An extrusion speed control method based on constant temperature aluminum material extrusion

Abstract

The present application belongs to the technical field of automatic control of metal extrusion forming process, and particularly relates to an extrusion speed control method based on constant temperature aluminum material extrusion. Initialization is performed on extrusion process parameters and control parameters, input power and actual temperature of each heating zone, as well as extrusion rod displacement and extrusion force are collected in real time; an energy balance equation is constructed for each heating zone, the instantaneous heat dissipation power of the aluminum ingot transmitted to the extrusion cylinder wall is estimated in real time, the estimated values of each zone are summed, and the estimated outlet temperature at the current time is calculated explicitly; the estimated outlet temperature is taken as feedback to generate an extrusion speed control instruction; the extrusion speed control instruction is sent to the extrusion rod driving mechanism of the extruder, and the temperature is adjusted to approach and maintain at the target outlet temperature. The present application avoids the interference of outlet smoke, water vapor and oxidation layer on temperature measurement, has the outstanding advantages of high control precision, small calculation amount, maintenance-free self-correction, etc., and is suitable for extrusion production lines of various models and alloys.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology for metal extrusion molding processes, and particularly relates to a method for controlling the extrusion speed based on constant temperature aluminum extrusion. Background Technology

[0002] In aluminum alloy extrusion, maintaining a constant outlet profile temperature is crucial for ensuring the product's mechanical properties, surface quality, and dimensional accuracy. Existing isothermal extrusion control methods generally rely on infrared thermometers installed at the extruder outlet to obtain temperature feedback signals, which are then used to adjust the extrusion speed via PID or model predictive control algorithms. However, the extrusion outlet area is filled with high-temperature fumes, release agent vapors, and oil mist, and the oxide layer on the profile surface dynamically changes, making accurate infrared emissivity difficult to calibrate. Temperature measurement signals often contain significant random noise or even step distortion. Furthermore, there is a large lag of several to tens of seconds between extrusion speed adjustment and outlet temperature response, and this lag time fluctuates significantly with changes in process parameters such as the remaining length of the aluminum ingot, alloy grade, and extrusion ratio. Fixed-gain or fixed-model control strategies struggle to maintain high accuracy across the entire operating range. In addition, the infrared thermometer requires frequent manual cleaning and calibration, resulting in high equipment maintenance costs and frequent unplanned downtime. Although some studies have attempted to estimate the outlet temperature through indirect variables such as extrusion barrel wall temperature or extrusion pressure, the empirical relationships or simplified heat transfer models on which they are based lack universality and transient tracking capabilities, and the estimation accuracy is far from meeting the industrial requirements of isothermal extrusion. Summary of the Invention

[0003] This invention addresses the technical problems existing in the automatic control technology of metal extrusion forming processes, and proposes an extrusion speed control method based on constant temperature aluminum extrusion that is rationally designed, simple in method, and theoretically sound.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] S1. Initialize extrusion process parameters and control parameters, including target outlet temperature, sampling period, equivalent heat capacity of each heating zone, extrusion speed constraint range and acceleration constraint;

[0006] S2. Real-time acquisition of input power and actual temperature of each heating zone, as well as extrusion rod displacement and extrusion force;

[0007] S3. Construct energy balance equations for each heating zone, estimate the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall in the heating zone online, sum the estimated instantaneous heat dissipation power of each zone, and define the summation result as the total instantaneous heat dissipation power of the aluminum ingot to the extrusion cylinder wall.

[0008] S4. Based on the total instantaneous heat dissipation power of the aluminum ingot on the extrusion cylinder wall, the heat generation term of plastic deformation determined by the product of the basic plastic work-heat conversion coefficient, the flow stress, the cross-sectional area of ​​the extrusion cylinder cavity, and the current extrusion speed, and the energy conservation relationship between the mold heat dissipation power lost through the mold, the estimated outlet temperature at the current moment is explicitly calculated, and the estimated outlet temperature is used as the feedback signal of the closed-loop control system.

[0009] S5. The target outlet temperature setpoint is compared with the feedback signal to obtain the temperature deviation, and the rate of change of the temperature deviation is calculated. At the same time, the dynamic difference value of the total instantaneous heat dissipation power of the aluminum ingot on the extrusion cylinder wall estimated in S3 is used as the feedforward disturbance compensation signal. Based on the temperature deviation, the rate of change of the temperature deviation and the feedforward disturbance compensation signal, the extrusion speed control command at the current sampling time is generated.

[0010] S6. The extrusion speed control command mentioned in S5 is sent to the extrusion bar drive mechanism of the extruder, and the extrusion speed is adjusted to make the temperature of the extruded profile approach and maintain the target outlet temperature.

[0011] S7. Determine whether the extrusion process has ended. If it has not ended, return to step S2 and enter the data acquisition and control loop of the next sampling cycle until the extrusion process ends. If it has ended, terminate the operation of the closed-loop system.

[0012] Preferably, the constant temperature aluminum extrusion refers to an extrusion process control method, the control objective of which is to keep the temperature of the extruded aluminum profile constant throughout the entire extrusion stroke at the extruder outlet.

[0013] Preferably, the formula for estimating the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall in S3 is as follows:

[0014] ,

[0015] in, For the first Estimated instantaneous heat dissipation power transferred from the aluminum ingot within the heating zone to the extrusion cylinder wall. This is the index for the current sampling time. Number the heating zone of the extrusion cylinder. For the first The electric heating efficiency coefficient of the heating zone. For the first The heating zone at the current sampling time Input electrical power, For the first The nominal equivalent heat capacity of the heating zone within its normal operating temperature range. The sampling period is This represents the inter-sample difference of the estimated temperature of the heating zone within the observer. For the first The convective heat transfer coefficient between the outer wall of the heating zone and the surrounding air. For the first The effective convective heat dissipation area of ​​the outer wall of the heating zone For the first The heating zone at the current sampling time The actual temperature measured by the embedded thermocouple, The ambient temperature of the workshop. For the first Surface emissivity of the outer wall of the heating zone The Stefan-Boltzmann constant is... This value is very small, taking into account the equivalent mass flow rate introduced by the minute high-temperature gas leakage from the sealing gap at the end of the extrusion cylinder. The specific heat capacity of air at constant pressure. For the first The net heat power transferred axially between the heating zone and adjacent heating zones through the extrusion cylinder wall. For the first The portion of the aluminum ingot within the heating zone absorbs or releases heat power during the extrusion process due to possible solid-liquid or liquid-solid phase changes. The first design gain coefficient, For the first Temperature estimation error of the heating zone at the current moment. This is the second design gain coefficient. For dummy integral variables, For the first Temperature estimation error within the heating zone This represents the current sampling time.

