Self-adaptive control method for steel processing equipment based on digital twinning

Abstract

The invention relates to the technical field of digital twinning, in particular to a steel processing equipment self-adaptive control method based on digital twinning, which comprises the following steps: acquiring real-time signals such as displacement, load, rotating speed and inter-unit tension of an actuating mechanism, inputting the real-time signals into a digital twinning model, and constructing an instantaneous dynamic geometric model to calculate an instantaneous feedback value of a controlled object; the influence coefficient between the first control loop and the second control loop is analyzed through virtual perturbation, and a partial derivative sensitivity matrix is generated; and then, inputting the instantaneous feedback value into a self-adaptive controller to obtain an original control increment, calculating a compensation control increment of a second execution mechanism in combination with an actually measured morphology deviation signal and an influence coefficient, and finally driving a controlled object to complete action response. A cyclic storage buffer area is established, and asynchronous timestamp alignment based on spatial displacement is executed. Through multi-physics field coupling and asynchronous correction, self-adaptive control over the steel machining equipment is achieved.

Description

Technical Field

[0001] This invention relates to the field of digital twin technology, specifically to an adaptive control method for steel processing equipment based on digital twins. Background Technology

[0002] In the steel processing industry, the performance indicators of the controlled object (such as thickness and morphology) are affected by multidimensional physical variables. In order to achieve high-quality continuous production, the control system needs to coordinate the actions of multiple actuators to ensure that the controlled object remains within the preset process range during the dynamic evolution process.

[0003] However, in complex dynamic processing environments, control systems face severe physical and logical challenges. First, the controlled object contains a large number of implicit state variables that are difficult to obtain directly through conventional physical sensors. These variables drift nonlinearly and over time with system operating parameters (such as energy input rate and load fluctuations), causing the preset control mechanism model to often deviate from the actual state of the physical entity, making it difficult to provide high-fidelity state feedback. Second, there are strong interactive coupling characteristics between different regulation loops within the control system. The control output of a single loop often causes instantaneous interference to the controlled variables of other loops, making the system prone to precision interference or control oscillations during multi-objective coordinated regulation.

[0004] Furthermore, due to the distributed displacement of the detection instruments and actuators in physical space, detection delays are prevalent in the feedback path. During the high-frequency evolution of the controlled object's state, this misalignment in the spatiotemporal dimensions makes it difficult for the feedback signal to reflect the physical state of the processing point in real time, further limiting the system's ability to promptly correct dynamic deviations. Therefore, how to achieve accurate perception of the controlled object's physical state and real-time adaptive decoupling of multiple control loops under conditions where the internal state of the controlled object is difficult to observe directly and where cross-loop interference and detection delays exist is a key technical problem currently facing the field of steel processing control systems.

[0005] To address this, an adaptive control method for steel processing equipment based on digital twins is proposed. Summary of the Invention

[0006] The purpose of this invention is to provide an adaptive control method for steel processing equipment based on digital twins. Through multi-physics coupling and asynchronous correction, adaptive control of the steel processing equipment is achieved. This includes acquiring real-time signals such as actuator displacement, load, speed, and inter-unit tension, and inputting them into a digital twin model to construct an instantaneous dynamic geometric model to calculate the instantaneous feedback value of the controlled object; using virtual perturbation to analyze the influence coefficients between the first and second control loops, generating a partial derivative sensitivity matrix; subsequently, inputting the instantaneous feedback value into the adaptive controller to obtain the original control increment, and combining the measured topographic deviation signal and influence coefficients to calculate the compensated control increment of the second actuator, ultimately driving the controlled object to complete the action response. This is achieved by establishing a circular storage buffer and performing asynchronous timestamp alignment based on spatial displacement.

[0007] To achieve the above objectives, the present invention provides the following technical solution: An adaptive control method for steel processing equipment based on digital twins, comprising: The system acquires the current displacement signal, preset load signal, drive unit speed signal, and real-time load signal of the actuator; and obtains the feed thickness signal and inter-unit tension signal. The acquired real-time displacement signal, real-time load signal, drive unit speed signal, and inter-unit tension signal are input into the digital twin model. An instantaneous dynamic geometric model is constructed based on the drive unit speed signal and the real-time displacement signal. The current instantaneous feedback value of the controlled object is calculated by combining the real-time load signal. Based on the change gradient of the instantaneous feedback value, real-time load signal, and drive unit speed signal, the influence coefficient between the first control loop and the second control loop is analyzed, and a sensitivity matrix is ​​generated. The instantaneous feedback value is used as the thickness feedback signal, and the deviation from the preset target thickness is input to the adaptive controller to calculate the original control increment signal of the first actuator; the measured shape deviation signal is obtained, and it is calculated with the influence coefficient and the first control increment signal to obtain the compensation control increment signal of the second actuator; The first and second control increment signals are converted into electronic control commands to drive the controlled object to complete the action response.

[0008] Preferably, the process of acquiring various signals from the actuator includes: acquiring the current displacement signal in real time using a displacement sensor installed in the hydraulic pressing system of the hot strip mill finishing stand; retrieving the set value corresponding to the current processing variety from the process database of the control system as the preset load signal; acquiring the speed signal of the drive unit through a rotary encoder coaxially connected to the drive motor; acquiring the real-time load signal in real time using a load sensor installed at the bottom of the hot strip mill finishing stand; acquiring the feed thickness signal through a X-ray thickness gauge installed at the entrance end of the hot strip mill finishing stand; and acquiring the inter-unit tension signal using a looper tension detection roller and its matching strain gauge tension sensor installed between adjacent stands.

[0009] Preferably, the process of constructing an instantaneous dynamic geometric model based on the drive unit rotation speed signal and the real-time displacement signal includes: using the drive unit rotation speed signal to analyze the frictional heat generation power and centrifugal stress distribution of the rotating component in the actuator at the current processing frequency in real time, and calculating the thermal dynamic expansion and centrifugal deformation of the controlled object; performing vector composite operation on the real-time load signal and the inter-unit tension signal to analyze the axial and radial instantaneous stress distribution of the material inside the controlled object in the processing area, and combining the real-time strain rate converted from the drive unit rotation speed signal to identify the real-time deformation resistance characteristics of the material under the current working condition in the digital twin model; using the thermal dynamic expansion and centrifugal deformation to perform multi-dimensional geometric compensation on the real-time displacement signal to generate an instantaneous dynamic geometric model; using the real-time deformation resistance characteristics as plastic deformation constraints, inputting them into the instantaneous dynamic geometric model for thermo-mechanical-plastic multiphysics coupling iteration, and outputting the outlet thickness estimate as the instantaneous feedback value.

[0010] Preferably, the process of generating the instantaneous dynamic geometric model includes: using the radial wear of the rotating component and the thermal convexity distribution of the controlled object calculated from the thermal dynamic expansion, reconstructing the nonlinear transverse profile model of the contact area of ​​the actuator in virtual space; extracting the real-time load signal, calculating the elastic flattening of the roll under the current load in the digital twin model using Hertzian contact theory, and geometrically rounding the transverse profile model using the elastic flattening of the roll; using the rotational speed signal of the drive unit, calculating the dynamic oil film thickness increment of the bearing and contact interface of the controlled object in real time through a fluid dynamics sub-model; and spatially coupling and superimposing the transverse profile model, the elastic flattening of the roll, and the dynamic oil film thickness increment to generate a curve characterizing the actual physical gap distribution from the center to the edge nodes of the contact area of ​​the controlled object at the current moment, as an effective instantaneous roll gap parameter output.

[0011] Preferably, the step of analyzing the influence coefficient between the first control loop and the second control loop and generating a sensitivity matrix includes: calculating the time-domain gradient of the real-time load signal and the drive unit speed signal within the current sampling period in real time; inputting the instantaneous feedback value, the effective instantaneous roll gap parameter, and the time-domain gradient into the digital twin model; applying a small control variable disturbance in the virtual model to analyze online the instantaneous derivative of the control quantity of the first control loop with respect to the output variable of the second control loop, and the instantaneous derivative of the control quantity of the second control loop with respect to the output variable of the first control loop; identifying the real-time interactive coupling coefficient characterizing the mutual interference strength between the thickness adjustment action and the shape adjustment action based on the change curve of the instantaneous derivative and the material rheological property value; and constructing a partial derivative sensitivity matrix that dynamically migrates with the processing conditions using the real-time interactive coupling coefficient as matrix elements.

