A heavy-load friction stir welding robot driving motor constraint tracking control method

Abstract

The application relates to the technical field of motor vector control, and discloses a driving motor constraint tracking control method for a heavy-load friction stir welding robot, which reconstructs the time-varying rotor flux and electromechanical dynamics equation of a permanent magnet synchronous motor through a thermal magnetic decay index; constructs an electromechanical thermal cross-domain generalized constraint vector by combining the space trajectory tracking requirement with a heat-induced demagnetization safety envelope and converts the generalized second-order servo constraint equation; introduces a diagonal penalty matrix to solve a nominal constraint control law, reconstructs a dynamic uncertainty boundary based on a decay index time domain gradient to generate a robust compensation control law, fuses a stable callback control law to generate a total constraint instruction, and generates a vector control instruction signal by using a current distribution reconstruction operator. The application can correct the flux distortion and torque estimation deviation caused by temperature rise, make the system follow the thermodynamic safety boundary while maintaining the trajectory tracking accuracy, inhibit the mechanical chatter caused by metal plastic friction, and reduce the additional heat generated by control chattering.

Description

Technical Field

[0001] This invention relates to the field of motor vector control technology, specifically to a constraint tracking control method for the drive motor of a heavy-duty friction stir welding robot. Background Technology

[0002] Friction stir welding (FSW), as an advanced solid-state joining technology, is widely used in the welding of thick plates in aerospace, rail transportation, and high-end manufacturing fields. With the development of industrial automation and intelligent manufacturing, heavy-duty industrial robots equipped with FSW end effectors have gradually become the mainstream equipment in this field due to their flexibility in planning complex spatial trajectories. In such heavy-duty FSW robots, the spindle drive motor (usually a permanent magnet synchronous motor) is the core actuator that provides the mechanical power required for the rotating friction heat generation of the stirring head and the plastic deformation of the metal. The servo control accuracy, torque output stability, and operational safety of the drive motor under extreme conditions determine the forming quality of the weld joint and the operational reliability of the entire robot system.

[0003] For drive motor control strategies, current technologies and methods primarily rely on conventional vector control architectures that decouple the electrical and mechanical domains. The mainstream solutions typically employ field-oriented control (FOC) with zero stator direct-axis current, using cascaded position, velocity, and current loops to track a set mechanical trajectory. When dealing with complex welding loads, representative works often establish feedforward control logic based on pure mechanical dynamics models, or introduce conventional disturbance observers (such as sliding mode observers or state observers) to estimate external contact resistance torque, thereby dynamically correcting the stator quadrature-axis reference current. Furthermore, some technical approaches incorporate compliant control theory to address the nonlinear force changes at the interface between the stirring head and the workpiece.

[0004] However, when facing the complex operating conditions of heavy-duty friction stir welding robots, existing permanent magnet synchronous motor drive control systems suffer from weak resistance to thermal degradation, easy decoupling failure under complex contact loads, and poor high-frequency disturbance suppression capabilities. This is because heavy loads and prolonged dwell times generate intense frictional heat at the tool interface and Joule heating in the stator. Existing technologies rely on constant flux linkage models under normal temperature conditions, which struggle to characterize rotor flux linkage distortion caused by temperature rise. This leads to deviations in electromagnetic torque estimation and increases the risk of thermal instability due to irreversible demagnetization of the motor's permanent magnets. Secondly, there is a cross-domain coupling between the mechanical trajectory accuracy requirements of heavy-duty friction stir welding and the safe operating envelope to prevent thermal demagnetization. Existing systems isolate electrical, mechanical, and thermodynamic control, making it difficult to achieve generalized servo constraint linkage across physical domains. Under complex contact loads, this easily leads to decoupling mechanism failure, making it difficult to simultaneously address trajectory tracking and thermal safety. Furthermore, the intense friction of metals in a non-Newtonian fluid state generates strong mechanical chatter and high-frequency impacts. Existing robust compensation methods based on static uncertainty boundaries are difficult to dynamically and adaptively adjust according to the system's thermomechanical state, and are prone to causing additional control chattering and abnormal heating when suppressing high-frequency disturbances. Therefore, a constraint tracking control method for the drive motor of a heavy-duty friction stir welding robot is urgently needed to solve the above problems. Summary of the Invention

[0005] To address the problems in related technologies, this invention provides a drive motor constraint tracking control method for a heavy-duty friction stir welding robot, thereby overcoming the aforementioned technical problems in existing related technologies.

[0006] To solve the aforementioned technical problem, the present invention is achieved through the following technical solution: In a first aspect, embodiments of the present invention provide a drive motor constraint tracking control method for a heavy-duty friction stir welding robot, specifically including: obtaining a thermomagnetic decay index characterizing the internal flux distortion of the drive motor under friction stir welding conditions; constructing an electromechanical dynamic equation for the time-varying rotor flux of a permanent magnet synchronous motor and the coupled thermomagnetic decay index; combining the spatial trajectory tracking requirements of heavy-duty friction stir welding with the safe operation envelope for preventing thermal demagnetization; constructing a generalized electromechanical-thermal cross-domain constraint vector; and transforming it into a generalized second-order servo constraint equation containing electromechanical joint acceleration state variables through second-order differentiation; based on the generalized... The constraint matrix of the second-order servo constraint equation is introduced with a diagonal penalty matrix modulated by the thermomagnetic decay index. The cross-domain nominal constraint control law is solved by minimizing the generalized torque deviation. The dynamic uncertainty envelope boundary is reconstructed based on the time-domain gradient of the thermomagnetic decay index to generate a robust compensation control law for handling nonlinear contact friction and unmodeled dynamics of the system. The stable callback control law is obtained and the nominal constraint control law and the robust compensation control law are fused to generate the total system constraint input command. Based on the thermomagnetic decay index, the setting of zero direct-axis current is dynamically broken by the current distribution reconstruction operator to generate a vector control command signal.

[0007] As a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot of the present invention, the construction of the electromechanical dynamics model includes: Real-time acquisition of stator quadrature shaft current of drive motor, actual motor speed, and friction stir welding load torque; Based on the electrical heating weighting coefficient, the mechanical frictional heat conduction coupling coefficient, and the heat dissipation hysteresis coefficient, the product of the square term of the stator quadrature axis current and the mechanical conduction heat power is integrally calculated with a forgetting factor to obtain the thermomagnetic decay index. By utilizing the thermal demagnetization sensitivity factor and the nominal flux linkage at room temperature, the time-varying rotor flux linkage is reconstructed through an exponential decay mapping relationship, and then substituted into the mechanical balance equation of the drive motor that incorporates the uncertainty of system parameters to reconstruct the electromechanical model.

[0008] As a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot described in this invention, the construction of the generalized second-order servo constraint equation includes: The boundary relationship between displacement-level target tracking error, thermomagnetic decay index and safety threshold, and electromagnetic reactive current distribution constraint are integrated into a unified cross-domain generalized constraint vector. Expanding the cross-domain generalized constraint vector with respect to time using the first-order derivative yields a system of first-order differential equations containing electrical dimension acceleration state variables. The second-order time chain derivative of the first-order differential equation system containing mechanical angular velocity and stator cross-axis current is further performed to force the exposure of the electromechanical joint acceleration state variables containing mechanical angular acceleration and stator cross-axis current change rate, and reconstruct it into a matrix equation form containing cross-domain constraint matrix and system second-order constraint boundary vector.