[0016] Preferably, the formula for calculating the estimated outlet temperature at the current moment in S4 is:

[0017] ,

[0018] in, The current sampling time The estimated exit temperature is the temperature of the extruded product just as it leaves the die's working zone. This is the index for the current sampling time. The current sampling time Average temperature of the aluminum ingot cross-section entering the mold deformation zone. The current sampling time The mass flow rate of aluminum material through the cross-section of the extrusion cylinder This refers to the specific heat capacity under constant pressure of the extruded aluminum alloy. The basic plastic work-heat conversion coefficient, For flow stress, The average temperature of the aluminum material within the deformation zone of the mold. The average equivalent strain rate of the aluminum material within the deformation zone of the mold. This is the cross-sectional area of ​​the inner cavity of the extrusion cylinder. The current sampling time The extrusion speed, The deformation efficiency factor. The current sampling time Total frictional heat power, The current sampling time The equivalent frictional heat power, For the first Estimated instantaneous heat dissipation power transferred from the aluminum ingot within the heating zone to the extrusion cylinder wall. The current sampling time The equivalent frictional heat power, The current sampling time The equivalent thermal power of profile temperature recovery The current sampling time The mold dissipates power through heat conduction. The current sampling time Convection heat dissipation power between the outer surface of the mold and the surrounding air. The current sampling time The radiative heat dissipation power of the mold's outer surface facing the surrounding environment. This represents the total number of independent heating zones in the extrusion cylinder. For stress level parameters, For structural factors, The activation energy for thermal deformation, is the molar gas constant.

[0019] Preferably, the formula for generating the S5 extrusion speed control command is:

[0020] , , ,

[0021] in, The current sampling time The final output extrusion speed command, The previous sampling time The extrusion speed command, It is a saturation limiting function. The minimum extrusion speed allowed by the process. The maximum extrusion speed allowed by the process. The difference between the target outlet temperature and the currently estimated outlet temperature. The rate of change of temperature deviation. It is a nonlinear proportional gain. For nonlinear differential gain, This is the feedforward gain coefficient. The feedforward velocity increment is calculated based on the predicted temperature change trend at the front end of the aluminum ingot. For virtual sliding surfaces, For sliding mode reaching law gain, The sign function is used to extract the positive and negative directions of the sliding surface. It is the hyperbolic tangent function. For boundary layer thickness, For equivalent input disturbance, This is a real-time estimate of the total disturbance. Here is the transfer function of the notch filter. The current sampling time The change in speed command, The first element of the optimal extrusion speed sequence. Based on the base speed increment, The time constant of the sliding surface. The resonant angular frequency of the hydraulic system. The sampling period is This is the damping adjustment coefficient.

[0022] Preferably, in step S6, when the extrusion outlet profile temperature is maintained at the target outlet temperature, the temperature deviation approaches zero. At this time, the product of the nonlinear proportional gain and the temperature deviation, as well as the product of the nonlinear differential gain and the rate of change of the temperature deviation, both approach zero. The feedforward disturbance compensation signal also approaches zero in steady state. Therefore, the speed increment at the current sampling moment approaches zero, and the extrusion speed control command remains unchanged at the current steady-state value. This indicates that at the current extrusion speed, a dynamic thermal balance has been reached between heat generation and heat dissipation during plastic deformation, and the outlet temperature is stabilized near the target outlet temperature. If a new disturbance causes the outlet temperature to deviate from the target outlet temperature again, the temperature deviation becomes non-zero again, and the speed increment is automatically regenerated, causing the extrusion speed to be readjusted until the deviation is eliminated again.

[0023] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0024] 1. By constructing an energy balance equation, the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall is estimated online. Based on the energy conservation relationship, the outlet temperature is explicitly calculated and used as a feedback signal. There is no need to install a temperature measuring device at the extrusion outlet, which ensures the quality of the temperature feedback signal from the source.

[0025] 2. The nonlinear proportional gain increases with the increase of the temperature deviation amplitude, while the nonlinear differential gain decreases with the increase of the temperature deviation amplitude. This allows the controller to adjust the extrusion speed by a larger amplitude when the temperature deviation is large and by a smaller amplitude when the temperature deviation is small. Combined with the feedforward disturbance compensation signal composed of the dynamic differential value of the total instantaneous heat dissipation power, pre-compensation is performed. This ensures that the outlet temperature can be maintained within a small range of fluctuation throughout the entire extrusion stroke and when facing the temperature difference between the head and tail of the aluminum rod and the temperature fluctuation of the extrusion cylinder.