[0012] Preferably, the process of calculating the original control increment signal of the first actuator includes: calculating the control residual error between the preset target thickness deviation and the instantaneous feedback value, and predicting the deviation evolution trajectory of the next sampling period in combination with the changing trend of the instantaneous feedback value; extracting the real-time deformation resistance characteristics and instantaneous structural yielding amount output by the digital twin model, and matching the control gain matrix adapted to the current processing condition online through an adaptive law; performing proportional-integral-differential operations on the control residual error using the control gain matrix to generate the original control increment driving the first actuator; obtaining the dynamic response frequency and hysteresis characteristics of the first actuator, performing high-frequency component correction and nonlinear region avoidance on the first original control increment, and outputting the original control increment signal.

[0013] Preferably, the process of obtaining the second actuator compensation control increment signal includes: extracting the first control increment signal and, in conjunction with the interaction coupling coefficient in the sensitivity matrix, calculating online the instantaneous disturbance prediction value generated by the adjustment action of the first actuator on the target variable of the second control loop; performing spatial spectrum decomposition on the acquired measured shape deviation signal to extract the components of each order characterizing the surface flatness feature of the controlled object, and calculating the error vector between each order component and the preset target shape; using the sensitivity matrix to perform inverse decoupling mapping on the instantaneous disturbance prediction value to generate a feedforward compensation component; simultaneously using an adaptive control algorithm to calculate the gain of the error vector to generate a feedback adjustment component; performing time-domain synchronous fusion of the feedforward compensation component and the feedback adjustment component, and dynamically scaling the fused signal according to the drive unit speed signal to output the final second actuator compensation control increment signal.

[0014] Preferably, the method further includes: assigning a unified system timestamp to the instantaneous feedback value output by the digital twin model, and storing it in a circular storage buffer of a preset window length according to the time sequence to form a first-in-first-out queue representing the virtual state trajectory of the controlled object; acquiring the measured feedback signal with detection time delay and its corresponding sampling timestamp, and determining the dynamic transmission time by dividing the physical distance between the sensor and the machining center line by the material outlet speed converted from the drive unit speed signal; subtracting the dynamic transmission time from the sampling timestamp, and retrieving and extracting the instantaneous feedback value at the corresponding moment from the circular storage buffer; performing a difference operation between the aligned measured feedback signal and the retrieved instantaneous feedback value to generate asynchronous identification residuals; constructing the partial derivative matrix of the instantaneous feedback value with respect to the frame stiffness parameters inside the digital twin model as the Jacobian matrix; calculating the gradient direction of the asynchronous identification residuals under the Jacobian matrix by combining the real-time load signal and the drive unit speed signal at the current moment; using an iterative optimization algorithm to find the frame stiffness correction amount that minimizes the sum of squares of the asynchronous identification residuals in the gradient direction, and compensating the correction amount to the digital twin model in real time.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. By integrating a fluid dynamics sub-model with Hertzian contact theory in virtual space, a deep perception of the microscopic geometric evolution of the actuator is achieved. It can calculate in real time the dynamic oil film thickness increment and roll elastic flattening amount, which cannot be directly accessed by physical sensors, and convert them into high-fidelity instantaneous physical gap distribution curves. This elevates the control reference from a single sensor reading to an effective gap field coupled with multiple physics fields, effectively eliminating thickness prediction errors caused by mechanical micro-deformation under high-speed, heavy-load conditions.

[0016] 2. By introducing virtual perturbation analysis and temporal gradient extraction into the digital twin model, a partial derivative sensitivity matrix that dynamically migrates with processing conditions was constructed. This allows for online analysis of the instantaneous interaction intensity between the thickness adjustment and shape adjustment loops, enabling the system to adjust decoupling weights in real time based on the current material rheological properties and equipment status. This not only significantly suppresses dynamic oscillations during multivariate adjustment but also achieves efficient coordination and precise response of multiple control objectives under complex varying conditions.

[0017] 3. By constructing a circular storage buffer and performing asynchronous timestamp alignment based on spatial displacement, the measured signal with hysteresis characteristics can be accurately traced back to the corresponding material processing slice, thereby accurately identifying the instantaneous drift of core physical parameters such as frame stiffness, ensuring that the digital twin model can dynamically evolve as the equipment service status changes. Attached Figure Description

[0018] Figure 1This is a schematic diagram of the adaptive control method for steel processing equipment based on digital twins according to the present invention. Figure 2 This is a schematic diagram of the process for generating the instantaneous dynamic geometric model according to the present invention; Figure 3 This is a schematic diagram illustrating the process of real-time compensation of correction amounts into the digital twin model according to the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Please see Figures 1 to 3 This invention provides an adaptive control method for steel processing equipment based on digital twins, the technical solution of which is as follows: Example 1: An adaptive control method for steel processing equipment based on digital twins, the specific process of which is as follows: Figure 1 As shown, it includes: The system acquires the current displacement signal, preset load signal, drive unit speed signal, and real-time load signal of the actuator; and obtains the feed thickness signal and inter-unit tension signal. The acquired real-time displacement signal, real-time load signal, drive unit speed signal, and inter-unit tension signal are input into the digital twin model. An instantaneous dynamic geometric model is constructed based on the drive unit speed signal and the real-time displacement signal. The current instantaneous feedback value of the controlled object is calculated by combining the real-time load signal. Based on the change gradient of the instantaneous feedback value, real-time load signal, and drive unit speed signal, the influence coefficient between the first control loop and the second control loop is analyzed, and a sensitivity matrix is ​​generated. The instantaneous feedback value is used as the thickness feedback signal, and the deviation from the preset target thickness is input to the adaptive controller to calculate the original control increment signal of the first actuator; the measured shape deviation signal is obtained, and it is calculated with the influence coefficient and the first control increment signal to obtain the compensation control increment signal of the second actuator; The first and second control increment signals are converted into electronic control commands to drive the controlled object to complete the action response.

[0021] Furthermore, the process of acquiring various signals from the actuator includes: acquiring the current displacement signal in real time using a displacement sensor installed in the hydraulic pressing system of the hot strip mill finishing stand; retrieving the set value corresponding to the current processing variety from the process database of the control system as the preset load signal; acquiring the drive unit speed signal through a rotary encoder coaxially connected to the drive motor; acquiring the real-time load signal in real time using a load sensor installed at the bottom of the hot strip mill finishing stand; acquiring the feed thickness signal through a X-ray thickness gauge installed at the entrance end of the hot strip mill finishing stand; and acquiring the inter-unit tension signal using a looper tension detection roller and its matching strain gauge tension sensor installed between adjacent stands.

[0022] Specifically, inside the hydraulic pressing system of the hot strip mill stand, a high-precision magnetostrictive displacement sensor is installed on the piston rod of the pressing cylinder or the servo actuator. When the servo valve adjusts the hydraulic oil to enter and exit the cylinder, causing the piston to move, the displacement sensor senses the physical stroke of the piston relative to the bottom of the cylinder in real time. This displacement is converted into a digital pulse or voltage signal by the non-contact probe inside the sensor and transmitted to the input interface of the controller via a shielded cable. The controller then interprets the electrical signal into the current displacement signal of the actuator according to a preset scale coefficient.

[0023] Regarding the acquisition of the preset load signal, the basic automated control system first retrieves the original physical properties of the steel to be processed from the upper-level process database, including steel composition, specifications, and target thickness. Based on the retrieved information, the control system matches the corresponding theoretical deformation force setting value in the preset process specification table. This setting value is then transmitted to the parameter register of the digital twin model via industrial Ethernet, serving as the benchmark for subsequent simulation calculations, i.e., the preset load signal.

[0024] Regarding the acquisition of the drive unit speed signal, an incremental rotary encoder is installed at the end of the output shaft of the drive main motor. When the motor drives the roller to rotate, the rotary encoder rotates synchronously with the output shaft and generates continuous orthogonal pulses. The counting module of the control system counts the number of pulses per unit time in real time, and uses the ratio between the total number of pulses and the number of rotations, combined with the sampling period, to convert the pulse frequency into rotational angular velocity or revolutions per minute through logical operations, thereby obtaining an accurate drive unit speed signal.

