to intervene as soon as the system completes synchronization, thus improving the timeliness and effectiveness of overshoot suppression. At the same time, it avoids missing the optimal zeroing opportunity due to waiting for the remaining delay time, making the control system more sensitive and accurate in responding to changes in operating conditions.

[0105] In a preferred embodiment, after the zeroing delay time is interrupted, the following steps are further included: Record the actual duration from the start of the zeroing delay to the interruption time, as well as the tracking deviation value and the rate of change of the tracking deviation at the interruption time; The actual duration, the tracking deviation value at the time of interruption, and the rate of change of the tracking deviation are stored as a complete sample in the sample library; When a preset temperature rise rate change occurs again within the same process segment and a new zeroing delay time is entered, historical samples with a similar rate change are retrieved from the sample library. The current zeroing delay time is then corrected based on the actual duration in the historical samples. Specifically, this includes: If the tracking deviation value at the time of interruption in the retrieved historical samples is less than the preset deviation threshold, the current zeroing delay time will be shortened to a preset proportion of the current preset delay time. If the rate of change of tracking deviation at the time of interruption is still positive in the retrieved historical samples, the current zeroing delay time will be extended to a preset proportion of the current preset delay time. If no similar historical samples are found, the current preset delay time will remain unchanged.

[0106] Specifically, after the zeroing delay time is truncated, the system obtains complete execution information for that delay process, including the actual duration of the delay, the tracking deviation value at the truncation moment, and the rate of change. This information reflects the time characteristics required for the actual temperature and the target trajectory to synchronize under the current operating conditions, and is valuable empirical data. If this data is discarded, the delay waiting process will have to be repeated when encountering similar operating conditions in the future, making it impossible to reuse and optimize experience.

[0107] To solve this problem, the PLC performs the sample storage operation after the zeroing delay time is truncated. The specific implementation method is as follows: After the zeroing delay time truncation operation is executed, the PLC immediately records the following data: the actual duration T_actual from the start of the zeroing delay time to the interruption time, which is read from the delay timer Delay_Timer in seconds; the tracking deviation value E_interrupt at the interruption time, which is the difference between the dynamic target temperature and the actual temperature at the truncation time; and the tracking deviation change rate dE / dt_interrupt at the interruption time, which is the change rate value at the truncation time.

[0108] The PLC associates the three data points T_actual, E_interrupt, and dE / dt_interrupt with the current operating parameters and stores them as a complete sample in the sample library. The sample library's storage structure is as follows: each sample contains five fields: preset heating slope K, thermal inertia characteristic parameter θ, actual duration T_actual, tracking deviation value at the interruption time E_interrupt, and tracking deviation change rate dE / dt_interrupt at the interruption time. The sample library is stored in the PLC's extended data storage area using a circular queue structure, capable of storing a maximum of 100 samples. When this limit is exceeded, the oldest stored sample is overwritten.

[0109] When a preset temperature rise rate change occurs again within the same process segment and a new zeroing delay time is reached, the PLC retrieves historical samples from the sample library that are similar to this rate change, and corrects the current zeroing delay time based on the retrieval results. The specific retrieval and correction methods are as follows: First, the PLC determines the characteristic parameters of the current slope change, including the first preset heating slope K_old, the second preset heating slope K_new, and the current thermal inertia characteristic parameter θ_current. The PLC calculates the slope ratio R_current = K_new / K_old.

[0110] Then, the PLC iterates through each sample in the sample library and calculates the similarity S between the sample and the current working condition. The similarity S is calculated as follows: S = w1×|K_old_sample - K_old_current| + w2×|K_new_sample-K_new_current| + w3×|θ_sample-θ_current|. Wherein, K_old_sample represents the preset heating slope before the slope change corresponding to the historical samples stored in the sample library; K_old_current represents the preset heating slope before the slope change under the current operating condition; K_new_sample represents the preset heating slope after the slope change corresponding to the historical samples stored in the sample library; K_new_current represents the preset heating slope after the slope change under the current operating condition; θ_sample represents the thermal inertia characteristic parameter corresponding to the historical samples stored in the sample library; θ_current represents the thermal inertia characteristic parameter identified in real time under the current operating condition; w1, w2, w3 are preset weighting coefficients, used to measure the influence of the difference in slope and thermal inertia before and after on the similarity, respectively, and their specific values ​​can be determined by experimental calibration according to the actual operating conditions. The smaller the S value, the more similar the sample is to the current operating condition. The PLC presets a similarity threshold S_th, and selects one or more samples with an S value less than S_th as similar historical samples. After retrieving similar historical samples, the PLC corrects the current zeroing delay time according to the actual duration T_actual in the historical samples. The revised rules are as follows: If, in the retrieved historical samples, the tracking deviation value E_interrupt at the moment of interruption is less than the preset deviation threshold E_th, it is determined that, under historical operating conditions, the actual temperature was already very close to the target trajectory before the end of the delay time, and the synchronization process was completed relatively quickly. In this case, the current zeroing delay time is shortened to a preset proportion of the current preset delay time, for example, shortened to 80%. The shortened delay time T_delay_new = T_delay_original × 0.8. The preset deviation threshold E_th is set by the host computer, for example, set to 0.5 degrees Celsius.