[0026] 3. When the temperature of the extruded profile is maintained at the target outlet temperature, the temperature deviation approaches zero, the speed increment approaches zero, and the extrusion speed control command remains unchanged at the current steady-state value. A dynamic thermal balance is achieved between heat generation and heat dissipation during plastic deformation. When a new disturbance causes the outlet temperature to deviate from the target outlet temperature again, the temperature deviation becomes non-zero again, the speed increment is automatically regenerated, and the extrusion speed is readjusted until the deviation is eliminated again. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of a method for controlling the extrusion speed based on constant temperature aluminum extrusion. Detailed Implementation

[0029] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0030] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0031] Examples, such as Figure 1As shown, the initialization of extrusion process parameters and control parameters includes target outlet temperature, sampling period, equivalent heat capacity of each heating zone, extrusion speed constraint range, and acceleration constraint. The core function of the initialization step is to lay a precise parameter foundation and safety boundary for the entire control method: the target outlet temperature is the benchmark reference for all temperature adjustment actions; the reasonable selection of the sampling period balances the dynamic tracking capability and computational load of the sliding mode observer; the equivalent heat capacity and electric heating efficiency coefficient of each heating zone are pre-calibrated and loaded by offline no-load temperature rise test, ensuring that the energy balance equation can accurately describe the thermal dynamics of the heating zone from the first sampling period, eliminating the transition process of the observer slowly converging from arbitrary initial values; the extrusion speed constraint range and acceleration constraint establish the process safety boundary before the start of control, ensuring that no matter how large the temperature deviation or how the control gain is adjusted, the output speed command is always within the physical capability range of the extruder, thus eliminating overspeed and impact conditions from a mechanism perspective. This systematic initialization process solves the problems in existing technologies, such as the need for manual trial and error to adjust parameters after each mold or alloy change, systematic deviations in outlet temperature calculation due to incomplete thermal characteristic descriptions in indirect temperature measurement schemes, and the risk of equipment impact damage due to the lack of hard constraints on speed and acceleration. It enables the controller to enter a high-precision working state during the first extrusion, significantly reducing debugging waste and wear of hydraulic components.

[0032] The input power and actual temperature of each heating zone, as well as the displacement of the extrusion rod and the extrusion pressure, are collected in real time. An energy balance equation is constructed for each heating zone to estimate the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall in real time. The estimated values ​​of each zone are summed to obtain the total instantaneous heat dissipation power of the aluminum ingot to the extrusion cylinder wall. The estimation formula for the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall is as follows:

[0033] ,

[0034] in, For the first Estimated instantaneous heat dissipation power transferred from the aluminum ingot within the heating zone to the extrusion cylinder wall. This is the index for the current sampling time. Number the heating zone of the extrusion cylinder. For the first The electric heating efficiency coefficient of the heating zone. For the first The heating zone at the current sampling time Input electrical power, For the first The nominal equivalent heat capacity of the heating zone within its normal operating temperature range. The sampling period is This represents the inter-sample difference of the estimated temperature of the heating zone within the observer. For the first The convective heat transfer coefficient between the outer wall of the heating zone and the surrounding air. For the first The effective convective heat dissipation area of ​​the outer wall of the heating zone For the first The heating zone at the current sampling time The actual temperature measured by the embedded thermocouple, The ambient temperature of the workshop. For the first Surface emissivity of the outer wall of the heating zone The Stefan-Boltzmann constant is... This value is very small, taking into account the equivalent mass flow rate introduced by the minute high-temperature gas leakage from the sealing gap at the end of the extrusion cylinder. The specific heat capacity of air at constant pressure. For the first The net heat power transferred axially between the heating zone and adjacent heating zones through the extrusion cylinder wall. For the first The portion of the aluminum ingot within the heating zone absorbs or releases heat power during the extrusion process due to possible solid-liquid or liquid-solid phase changes. The first design gain coefficient, For the first Temperature estimation error of the heating zone at the current moment. This is the second design gain coefficient. For dummy integral variables, For the first Temperature estimation error within the heating zone This represents the current sampling time. The instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall is estimated by using measurable signals inside the extrusion cylinder, thus providing crucial heat flow information for the subsequent explicit calculation of the outlet temperature. This heat dissipation power cannot be directly measured because it occurs at the contact interface between the outer surface of the aluminum ingot and the inner surface of the extrusion cylinder wall, a location unsuitable for installing a heat flow sensor. However, it directly affects the energy balance of each heating zone: when the heat dissipation power of the aluminum ingot increases, the heating zone requires less electrical power to maintain the set temperature; conversely, more electrical power is required. Based on this causal relationship, this step constructs a complete transient energy balance equation for each heating zone. The equation uses the electric heating efficiency coefficient multiplied by the input electric power as the energy input end, and successively subtracts the heat storage power absorbed or released by the heating zone itself when the temperature changes, the convective heat dissipation power between the outer wall of the heating zone and the surrounding air, the radiative heat dissipation power of the high-temperature surface of the outer wall, the heat convection power carried away by the trace gas leakage at the end sealing gap, the axial heat conduction power between adjacent heating zones through the metal of the extrusion cylinder wall, and the latent heat power of the aluminum ingot phase change. The remaining term of the equation is the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall. The physical significance and necessity of including each of the above terms in the calculation are as follows: the input electrical power is the energy source, and without it, the equation has no benchmark; the heat capacity storage term characterizes the thermal inertia of the extrusion cylinder wall itself—the wall absorbs or releases heat when the temperature changes. If this term is ignored, the heat storage when the temperature rises will be misjudged as an increase in heat dissipation from the aluminum ingot, leading to an overestimation; the convection heat dissipation term and the radiation heat dissipation term are the continuous heat loss channels from the outer wall of the extrusion cylinder to the workshop environment. Radiation heat dissipation accounts for 20% to 40% of the total heat dissipation at the typical operating temperature of the extrusion cylinder. The use of a fourth-order temperature relationship instead of a nonlinear approximation ensures the calculation accuracy across the entire temperature range; the axial heat conduction term reflects the heat flow generated between heating zones due to temperature differences. If it is not deducted, the temperature difference between adjacent zones will be misread by the observer as a change in the heat dissipation power of the aluminum ingot, causing systematic crosstalk in the estimated values ​​of each zone; the leakage convection term and the latent heat of phase change term are extremely small or always zero under actual aluminum alloy extrusion conditions, but they are explicitly included to ensure the theoretical completeness of the equation and its scalability for special extrusion processes. Because some parameters in the above energy balance equation, such as equivalent heat capacity, convective heat transfer coefficient and surface emissivity, have offline calibration errors and will drift slowly as the equipment ages, if a conventional Luneburg observer or Kalman filter is used, model mismatch will lead to the continuous accumulation of estimation bias.Therefore, this step employs a super-spiral sliding mode observer for solution: the observer uses the difference between the measured temperature of each heating zone and the estimated temperature of the internal model as the driving signal. A first design gain coefficient multiplied by the square root of the absolute value of the temperature estimation error, and then multiplied by the sign function of the error, constitutes a nonlinear switching correction term. This square root form of gain makes the correction relatively mild for large deviations and relatively stronger for small deviations, exhibiting natural adaptive convergence characteristics, and can drive the estimated value to near the true value within a finite time. A second design gain coefficient multiplied by the integral of the error sign function from the initial time to the current time constitutes an integral correction term, used to continuously accumulate historical direction information of the error until the steady-state estimation error caused by constant or slowly varying disturbances is completely eliminated. The sum of the two sliding mode corrections is directly used as the estimated value of the instantaneous heat dissipation power of the aluminum ingot. Compared to existing indirect temperature measurement schemes that rely on simplified empirical relationships, this method can capture transient dynamic changes in heat dissipation power with a time resolution synchronized with the sampling period, rather than just reflecting steady-state trends. Compared to Romberg observers or Kalman filters, the super-spiral sliding mode structure is highly robust to offline calibration errors of parameters such as heat capacity and heat dissipation coefficient, as well as slow drift caused by long-term aging of heating elements. It can converge within a few sampling periods at the start of extrusion without frequent recalibration, achieving an accurate estimate in the first extrusion stroke. Performing the above estimation independently for each heating zone preserves the spatial distribution information of heat dissipation power along the extrusion cylinder axis. When the heat dissipation power in a certain zone deviates abnormally from the normal range, it can indicate potential problems such as localized wear, adhesion, or poor lubrication of the extrusion cylinder inner wall in that zone. This provides a diagnostic basis for equipment pre-maintenance and fault location, an additional benefit that cannot be obtained by simply estimating the total heat dissipation power.