[0025] Regarding the acquisition of real-time load signals, load sensors are installed between the base of the hot strip mill finishing stand and the stress point of the stand. When steel enters the processing zone and generates rolling resistance, this resistance acts directly on the stress surface of the load sensor through the roll system and bearing housing. The elastic body inside the sensor generates minute physical strain, causing a change in the resistance value of the strain gauge attached to it. This change is amplified by a bridge circuit and converted into a standard current or voltage signal. Finally, the signal acquisition card summarizes and calculates the total physical pressure value, i.e., the real-time load signal.

[0026] Regarding the acquisition of the feed thickness signal, a radiographic thickness gauge is installed at the entrance end of the hot strip mill stand. A radiographic source emits high-energy rays into the strip passing through it. A detector located on the other side of the strip receives the intensity of the residual rays after penetration in real time. Based on the difference in the attenuation rate of the rays passing through materials of different thicknesses, the detector outputs an electrical signal inversely proportional to the material thickness. The control system calculates the actual physical thickness of the strip before it enters the stand based on the received electrical signal intensity and a preset material density compensation parameter, using this as the feed thickness signal.

[0027] Regarding the acquisition of inter-unit tension signals, a looper tension detection roll is installed between two adjacent finishing mill stands, and a strain gauge tension sensor is installed below the bearing support of the detection roll. When the running strip passes through the detection roll and generates a certain wrap angle, the strip tension will generate a vertically downward component force on the detection roll. The tension sensor detects the elastic strain caused by this component force in real time and converts the strain variable into an electrical signal. The control system, combined with the geometric installation angle of the detection roll and the principle of mechanical balance, restores this vertical component force to the axial tension of the strip in the horizontal running direction, thereby acquiring the inter-unit tension signal.

[0028] By accurately acquiring key signals such as displacement, load, rotational speed, and tension, this application constructs a multi-dimensional, synchronous data foundation for the digital twin model. The real-time mapping mechanism of high-precision sensors ensures that the virtual image can objectively reproduce the instantaneous dynamic response of the controlled object, providing a reliable sensing basis for subsequent implicit parameter identification and decoupling of complex loops.

[0029] Furthermore, the process of constructing an instantaneous dynamic geometric model based on the drive unit rotation speed signal and real-time displacement signal includes: using the drive unit rotation speed signal to analyze the frictional heat generation power and centrifugal stress distribution of the rotating component in the actuator at the current processing frequency in real time, and calculating the thermal dynamic expansion and centrifugal deformation of the controlled object; performing vector composite operation on the real-time load signal and the inter-unit tension signal to analyze the axial and radial instantaneous stress distribution of the material inside the controlled object in the processing area, and combining the real-time strain rate converted from the drive unit rotation speed signal to identify the real-time deformation resistance characteristics of the material under the current working condition within the digital twin model; using the thermal dynamic expansion and centrifugal deformation to perform multidimensional geometric compensation on the real-time displacement signal to generate an instantaneous dynamic geometric model; using the real-time deformation resistance characteristics as plastic deformation constraints, inputting them into the instantaneous dynamic geometric model for thermo-mechanical-plastic multiphysics coupling iteration, and outputting the outlet thickness estimate as the instantaneous feedback value.

[0030] Specifically, the digital twin model is functionally divided into several sub-modules, including: a heat conduction sub-model for solving the radial temperature field of rotating components; a material rheology sub-model for analyzing the stress-strain distribution and real-time deformation resistance characteristics of materials; a geometric compensation sub-model for reconstructing the geometric profile of the contact area; a virtual perturbation and sensitivity matrix sub-model for simulating the interactive effects of multiple control loops; and a Jacobian matrix and iterative optimization sub-model for performing online correction of frame stiffness. All of these sub-models are integrated within the digital twin model in software form, jointly calculating instantaneous feedback values ​​and identifying parameters by sharing real-time acquired displacement, load, tension, and rotational speed signals.

[0031] The digital twin model first acquires the rotational speed signal of the drive unit collected by the rotary encoder and converts it into the angular velocity of the rotating component. It then retrieves preset bearing geometric parameters and friction coefficients, and calculates the instantaneous heat generation power at the bearing position using real-time load signals. This power is input as a thermal boundary condition into the unsteady radial heat conduction analytical logic constructed based on the finite difference method. Simultaneously, the surface comprehensive heat transfer coefficient (including the convective heat transfer components of cooling water and the radiative heat transfer components of air) and the ambient reference temperature are introduced as thermal equilibrium boundary constraints. The radial temperature field distribution of the rotating component from the center to the surface is simulated through numerical temperature rise iteration. Based on the thermal expansion coefficient of the material, radial full-size integration is performed to calculate the thermal dynamic expansion of the controlled object. Simultaneously, the model uses the angular velocity and the mass distribution density of the rotating component to calculate the centrifugal stress field generated by rotation, and combines this with the elastic modulus of the material to calculate the radial strain, thereby calculating the geometric radial elongation caused by high-speed rotation, i.e., the centrifugal deformation.

[0032] Subsequently, the vertical pressure vector represented by the real-time load signal and the horizontal tension vector represented by the inter-unit tension signal are combined into a vector composite operation. By establishing a stress balance differential equation based on the slice method in the contact arc region, the deformation zone is discretized into several unit slices along the running direction. The axial and radial stress distribution states inside the strip at the moment of processing are analyzed. At the same time, the digital twin model uses the rotation speed signal of the drive unit to calculate the outlet flow rate of the strip. Combined with the gap geometric parameters in the instantaneous dynamic geometric model, the rate of change of unit strain with time when the material passes through the deformation zone is calculated, i.e., the real-time strain rate. The model uses the analyzed instantaneous stress distribution and real-time strain rate as independent variables and performs matching and optimization in the preset material constitutive feature space (such as the parameter matrix constructed based on the Hensel-Spittel model). The Levenberg-Marquardt optimization algorithm is used to perform iterative search to find the physical feature value that minimizes the mechanical residual, thereby identifying the real-time deformation resistance characteristics of the material under the current working condition.

[0033] The pre-defined material constitutive feature space is constructed based on rheological test data of various typical steel grades in the hot working process. By performing thermal simulation compression tests on the specimens under different temperature gradients, deformation degrees and strain rates, the corresponding true stress-true strain curve set is obtained and used as the underlying data support. These test data are digitally regressed and formed a parametric feature matrix covering multi-dimensional processing conditions within the digital twin model.

[0034] In this feature space, the Hensel-Spittel model is used as the mathematical benchmark to describe the thermoplastic deformation behavior of materials. This model quantitatively correlates the work hardening effect, dynamic softening effect and strain rate sensitivity of materials under different thermodynamic states through a set of specific material characteristic coefficients. For different steel grades to be processed, the corresponding set of characteristic coefficients constitutes the feature vector in this space, providing a standardized physical reference for the real-time parameter identification of digital twin models under complex and variable working conditions.

[0035] In the real-time control logic, the digital twin model uses the analyzed instantaneous axial and radial stress distributions, as well as the real-time strain rate converted from the drive unit's rotational speed, as input variables. It then employs the Lewenberg-Marquardt optimization algorithm to perform iterative optimization within a predefined material constitutive feature space. The algorithm compares the mechanical load signals fed back from the physical entity with the theoretical calculations within the model, searching for and locking down the characteristic coefficients that minimize the mechanical residuals within the space. This identifies the real-time deformation resistance characteristics of the material under the current processing condition, providing precise physical constraints for subsequent adaptive closed-loop control.

[0036] The digital twin model uses the initial coordinates of the hydraulic pressing system fed back in real time by the displacement sensor as a reference. It introduces the thermal dynamic expansion and centrifugal deformation calculated above as geometric correction operators. In the virtual three-dimensional coordinate system, the model performs subtraction on the coordinates of the contact boundary nodes of the actuator to deduct the bulge increment caused by thermal expansion and superimpose the radial displacement increment caused by centrifugal force. Through this multi-dimensional geometric compensation, the system updates the real physical boundary between the actuator and the processed material in memory in real time, generating an instantaneous dynamic geometric model that can characterize the real position of the physical entity under the current thermal state.