[0009] As a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot described in this invention, the solution of the cross-domain nominal constraint control law includes: Define a generalized constraint diagonal penalty matrix that includes mechanical trajectory tracking weight, thermodynamic safety constraint weight, and electromagnetic reactive current allocation weight. Configure the mechanical trajectory tracking weight through a reverse smoothing decay function, configure the thermodynamic safety constraint weight through a logarithmic barrier penalty function, and set the electromagnetic reactive current allocation weight as a constant factor. The rotor kinetic energy equation from the mechanical domain and the magnetic field co-energy equation from the electrical domain are combined to form the generalized kinetic energy term of the system. The second-order partial derivatives of the electromechanical joint velocity state variables are then calculated to derive the original dimensional equivalent inertia matrix. The rated operating parameters of the drive motor are extracted to construct the system's total nominal energy reference and dimensionless state transformation matrix. The dimensionless state transformation matrix is ​​then used to map the original dimensional equivalent inertia matrix to derive the dimensionless electromechanical joint equivalent inertia matrix. A weighted constraint space projection matrix is ​​constructed by combining the electromechanical joint equivalent inertia matrix and the generalized constraint diagonal penalty matrix. An adaptive damping factor is obtained based on the stator quadrature axis current state and a preset singular threshold. The adaptive damping factor is used to solve the regularized damping pseudo-inverse of the weighted constraint space projection matrix to obtain the damping pseudo-inverse. The damping pseudo-inverse is used to map and transform the second-order constraint boundary vector of the system containing the natural acceleration state vector of the drive motor. The electromechanical cross-domain joint compensation control quantity is obtained as the cross-domain nominal constraint control law.

[0010] In a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot described in this invention, the generation of the robust compensation control law includes: The dynamic perturbation, which includes uncertainties in external friction, load, and moment of inertia, is factored into a linear relationship and an equivalent uncertainty matrix is ​​synthesized. Extract the time-domain gradient of the thermomagnetic decay index, and construct the dynamic uncertainty boundary of the joint dynamic error of the envelope thermoengine by combining the decay gradient sensitive gain and the equivalent uncertainty matrix. A robust compensation control law with an integral sliding surface joint switching vector is generated based on the reconstructed dynamic uncertainty boundary, and an adaptive smoothing factor that automatically decreases with the thermomagnetic decay exponent is introduced to reduce control chattering.

[0011] In a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot described in this invention, the step of determining the decay gradient sensitive gain includes: The equivalent uncertainty matrix of the drive motor in a cold state and under the nominal working condition of translational welding is obtained, and the minimum stable boundary gain required to resist conventional mechanical friction and load disturbance is calculated based on stability theory as the reference sensitive gain. Obtain the heat margin approximation rate index, which represents the ratio of the current thermomagnetic decay index to the set decay trigger threshold. Construct a nonlinear adaptive mapping relationship using the square term of the heat margin approximation rate index to dynamically amplify the benchmark sensitive gain when the temperature rise approaches the decay trigger threshold to obtain the initial sensitive gain. The maximum safe current magnitude of the servo driver inverter power module is extracted. The maximum safe current magnitude is projected onto the generalized actuation space by combining the electromechanical equivalent inertia matrix to obtain the extreme value of the total generalized actuation vector magnitude. The generalized control margin is calculated based on the extreme value of the total generalized actuation vector magnitude and the current feedforward control quantity of the system. The maximum allowable sensitive gain threshold within the current calculation cycle is calculated using the generalized control margin. The initial sensitive gain is dynamically truncated by the smoothing saturation function to obtain the decay gradient sensitive gain.

[0012] In a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot described in this invention, the step of obtaining the stable callback control law includes: Extract the cross-domain generalized constraint vector and its first-order time derivative, and introduce a positive definite diagonal gain matrix to construct a cross-domain generalized constraint tracking error vector to measure the degree of deviation of the system from the ideal constraint manifold; Using the transpose of the cross-domain constraint matrix in the generalized second-order servo constraint equation as the Jacobian mapping operator, the error vector in the constraint space is projected back to the physical actuation space. Combined with the inverse matrix of the electromechanical joint equivalent inertia matrix, the mathematical error penalty term is mapped to the physical voltage compensation quantity to generate the stable callback control law.

[0013] As a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot described in this invention, the generation of vector control command signals by dynamically breaking the setting of zero direct-axis current through a current distribution reconstruction operator based on the thermomagnetic decay index includes: When the thermomagnetic decay index is less than or equal to the set decay trigger threshold, the current distribution reconstruction operator outputs the maximum torque current ratio distribution vector, making the stator direct axis reference current command zero. When the thermomagnetic decay index is greater than the set decay trigger threshold, the current distribution reconstruction operator dynamically outputs a vector command to force the direct axis current to be set to zero, injecting negative reactive current into the stator direct axis to generate reluctance torque compensation to share the load of quadrature axis active current.

[0014] In a preferred embodiment of the drive motor constraint tracking control method for the heavy-duty friction stir welding robot of the present invention, the step of determining the decay trigger threshold includes: Extract the intrinsic thermodynamic limit boundary of the core component of the drive motor, and obtain the maximum safe temperature rise of the system by subtracting the reference temperature of the working environment and the preset calibration error margin from the minimum temperature extreme value in the intrinsic thermodynamic limit boundary. Then, the maximum safe temperature rise is equivalently assigned to the safe demagnetization limit index. The time-domain derivative of the thermomagnetic decay index is extracted as the transient thermal gradient. The transient thermal gradient is smoothed by using an asymmetric low-pass filter to obtain a smooth thermal gradient. The thermal relaxation safety time window determined by the motor's heat transfer hysteresis characteristics and the overload feedforward weight reflecting the ratio of real-time contact resistance torque to physical peak overload torque are combined to calculate the dynamic buffer margin used to prevent thermal inertia overshoot. The decay trigger threshold is obtained by subtracting the dynamic buffer margin from the safe demagnetization limit index.

[0015] Secondly, embodiments of the present invention provide a drive motor constraint tracking control system for a heavy-duty friction stir welding robot, comprising: a decay dynamics modeling module for constructing a dynamic decay electromechanical dynamics model; a cross-domain constraint equation construction module for constructing a generalized second-order servo constraint equation; a nominal control torque solving module for solving the cross-domain nominal constraint control law; a robust compensation control law generation module for generating a robust compensation control law; and an instruction generation and output module for generating vector control instruction signals to generate underlying inverter drive instructions.

[0016] The present invention has the following beneficial effects: 1. This invention establishes a dynamic decay electromechanical model based on thermo-magnetic energy flow coupling, and uses the thermo-magnetic decay index to couple stator electrical Joule heat and tool interface friction heat. By reconstructing the time-varying rotor flux of the permanent magnet synchronous motor, it can overcome the influence of flux distortion caused by temperature rise, correct the electromagnetic torque estimation deviation under complex working conditions, and thus reduce the risk of irreversible demagnetization of the permanent magnet thermal instability of the motor.

[0017] 2. This invention constructs a cross-domain enhanced generalized servo constraint equation, which combines the spatial trajectory tracking requirements with the thermal demagnetization safety operation envelope. Based on the pseudo-inverse matrix modulated by the thermomagnetic decay index, it solves the nonlinear nominal control torque and outputs vector control commands by combining the underlying non-zero direct-axis current redistribution mechanism. This can break the control boundaries of the pure mechanical or pure electrical domains and realize the joint underlying constraints of the mechanical, electrical, and thermal multi-physical domains. This avoids the failure of the decoupling mechanism under complex working conditions, and enables the system to maintain the accuracy of spatial trajectory tracking while following the thermodynamic safety boundary.

[0018] 3. This invention designs an adaptive boundary layer robust compensation control law based on thermomagnetic gradient feedback. It reconstructs the dynamic uncertainty boundary of the envelope thermo-mechanical joint dynamic error based on the time-domain gradient of the thermomagnetic decay index. This enables the control system to adaptively adjust the robust compensation range according to the real-time thermo-mechanical state. While suppressing mechanical chatter and high-frequency impact caused by metal plastic friction, it also reduces the additional stator heating caused by control chattering. This solves the problem that existing robust compensation methods using static uncertainty boundaries are prone to additional control chattering and abnormal heating when suppressing high-frequency disturbances.

[0019] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, the drawings can be obtained from these drawings without creative effort.

[0021] Figure 1 The present invention provides a flowchart of a drive motor constraint tracking control method for a heavy-duty friction stir welding robot.

[0022] Figure 2 This is a schematic diagram of the S5 process provided by the present invention.