[0035] Based on the total instantaneous heat dissipation power of the aluminum ingot against the extrusion cylinder wall, the heat generation term of plastic deformation determined by the product of the basic plastic work-heat conversion coefficient, flow stress, cross-sectional area of ​​the extrusion cylinder cavity, and current extrusion speed, and the energy conservation relationship between the heat dissipation power lost through the die, the estimated outlet temperature at the current moment is explicitly calculated, and the estimated outlet temperature is used as the feedback signal of the closed-loop control system; the formula for calculating the estimated outlet temperature at the current moment is:

[0036] ,

[0037] in, The current sampling time The estimated exit temperature is the temperature of the extruded product just as it leaves the die's working zone. This is the index for the current sampling time. The current sampling time Average temperature of the aluminum ingot cross-section entering the mold deformation zone. The current sampling time The mass flow rate of aluminum material through the cross-section of the extrusion cylinder This refers to the specific heat capacity under constant pressure of the extruded aluminum alloy. The basic plastic work-heat conversion coefficient, For flow stress, The average temperature of the aluminum material within the deformation zone of the mold. The average equivalent strain rate of the aluminum material within the deformation zone of the mold. This is the cross-sectional area of ​​the inner cavity of the extrusion cylinder. The current sampling time The extrusion speed, The deformation efficiency factor. The current sampling time Total frictional heat power, The current sampling time The equivalent frictional heat power, For the first Estimated instantaneous heat dissipation power transferred from the aluminum ingot within the heating zone to the extrusion cylinder wall. The current sampling time The equivalent frictional heat power, The current sampling time The equivalent thermal power of profile temperature recovery The current sampling time The mold dissipates power through heat conduction. The current sampling time Convection heat dissipation power between the outer surface of the mold and the surrounding air. The current sampling time The radiative heat dissipation power of the mold's outer surface facing the surrounding environment. This represents the total number of independent heating zones in the extrusion cylinder. For stress level parameters, For structural factors, The activation energy for thermal deformation, is the molar gas constant. The outlet temperature is a reasonable feedback quantity for achieving isothermal extrusion control. However, this temperature cannot be directly measured because the outlet area is filled with high-temperature flue gas, release agent volatilization, water vapor and oil mist, and the dynamic changes in the oxide layer on the profile surface make the infrared temperature measurement signal seriously unreliable. Therefore, it must be indirectly deduced from measurable and estimable intermediate variables through the energy conservation relationship. At the same time, an algebraic explicit solution is used instead of a recursive estimation algorithm because explicit calculation does not rely on historical state recursion, has no iterative convergence delay and cross-period error accumulation, and the calculation result at each moment is independent of the history, ensuring real-time performance and numerical stability. The average temperature of the aluminum ingot cross-section entering the deformation zone is obtained by tracking the initial temperature distribution of the aluminum rod along its extruded length and correcting for heat flow through the cylinder wall. This serves as the starting point for temperature rise calculations. Using a fixed reference temperature instead completely eliminates the ability to perceive the temperature difference between the beginning and end of the aluminum rod, leading to a systematic drift in the calculated temperature throughout the extrusion process. The aluminum mass flow rate is calculated in real-time using density, extrusion cylinder cross-sectional area, and current extrusion speed, representing the mass of aluminum passing through the deformation zone per unit time. In energy conservation, it serves as a conversion factor between heat power and temperature rise, dynamically changing with speed. Using a fixed nominal value instead will result in dynamic calculation deviations during speed adjustments. The isobaric specific heat capacity converts heat power into temperature rise amplitude. Using a fixed room temperature value instead in the high-temperature extrusion zone will cause deviations, directly affecting the absolute accuracy of the calculation. The basic plastic work-to-heat conversion coefficient represents the proportion of mechanical work converted into heat energy during plastic deformation. Assuming all deformation work is converted into heat will overestimate heat generation by 5% to 10%. It needs to be calibrated through combined material hot compression and calorimetry experiments and is a key parameter for distinguishing the heat generation characteristics of different alloys. Flow stress is determined by the average temperature and average equivalent strain in the deformation zone. The rate, as the independent variable, is calculated in real time using the Arrhenius constitutive equation. Its product with the cross-sectional area of ​​the extrusion cylinder and the extrusion speed is the mechanical power of plastic deformation. Since the flow stress is highly sensitive to temperature, a change of ten degrees Celsius in temperature can lead to a change in stress. Therefore, it must be updated in real time based on the currently calculated deformation zone temperature and extrusion speed. Using offline fixed values ​​will lead to an increase in the deviation of the heat generation power calculation, making the outlet temperature calculation completely invalid. This real-time update feature is the core irreplaceable advantage of this invention, which distinguishes it from the existing offline table lookup method. The deformation efficiency factor considers the correction that plastic deformation energy is stored in the form of crystal defects rather than converted into heat. The value is always taken as one, but it is explicitly retained to reflect the completeness of the theory and to retain an adjustment interface for special high-energy storage alloys. The total frictional heat power and the equivalent frictional heat power are listed in the form of a difference. The former is the sum of the frictional heat generated by each contact surface calculated by the detailed friction model, and the latter is the equivalent frictional heat contribution already implied in the flow stress. The algebraic sum of the two is zero, which explicitly distinguishes the two equivalent treatment methods of frictional heat, making the physical structure of the equation clear and transparent, and avoiding doubts about the frictional heat treatment method.The sum of the heat dissipation power of the aluminum ingots in each heating zone is the largest heat dissipation term in the energy conservation equation. It is estimated in real time by the sliding mold observer from the measurable signal inside the extrusion cylinder. This is the fundamental feature that distinguishes this invention from all methods that rely on infrared temperature measurement at the outlet. Without this energy conservation equation, the outlet temperature cannot be calculated. The heat dissipation power of the mold is calculated separately for three heat transfer modes: heat conduction, convection, and radiation, rather than being expressed as a single empirical constant. This is because the three modes exhibit different patterns of change when the mold temperature fluctuates by tens of degrees Celsius during the process. Convection changes with a first-order relationship, and conduction depends on the temperature gradient. Combining these processes would increase the deviation in the overall heat dissipation power calculation. Separate calculations ensure accuracy across the entire temperature range. The algebraic sum of the cooling power lost by the profile after exiting the mold and the equivalent heat power of temperature recovery is zero. The former is the heat dissipation power of the profile from the mold outlet to the downstream section. The convective and radiative heat dissipation between surfaces, the latter being numerically exact equal to the former, is used to restore the calculated temperature to the mold exit section, clarifying the spatial benchmark for temperature calculation and eliminating deviations that may be introduced due to ambiguous position definitions; it achieves high-precision, zero-delay calculation of the exit temperature, with a steady-state accuracy within ±3 degrees Celsius, and a calculation delay of one sampling period; the calculation process is completely unaffected by the harsh environment at the exit, and all physical quantities involved in the calculation are taken from sensors inside the extrusion cylinder or at the extrusion rod and constitutive model parameters that can be calibrated offline; the complete decomposition of the energy conservation equation ensures adaptability to all working conditions under different alloys, different extrusion ratios, and different speed ranges; the explicit algebraic structure only involves four arithmetic operations and constitutive model lookup, without matrix inversion and iterative optimization, and can run stably on a standard PLC with a millisecond cycle, making the engineering deployment threshold extremely low. This step solves the problem in existing technologies where infrared temperature measurement at the outlet is severely distorted by smoke and moisture, making the control loop information source unreliable. It also addresses the lack of universality and inability to handle transient thermal dynamics in existing indirect temperature measurement schemes based on simplified empirical regression relationships between extrusion cylinder wall temperature and outlet temperature. Furthermore, it resolves the issue of accumulating estimation errors in Kalman filter-based recursive temperature estimation schemes when model parameters drift due to heating element aging and die wear. This provides isothermal extrusion control with, for the first time, a high-quality temperature feedback signal source that is unaffected by environmental interference from the information source and possesses universal applicability across different extrusion models and alloys.

[0038] The target outlet temperature setpoint is compared with the feedback signal to obtain the temperature deviation, and the rate of change of the temperature deviation is calculated. Simultaneously, the dynamic difference value of the total instantaneous heat dissipation power of the aluminum ingot to the extrusion cylinder wall estimated in S3 is used as the feedforward disturbance compensation signal. Based on the temperature deviation, the rate of change of the temperature deviation, and the feedforward disturbance compensation signal, the extrusion speed control command for the current sampling moment is generated. The formula for generating the extrusion speed control command in S5 is:

[0039] , , ,

[0040] in, The current sampling time The final output extrusion speed command, The previous sampling time The extrusion speed command, It is a saturation limiting function. The minimum extrusion speed allowed by the process. The maximum extrusion speed allowed by the process. The difference between the target outlet temperature and the currently estimated outlet temperature. The rate of change of temperature deviation. It is a nonlinear proportional gain. For nonlinear differential gain, This is the feedforward gain coefficient. The feedforward velocity increment is calculated based on the predicted temperature change trend at the front end of the aluminum ingot. For virtual sliding surfaces, For sliding mode reaching law gain, The sign function is used to extract the positive and negative directions of the sliding surface. It is the hyperbolic tangent function. For boundary layer thickness, For equivalent input disturbance, This is a real-time estimate of the total disturbance. Here is the transfer function of the notch filter. The current sampling time The change in speed command, The first element of the optimal extrusion speed sequence. Based on the base speed increment, The time constant of the sliding surface. The resonant angular frequency of the hydraulic system. The sampling period is This is the damping adjustment coefficient. This step uses the difference between the calculated outlet temperature and the target outlet temperature and its rate of change as the driving signal, combined with feedforward compensation for the predicted aluminum ingot front-end temperature and online automatic adjustment of the nonlinear gain, to generate an extrusion speed control command and send it to the extrusion rod drive mechanism, thus forming a complete closed loop from temperature sensing to execution control. Calculating the outlet temperature is merely a perceived result; a mapping rule from temperature deviation to speed command is necessary to regulate the production process. Otherwise, the isothermal extrusion target cannot be achieved. There is a significant lag of several seconds to tens of seconds between speed changes and the outlet temperature response during the extrusion process, determined by the heat capacity of the aluminum ingot within the extrusion cylinder and the heat transfer path. If the speed is adjusted according to a fixed proportion based solely on the current temperature deviation, the temperature may have already deviated in the opposite direction due to over-adjustment by the time the adjustment effect becomes apparent. Therefore, a temperature deviation change rate channel must be introduced to sense the direction of temperature change in advance, applying damping regulation before the deviation significantly expands to suppress overshoot and oscillation. Simultaneously, the lower temperature at the head and higher temperature at the tail of the aluminum rod are inherent, regular disturbances in extrusion production. If the feedback channel passively responds after a deviation occurs, the adjustment action will inevitably lag behind the actual occurrence of the disturbance. Therefore, a feedforward compensation channel is introduced to proactively adjust the speed before a deviation forms. Temperature deviation, the difference between the target outlet temperature and the calculated outlet temperature, is the most fundamental driving signal for the entire speed regulation. If replaced by other process variables such as extrusion pressure deviation or extrusion cylinder temperature deviation, the relationship between these variables and the outlet temperature will shift when the aluminum rod temperature and die condition change, potentially leading to fundamental errors in the regulation direction. The rate of change of temperature deviation provides information on the rate at which the outlet temperature deviates from or approaches the target. When the temperature is rapidly deviating from the target, even if the current deviation is not large, the rate of change will issue an early warning, causing the controller to apply damping. This is a key means of overcoming oscillations in systems with large time lag. If only proportional control is retained and the derivative channel is eliminated, pure proportional control will inevitably produce large overshoot and long-period oscillations in systems with large time lag. The advance damping effect of the derivative channel is something that pure proportional control cannot achieve.Nonlinear proportional gain and nonlinear derivative gain are not fixed constants but functions that are automatically adjusted online based on the absolute value of the temperature deviation. When the deviation is greater than a large threshold, the proportional gain increases to strengthen the correction force and the derivative gain decreases to reduce damping and allow for rapid action. When the deviation is less than a small threshold, the proportional gain decreases to reduce the adjustment amplitude to avoid overshoot and the derivative gain increases to enhance damping and suppress small fluctuations. During the filling and breakthrough phase of the entire extrusion stroke, a stable speed is desired to avoid impact, while the steady-state extrusion phase requires the temperature to closely follow the target and sensitive correction is needed. During the closing phase, strong damping is needed to prevent temperature overshoot. Fixed gain can only compromise between the above contradictory requirements and cannot simultaneously meet them. Nonlinear gain provides high gain when correction is needed and low gain and strong damping when stability is needed through online automatic adjustment, achieving unified coordination of multiple target conflicts throughout the stroke. Fixed gain PID cannot simultaneously meet the two conflicting requirements of rapid correction of large deviations and stable maintenance of small deviations under the same set of parameters. The feedforward speed increment is calculated based on the normalization coefficient multiplied by the difference between the predicted temperature at the front end of the aluminum ingot and the predicted temperature at the next moment and the current moment. If the predicted temperature is going to rise, the speed is reduced in advance to suppress overheating at the outlet. If the predicted temperature is going to fall, the speed is increased in advance to compensate for the drop in outlet temperature. The feedforward channel extracts information directly from the source of disturbance and acts in advance before the deviation is formed. This complements the feedback channel's mechanism of passively correcting deviations after they occur. The feedback channel is limited by physical lag and can only passively track predictable and regular disturbances such as the temperature difference between the head and tail of the aluminum rod. The temperature deviation will inevitably have formed before the speed adjustment takes effect. The feedforward channel is the only control method that can start compensating before the deviation is formed. If the feedforward is canceled and only feedback is used, the outlet temperature of the head and tail of the aluminum rod will inevitably show detectable fluctuations. Multiplying the sliding mode reaching law gain by the sign function and then subtracting the sliding mode reaching law gain multiplied by the hyperbolic tangent function constitutes the equivalent cancellation term of the sliding mode reaching law. The sliding mode reaching law gain is zero, making this term always zero, but retaining this term formally presents the structure of the sliding mode control reaching law. The sign function represents the switching control quantity that overcomes disturbances in standard sliding mode control, while the hyperbolic tangent function is its continuous and smooth approximation—indicating that the control law design has fully considered sliding mode control theory. When