[0037] The digital twin model assigns the identified real-time deformation resistance characteristics as physical properties to the computational grid cells in the instantaneous dynamic geometric model, initiating a thermo-mechanical-plastic multiphysics coupling iterative program. The real-time load signal is used as the target load constraint, and the von Mises yield criterion is employed to determine the plastic flow state of the grid cells to search for the mechanical equilibrium point. In each iteration, the model verifies whether the theoretical deformation force under the current geometric state is consistent with the actual load signal fed back by the sensor, and simultaneously checks whether the flow rates per second at the inlet and outlet satisfy the material flow continuity equation. When the L2 norm of the mechanical equilibrium residual converges to a preset threshold range (10 in this embodiment), the model continues to operate. -3 When the displacement increment of the grid nodes tends to stabilize (on the order of magnitude), the model locks the current grid geometry and extracts the vertical coordinate deviation of the center node of the outlet end face from the coordinate system. This coordinate difference is defined as the estimated outlet thickness and transmitted to the closed-loop control loop of the controller in real time as an instantaneous feedback value.

[0038] By constructing an instantaneous dynamic geometric model and executing thermo-mechanical-plastic multiphysics coupling iterations, online identification of the microscopic deformation and rheological properties of the controlled object was achieved. This effectively compensates for the deficiency of traditional static models in mapping implicit physical characteristics and can correct geometric deviations caused by fluctuations in thermal expansion, centrifugal force, and material resistance in real time. This real-time mapping logic based on physical mechanisms provides a physically realistic feedback benchmark for achieving high-response, high-precision adaptive closed-loop control.

[0039] Further, the process of generating the instantaneous dynamic geometric model includes: using the radial wear of the rotating component, combined with the thermal convexity distribution of the controlled object calculated from the thermal dynamic expansion, to reconstruct the nonlinear transverse profile model of the actuator contact area in virtual space; extracting the real-time load signal, using Hertzian contact theory to calculate the elastic flattening of the roll under the current load within the digital twin model, and using the elastic flattening of the roll to geometrically reduce the transverse profile model; using the rotational speed signal of the drive unit, calculating the dynamic oil film thickness increment of the controlled object bearing and contact interface in real time through a fluid dynamics sub-model; spatially coupling and superimposing the transverse profile model, the elastic flattening of the roll, and the dynamic oil film thickness increment to generate a curve characterizing the actual physical gap distribution curve from the center to the edge nodes of the contact area of ​​the controlled object at the current moment, as an effective instantaneous roll gap parameter output, the specific process is as follows: Figure 2 As shown.

[0040] Specifically, the digital twin model first acquires the initial geometric properties and surface curve data of the rotating component, extracts the real-time accumulated radial wear value, and then calculates the microscopic wear increment within a unit sampling period and accumulates it in the time domain using the Arcard wear theory model, combined with the real-time load signal, material contact length, and surface hardness parameters of the rotating component, thereby obtaining the radial wear value. Combining the thermal convexity distribution function of the controlled object obtained by the aforementioned thermal dynamic expansion calculation, several discrete transverse coordinate nodes are defined in the three-dimensional coordinate system of the virtual space with the axial center of the rotating component as the origin and along the axial width direction. The model subtracts the radial wear value at the corresponding node from the initial radius value and superimposes the thermal expansion increment calculated by the thermal convexity distribution, thereby constructing a nonlinear transverse contour model that characterizes the evolution of the original geometric contour of the actuator contact area with thermal wear.

[0041] The digital twin model extracts the real-time load signal collected by the load sensor and converts it into linear pressure acting on a unit length of the contact area. It introduces physical parameters such as the elastic modulus and Poisson's ratio of the material and uses Hertz contact theory. Specifically, it adopts a numerical integral model of a semi-infinite elastic body based on the Hitchcock improved radius of curvature to convert the non-uniformly distributed linear pressure into the radial geometric shrinkage of each transverse coordinate node in the contact area. Then, the elastic flattening amount is used as a geometric rounding operator to be applied to the previously generated transverse contour model. By performing coordinate offset correction on each transverse coordinate node, it compensates for the microscopic concave deformation of the rotating component surface caused by high pressure extrusion.

[0042] The instantaneous linear velocity of the rotating component is determined using the rotational speed signal of the drive unit and input into a built-in hydrodynamic sub-model. This sub-model combines the viscosity-temperature characteristics of the lubricating medium with the geometric curvature of the contact interface, and uses simplified analytical logic of the Reynolds equation to calculate the hydrodynamic pressure effect. The model calculates in real time the pressure oil wedge thickness formed by the lubricating medium at the contact interface due to changes in rotational speed. Specifically, using simplified analytical logic of the Reynolds equation, the Dowson-Higginson minimum oil film thickness formula is introduced. Combining the pressure-viscosity coefficient of the lubricating medium and the equivalent radius of curvature of the rotating component, the hydrodynamic oil film increment under instantaneous speed fluctuations is calculated. This thickness increment is defined as the displacement offset of the bearing clearance and contact interface of the controlled object, used to characterize the slight rise or fall of the center position of the rotating component due to hydrodynamic support.

[0043] Under a unified transverse coordinate system, for each transverse coordinate node, the geometrically rounded transverse contour coordinates, the calculated dynamic oil film thickness increment, and the initial frame structure dimensions are linearly superimposed and calculated. By calculating the geometric net distance from the top contact point to the bottom contact point of the actuator, an actual physical gap distribution curve representing the actual geometric distance from the center of the contact area to each edge node of the controlled object at the current moment is generated. This curve serves as the final output parameter of the instantaneous dynamic geometric model, obtaining the effective instantaneous roll gap parameters, which are provided in real time to the subsequent sensitivity matrix analysis logic.

[0044] By integrating multi-dimensional geometric compensation operators such as radial wear, thermal convexity, elastic flattening, and dynamic oil film into the digital twin model, a microscopic restoration of the actual physical clearance of the actuator is achieved. This enables precise capture of instantaneous geometric deviations caused by load fluctuations and speed changes. This full-contour geometric mapping logic provides a high-fidelity physical benchmark for eliminating plate shape defects and improving the consistency of thickness control.

[0045] Furthermore, the step of analyzing the influence coefficients between the first and second control loops and generating a sensitivity matrix includes: calculating the time-domain gradient of the real-time load signal and the drive unit speed signal within the current sampling period; inputting the instantaneous feedback value, the effective instantaneous roll gap parameter, and the time-domain gradient into the digital twin model; applying small control variable perturbations in the virtual model to analyze online the instantaneous derivative of the control quantity of the first control loop with respect to the output variable of the second control loop, and the instantaneous derivative of the control quantity of the second control loop with respect to the output variable of the first control loop; identifying the real-time interactive coupling coefficient characterizing the mutual interference strength between the thickness adjustment action and the shape adjustment action based on the change curve of the instantaneous derivative and the material rheological property value; and constructing a partial derivative sensitivity matrix that dynamically migrates with the processing conditions using the real-time interactive coupling coefficient as matrix elements.

[0046] Specifically, the actual physical gap distribution curve generated by the instantaneous dynamic geometric model is first defined as the effective instantaneous roll gap parameter. This effective instantaneous roll gap parameter serves as the initial geometric boundary condition when the digital twin model performs virtual perturbations, characterizing the comprehensive roll gap morphology including roll thermal expansion, elastic flattening, and dynamic oil film increment. Simultaneously, real-time load signals and drive unit speed signals are captured and stored in a first-in-first-out buffer queue. A hardware synchronous trigger clock is used to achieve nanosecond-level time alignment, and high-frequency noise is removed through low-pass filtering. The system calculates the difference between the current sampling time value and the previous time value through a logic operation unit, and divides it by the time span of the sampling period to obtain the time-domain gradient reflecting the load fluctuation and speed change rate.

[0047] Subsequently, the generated instantaneous feedback value, the aforementioned effective instantaneous roll gap parameters, and the time-domain gradient are input into the digital twin model. The model starts a parallel computing thread in the software simulation layer and performs virtual perturbation analysis while keeping the current physical state constant. Small numerical perturbations (usually 1% of the current control quantity) are applied to the control quantity of the first control loop (such as hydraulic position command) and the control quantity of the second control loop (such as bending roll force command). The model recalculates the output response under the perturbation state, compares the changes in the thickness prediction and the shape deviation prediction before and after the perturbation, and calculates the ratio between the output increment and the input perturbation. Specifically, the digital twin model pre-constructs an analytical mapping logic based on the coupling of the rolling force equation and the roll gap geometry. After applying the numerical perturbation, a new mechanical equilibrium point is found using a thermo-mechanical-plastic multiphysics coupling iterative program, thereby obtaining the output response value after the perturbation, ensuring that the calculation of the instantaneous derivative is based on the real metal rheological laws. This ratio represents the instantaneous derivative of the control quantity of the first control loop with respect to the output variable of the second control loop, and the instantaneous derivative of the control quantity of the second control loop with respect to the output variable of the first control loop, thereby quantitatively analyzing the influence coefficient between the two loops.