[0023] Figure 3 This invention provides a schematic block diagram of a drive motor constraint tracking control system for a heavy-duty friction stir welding robot. Detailed Implementation

[0024] 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.

[0025] Example 1 When facing the complex working conditions of heavy-duty friction stir welding robots, the existing permanent magnet synchronous motor drive control system is not perfect enough. It still has problems such as weak resistance to thermal degradation, easy failure of decoupling under complex contact loads, and poor high-frequency disturbance suppression.

[0026] To solve the above technical problems, such as Figure 1As shown, Embodiment 1 of the present invention provides a constraint tracking control method for the drive motor of a heavy-duty friction stir welding robot. Specifically, Embodiment 1 takes the spindle drive motor of a heavy-duty friction stir welding robot as an example. By constructing a generalized constraint control architecture spanning multiple physical domains including electrical, magnetic, thermal, and mechanical, an adaptive thermal decay closed-loop tracking control framework is formed. The specific steps include: S1. Construct a dynamic decay electromechanical model based on thermo-magnetic energy flow coupling: Establish a thermo-magnetic decay index characterizing the internal flux distortion of the drive motor under friction stir welding conditions, and reconstruct the time-varying rotor flux of the permanent magnet synchronous motor and the electromechanical equations of the coupled thermo-magnetic decay index. S2. Constructing a cross-domain enhanced generalized servo constraint equation: Combine the spatial trajectory tracking requirements of heavy-duty friction stir welding with the safe operation envelope of thermal demagnetization prevention to construct a cross-domain electromechanical-thermal generalized constraint vector, and transform it into a generalized second-order servo constraint equation containing electromechanical joint acceleration state variables through second-order differentiation. S3. Solving the nonlinear nominal control torque based on the thermal weight pseudo-inverse matrix: For the constraint matrix of the generalized second-order servo constraint equation, a diagonal penalty matrix modulated by the thermomagnetic decay index is introduced, and the cross-domain nominal constraint control law is solved by minimizing the generalized torque deviation. S4. Design an adaptive boundary layer robust compensation control law based on thermomagnetic gradient feedback: Reconstruct the dynamic uncertainty envelope boundary based on the time-domain gradient of the thermomagnetic decay index to generate a robust compensation control law for handling nonlinear contact friction and unmodeled dynamics of the system. S5. Generate non-zero direct-axis reassignment vector control command signal: Integrate the nominal constraint control law, stable callback control law and robust compensation control law to generate the system total constraint input command. Based on the thermomagnetic decay index, the current distribution reconstruction operator dynamically breaks the setting of zero direct-axis current, generates stator quadrature-direct-axis reference current command and outputs it to the underlying space vector pulse width modulator.

[0027] In this invention, the dynamic decay dynamic model constructed in step S1 serves as the physical benchmark for cross-domain constraints and parameter reconstruction in steps S2 to S5; the generalized servo constraint equation constructed in step S2 serves as the mathematical load for solving the nominal control torque in step S3; the nominal constraint control law calculated based on the thermal weight pseudo-inverse matrix in step S3 is the core input for maintaining the system's adherence to the ideal trajectory and thermal boundary; the robust compensation law generated based on the thermomagnetic decay gradient in step S4 effectively suppresses high-frequency impacts and parameter perturbations during heavy-duty friction stir welding; and the dynamic adjustment of stator current distribution using the current distribution reconstruction operator in step S5 is the physical execution link for avoiding motor thermal instability and realizing the underlying implementation of cross-domain control commands. The above steps work together to break the control boundaries of the traditional pure mechanical or pure electrical domains, achieving high-precision and robust constraint tracking control of heavy-duty friction stir welding motors under complex working conditions.

[0028] Furthermore, to better illustrate the technical solution of Embodiment 1 of the present invention, a detailed description of the drive motor constraint tracking control method for a heavy-duty friction stir welding robot is provided, including the following: First, S1 establishes a dynamic decay electromechanical model by coupling stator Joule heating with tool interface frictional heating, including the following sub-steps: S11. Real-time acquisition of stator quadrature-axis current of the drive motor. Actual motor speed and friction stir welding load torque Among them, load torque Nonlinear contact resistance torque including the welding stages of stirring head pressing down, dwelling and translation.

[0029] S12. Construct an integral equation containing an exponential forgetting factor to calculate the thermomagnetic decay index. : ; In the formula, This is the electrical heating weighting coefficient; The mechanical frictional heat conduction coupling coefficient; The heat dissipation hysteresis coefficient is determined by the heat dissipation conditions of the motor stator and the housing.

[0030] S13. Thermomagnetic decay index based on calculation Reconstructing the time-varying rotor flux of a permanent magnet synchronous motor Then, substituting these equations into the mechanical balance equations of the drive motor, which incorporate the uncertainties in system parameters, we reconstruct the electromechanical equations with coupled thermomagnetic decay exponents: In the formula, The nominal flux linkage of the motor at room temperature; It is a thermal demagnetization sensitive factor; It is the extreme logarithm; These are direct-axis and quadrature-axis inductors, respectively. It is the moment of inertia; The system friction torque; These are the uncertainty parameters of the system.

[0031] Specifically, for example: A heavy-duty friction stir welding robot is configured to perform welding of thick aluminum alloy plates, and the drive motor has a nominal flux linkage... The thermal demagnetization sensitivity factor is 0.15 Wb. The value is 0.02. During the intense dwell period under pressure, the motor continuously outputs extremely high quadrature-axis current and the frictional heat generated by the stirring head increases dramatically. If the sensor collects and calculates the thermomagnetic decay index obtained by integrating at the current moment... The system calculates the current time-varying rotor flux in real time. Wb. At this point, the flux linkage has decreased by approximately 9.5% compared to the nominal value. By substituting the decreased actual flux linkage into the dynamic model, the electromagnetic torque estimation error caused by the traditional constant flux linkage model can be avoided, providing an accurate physical reference for subsequent constraint control.

[0032] As an optional embodiment, considering the complex working conditions of heavy-duty friction stir welding, such as high-frequency switching noise, mechanical torsional chatter, and the vulnerability of physical torque sensors, the specific implementation steps of step S11 include: S111. High signal-to-noise ratio acquisition and decoupling extraction of stator quadrature-axis current, including: addressing the switching noise and thermal drift caused by the high-frequency operation of insulated-gate bipolar transistors (IGBTs) in heavy-duty drivers, abandoning traditional continuous asynchronous sampling, utilizing the hardware timer of the main control chip to generate a synchronous trigger signal strictly aligned with the pulse width modulation (PWM) carrier, performing analog-to-digital conversion (A / D) synchronous sampling at the peaks and valleys of the PWM waveform without dead zones, physically shielding electromagnetic transient switching noise, and obtaining high-fidelity three-phase stator current. The three-phase stator current is input to a low-pass filter with adaptive bandwidth adjustment to filter out high-frequency glitches caused by grid harmonics. Then, precise Clark and Park transforms are performed sequentially to extract the stator quadrature-axis current, which is stripped of quadrature-axis coupling interference and has no phase delay. .

[0033] S112. Acquisition of the actual motor speed, including: During the dwell and translation phases of heavy-duty friction stir welding, the intense friction between the stirring pin and the non-Newtonian fluid-state metal excites strong mechanical chatter. This chatter is transmitted in reverse to the motor shaft end through the reduction mechanism, causing high-frequency flexible torsional vibration components to be mixed into the original position signal output by the photoelectric encoder. The discrete rotor mechanical angular position signal acquired by the absolute encoder is input into a pre-constructed digital phase-locked loop (PLL) speed observer; the original position signal is subjected to phase-locked filtering and smoothing differentiation processing using the proportional-integral (PI) adjustment network and orthogonal phase tracking mechanism inside the PLL. By setting a cutoff frequency that matches the first-order natural resonant frequency of the mechanical transmission chain, the high-frequency torsional vibration noise is removed, and the actual motor speed, representing the true rigid body motion of the motor rotor, is output. .