[0111] If the tracking deviation change rate dE / dt_interrupt at the moment of interruption is still positive in the retrieved historical samples, it is determined that under historical operating conditions, the actual temperature was still lagging when the delay time was truncated. The truncation was triggered by other conditions, and the actual synchronization time may be longer. In this case, the current zeroing delay time is extended to a preset percentage of the current preset delay time, for example, extended to 120%. The extended delay time T_delay_new = T_delay_original × 1.2.

[0112] If no similar historical sample is found, the current preset delay time will remain unchanged, i.e., T_delay_new=T_delay_original.

[0113] Taking a specific scenario as an example, assume the current slope ratio R_current = 2.5, θ_current = 0.6, and the current preset delay time is 4 seconds. The PLC retrieves a similar sample from the sample library, whose K_old and K_new are similar to the current one, θ is 0.55, and the sample's E_interrupt = 0.3 degrees Celsius, which is less than the preset deviation threshold of 0.5 degrees Celsius. According to the correction rule, the current delay time is shortened to 4 × 0.8 = 3.2 seconds. In another scenario, if the retrieved sample has a positive dE / dt_interrupt value, the current delay time is extended to 4 × 1.2 = 4.8 seconds.

[0114] After determining the corrected zeroing delay time, the PLC executes the zeroing delay mechanism according to the corrected delay time. At the same time, when the delay process ends, whether it ends normally or is truncated, the PLC stores the actual execution data of this delay process as a new sample in the sample library for subsequent retrieval and correction.

[0115] The technical principle behind this solution lies in storing actual execution data for each zeroing delay process in a sample library, allowing the system to accumulate historical experience. When encountering similar operating conditions again, the optimal delay time for the current condition can be predicted by retrieving historical samples. If historical samples show a fast synchronization process, the delay time is shortened to improve response speed; if historical samples show a slow synchronization process, the delay time is extended to ensure sufficient synchronization. This experience-driven delay time correction mechanism transforms the delay time setting from a fixed open-loop calculation to a closed-loop optimization based on historical data.

[0116] The technical advantages of this solution are: it enables the zeroing delay time to be adaptively adjusted based on historical experience, gradually approaching the optimal value under current operating conditions. Through the accumulation and reuse of a sample library, the system acquires learning capabilities. When running the same or similar processes multiple times, the delay time setting becomes increasingly precise, avoiding zeroing timing mismatch problems caused by inappropriate delay times, and improving control efficiency and overshoot suppression in multi-stage heating processes. Simultaneously, the introduction of the sample library allows the control system to adapt to changes in operating conditions under different batches and loads, improving the versatility and robustness of the control system.

[0117] Example 2 This embodiment proposes a linear slope temperature rise control system for a vacuum welding furnace, used to implement the method described above, including: The calculation module is configured to obtain the initial temperature and preset heating slope of the current process segment, and calculate the dynamic target temperature in real time according to the running time of the current process segment and at a refresh frequency that matches the PID control cycle; wherein the dynamic target temperature changes continuously and linearly with time, and the difference between two adjacent calculated dynamic target temperatures is a constant minimum value, so that the change trajectory of the dynamic target temperature is a smooth straight line. An output module, configured to output the dynamically calculated target temperature as a set value in real time; The control module is configured to collect the actual temperature value of the vacuum welding furnace as a feedback value, and use the dynamic target temperature and the actual temperature value as inputs to perform PID calculations to generate control quantities, driving the actuator to perform closed-loop control of the furnace body temperature; wherein, the actual temperature tracks a continuously moving smooth target trajectory, rather than discrete step-like target points.