[0048] The first control loop is specifically an automatic thickness control loop. Its core control objective is to ensure that the exit thickness of the controlled object (such as strip steel) remains within the preset target process range. During operation, the first control loop receives the estimated exit thickness (i.e., instantaneous feedback value) output by the digital twin model in real time and compares it with the preset target thickness to calculate the control residual error. This loop generates the original control increment signal through an adaptive control algorithm and ultimately drives the first actuator (hydraulic pressing system) to perform physical actions, achieving closed-loop correction of thickness deviations during processing.

[0049] The second control loop is specifically an automatic shape control loop, also known as a flatness control loop. Its core control objective is to adjust the surface flatness, lateral convexity, and complex morphological features of the controlled object. This loop acquires the measured morphological deviation signal through a detection unit and uses a partial derivative sensitivity matrix to analyze online the instantaneous interference effect of the first control loop (thickness adjustment) on the morphological variables. By performing inverse decoupling mapping, the second control loop generates feedforward compensation components and feedback adjustment components, and ultimately drives the second actuator (bending roller system) to adjust the bending roller force. This ensures thickness accuracy while eliminating shape defects caused by the pressing action, achieving multi-objective adaptive decoupling control.

[0050] The instantaneous derivative sequence obtained from the analysis is associated with the material rheological property parameters in the database. The specific identification logic is as follows: the deviation of the strain hardening coefficient of the current material from the reference value is compared in real time. When the material hardness causes fluctuations in deformation resistance, the gain weight of the corresponding derivative is adjusted proportionally. Specifically, the strain hardening coefficient reference of the current steel grade is extracted from the process database, the deviation ratio between the measured value and the reference value is calculated, and this ratio is linearly applied to the instantaneous derivative. Subsequently, the dimensions of the derivatives of each loop are normalized using the rated adjustment range of the actuator as the denominator. The thickness control unit and the shape control unit (IU or stress value) are uniformly converted to the value range of [0,1] for comparison, thereby identifying the interactive coupling coefficient that can truly characterize the physical interference strength between the thickness adjustment action and the shape adjustment action.

[0051] Finally, the digital twin model, following the control matrix mapping rules, constructs a partial derivative sensitivity matrix that dynamically shifts with the processing conditions, using real-time interactive coupling coefficients and various derivatives as matrix elements. This matrix uses the sensitivity of the first control loop to itself and the interactive coupling coefficient between the first and second loops as its first row elements, and the interactive coupling coefficient between the second and first control loops and their own sensitivity as its second row elements. This matrix is ​​refreshed and output in real-time with the processing data during each sampling period, providing the compensation algorithm module with the opportunity to perform inverse decoupling operations. This determines the interference generated by the first control loop's actions on the second control loop and ultimately calculates the compensation control increment signal for the second actuator. During the inverse decoupling operation, if the condition number of the partial derivative sensitivity matrix exceeds a preset threshold (e.g., 10), the algorithm will terminate the process. 3 Then, Tikhonov regularization is introduced, which suppresses numerical singularity by adding a damping factor to the matrix diagonal, ensuring that the generated feedback correction load evolves smoothly within the physical response frequency range.

[0052] By capturing signal gradients in real time and performing virtual perturbation analysis, quantitative analysis of cross-loop interference intensity is achieved. Combined with the sensitivity matrix modified by material properties to dynamically generate compensation, the physical coupling interference between multiple loops can be effectively reduced, improving the decoupling control accuracy and adaptive stability of the system under complex transient conditions, and ensuring the consistency of processing quality under different working conditions.

[0053] Furthermore, the process of calculating the original control increment signal of the first actuator includes: calculating the control residual error between the preset target thickness deviation and the instantaneous feedback value, and predicting the deviation evolution trajectory of the next sampling period in combination with the changing trend of the instantaneous feedback value; extracting the real-time deformation resistance characteristics and instantaneous structural yielding amount output by the digital twin model, and matching the control gain matrix adapted to the current processing condition online through an adaptive law; performing proportional-integral-differential operations on the control residual error using the control gain matrix to generate the original control increment driving the first actuator; obtaining the dynamic response frequency and hysteresis characteristics of the first actuator, performing high-frequency component correction and nonlinear region avoidance on the first original control increment, and outputting the original control increment signal.

[0054] Specifically, the system first synchronously retrieves the preset thickness target value signal and the instantaneous measured signal fed back by the sensing unit through the controller interface. The instantaneous difference between the two is calculated by the subtraction logic unit to obtain the current control residual error. The residual error values ​​for five consecutive sampling cycles are stored in the buffer. The trend of residual error change is analyzed by the slope comparison logic: if the residual error value shows an increasing trend in the continuous cycle, the system pre-superimposes a correction bias in the opposite direction in the feedforward channel according to the current deviation change rate. Specifically, the magnitude of the correction bias is obtained by multiplying the current deviation change rate by a preset advance compensation coefficient. The advance compensation coefficient is preset according to the length of the system sampling cycle (set to 0.5 to 1.2 times the sampling cycle), so that the bias can offset the estimated evolution trend of the next cycle in advance, and complete the linear prediction of the deviation evolution trajectory of the next cycle.

[0055] The digital twin model outputs two key physical parameters representing the current processing state in real time: deformation resistance (reflecting changes in material hardness) and structural yield (reflecting the elastic deformation of the frame). The system uses these two values ​​as index coordinates and inputs them into a pre-stored condition-gain correlation database. This database pre-stores discrete control parameter sets for different material hardness levels (e.g., resistance ranges corresponding to low-carbon steel, high-alloy steel, etc.) and different frame stiffness states. The preset judgment rule is: when the deformation resistance increases by more than 10% compared to the initial set value, it is determined as an increase in resistance, and a high-sensitivity gain is output; when the structural yield exceeds 80% of the frame's design elastic limit, the integral term weakening logic is triggered. If the real-time parameter is between two discrete levels in the database, the final gain value is calculated using linear interpolation logic. If the deformation resistance increases, the database outputs a set of increased proportional term gains to enhance control sensitivity; if the structural yield exceeds a preset threshold, the database outputs a weakened integral term gain to prevent oscillations caused by insufficient mechanical rigidity.

[0056] The deviation prediction signal generated in the first step is input into the proportional-integral-derivative (PI-DE) operation module, and the control gain matrix obtained in the second step is loaded. The module first performs proportional scaling on the instantaneous deviation, then performs integral summation on the historical deviation accumulation sequence to eliminate steady-state error, and extracts the differential rate of deviation change. The operation unit performs weighted summation on the calculation results of the above three dimensions to generate a preliminary control command representing the amplitude and direction of the action of the first actuator. During the weighted summation process, the system allocates weights according to whether it is in the acceleration stage or the stable rolling stage. Under the preset transient switching logic, if the speed gradient is detected to exceed the preset threshold, the weight ratio of the derivative term (deviation change rate) will be automatically increased to suppress response overshoot. In the stable stage, the proportional term and the integral term are used as the main outputs. In this embodiment, the weight ratio is set to 70% for the proportional term and 30% for the integral term.

[0057] Based on the physical characteristics of the actuator (such as a hydraulic servo system), a final safety and accuracy correction is performed on the initial command: the command signal is passed through a low-pass filter logic unit to intercept high-frequency fluctuation components whose frequency exceeds the actuator's response limit, preventing mechanical fatigue. A preset hysteresis characteristic threshold is used, and a numerical comparator determines whether the absolute value of the initial command is less than the threshold. If the increment is too small to overcome mechanical static friction, the increment is forcibly cleared to avoid invalid action. If the command exceeds the threshold, a fixed-step starting increment is compensated according to the hysteresis direction to ensure that the actuator can accurately cross the nonlinear response region. The hysteresis characteristic threshold is preset to 1.2 times the mechanical backlash value of the actuator. The specific avoidance and compensation logic is as follows: when the command increment is insufficient to overcome the mechanical dead zone, it is forcibly cleared to protect the valve body; once the command exceeds the threshold, an additional fixed-step start increment will be added. This step size is preset to the minimum pressure command value required to overcome the static friction of the actuator, so that the actuator directly crosses the static friction range and enters the linear response range, and finally outputs the original control increment signal. The hysteresis characteristic refers to the physical characteristic caused by the mechanical backlash and static friction of the actuator, which leads to a nonlinear response between the command increment and the actual action.