[0034] S113. Virtual observation of nonlinear contact resistance torque based on electromechanical-thermal coupling feedforward, including: Considering that under heavy-load high-frequency impact conditions, the physical torque sensor installed in series is prone to fatigue fracture and has an extremely low signal-to-noise ratio, a multivariable fusion sliding mode variable structure load torque observer (SM-LTO) is constructed as a virtual torque sensor. Extract the torque obtained in step S111. With the information obtained in step S112 The electromagnetic drive equations of the observer are constructed; simultaneously, the axial forging force of the stirring head is acquired in real time through a tension / compression sensor deployed at the rear end of the robot's Z-axis spindle. An empirical nonlinear mapping function between axial upsetting force and horizontal tangential frictional resistance is established, and the feedforward compensation term of the resistance torque caused by the sudden change in the downward pressure is extracted. The feedforward compensation term is injected into the sliding mode variable structure load torque observer: In the formula, and These are the observed values ​​for rotational speed and load torque, respectively. The coefficient of viscous friction is... and This is the sliding mode gain coefficient. For switching functions, The coupling weighting coefficient for upsetting force is used. By solving the above state equations, the nonlinear contact resistance torque, which includes the transient impact of downward pressure, the stationary steady-state friction, and the periodic fluctuations of translation, is calculated in real time as the load torque for friction stir welding. .

[0035] As an optional embodiment, feature parameters , , The calibration steps include: S121, heat dissipation hysteresis coefficient Calibration includes: obtaining the baseline heat dissipation factor under different cooling modes in zero-load free cooling experiments of standard motors of the same family. Extract the geometric feature parameters of the cooling channel of the target drive motor, and obtain the kinematic viscosity and Prandtl number of the cooling medium (air or coolant) in real time. Establish a generalized reconstruction model of the dynamic heat dissipation hysteresis coefficient coupled with online fluid state: ; in, This is the conversion factor for cooling efficiency; The Nusselt number represents the ratio of convective to conductive heat transfer; the Reynolds number... Based on the real-time flow rate of the cooling medium Dynamic calculations are performed, and for natural cooling configurations, real-time flow rates are forcibly set. Setting the coefficient to zero causes the coefficient to automatically degenerate into a state of pure natural radiation and convection, which will be dynamically updated. To replace the constant value, in order to cope with the fluctuations in cooling capacity caused by continuous welding.

[0036] S122, Electrical Heating Weighting Coefficient The determination method includes: in the stall-rotor pure electric heating decoupling test of the standard model, using the steady-state limiting temperature rise to calculate the intrinsic electrical heating constant stripped of physical dimensional properties. When the control system is adapted to different models of drive motors, the nameplate constants of the target motor are extracted, including the stator phase resistance at 20 degrees Celsius. Stator winding quality and the specific heat capacity of copper materials An adaptive electrical heating weighting coefficient is generated based on the physical capacity of the target motor. : ; in, is the temperature coefficient of resistance of copper; To monitor the temperature of the stator in real time.

[0037] S123, Mechanical-thermal conduction coupling coefficient Cross-configuration mapping includes: in the constant power simulation loading decoupling experiment of the standard model, separating the dimensionless fundamental factor of heat flow conduction from tool interface frictional heat to the motor rotor. For the physical heat transfer path from the spindle flange to the motor shaft in friction stir welding, the equivalent thermal conductivity of the spindle drive rod of the target system is extracted. thermal conductivity cross-sectional area With the effective length of the heat transfer axis A mechanical conduction thermal impedance network is established, and the mechanical friction thermal conduction coupling coefficient is calculated. : ; in, This refers to the combined mechanical heat capacity of the motor rotor and connecting flange. Utilizing the aforementioned cross-configuration mapping, the control system can adaptively match the differences in interfacial frictional heat backflow caused by changing the diameter or material of the stirring head base, by inputting simple mechanical dimensional parameters, and then calculate the parameter group... , , Substitute this into the thermomagnetic decay exponent equation.

[0038] As an optional embodiment, to ensure the stability of the control system during online operation, a thermal demagnetization sensitive factor is used. Moment of inertia and frictional torque The determination process includes: S131. Determine the thermal demagnetization sensitivity factor through offline back-EMF thermistor experiment. : The unloaded drive motor is placed in a programmable high and low temperature alternating test chamber. A series of discrete target ambient temperature gradients are set, and the motor is kept sufficiently warm until thermal equilibrium is reached inside and outside the motor. Based on the heat generation and dissipation mechanism established in step S12, each steady-state temperature is converted and mapped to the corresponding calibrated thermomagnetic decay index. .

[0039] At each thermal steady-state gradient, the test motor was driven by an external prime mover at a constant speed. Rotation, the driver side remains open circuit, stator current The peak value of the stator three-phase line back electromotive force is captured using a high-precision oscilloscope or power analyzer. .

[0040] Based on the principle of back electromotive force, the actual rotor flux linkage under different decay indices is calculated. Substitute the test data set into the logarithmically processed demagnetization equation: Linear regression was performed using the least squares method, and the absolute value of the slope of the fitted line is the determined thermal demagnetization sensitivity factor. .

[0041] S132. Determine the moment of inertia through acceleration / deceleration frequency sweep experiments and configuration envelope. and uncertainties: The total rotational inertia of the spindle in heavy-duty friction stir welding is composed of the motor rotor, the reduction gearbox, and the stirring head. This inertia is decomposed into specific nominal moments of inertia. With the uncertain part .

[0042] When the crane or robot is not equipped with the mixing head (basic unloaded configuration), a known quadrature-axis current of a step or pseudo-random binary sequence (PRBS) is injected into the motor via a servo driver. Ignoring low-speed friction, angular acceleration during the high-frequency acceleration phase was collected. Using the equations of motion The fundamental nominal moment of inertia was identified offline using the recursive least squares (RLS) method. .

[0043] Friction stir welding requires frequent replacement of heavy-duty stirring heads with different shoulder diameters and needle lengths, and the gearbox gears will wear over time. This paper extracts parameters for all permissible stirring head models, calculates the maximum inertial perturbation caused by their physical mass distribution, and defines the boundary envelope set of inertial uncertainty based on mechanical wear margin. The moment of inertia in the final online control equations is expressed as: ,in For bounded unknowns, the robust compensation law in step S4 is applied. A unified, comprehensive solution will be provided.

[0044] S133. Determine the friction torque through graded constant speed calibration and high / low temperature drift constraint. and uncertainties: Frictional torque is influenced by both bearing assembly preload and grease viscosity (which is strongly temperature-dependent), and can be decomposed into a nominal friction model. With uncertain drift part .

[0045] Under normal temperature and no-load conditions with no pressure, the motor is controlled to operate at multiple discrete constant speeds covering the range from low speed to maximum speed. Running at constant speed. And external load At this point, the output electromagnetic torque is exactly equal to the nominal friction torque, that is... Record the constant speeds. The values ​​are used to fit the complete Stribeck friction characteristic curve and obtain the nominal values ​​of Coulomb friction torque, static friction torque and viscous friction coefficient.

[0046] To decouple the severe nonlinear effect of temperature changes on grease viscosity, constant-speed experiments were repeated under extreme low-temperature cold start and extreme high-temperature overload conditions. The frictional torque under these two extreme conditions was extracted and compared with the nominal model. The maximum envelope difference between them is defined as the friction uncertainty boundary parameter set. During online operation, the frictional torque is expressed as... The control algorithm directly uses a deterministic nominal model feedforward, and the deviation is also included in the robust uncertainty set. absorb.

[0047] As a preferred embodiment, to ensure the calculability of the upper bound of the uncertainty in the robust compensation control law, the uncertainty of the moment of inertia... Friction uncertainty The specific boundary determination steps include: S133, Upper bound of rotational inertia perturbation based on the geometric envelope of the stirring head. The quantification includes: The identification results under the basic execution end configuration are used as the nominal moment of inertia. Establish the mass distribution matrix for all models of stirring heads in the library, and calculate the maximum configuration inertia. (Long needle / large diameter shoulder combination) and minimum configuration inertia Define the absolute upper bound of the moment of inertia perturbation. : ; In the formula, To account for the backlash of the reducer and the elastic distortion of the transmission chain, the empirical coefficient is usually taken to a range of values. This establishes the range of inertia perturbation. For the follow-up The computation provides closed set constraints.