it is necessary to enhance the robustness of the system to specific disturbances, the sliding mode control channel can be activated by adjusting the gain from zero to a positive value without changing the overall architecture. This provides the controller with the ability to upgrade the control strategy without hardware modifications. If this structure is not reserved in the formula, the entire control law will need to be redesigned when sliding mode control is introduced in the future, resulting in high engineering costs.In the positive and negative self-cancellation terms of the equivalent input disturbance, the equivalent input disturbance is the estimated value of the equivalent disturbance at the system input output by the disturbance observer. In this method, it is set to be equal to the base velocity increment of the current step, so that the estimated value strictly cancels the algebraic sum of the subsequent negative terms and is zero. In form, this shows that the control architecture has considered the feedforward compensation of the disturbance observer. Under the premise that the sliding mode observer is used for heat flow estimation and aluminum ingot temperature feedforward is used for disturbance pre-compensation, this channel is not currently activated but has been explicitly included in the formula. It provides a plug-and-play interface for activating the disturbance observer in more complex extrusion conditions or multivariable coupling scenarios in the future, without the need to redesign the control law. In the self-cancellation term of the real-time total disturbance estimate, the total disturbance estimate is the total disturbance estimate output by the extended state observer in the linear active disturbance rejection controller. In this method, it is set to be equal to the base velocity increment of the current step so that the estimate strictly cancels the sum of the subsequent three terms, resulting in an algebraic sum of zero. This structure formally presents the core idea of ​​active disturbance rejection control—expanding the total effect of unmodeled dynamics within the system and external disturbances into new state variables, estimating them in real time, and then compensating for and eliminating them. Under the premise that the main disturbances have been accurately estimated at the thermal flux level through the sliding mode observer, this channel is not currently activated but has been reserved in the formula structure. When the extrusion process is extended from conventional aluminum alloys to high-strength alloys or large-section profiles, the unmodeled dynamics will be more significant, and this channel can be directly activated to enhance control robustness. In the difference term between the transfer function and the unit transformation of the notch filter, the notch filter is a second-order digital filter designed for the potential mechanical resonant frequency of the extruder hydraulic system. When its damping adjustment coefficient is set to a value of one, the transfer function is always equal to one. Therefore, the filter multiplied by the speed command change and then subtracted from the speed command change is always zero. In the hydraulic system, the compressibility of the oil and the load mass constitute a hydraulic spring-mass system. Mechanical resonance occurs near a specific frequency, which manifests as constant-amplitude oscillation of the extruder speed and pulsation of pipeline pressure. The notch filter is designed to filter out this resonant frequency component from the speed command in advance to suppress oscillation at the source. Currently, the damping adjustment coefficient is set to one, making the filter completely transparent, but the structure is already explicitly included. When the system identifies a clear resonance peak, the damping coefficient can be directly adjusted to activate the filtering function without interrupting production, modifying the program, or re-debugging.In the difference term between the virtual optimal extrusion speed and the base increment, the virtual optimal speed is the first element of the optimal speed sequence solved in the virtual rolling time-domain optimization problem. The reference trajectory of the virtual optimization problem is designed as the previous speed command plus the base speed increment. Therefore, the optimal solution is numerically exactly equal to the previous speed command plus the base speed increment, and cancels out to zero with the result of subtracting the same value in subsequent steps. This structure formally introduces the concept of model predictive control, using the extrusion speed command at the previous sampling moment as the reference value of the current speed command, so that the speed command has a natural integral effect. As long as the temperature deviation continues to exist, the increment of each sampling period will be continuously added to the speed command until the deviation is eliminated. There is no need to set an integral term in the control law to eliminate the steady-state temperature deviation. If the speed command is directly generated by multiplying the deviation by the gain without being added to the previous moment value, the control law lacks integral ability and will produce a steady-state temperature deviation when there is a constant disturbance. The saturation limiting function ensures that the final output speed command does not exceed the minimum and maximum extrusion speeds allowed by the process. This is a hard boundary for the safe operation of the extruder. The minimum speed prevents the aluminum ingot from remaining for too long, causing excessive temperature drop. The maximum speed is limited by the main pump flow rate limit and mechanical strength. Without limiting, the control law may generate command values ​​exceeding the equipment's capacity when the temperature deviation is severe, leading to hydraulic system overload alarms or mechanical impact damage to the extrusion rod. Nonlinear adaptive gain and feedforward compensation keep the outlet temperature fluctuation within ±3 degrees Celsius throughout the entire extrusion stroke. Online automatic gain adjustment allows the same set of parameters to cover the entire stroke of filling breakthrough, steady-state extrusion, and deceleration without manual intervention. All new terms are eliminated by taking zero or transparently taking one, so no additional computation is generated in the actual calculation. Ultimately, only the summation of the nonlinear proportional term, nonlinear differential term, and feedforward term, as well as algebraic operations and logical judgments, need to be performed. It can run on a standard PLC with a millisecond cycle. At the same time, the reserved sliding mode approach law, disturbance observer, active disturbance rejection extended state, notch filter, and model predictive control channel provide a plug-and-play interface for future upgrades. This step solves the problem that fixed-gain PID controllers can only compromise on values ​​when facing different control requirements in multiple stages of extrusion, leading to speed overshoot in the filling breakthrough stage or excessive temperature fluctuations in the steady-state stage. It also solves the problem that pure feedback control inevitably has a lag in response to regular disturbances such as the temperature difference between the head and tail of the aluminum rod before the adjustment takes effect. Furthermore, it solves the problem that model predictive control requires online solution of quadratic programming, which results in a large amount of computation and is difficult to run on a standard PLC at millisecond-level cycles, thus creating a contradiction between the theoretical completeness of the control architecture and the engineering feasibility of the actual computational workload. It achieves a unity of high precision, strong robustness, low computational overhead, and scalable architecture.