[0058] By linearly predicting the deviation trajectory and dynamically retrieving operating parameters, the command output can proactively adapt to the real-time changes in material hardness and frame stiffness. Combined with dead-zone compensation and high-frequency filtering of the actuator, the motion lag caused by mechanical backlash is effectively eliminated, significantly reducing the physical impact of invalid control commands on the valve body and maintaining continuous and consistent processing actions.

[0059] Further, the process of obtaining the second actuator compensation control increment signal includes: extracting the first control increment signal and, in conjunction with the interaction coupling coefficient in the sensitivity matrix, calculating online the instantaneous disturbance prediction value generated by the adjustment action of the first actuator on the target variable of the second control loop; performing spatial spectrum decomposition on the acquired measured shape deviation signal to extract the components of each order characterizing the surface flatness feature of the controlled object, and calculating the error vector between each order component and the preset target shape; using the sensitivity matrix to perform inverse decoupling mapping on the instantaneous disturbance prediction value to generate a feedforward compensation component; simultaneously using an adaptive control algorithm to calculate the gain of the error vector to generate a feedback adjustment component; performing time-domain synchronous fusion of the feedforward compensation component and the feedback adjustment component, and dynamically scaling the fused signal according to the drive unit speed signal to output the final second actuator compensation control increment signal.

[0060] Specifically, the controller extracts the calculated first control increment signal (such as the displacement correction of the hydraulic pressing system) in real time and retrieves the sensitivity matrix of the current cycle from the memory register of the digital twin model. The logic operation unit identifies the partial derivative cross-gain term in the matrix that represents the influence of the first actuator action on the controlled variables of the second loop (such as the shape component). The first control increment signal is multiplied with the gain term to quantitatively calculate the instantaneous disturbance prediction of the shape target variable caused by the change in roll gap geometry due to the pressing action in the virtual space.

[0061] The measured morphological deviation signal of the strip in the width direction is acquired by a flatness detection sensor and processed using spatial spectrum decomposition logic based on the least squares method. This process fits the discrete deviation data to a preset fourth-order orthogonal polynomial basis function space, thereby independently separating the components characterizing the surface flatness features, including symmetric second-order components and asymmetric fourth-order components. Specifically, Chebyshev polynomials are used as orthogonal basis functions, and the fitting coefficients are calculated using the least squares method to minimize the sum of squared residuals between the measured stress distribution curve and the fitted curve. This deconstructs the complex transverse flatness signal into independent geometric components of various orders, achieving accurate decoupling and extraction of the wave and edge wave characteristics of the strip. Subsequently, the difference between the measured values ​​of each component and the preset target morphological values ​​in the process database is calculated to generate a multi-dimensional error vector.

[0062] For the obtained instantaneous disturbance prediction, a mapping operation is performed using the inverse decoupling operator of the sensitivity matrix. This step calculates the compensation action required by the second actuator (such as the bending roller system) to offset the disturbance by projecting the disturbance prediction back from the output variable space to the control space of the actuator. This compensation action is defined as the feedforward compensation component. During the calculation, if the matrix tends to be singular, a pseudo-inverse algorithm is used to perform numerical correction to maintain the stability of the calculation. In order to prevent the matrix from exploding due to ill-conditioning, Tikhonov regularization is introduced when performing the pseudo-inverse operation. By setting a damping coefficient for smaller singular values, the continuity and smoothness of the feedforward compensation component during the command switching transient are ensured.

[0063] When processing the generated error vector, the system synchronously starts the adaptive control algorithm. The controller uses the real-time identified material deformation resistance characteristics and frame stiffness parameters as indexes to perform bilinear interpolation in a preset two-dimensional gain lookup table to match the control gain matrix under the current operating condition. The gain matrix is ​​then used to perform proportional-integral operation on the error vector to generate feedback adjustment components for correcting steady-state residual deviations. The gain lookup table uses material deformation resistance of 100MPa to 500MPa and frame online stiffness of 4000kN / mm to 6000kN / mm as index axes and is gridded according to a quantization step size of 5%. Based on the real-time resistance and stiffness feedback, bilinear interpolation is performed between four adjacent grid nodes to output the optimal PID gain constant under the current operating condition.

[0064] The timing synchronization operator superimposes and fuses the feedforward compensation component and the feedback adjustment component at the same timestamp. To achieve dynamic gain scaling, the controller executes the following technical logic: A reference speed node (e.g., 40% of the rated speed) and a maximum speed node (100% of the rated speed) are preset, and corresponding to a high gain coefficient (1.0) and a low gain coefficient (e.g., 0.7) respectively.

[0065] The controller captures the drive unit speed signal in real time and calculates the percentage position of the current speed within the preset speed range.

[0066] Based on this ratio, a linear subtraction mapping is performed between preset high and low gain coefficients to obtain a real-time scaling factor. The calculation logic of this scaling factor is as follows: a reference speed (such as 40% of the rated speed) and a maximum speed (such as 100% of the rated speed) are preset as adjustment ranges; when the measured speed increases within this range, the scaling factor decreases linearly from 1.0 to 0.7; the higher the speed, the lower the global output weight, thereby actively compensating for mechanical resonance that may be caused by the hypersensitive response of the hydraulic system at high speeds, and ensuring the damping stability of the control system.

[0067] The synthesized signal after dynamic gain scaling is used as the final compensation control incremental signal output of the second actuator. This signal is converted into an electronic control command and sent to the servo drive unit of the second actuator (such as the bending roller force electro-hydraulic servo valve) to drive the controlled object to complete the final action response.

[0068] The first actuator is the hydraulic pressing system of the intermediate hot continuous rolling mill stand in this embodiment. This actuator is the core physical unit for realizing automatic control of plate thickness. Its hardware mainly consists of a double-acting large-diameter hydraulic cylinder installed on the top of the stand, a high-performance electro-hydraulic servo valve, and a high-precision magnetostrictive displacement sensor.

[0069] In this embodiment, the second actuator specifically refers to the bending roll system used to adjust the straightness and cross-sectional shape of the strip (in some working conditions, it may also include the rolling mechanism). The main function of this actuator is to perform automatic control of the strip shape. Its physical entity includes bending roll hydraulic cylinders set on both sides of the roll bearing seat and matching electro-hydraulic servo drive units.

[0070] By combining feedforward decoupling with feedback adaptive adjustment, this step effectively suppresses physical interference between loops, reduces the instantaneous interference of thickness adjustment on topography quality, quantifies multi-order topography components using spatial spectrum decomposition technology, improves the control accuracy of surface flatness, and compensates for system damping fluctuations under high-speed conditions with a dynamic gain scaling mechanism based on drive speed.

[0071] Furthermore, it also includes: assigning a unified system timestamp to the instantaneous feedback value output by the digital twin model, and storing it in a circular storage buffer of a preset window length according to the time sequence, forming a first-in-first-out queue representing the virtual state trajectory of the controlled object; acquiring the measured feedback signal with detection time delay and its corresponding sampling timestamp, and determining the dynamic transmission time by dividing the physical distance between the sensor and the machining center line by the material outlet speed converted from the drive unit rotation speed signal; subtracting the dynamic transmission time from the sampling timestamp, and retrieving and extracting the corresponding data from the circular storage buffer. The instantaneous feedback value at the given moment is obtained; the difference between the aligned measured feedback signal and the retrieved instantaneous feedback value is calculated to generate the asynchronous identification residual; the partial derivative matrix of the instantaneous feedback value with respect to the frame stiffness parameters inside the digital twin model is constructed as the Jacobian matrix; the gradient direction of the asynchronous identification residual under the Jacobian matrix is ​​calculated by combining the real-time load signal and the drive unit speed signal at the current moment; the frame stiffness correction amount that minimizes the sum of squares of the asynchronous identification residual is found in the gradient direction using an iterative optimization algorithm, and the correction amount is compensated into the digital twin model in real time. The specific process is as follows: Figure 3 As shown.