[0048] S134. Quantification basis of frictional uncertainty based on Arrhenius law and temperature drift constraint ,include: The nominal friction torque at room temperature was fitted using the Stribeck model. Introducing the dynamic viscosity of lubricating grease as a function of thermomagnetic decay index. A changing exponential correction operator defines an upper bound on the uncertainty of frictional torque. : ; In the formula, The modeling error coefficient reflects the unmodeled dynamics of Coulomb friction. and This is the thermoviscosity constant of the lubricating grease; The absolute temperature of the environment.

[0049] Dynamic boundary generation: frictional uncertainty In real time, it is bounded by a dynamic envelope centered on the nominal model that contracts with temperature rise, i.e. .

[0050] Furthermore, S2 constructs generalized servo constraint equations by simultaneously solving cross-domain variables, including the following sub-steps: S21. Express the mechanical spindle spatial trajectory tracking requirements of the friction stir welding process specifications as zero-order kinematic constraints. Simultaneously, the safe operating envelope preventing irreversible thermal demagnetization of the motor's permanent magnets is represented as a thermodynamic constraint. (Equality constraints are activated when the critical value is approached). Combining these two equations constitutes a transdomain generalized constraint vector for electromechanical-thermal systems. .

[0051] S22. Following the chain rule, perform second-order differentiation on the generalized constraint vector to separate the vector containing mechanical angular acceleration. With stator current change rate The augmented state terms are transformed into generalized second-order servo constraint equations: ; In the formula, For electromechanical combined acceleration state quantities; It is a cross-domain constraint matrix that includes the dynamic flux gradient and the trajectory Jacobian matrix; This is the second-order constraint boundary vector of the system.

[0052] As an optional embodiment, considering the strong cross-domain coupling between mechanical trajectory tracking and electrothermal demagnetization during heavy-duty friction stir welding, conventional second-order constraint equations in a single mechanical domain cannot directly impose low-level constraints on electrical variables. To address this issue, this embodiment extends the Udwadia-Kalaba (UK) theory from the pure mechanical dynamics domain to the electromechanical-thermal coupled dynamics domain. The specific implementation process of step S22 includes: S221. Definition and construction of cross-domain generalized constraint vectors, including: The multi-dimensional objectives that the control system of a heavy-duty friction stir welding robot must satisfy are integrated into a unified generalized constraint vector. .

[0053] Mechanical trajectory constraint: Target angular displacement set according to the friction stir welding process specification. Construct displacement-level target tracking error .

[0054] Thermodynamic safety boundary constraints: Extract the thermomagnetic decay index calculated in step S1 Compared with the set thermal demagnetization critical safety threshold Constructing thermal boundary constraints In the control algorithm, when When approaching the safety threshold boundary (i.e., entering the decay activation region), it is transformed into an active equality constraint. .

[0055] Electromagnetic reactive current distribution constraints: Setting a non-zero direct-axis current distribution reconstruction operator Constructing electrical constraints .

[0056] S222. First-order expansion of cross-domain state variables based on time derivative, including: Following the chain rule, the generalized equality constraint vector is... Regarding time Perform a first derivative expansion: For mechanical trajectory constraints: .

[0057] For thermodynamic safety boundary constraints, the integral equation in step S12 is transformed into differential form: .

[0058] For electromagnetic reactive current distribution constraints: .

[0059] After first differentiation, the constraint equations The rate of change of current has been explicitly shown. That is, the acceleration state quantity in the electrical control dimension, and and Includes only velocity-level state variables (rotational speed) With stator current (This requires a second step of stripping down to a lower level).

[0060] S223. Extracting the second-order chain rule derivative of the joint acceleration state variables, including: For only velocity-level state variables and Continuing with the discussion about time By performing second-order chain rule differentiation, the mechanical angular acceleration is forcibly exposed. Stator cross-axis current change rate .

[0061] For mechanical trajectory constraints: .

[0062] For thermodynamic safety boundary constraints, the partial derivative chain expansion is applied: Substituting the first-order differential form and calculating the partial derivatives, where the partial derivative for the electrical heating of the dynamic flux is... The partial derivative of mechanical frictional heat conduction is .

[0063] The linearized result is obtained by rearranging. and The second-order thermal constraint equation: .

[0064] S224, Matrix mapping of generalized second-order servo constraint equations, including: The above contains , and The equations are combined to extract the electromechanical combined acceleration state variables. Reconstructed into the standard Pfaffian matrix equation form .

[0065] Among them, the cross-domain constraint matrix Mapped to: ; System second-order constraint boundary vector Mapped to: ; Real-time calculation of the absolute value of the determinant of the above constraint matrix Set the noise floor factor of the underlying current sensor as the singular threshold. Define the system's dynamic runtime space: when When, the system is on a regularly constrained manifold; when When the system enters the singularity domain of the thermodynamic derivative, the regularization reconstruction mapping mechanism needs to be activated to prevent the control torque from diverging.

[0066] As a preferred embodiment, a second-order chain expansion of joint acceleration, incorporating precise observations of load rate variation, is constructed, including: S223-a, Obtain the estimated value of the friction stir welding load torque output in real time by the sliding mode variable structure load torque observer in step S113. To address the load step and high-frequency mechanical chatter caused by heavy-load pressure and complex contact conditions, and to avoid noise amplification and phase delay caused by direct numerical difference, a finite-time robust exact differentiator based on the superspiral algorithm is constructed. ; In the formula, For smooth tracking of load torque; The precise observed value of the time derivative of the phase-shift-free load torque output by the system is... ; and The positive definite feedback gain constant of the differentiator is set according to the Lipschitz constant to ensure that the state variables converge to the real differential manifold in a finite time.

[0067] S223-b, For mechanical displacement level constraints that only contain velocity-level state variables Thermodynamic safety constraints Continuing with the discussion about time By performing second-order chain rule differentiation, the mechanical angular acceleration is forcibly exposed. Stator cross-axis current change rate Expanding the thermodynamic boundary equations using the partial derivative chain formula: ; Substituting the first-order differential form and calculating each partial derivative term, where the partial derivative for the electrical heating of the dynamic flux is: The partial derivative of mechanical frictional heat conduction is .

[0068] S223-c, The load variability observations extracted in step S223-a Inject this into the above second-order expansion, replacing the ideal derivative term. Rearrange to obtain a linearized form that includes... and Robust second-order thermal constraint equations: ; The reconstructed equations eliminate the high-frequency divergence terms introduced by direct difference calculations, ensuring the second-order constraint boundary vectors of the system. Numerical stability and physical boundedness when encountering nonlinear indentation and abrupt tool wear.

[0069] Furthermore, S3 solves for the nonlinear nominal control torque based on the restricted Gaussian principle, including the following sub-steps: S31. For generalized constraint matrices Introducing the thermomagnetic decay index Real-time modulated diagonal penalty matrix .when When the matrix weights are low, they tend to prioritize ensuring the accuracy of the mechanical trajectory; when... When approaching the safety threshold, the matrix weights are nonlinearly transferred to the thermal constraint term to forcibly reduce the heat generation index.

[0070] S32, Combining electromechanical equivalent inertia matrix Using the thermal weight pseudo-inverse matrix, the nominal constraint control law that maintains the system's satisfaction of the ideal transdomain constraints is solved. : ; In the formula, Indicates Penalized weighted Moore-Penrose pseudoinverse operator; Let be the natural acceleration state vector of the drive motor when it is not subject to the generalized constraints.

[0071] As a preferred embodiment, a nonlinear diagonal penalty matrix based on exponential decay and logarithmic barrier functions is constructed. The specific steps include: S311. Define the generalized constraint diagonal penalty matrix: Its diagonal elements correspond to the cross-domain constraint matrix. The mechanical, thermodynamic, and electrical terms in the text.