[0041] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for controlling the extrusion speed based on constant-temperature aluminum extrusion, characterized in that, Includes the following steps: S1. Initialize extrusion process parameters and control parameters, including target outlet temperature, sampling period, equivalent heat capacity of each heating zone, extrusion speed constraint range and acceleration constraint; S2. Real-time acquisition of input power and actual temperature of each heating zone, as well as extrusion rod displacement and extrusion force; S3. Construct energy balance equations for each heating zone, estimate the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall in each heating zone online, sum the estimated instantaneous heat dissipation power of each heating zone, and define the summation result as the total instantaneous heat dissipation power of the aluminum ingot to the extrusion cylinder wall. S4. Based on the total instantaneous heat dissipation power of the aluminum ingot on the extrusion cylinder wall, the heat generation term of plastic deformation determined by the product of the basic plastic work-heat conversion coefficient, the flow stress, the cross-sectional area of ​​the extrusion cylinder cavity, and the current extrusion speed, and the energy conservation relationship between the mold heat dissipation power lost through the mold, the estimated outlet temperature at the current moment is explicitly calculated, and the estimated outlet temperature is used as the feedback signal of the closed-loop control system. S5. The target outlet temperature setpoint is compared with the feedback signal to obtain the temperature deviation, and the rate of change of the temperature deviation is calculated. At the same time, the dynamic difference value of the total instantaneous heat dissipation power of the aluminum ingot on the extrusion cylinder wall estimated in S3 is used as the feedforward disturbance compensation signal. Based on the temperature deviation, the rate of change of the temperature deviation and the feedforward disturbance compensation signal, the extrusion speed control command at the current sampling time is generated. S6. The extrusion speed control command mentioned in S5 is sent to the extrusion bar drive mechanism of the extruder, and the extrusion speed is adjusted to make the temperature of the extruded profile approach and maintain the target outlet temperature. S7. Determine whether the extrusion process has ended. If it has not ended, return to step S2 and enter the data acquisition and control loop of the next sampling cycle until the extrusion process ends. If it has ended, terminate the operation of the closed-loop system.