[0072] Specifically, the controller receives instantaneous feedback values ​​(such as the estimated export thickness) output by the digital twin model in real time and synchronously calls the system's high-precision clock to assign a unique system timestamp to each feedback value. Subsequently, the "timestamp-feedback value" pairs are stored in chronological order in a circular storage buffer with a preset window length (such as the time length covering the maximum transmission cycle of the material from the processing center to the detection point). Specifically, the preset window length is determined based on the ratio of the maximum distance of the production line to the minimum running speed of the material, and is usually set to 1.2 to 1.5 times the actual transmission time. In this embodiment, the buffer storage frequency is synchronized with the calculation step size of the digital twin model (such as 10ms to 20ms) to ensure that the stored virtual trajectory covers the complete material dynamic evolution cycle. The buffer executes a first-in-first-out management logic. When new data is stored and exceeds the window capacity, the oldest historical data is automatically overwritten, thereby forming a time series trajectory in memory that represents the virtual evolution state of the controlled object.

[0073] The system acquires the measured signal and its original sampling timestamp from a sensor (such as a X-ray thickness gauge) located downstream of the machining center. The controller extracts the real-time drive unit rotation speed signal and, combined with the preset effective roll radius, calculates the instantaneous exit velocity of the material. By dividing the known physical distance between the sensor and the machining center line by this exit velocity, the system determines online the dynamic transmission time of the material at the sampling point between the processing area and the detection point. Subsequently, the transmission time is subtracted from the sampling timestamp of the measured signal to obtain the actual processing time of the material slice at the machining center line.

[0074] The controller uses the calculated actual processing time as an index to perform a retrieval in the virtual state trajectory of the circular storage buffer. Through timestamp matching logic (if no exact matching point is found, linear interpolation is performed between two adjacent virtual state points), the instantaneous feedback value at the corresponding time is extracted. The difference between the aligned measured feedback signal and the retrieved instantaneous feedback value is calculated to generate an asynchronous identification residual that represents the prediction deviation of the digital twin model.

[0075] The digital twin model initiates a sensitivity analysis procedure. By applying a small positive perturbation to the frame stiffness parameters within the current calculation cycle, it analyzes the partial derivatives of the instantaneous feedback value with respect to the change in stiffness parameters. The small positive perturbation is selected to be 0.1% to 0.5% of the current nominal frame stiffness value. The partial derivatives calculated using this step size can linearize the nonlinear mapping relationship between the frame elastic deformation and the outlet thickness online, ensuring the local effectiveness of the Jacobian matrix at the current operating point. The partial derivatives are used as matrix elements to construct the Jacobian matrix, which quantitatively describes the mapping strength of a small change in the core implicit parameter of frame stiffness to the model output (thickness prediction).

[0076] By combining the real-time load signal and the drive unit speed signal at the current moment, the current physical operating condition coordinates are determined. The Jacobian matrix is ​​used to map the asynchronous identification residuals to a direction, and the gradient direction with the fastest deviation reduction is calculated. Then, an iterative optimization algorithm based on Levenberg-Marquardt logic is executed. Through multiple numerical approximations in the gradient direction, the rack stiffness correction amount that minimizes the sum of squares of the asynchronous identification residuals within the current observation window is found. In order to prevent the model parameters from becoming unstable under extreme transient conditions, the system sets a single compensation step size limit (usually not exceeding 2% of the original parameter value) and a physical range limit for the rack stiffness correction amount. If the calculated correction amount exceeds the safe domain, truncation is performed to ensure the physical rationality of the model evolution process.

[0077] The controller writes the calculated frame stiffness correction amount into the parameter register of the digital twin model in real time in the form of incremental compensation. In the thermo-mechanical-plastic multiphysics coupling iteration of the next sampling cycle, the model directly calls the corrected frame stiffness coefficient for gap compensation and thickness prediction. Through this closed-loop correction mechanism based on measured trajectory backtracking, the internal physical parameters of the digital twin model evolve synchronously with the changes in the service status of the equipment.

[0078] By constructing a circular storage buffer and performing asynchronous timestamp alignment based on spatial displacement, this step effectively eliminates signal time-delay interference commonly found in physical detection paths. Utilizing the real-time correlation between sensor sampling timestamps and material outlet velocity, measured data with time-delay characteristics are accurately traced back to the virtual state trajectory nodes of the digital twin model. By analyzing the partial derivatives of instantaneous feedback values ​​with respect to frame stiffness using the Jacobian matrix, implicit physical parameter drifts caused by mechanical wear, thermal deformation, or component aging can be identified online. This iterative optimization mechanism based on asynchronous residual identification ensures that the digital twin model can dynamically evolve as the actual service status of the equipment changes.

[0079] By integrating a digital twin model with multi-physics coupling in virtual space, precise sensing of the microscopic deformation of the actuator and the rheological properties of the material is achieved. Utilizing an online analytical partial derivative sensitivity matrix, dynamic coupling interference between thickness and morphology adjustment loops can be effectively identified and suppressed, enabling efficient coordination of multiple control targets. Combined with timestamp alignment technology based on spatial displacement compensation, the detection time lag effect of measured feedback is eliminated, and asynchronous residual identification enables dynamic correction of core physical parameters such as frame stiffness, ensuring long-term, high-fidelity mapping between the virtual image and the physical entity.

[0080] Example 2: During the processing of high-strength steel plates, the current displacement is first collected by a displacement sensor integrated into the pressing cylinder, and the set load corresponding to this type of steel is retrieved from the process database. Simultaneously, the rotational speed is obtained through a rotary encoder connected to the main drive motor, and the real-time load during processing is monitored by a load sensor at the bottom of the frame. Furthermore, a thickness measuring device at the inlet provides real-time feedback on the feed thickness, and tension detection rollers and their associated strain gauges between adjacent frames are responsible for acquiring the dynamic tension signal of the strip. These data form the basic input stream for the digital twin model.

[0081] After the acquired data stream is input into the digital twin model, the frictional heat generation and centrifugal force distribution of the rotating component under the current processing frequency are analyzed using the drive speed. The thermal expansion and centrifugal deformation of the controlled object are calculated. The model performs vector composite operation on the real-time load and tension to analyze the axial and radial stress distribution inside the material of the processing area. Subsequently, the thermal expansion and centrifugal deformation are used to perform geometric compensation on the initial displacement signal. In the virtual space, multi-physics coupling iteration is performed in combination with the real-time deformation resistance characteristics of the material to output the theoretical estimate of the outlet thickness, which is used as the instantaneous feedback value.

[0082] The system calculates the time-domain gradients of load and rotational speed within the current sampling period in real time and inputs them into the model along with the instantaneous feedback values. Small control variable perturbations are applied within the model, and the instantaneous derivatives of the first control loop (e.g., thickness adjustment) with respect to the output variables of the second loop (e.g., shape adjustment) are analyzed online, and vice versa. Combining this with the rheological properties of the material, the system identifies the interactive coupling coefficients characterizing the interference strength between thickness adjustment and shape adjustment actions. These coefficients are then used to construct a partial derivative sensitivity matrix that dynamically shifts with the operating conditions, providing a quantitative basis for multi-objective decoupling.

[0083] The controller calculates the control steady-state error by comparing the target thickness deviation with the instantaneous feedback value, and extracts the real-time deformation resistance characteristics and structural yield from the model output, matching the optimal control gain matrix online. Using this gain matrix, proportional-integral-differential operations are performed on the steady-state error to generate the initial control increment for the first actuator. Subsequently, the dynamic response frequency and hysteresis characteristics of the actuator are acquired, and high-frequency component correction and nonlinear region avoidance are applied to the initial increment, outputting the final initial control increment signal.

[0084] For topography control, the system utilizes the aforementioned sensitivity matrix to calculate online the instantaneous disturbance prediction caused by the action of the first actuator to the topography target variable. The measured topography deviation signal is decomposed into spatial spectrum to extract components representing surface flatness characteristics (such as second-order intermediate waves or fourth-order composite waves), and the error vector between these components and the target topography is calculated. The sensitivity matrix is ​​used to perform inverse decoupling mapping to generate feedforward compensation components, while an adaptive algorithm is simultaneously used to generate feedback adjustment components. After the two signals are fused, dynamic gain scaling is performed based on the current rotational speed signal; the gain is proportionally reduced as the rotational speed increases to prevent system oscillation, ultimately driving the bending or rolling mechanism.