[0072] S312, Weighting for machine trajectory tracking Introducing the inverse Sigmoid smooth decay function: ; In the formula, The initial maximum mechanical weight; To switch the steepness coefficient; This is the set thermal degradation warning threshold. This function ensures that a very high trajectory tracking weight is assigned when the motor is at normal temperature, while the weight smoothly decreases when the temperature exceeds the warning threshold, releasing mechanical control stiffness in exchange for electrical cooling space.

[0073] S313, Weights for Thermodynamic Safety Constraints Introduce a logarithmic barrier penalty function: ; In the formula, This is the fundamental thermodynamic penalty coefficient; This represents the safe limit value for irreversible demagnetization of permanent magnets.

[0074] S314, Weighting of Electromagnetic Reactive Current Allocation To ensure The stability of the shaft current regulation during the fundamental period is set as a thermodynamic constant factor: .

[0075] As a preferred embodiment, the electromechanical joint equivalent inertia matrix is ​​constructed using the principle of energy conservation in electromechanical systems. The specific steps include: S321. Extract the rotor kinetic energy equation from the mechanical domain of the permanent magnet synchronous motor. Co-energy equations of magnetic fields in the electrical domain .

[0076] Read the nameplate specifications of the servo drive system, including the rated mechanical angular velocity. With the rated stator current amplitude The basic mechanical kinetic energy benchmark for system operation is defined using nominal parameters. Energy reference with the basic magnetic field : ; ; Define a dimensionless state transformation matrix and the system's total nominal energy reference .

[0077] S322. Based on the Lagrangian dynamics system, the sum of kinetic energy and magnetic field energy is taken as the generalized kinetic energy term in the generalized Lagrangian quantity of the system. This is for the original electromechanical combined velocity state quantity. Taking its second-order partial derivatives, we can derive the electromechanical equivalent inertia matrix with the original dimensions. Using the dimensionless state transformation matrix Compared with the total nominal energy benchmark Homeomorphism mapping is performed on the original matrix to generate a dimensionless electromechanical equivalent inertia matrix. : ; After expansion, the diagonal elements of the dimensionless matrix are respectively , and .

[0078] S323, in a clear manner and Then, the control system performs the following deterministic algebraic operations in each calculation cycle: Extract real-time sensor parameters and update them synchronously to refresh the electromechanical equivalent inertia matrix. Diagonal penalty matrix of generalized constraints .

[0079] Constructing the weighted constrained space projection matrix .

[0080] For the singularity domain of the thermodynamic derivative defined in step S224, an adaptive damping factor dependent on the cross-axis current state is introduced. : ; In the formula, The maximum allowable damping coefficient to prevent numerical divergence.

[0081] The damping pseudo-inverse is obtained using the Levenberg-Marquardt regularization algorithm that includes the damping factor. : In the formula, It is a third-order identity matrix.

[0082] Will The standard pseudo-inverse is replaced by a mapping transformation and substituted into the nominal control law formula: ; The final electromechanical cross-domain joint compensation control quantity with global boundedness and resistance to zero-point singularity is obtained through calculation.

[0083] Furthermore, the S4 design utilizes an adaptive robust compensation control law based on thermomagnetic gradient feedback to handle strong nonlinear disturbances in friction stir welding, comprising the following sub-steps: S41, Regarding uncertainties involving external friction Load uncertainty and uncertainty of rotational inertia We decompose the matrix and let the equivalent uncertainty matrix be... .

[0084] S42. Extract the time-domain gradient of the thermomagnetic decay exponent. Abandoning the traditional static boundary, a dynamic uncertainty boundary is constructed for the envelope of the thermo-mechanical joint dynamic error. : ; In the formula, This is the first positive definite matrix selected according to Lyapunov stability theory; This is a gradient-sensitive gain used to expand the robust compensation boundary during periods of rapid temperature deterioration. It is an identity matrix.

[0085] The above-mentioned quantified physical upper bound and Substitute into the equivalent uncertainty matrix In the calculation of the modulus, the norm inequality is used for expansion, and... The operation can be transformed into the following computable form: ; in This is the upper bound of the load disturbance determined based on the residual error envelope of the S113 sliding mode observer.

[0086] S43. Generate a robust compensation control law based on the reconstructed dynamic boundary. : ; In the formula, To introduce a joint switching vector for the integral sliding surface; It is the second positive definite constant matrix; It is an adaptive smoothing factor used to automatically reduce the high-frequency switching gain as the temperature rises, while ensuring system convergence, thereby reducing the additional electrical heating caused by control chattering.

[0087] As an optional embodiment, the equivalent uncertainty matrix The construction steps include: S411. Based on the prior offline identification model and online virtual observation results, the spindle mechanical dynamics parameters of the friction stir welding drive motor are separated into a deterministic nominal part and an unknown bounded uncertain part: ; ; ; In the formula, The nominal moment of inertia identified in advance; The nominal frictional torque is based on the Stribeck model; The nominal contact resistance torque is the real-time output of the sliding mode variable structure load torque observer (SM-LTO). These are the dynamic perturbations of rotational inertia, frictional torque, and load resistance torque, respectively. These perturbations encompass the unmodeled dynamics of the system and are strictly bounded by a predefined physical set. Inside.

[0088] S412. In the governing equations, the uncertainty of the moment of inertia is often nonlinearly coupled to the acceleration terms of the system through the inverse of the inertia matrix. Define the nominal inertia inverse matrix. and the system's actual inertia inverse matrix Construct the inverse nonlinear perturbation matrix of inertia. To facilitate the subsequent derivation of robust boundaries based on Lyapunov stability theory, a dimensionless intermediate mapping matrix is ​​introduced. : ; Through the above construction, the nonlinear inertia inverse perturbation equivalent factor is decomposed into a linear mapping relationship: .

[0089] S413. Substitute the separated physical parameters from step S411 into the fundamental dynamic equations of the permanent magnet synchronous motor in the mechanical domain, and separate the actual acceleration of the system into the superposition of nominal driving acceleration and perturbation distortion acceleration. Extract the absolute deviation term in acceleration space caused by parameter uncertainty, and synthesize an equivalent uncertainty matrix. : ; In the formula, This represents the actual electromagnetic torque output by the motor at the current moment.

[0090] As an optional embodiment, the decay gradient sensitive gain in S42 The specific methods for determining this include: S421, Offline calibration reference sensitive gain When the system is in a cold state and operating under the nominal translation welding condition (at this time) Based on the classical Lyapunov stability theory, this paper addresses the equivalent uncertainty matrix in a purely mechanical domain. Calculate the required minimum stable boundary gain and use it as the reference sensitive gain. This parameter characterizes the fundamental robustness cost required for the system to suppress conventional mechanical friction and load disturbances under thermal equilibrium conditions.

[0091] S422. Parameter analytical mapping based on thermophysical energy scale and boundary constraint theorem, including: introducing a heat margin approximation rate index to characterize the proximity of the current system's thermomagnetic decay exponent to the decay trigger threshold. To eliminate the empirical blind spot in parameter tuning, a nonlinear adaptive mapping equation is constructed: ; Based on the law that the electrical Joule heat generation of the system is directly proportional to the square of the stator current ( Forced setting This is to ensure that the expansion rate of the robust gain matches the physical intrinsic evolution law of thermal energy accumulation. The system is assumed to be in an absolutely critical state, i.e. , Below, the theoretical limit gain required to withstand the maximum transient impact is: Applying the boundary constraint theorem, the dynamic amplification factor is calculated in reverse: .