[0118] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for controlling the linear slope temperature rise of a vacuum welding furnace, characterized in that, Includes the following steps: The initial temperature and preset heating slope of the current process segment are obtained, and the dynamic target temperature is calculated in real time according to the running time of the current process segment and the refresh frequency is matched with the PID control cycle. The dynamic target temperature changes continuously and linearly with time, and the difference between two adjacent calculated dynamic target temperatures is a constant minimum value, so that the change trajectory of the dynamic target temperature is a smooth straight line. The dynamically calculated target temperature is output as the set value. The actual temperature value of the vacuum welding furnace is collected as a feedback value, and the dynamic target temperature and the actual temperature value are used as inputs to perform PID calculation to generate control quantity, which drives the actuator to perform closed-loop control of the furnace body temperature; wherein, the actual temperature tracks a continuously moving smooth target trajectory, rather than a discrete step-like target point.

2. The linear slope temperature rise control method for a vacuum welding furnace according to claim 1, characterized in that, The closed-loop control process also includes the following steps: When the actual temperature tracks the smooth target trajectory to enter the preset static target temperature range, the integral zeroing trigger threshold is dynamically determined according to the preset heating slope, and multiple zeroing operations are performed on the integral term in the PID calculation to suppress the overshoot of the actual temperature when it reaches the static target temperature. The integral zeroing trigger threshold is positively correlated with the preset heating slope. The larger the preset heating slope, the larger the integral zeroing trigger threshold, and the earlier the zeroing operation is initiated.

3. The linear slope temperature rise control method for a vacuum welding furnace according to claim 2, characterized in that, The step of dynamically determining the integral zeroing trigger threshold based on the preset heating slope includes the following steps: The thermal inertia characteristic parameters of the vacuum welding furnace under the current operating conditions are identified in real time, and the thermal inertia characteristic parameters are dynamically updated according to the tracking lag deviation of the actual temperature to the dynamic target temperature. Based on the preset heating slope of the current process section and the real-time identified thermal inertia characteristic parameters, the integral zeroing trigger threshold is dynamically calculated, so that the integral zeroing trigger threshold increases with the increase of the preset heating slope and also increases with the increase of the thermal inertia characteristic parameters. When the difference between the actual temperature and the static target temperature is less than or equal to the dynamically calculated integral zeroing trigger threshold, multiple progressive zeroing operations are performed on the integral term in the PID calculation. Specifically, this includes: performing a zeroing operation once; if the actual temperature is still on an upward trend within a preset time window and the difference between it and the static target temperature is still less than or equal to the integral zeroing trigger threshold, then performing the zeroing operation again, and so on, until the integral term is completely zeroed or the actual temperature enters the stable range of the static target temperature.

4. The linear slope temperature rise control method for a vacuum welding furnace according to claim 3, characterized in that, The process of dynamically determining the threshold for resetting the integral to zero also includes the following steps: The preset heating slope of the current process section is monitored in real time, and the difference between the preset heating slope of the current control cycle and the previous control cycle is calculated. When the difference exceeds the preset slope change threshold, it is determined that the preset heating slope has changed. In response to changes in the preset heating slope, a threshold smoothing transition operation is performed, specifically including: Obtain the first integral zeroing trigger threshold before the slope change and the second integral zeroing trigger threshold after the slope change; A transition time length is determined, which is positively correlated with thermal inertia characteristic parameters; Within the specified transition time, the integral zeroing trigger threshold is calculated and updated periodically using linear interpolation, with each control cycle as the unit, so that the integral zeroing trigger threshold gradually changes from the first integral zeroing trigger threshold to the second integral zeroing trigger threshold.

5. The linear slope temperature rise control method for a vacuum welding furnace according to claim 4, characterized in that, Within the said transition time length, the following steps are also included: Adjust the identification update cycle of thermal inertia characteristic parameters and shorten the identification update cycle to a preset ratio of the identification update cycle under normal operating conditions in order to accelerate the convergence of the tracking lag deviation of the actual temperature to the dynamic target temperature after the slope change. After the transition time ends, the identification and update cycle of the thermal inertia characteristic parameters will be restored to the identification and update cycle under normal operating conditions.