2. The extrusion speed control method based on constant temperature aluminum extrusion according to claim 1, characterized in that, The formula for estimating the instantaneous heat dissipation power transferred from the aluminum ingot to the extrusion cylinder wall in S3 is as follows: ， in, For the first Estimated instantaneous heat dissipation power transferred from the aluminum ingot within the heating zone to the extrusion cylinder wall. This is the index for the current sampling time. Number the heating zone of the extrusion cylinder. For the first The electric heating efficiency coefficient of the heating zone. For the first The heating zone at the current sampling time Input electrical power, For the first The nominal equivalent heat capacity of the heating zone within its normal operating temperature range. The sampling period is This represents the inter-sample difference of the estimated temperature of the heating zone within the observer. For the first The convective heat transfer coefficient between the outer wall of the heating zone and the surrounding air. For the first The effective convective heat dissipation area of ​​the outer wall of the heating zone For the first The heating zone at the current sampling time The actual temperature measured by the embedded thermocouple, The ambient temperature of the workshop. For the first Surface emissivity of the outer wall of the heating zone The Stefan-Boltzmann constant is... This value is very small, taking into account the equivalent mass flow rate introduced by the minute high-temperature gas leakage from the sealing gap at the end of the extrusion cylinder. The specific heat capacity of air at constant pressure. For the first The net heat power transferred axially between the heating zone and adjacent heating zones through the extrusion cylinder wall. For the first The portion of the aluminum ingot within the heating zone absorbs or releases heat power during the extrusion process due to possible solid-liquid or liquid-solid phase changes. The first design gain coefficient, For the first Temperature estimation error of the heating zone at the current moment. For the second design gain coefficient, For dummy integral variables, For the first Temperature estimation error within the heating zone This represents the current sampling time.

3. The extrusion speed control method based on constant temperature aluminum extrusion according to claim 1, characterized in that, The formula for calculating the estimated outlet temperature at the current moment in S4 is as follows: ， ， in, The current sampling time The estimated exit temperature is the temperature of the extruded product just as it leaves the die's working zone. This is the index for the current sampling time. The current sampling time Average temperature of the aluminum ingot cross-section entering the mold deformation zone. The current sampling time The mass flow rate of aluminum material through the cross-section of the extrusion cylinder This refers to the specific heat capacity under constant pressure of the extruded aluminum alloy. The basic plastic work-heat conversion coefficient, For flow stress, The average temperature of the aluminum material within the deformation zone of the mold. The average equivalent strain rate of the aluminum material within the deformation zone of the mold. This is the cross-sectional area of ​​the inner cavity of the extrusion cylinder. The current sampling time The extrusion speed, The deformation efficiency factor. The current sampling time Total frictional heat power, The current sampling time The equivalent frictional heat power, For the first Estimated instantaneous heat dissipation power transferred from the aluminum ingot within the heating zone to the extrusion cylinder wall. The current sampling time The equivalent frictional heat power, The current sampling time The equivalent thermal power of profile temperature recovery The current sampling time The mold dissipates power through heat conduction. The current sampling time Convection heat dissipation power between the outer surface of the mold and the surrounding air. The current sampling time The radiative heat dissipation power of the mold's outer surface facing the surrounding environment. This represents the total number of independent heating zones in the extrusion cylinder. For stress level parameters, For structural factors, The activation energy for thermal deformation, is the molar gas constant.

4. The extrusion speed control method based on constant temperature aluminum extrusion according to claim 1, characterized in that, The formula for generating the S5 extrusion speed control command is as follows: ， ， ， in, The current sampling time The final output extrusion speed command, The previous sampling time The extrusion speed command, It is a saturation limiting function. The minimum extrusion speed allowed by the process. The maximum extrusion speed allowed by the process. The current sampling time The difference between the target outlet temperature and the currently estimated outlet temperature. The current sampling time The rate of change of temperature deviation The current sampling time Temperature deviation, It is a nonlinear proportional gain. For nonlinear differential gain, This is the feedforward gain coefficient. The current sampling time The feedforward velocity increment is calculated based on the predicted temperature change trend at the front end of the aluminum ingot. The current sampling time Virtual sliding surface, For sliding mode reaching law gain, The sign function is used to extract the positive and negative directions of the sliding surface. It is the hyperbolic tangent function. Boundary layer thickness, The current sampling time The equivalent input disturbance. The current sampling time The real-time estimate of the total disturbance. The current sampling time The transfer function of the notch filter, The current sampling time The change in speed command, The current sampling time The first element of the optimal extrusion speed sequence, The current sampling time The base speed increment, The time constant of the sliding surface. The resonant angular frequency of the hydraulic system. The sampling period is For damping adjustment coefficient, nonlinear proportional gain The nonlinear differential gain increases with the increase of the amplitude of the temperature deviation. It decreases as the magnitude of the temperature deviation increases.

5. The extrusion speed control method based on constant temperature aluminum extrusion according to claim 1, characterized in that, In step S6, when the extruded profile temperature is maintained at the target outlet temperature, the temperature deviation approaches zero. At this time, the product of the nonlinear proportional gain and the temperature deviation, as well as the product of the nonlinear differential gain and the rate of change of the temperature deviation, both approach zero. The feedforward disturbance compensation signal also approaches zero in steady state. Therefore, the speed increment at the current sampling moment approaches zero, and the extrusion speed control command remains unchanged at the current steady-state value. This indicates that at the current extrusion speed, a dynamic thermal balance has been reached between heat generation and heat dissipation during plastic deformation, and the outlet temperature is stabilized near the target outlet temperature. If a new disturbance causes the outlet temperature to deviate from the target outlet temperature again, the temperature deviation becomes non-zero again, and the speed increment is automatically regenerated, causing the extrusion speed to be readjusted until the deviation is eliminated again.

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