[0092] S423, Maximum Sensitivity Gain Threshold Based on Action Space Inverse Mapping Dynamic inverse calculation and clamping, including: extracting the maximum safe current module allowed by the servo driver inverter power module. Using the electromechanical equivalent inertia matrix Based on the fundamental mapping of the current distribution reconstruction operator, the underlying nominal current limit is projected onto the generalized actuation space, and the extreme value of the current allowed total generalized actuation vector magnitude is calculated. Real-time extraction of nominal constraint control laws With stable callback control law Calculate the generalized control margin within the current calculation cycle. : ; Extracting the compensation modulus caused by the fundamental perturbation term in the robust uncertainty boundary formula ,Right now Not included This part utilizes the generalized control margin to inversely calculate the theoretical threshold of the maximum sensitive gain that the current hardware allows for injection. : ; A smooth saturation function is used to dynamically truncate the final effective decay gradient-sensitive gain: .

[0093] Furthermore, S5 generates vector control command signals by dynamically configuring the stator quadrature and direct-axis current distribution, such as... Figure 2 The process includes the following sub-steps: S51. In practical heavy-duty friction stir welding control systems, due to sensor measurement noise, discretization truncation error, and unknown transient strong impacts, the system state will inevitably deviate from the ideal cross-domain generalized constrained manifold, i.e. It cannot be absolutely maintained. If only the nominal control law is relied upon... Even minute numerical drifts accumulate over time, eventually leading to trajectory distortion or thermal protection failure. Therefore, an explicit stability callback control law is introduced. Specifically, it includes: S511. Construct the cross-domain generalized constraint tracking error vector: Extract the cross-domain generalized constraint vector defined in step S22. and its first time derivative Introducing a positive definite diagonal gain matrix. Construct a cross-domain generalized constraint tracking error vector to measure the degree to which the system deviates from the ideal constraint manifold. : ; In the formula, These represent the exponentially decaying convergence rates of the mechanical trajectory, thermodynamic safety boundary, and electromagnetic current distribution error, respectively. By adjusting the elements of this diagonal matrix, the recovery speed after deviations from the state in different physical domains can be independently set.

[0094] S512, Solve the stable callback control law based on electromechanical co-mapping. Based on the Lyapunov direct method, a stable callback control law is designed to ensure the global asymptotic stability of the nominal control system under no-uncertainty disturbances. The specific mathematical expression is: ; In the formula, This is a positive definite diagonal callback gain matrix, used to adjust the overall strength of the callback control force; It is the inverse matrix of the electromechanical joint equivalent inertia matrix defined in step S3, used to map the error penalty term at the purely mathematical level into electromechanical generalized torque / voltage compensation quantities that conform to physical dimensions. It is the transpose of the cross-domain constraint matrix, which serves as the Jacobian mapping operator to precisely project the error vector in the three-dimensional constraint space back into the physical action space. According to the Lyapunov equation ( The first positive definite matrix obtained by solving for any positive definite matrix.

[0095] S52, Stabilize the callback control law The nominal control law obtained in step S3 The robust compensation control law obtained in step S4 Linear superposition is used to calculate the total system constraint input command for the drive motor. .

[0096] The physical essence of this superposition logic lies in: This is equivalent to the system's active feedforward guidance, which drives the motor to run along a planned multi-dimensional mechanical, electrical, and thermal trajectory; Equivalent to the elastic tension spring of the system, once the motor's state deviates from the trajectory due to internal accumulated errors, it immediately... A normal corrective moment orthogonal to the constraint surface is generated to forcefully pull back; It can withstand unpredictable external nonlinear contact and temperature drift impacts during friction stir welding. The synergistic effect under a unified energy metric ultimately ensures closed-loop tracking accuracy under extreme operating conditions.

[0097] S53, Continuously monitor the thermomagnetic decay index and the set decay trigger threshold Compare them.

[0098] Among them, the decay trigger threshold The methods for determining this include: S531. Extract the intrinsic thermodynamic limit boundary of the core components of the drive motor: Refer to the manufacturer's material data sheet of the selected drive motor to extract the critical yield temperature at which irreversible demagnetization occurs in the permanent magnet material (such as NdFeB). And the ultimate withstand temperature of stator winding insulation materials (such as Class H insulation). Combined with the highest benchmark ambient temperature of the working environment of the crane or robot. and engineering calibration error margin The maximum safe temperature rise allowed by the computing system : .

[0099] S532, Establish the safe demagnetization limit index Based on the offline calibration logic in step S12, the thermomagnetic decay index The physical dimensions and numerical values ​​have been orthogonally mapped to the equivalent average temperature rise inside the motor. Therefore, the maximum safe temperature rise calculated in step S521 is... The direct equivalent value is the safe demagnetization limit index. : This parameter represents the thermodynamic red line boundary that the motor cannot cross under any operating condition.

[0100] S533. Calculate the transient thermal shock buffer margin and establish the trigger threshold. : Determining the thermal relaxation safety time window by extracting the heat transfer hysteresis characteristics of the motor The time-domain derivative of the thermomagnetic decay exponent within the current calculation period is extracted as the transient thermal gradient. To eliminate high-frequency glitches from the sensor, the transient thermal gradient is input into an asymmetric low-pass filter to obtain a smooth thermal gradient. The asymmetric filtering mechanism uses a smaller time constant during the thermal gradient ascent phase to ensure hysteresis-free response, and a larger time constant during the thermal gradient descent phase to prevent drastic threshold fluctuations. A nonlinear feedforward weight modulation based on load severity is introduced to construct a dynamic buffer margin. The solution equation is: ; In the formula, To maintain the static lower limit constant of the system's sensor basic calibration error margin; The absolute physical peak overload torque allowed for the drive motor; For overload feedforward sensitive gain; Finally, by subtracting the dynamic buffer margin from the safety limit, the decay trigger threshold is calculated and fixed. .

[0101] S54, Reconstruction operator via current distribution Input the total constraint command Solving for stator direct-axis reference current With cross-axis reference current : ; when At that time, the motor is in a good hot state, and the reconstruction operator... Output the maximum torque-to-current ratio allocation vector in normal mode. ,Right now ; when At this time, the motor enters the severe thermal decay region, and the reconstruction operator... Dynamic output (in ), forced break Setting: By injecting negative reactive current into the stator direct shaft to generate reluctance torque compensation, the peak load requirement of the quadrature shaft active current is shared, thereby reducing the local temperature rise rate of the winding.

[0102] The final solution The inverter drive is passed to the underlying space vector pulse width modulator (SVPWM).

[0103] Example 2 As a second embodiment of the present invention, such as Figure 3 As shown, based on Embodiment 1, this embodiment also discloses a drive motor constraint tracking control system for a heavy-duty friction stir welding robot, specifically including: The decay dynamics modeling module is used to construct a dynamic decay electromechanical dynamics model to generate a physical benchmark. Specifically, this module obtains the thermomagnetic decay index, which characterizes the internal flux distortion of the drive motor under friction stir welding conditions. Constructing the time-varying rotor flux of a permanent magnet synchronous motor and the coupled thermomagnetic decay index The electromechanical equations.

[0104] A cross-domain constraint equation construction module is used to construct generalized second-order servo constraint equations to generate mathematical loads. Specifically, this module combines the spatial trajectory tracking requirements of heavy-duty friction stir welding with the safe operation envelope for preventing thermal demagnetization to construct an electromechanical-thermal cross-domain generalized constraint vector. It is then transformed into a generalized second-order servo constraint equation containing electromechanical joint acceleration state variables through second-order differentiation.

[0105] The nominal control torque solving module is used to solve the cross-domain nominal constraint control law to generate the core input. Specifically, this module is based on the constraint matrix of the generalized second-order servo constraint equation. Introducing the thermal magnetic decay index Modulated diagonal penalty matrix The cross-domain nominal constraint control law is solved by minimizing the generalized torque deviation. .

[0106] A robust compensation control law generation module is used to generate a robust compensation control law to produce high-frequency impact suppression. Specifically, this module is based on the thermomagnetic decay index. Temporal gradient reconstruction of dynamic uncertainty envelope boundary Generate robust compensation control laws for handling nonlinear contact friction and unmodeled system dynamics. .