[0085] To eliminate hysteresis caused by the physical location of the measuring instruments, the system assigns a unified timestamp to the instantaneous feedback value and stores it in a circular storage buffer. When a measured signal with hysteresis characteristics is acquired, the transmission time is calculated based on the sensor's physical distance and the real-time exit velocity. This time is then subtracted from the timestamp, allowing the corresponding instantaneous feedback value to be retrieved from the buffer. Asynchronous identification residuals are generated by subtracting the aligned measured value from the virtual value, and a Jacobian matrix is ​​constructed. An iterative optimization algorithm is then used to find the rack stiffness correction that minimizes the sum of squared residuals. This correction is applied to the model in real time, ensuring continuous alignment between the virtual state and the physical entity.

[0086] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An adaptive control method for steel processing equipment based on digital twins, characterized in that, include: Collect the current displacement signal, preset load signal, drive unit speed signal, and real-time load signal of the actuator; Acquire the feed thickness signal and the inter-unit tension signal; The acquired real-time displacement signal, real-time load signal, drive unit speed signal, and inter-unit tension signal are input into the digital twin model. An instantaneous dynamic geometric model is constructed based on the drive unit speed signal and the real-time displacement signal. The current instantaneous feedback value of the controlled object is calculated by combining the real-time load signal. Based on the change gradient of the instantaneous feedback value, real-time load signal, and drive unit speed signal, the influence coefficient between the first control loop and the second control loop is analyzed, and a sensitivity matrix is ​​generated. The instantaneous feedback value is used as the thickness feedback signal, and the deviation from the preset target thickness is input to the adaptive controller to calculate the original control increment signal of the first actuator; the measured shape deviation signal is obtained, and it is calculated with the influence coefficient and the first control increment signal to obtain the compensation control increment signal of the second actuator; The first and second control increment signals are converted into electronic control commands to drive the controlled object to complete the action response.

2. The adaptive control method for steel processing equipment based on digital twins according to claim 1, characterized in that, The process of acquiring various signals from the actuator includes: acquiring the current displacement signal in real time using a displacement sensor installed in the hydraulic pressing system of the hot strip mill finishing stand; retrieving the set value corresponding to the current processing variety from the process database of the control system as the preset load signal; acquiring the speed signal of the drive unit through a rotary encoder coaxially connected to the drive motor; acquiring the real-time load signal in real time using a load sensor installed at the bottom of the hot strip mill finishing stand; acquiring the feed thickness signal through a X-ray thickness gauge installed at the entrance end of the hot strip mill finishing stand; and acquiring the inter-unit tension signal using a looper tension detection roller and its matching strain gauge tension sensor installed between adjacent stands.

3. The adaptive control method for steel processing equipment based on digital twins according to claim 1, characterized in that, The process of constructing an instantaneous dynamic geometric model based on the drive unit rotation speed signal and real-time displacement signal includes: using the drive unit rotation speed signal to analyze the frictional heat generation power and centrifugal stress distribution of the rotating parts in the actuator at the current processing frequency in real time, and calculating the thermal dynamic expansion and centrifugal deformation of the controlled object; performing vector composite operation on the real-time load signal and the inter-unit tension signal to analyze the axial and radial instantaneous stress distribution of the material inside the controlled object in the processing area, and combining the real-time strain rate converted from the drive unit rotation speed signal to identify the real-time deformation resistance characteristics of the material under the current working condition in the digital twin model; using the thermal dynamic expansion and centrifugal deformation to perform multidimensional geometric compensation on the real-time displacement signal to generate an instantaneous dynamic geometric model; using the real-time deformation resistance characteristics as plastic deformation constraints, inputting them into the instantaneous dynamic geometric model for thermo-mechanical-plastic multiphysics coupling iteration, and outputting the outlet thickness estimate as the instantaneous feedback value.

4. The adaptive control method for steel processing equipment based on digital twins according to claim 3, characterized in that, The process of generating the instantaneous dynamic geometric model includes: using the radial wear of the rotating component and the thermal convexity distribution of the controlled object calculated from the thermal dynamic expansion, reconstructing the nonlinear transverse profile model of the actuator contact area in virtual space; extracting the real-time load signal, calculating the elastic flattening of the roll under the current load in the digital twin model using Hertzian contact theory, and geometrically rounding the transverse profile model using the elastic flattening of the roll; using the rotational speed signal of the drive unit, calculating the dynamic oil film thickness increment of the controlled object bearing and contact interface in real time through a fluid dynamics sub-model; and spatially coupling and superimposing the transverse profile model, the elastic flattening of the roll, and the dynamic oil film thickness increment to generate a curve characterizing the actual physical gap distribution from the center to the edge nodes of the contact area of ​​the controlled object at the current moment, which is output as an effective instantaneous roll gap parameter.

5. The adaptive control method for steel processing equipment based on digital twins according to claim 4, characterized in that, The process of analyzing the influence coefficients between the first and second control loops and generating a sensitivity matrix includes: calculating the time-domain gradient of the real-time load signal and the drive unit speed signal within the current sampling period; inputting the instantaneous feedback value, the effective instantaneous roll gap parameter, and the time-domain gradient into the digital twin model; applying control variable perturbation to the virtual model to analyze online the instantaneous derivative of the control quantity of the first control loop with respect to the output variable of the second control loop, and the instantaneous derivative of the control quantity of the second control loop with respect to the output variable of the first control loop; identifying the real-time interactive coupling coefficient characterizing the mutual interference strength between the thickness adjustment action and the shape adjustment action based on the change curve of the instantaneous derivative and the material rheological property value; and constructing a partial derivative sensitivity matrix that dynamically migrates with the processing conditions using the real-time interactive coupling coefficient as matrix elements.

6. The adaptive control method for steel processing equipment based on digital twins according to claim 1, characterized in that, The process of calculating the original control increment signal of the first actuator includes: calculating the control residual error between the preset target thickness deviation and the instantaneous feedback value, and predicting the deviation evolution trajectory of the next sampling period based on the changing trend of the instantaneous feedback value; extracting the real-time deformation resistance characteristics and instantaneous structural yielding amount output by the digital twin model, and matching the control gain matrix adapted to the current processing condition online through an adaptive law; performing proportional-integral-differential operations on the control residual error using the control gain matrix to generate the original control increment driving the first actuator; obtaining the dynamic response frequency and hysteresis characteristics of the first actuator, performing high-frequency component correction and nonlinear region avoidance on the first original control increment, and outputting the original control increment signal.

7. The adaptive control method for steel processing equipment based on digital twins according to claim 1, characterized in that, The process of obtaining the second actuator compensation control increment signal includes: extracting the first control increment signal and, in conjunction with the interaction coupling coefficient in the sensitivity matrix, calculating online the instantaneous disturbance prediction value generated by the adjustment action of the first actuator on the target variable of the second control loop; performing spatial spectrum decomposition on the acquired measured shape deviation signal to extract the components of each order characterizing the surface flatness feature of the controlled object, and calculating the error vector between each order component and the preset target shape; using the sensitivity matrix to perform inverse decoupling mapping on the instantaneous disturbance prediction value to generate a feedforward compensation component; simultaneously using an adaptive control algorithm to calculate the gain of the error vector to generate a feedback adjustment component; performing time-domain synchronous fusion of the feedforward compensation component and the feedback adjustment component, and dynamically scaling the fused signal according to the drive unit speed signal to output the final second actuator compensation control increment signal.

8. The adaptive control method for steel processing equipment based on digital twins according to claim 1, characterized in that, Also includes: A unified system timestamp is assigned to the instantaneous feedback value output by the digital twin model, and the data is stored in a circular storage buffer of a preset window length according to the time sequence, forming a first-in-first-out queue representing the virtual state trajectory of the controlled object; the measured feedback signal with detection time delay and its corresponding sampling timestamp are acquired, and the dynamic transmission time is determined by dividing the physical distance between the sensor and the machining center line by the material outlet speed converted from the drive unit speed signal; the dynamic transmission time is subtracted from the sampling timestamp, and the instantaneous feedback value at the corresponding moment is retrieved and extracted from the circular storage buffer; the difference between the aligned measured feedback signal and the retrieved instantaneous feedback value is calculated to generate the asynchronous identification residual; the partial derivative matrix of the instantaneous feedback value with respect to the frame stiffness parameter inside the digital twin model is constructed as the Jacobian matrix; the gradient direction of the asynchronous identification residual under the Jacobian matrix is ​​calculated by combining the real-time load signal and the drive unit speed signal at the current moment; the frame stiffness correction amount that minimizes the sum of squares of the asynchronous identification residual is found in the gradient direction using an iterative optimization algorithm, and the correction amount is compensated to the digital twin model in real time.

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