6. The linear slope temperature rise control method for a vacuum welding furnace according to claim 4, characterized in that, Within the said transition time length, the following steps are also included: Real-time calculation of the tracking deviation between the current dynamic target temperature and the actual temperature, as well as the rate of change of the tracking deviation; When the tracking deviation is less than or equal to the integral zeroing trigger threshold in the current transition, and the rate of change of the tracking deviation is positive, the execution of the multiple progressive zeroing operations is paused. Obtain the first preset heating slope before the slope change and the second preset heating slope after the slope change, and calculate the slope ratio; The zeroing delay time is dynamically determined based on the product of the slope ratio and the thermal inertia characteristic parameter. During the zeroing delay period, the zeroing operation is paused; after the zeroing delay period ends, the determination of the integral zeroing trigger threshold is resumed, and the multiple progressive zeroing operations are allowed to be executed.

7. The linear slope temperature rise control method for a vacuum welding furnace according to claim 3, characterized in that, The process of repeated gradual zeroing operations also includes the following steps: Record the actual temperature value each time a zeroing operation is performed, as well as the trajectory of the actual temperature change after each zeroing operation. The suppression efficiency of a single zeroing operation is calculated based on the temperature change between two adjacent zeroing operations. The suppression efficiency is positively correlated with the decrease in the actual temperature rise rate after the zeroing operation. When the suppression efficiency of two consecutive zeroing operations is lower than the preset efficiency threshold, it is determined that the current integral zeroing trigger threshold is too high, and an adaptive threshold shrinkage operation is performed, which specifically includes: The current integral zeroing trigger threshold is gradually reduced by a preset step size until the suppression efficiency when the zeroing operation is performed again is restored to a level higher than the preset efficiency threshold. The shrinkage integral zeroing trigger threshold is used as the subsequent integral zeroing trigger threshold for the current process segment, and the correspondence between this threshold and the current thermal inertia characteristic parameter and the preset heating slope is recorded for subsequent threshold initialization under the same operating conditions.

8. The linear slope temperature rise control method for a vacuum welding furnace according to claim 6, characterized in that, The zeroing delay time also includes the following steps: Monitor the sign change of the rate of change; When the rate of change of the tracking deviation is detected to change from a positive value to a negative value, it is determined that the actual temperature has changed from lagging behind the dynamic target temperature to leading the dynamic target temperature. In response to the sign change, a zeroing delay truncation operation is performed, specifically including: Immediately interrupt the remaining countdown of the reset delay time; In the next control cycle after the interruption, the determination of the integral zeroing trigger threshold is immediately resumed, and the multiple progressive zeroing operations are allowed to be executed.

9. The linear slope temperature rise control method for a vacuum welding furnace according to claim 8, characterized in that, After the zeroing delay is interrupted, the following steps are also included: Record the actual duration from the start of the zeroing delay to the interruption time, as well as the tracking deviation value and the rate of change of the tracking deviation at the interruption time; The actual duration, the tracking deviation value at the time of interruption, and the rate of change of the tracking deviation are stored as a complete sample in the sample library; When a preset temperature rise rate change occurs again within the same process segment and a new zeroing delay time is entered, historical samples with a similar rate change are retrieved from the sample library. The current zeroing delay time is then corrected based on the actual duration in the historical samples. Specifically, this includes: If the tracking deviation value at the time of interruption in the retrieved historical samples is less than the preset deviation threshold, the current zeroing delay time will be shortened to a preset proportion of the current preset delay time. If the rate of change of tracking deviation at the time of interruption is still positive in the retrieved historical samples, the current zeroing delay time will be extended to a preset proportion of the current preset delay time. If no similar historical samples are found, the current preset delay time will remain unchanged.

10. A linear slope temperature rise control system for a vacuum welding furnace, used to implement the method as described in any one of claims 1-9, characterized in that, include: The calculation module is configured to obtain the initial temperature and preset heating slope of the current process segment, and calculate the dynamic target temperature in real time according to the running time of the current process segment and at a refresh frequency that matches the PID control cycle; wherein the dynamic target temperature changes continuously and linearly with time, and the difference between two adjacent calculated dynamic target temperatures is a constant minimum value, so that the change trajectory of the dynamic target temperature is a smooth straight line. An output module, configured to output the dynamically calculated target temperature as a set value in real time; The control module is configured to collect the actual temperature value of the vacuum welding furnace as a feedback value, and use the dynamic target temperature and the actual temperature value as inputs to perform PID calculations to generate control quantities, driving the actuator to perform closed-loop control of the furnace body temperature; wherein, the actual temperature tracks a continuously moving smooth target trajectory, rather than discrete step-like target points.