[0107] The instruction generation and output module generates vector control instruction signals to produce underlying inverter drive instructions. Specifically, this module obtains the stable callback control law. and integrate the nominal constraint control law With the robust compensation control law Generate system total constraint input instructions According to the thermomagnetic decay index Reconstructing operator through current distribution Dynamically break the zero setting of direct-axis current to generate vector control command signals. .

[0108] In the specific implementation of Embodiment 2 above, data interaction between various control modules is achieved through an industrial-grade data bus. The decay dynamics modeling module runs continuously and provides real-time physical parameter references for the cross-domain constraint equation construction module; the mathematical load matrix output by the cross-domain constraint equation construction module is synchronously transmitted to the nominal control torque solving module for core torque calculation; simultaneously, the robust compensation control law generation module independently calculates the high-frequency disturbance suppression quantity; finally, the instruction generation and output module superimposes and integrates the multi-domain compensation quantities, transforming the electromechanical-thermal multi-domain coupled control algorithm into a hardware-level executable low-level current vector signal output to the inverter driver, completing the closed-loop constraint control link.

Claims

1. A drive motor constraint tracking control method for a heavy-duty friction stir welding robot, characterized by, include: The thermomagnetic decay index, which characterizes the internal flux distortion of the drive motor under friction stir welding conditions, is obtained, and the time-varying rotor flux and coupled thermomagnetic decay index of the permanent magnet synchronous motor are constructed as electromechanical equations. By combining the spatial trajectory tracking requirements of heavy-duty friction stir welding with the safe operation envelope of thermal demagnetization prevention, a generalized cross-domain electromechanical-thermal constraint vector is constructed, and then transformed into a generalized second-order servo constraint equation containing electromechanical joint acceleration state variables through second-order differentiation. Based on the constraint matrix of the generalized second-order servo constraint equation, a diagonal penalty matrix modulated by the thermomagnetic decay index is introduced, and the cross-domain nominal constraint control law is solved by minimizing the generalized torque deviation. Based on the time-domain gradient reconstruction of the thermomagnetic decay index, a robust compensation control law is generated to handle nonlinear contact friction and unmodeled dynamics of the system. A stable callback control law is obtained, and the cross-domain nominal constraint control law and the robust compensation control law are fused to generate a total system constraint input command. Based on the thermomagnetic decay index, the setting of zero direct-axis current is dynamically broken through the current distribution reconstruction operator to generate a vector control command signal.

2. The drive motor constraint tracking control method for a heavy-duty friction stir welding robot according to claim 1, characterized by, The construction of the electromechanical model includes: Real-time acquisition of stator quadrature shaft current of drive motor, actual motor speed, and friction stir welding load torque; Based on the electrical heating weighting coefficient, the mechanical frictional heat conduction coupling coefficient, and the heat dissipation hysteresis coefficient, the product of the square term of the stator quadrature axis current and the mechanical conduction heat power is integrally calculated with a forgetting factor to obtain the thermomagnetic decay index. By utilizing the thermal demagnetization sensitivity factor and the nominal flux linkage at room temperature, the time-varying rotor flux linkage is reconstructed through an exponential decay mapping relationship, and then substituted into the mechanical balance equation of the drive motor that incorporates the uncertainty of system parameters to reconstruct the electromechanical model.

3. The drive motor constraint tracking control method for heavy-duty friction stir welding robots of claim 1, wherein, The construction of the generalized second-order servo constraint equations includes: The boundary relationship between displacement-level target tracking error, thermomagnetic decay index and safety threshold, and electromagnetic reactive current distribution constraint are integrated into a unified cross-domain generalized constraint vector. Expanding the cross-domain generalized constraint vector with respect to time using the first-order derivative, we obtain a system of first-order differential equations that include the electrical dimension acceleration state variables. The second-order time chain derivative of the first-order differential equation system containing mechanical angular velocity and stator cross-axis current is further performed to force the exposure of the electromechanical joint acceleration state variables containing mechanical angular acceleration and stator cross-axis current change rate, and reconstruct it into a matrix equation form containing cross-domain constraint matrix and system second-order constraint boundary vector.

4. The drive motor constraint tracking control method for a heavy-duty friction stir welding robot according to claim 1, characterized in that, Solving the cross-domain nominal constraint control law includes: Define a generalized constraint diagonal penalty matrix that includes mechanical trajectory tracking weight, thermodynamic safety constraint weight, and electromagnetic reactive current allocation weight. Configure the mechanical trajectory tracking weight through a reverse smoothing decay function, configure the thermodynamic safety constraint weight through a logarithmic barrier penalty function, and set the electromagnetic reactive current allocation weight as a constant factor. The rotor kinetic energy equation from the mechanical domain and the magnetic field co-energy equation from the electrical domain are combined to form the generalized kinetic energy term of the system. The second-order partial derivatives of the electromechanical joint velocity state variables are then calculated to derive the original dimensional equivalent inertia matrix. The rated operating parameters of the drive motor are extracted to construct the system's total nominal energy reference and dimensionless state transformation matrix. The dimensionless state transformation matrix is ​​then used to map the original dimensional equivalent inertia matrix to derive the dimensionless electromechanical joint equivalent inertia matrix. A weighted constraint space projection matrix is ​​constructed by combining the electromechanical joint equivalent inertia matrix and the generalized constraint diagonal penalty matrix. An adaptive damping factor is obtained based on the stator quadrature axis current state and a preset singular threshold. The adaptive damping factor is used to solve the regularized damping pseudo-inverse of the weighted constraint space projection matrix to obtain the damping pseudo-inverse. The damping pseudo-inverse is used to map and transform the second-order constraint boundary vector of the system containing the natural acceleration state vector of the drive motor. The electromechanical cross-domain joint compensation control quantity is obtained as the cross-domain nominal constraint control law.

5. The drive motor constraint tracking control method for a heavy-duty friction stir welding robot according to claim 1, characterized in that, The generation of the robust compensation control law includes: The dynamic perturbation, which includes uncertainties in external friction, load, and moment of inertia, is factored into a linear relationship and an equivalent uncertainty matrix is ​​synthesized. Extract the time-domain gradient of the thermomagnetic decay index, and construct the dynamic uncertainty boundary of the joint dynamic error of the envelope thermoengine by combining the decay gradient sensitive gain and the equivalent uncertainty matrix. A robust compensation control law with an integral sliding surface joint switching vector is generated based on the reconstructed dynamic uncertainty boundary, and an adaptive smoothing factor that automatically decreases with the thermomagnetic decay exponent is introduced to reduce control chattering.

6. The drive motor constraint tracking control method for a heavy-duty friction stir welding robot according to claim 5, characterized in that, The steps for determining the decay gradient sensitive gain include: The equivalent uncertainty matrix of the drive motor in a cold state and under the nominal working condition of translational welding is obtained, and the minimum stable boundary gain required to resist conventional mechanical friction and load disturbance is calculated based on stability theory as the reference sensitive gain. Obtain the heat margin approximation rate index, which represents the ratio of the current thermomagnetic decay index to the set decay trigger threshold. Construct a nonlinear adaptive mapping relationship using the square term of the heat margin approximation rate index to dynamically amplify the benchmark sensitive gain when the temperature rise approaches the decay trigger threshold to obtain the initial sensitive gain. The maximum safe current magnitude of the servo driver inverter power module is extracted. The maximum safe current magnitude is projected onto the generalized actuation space by combining the electromechanical equivalent inertia matrix to obtain the extreme value of the total generalized actuation vector magnitude. The generalized control margin is calculated based on the extreme value of the total generalized actuation vector magnitude and the current feedforward control quantity of the system. The maximum allowable sensitive gain threshold within the current calculation cycle is calculated using the generalized control margin. The initial sensitive gain is dynamically truncated by the smoothing saturation function to obtain the decay gradient sensitive gain.

7. The drive motor constraint tracking control method for a heavy-duty friction stir welding robot according to claim 1, characterized in that, The steps for obtaining the stable callback control law include: Extract the cross-domain generalized constraint vector and its first-order time derivative, and introduce a positive definite diagonal gain matrix to construct a cross-domain generalized constraint tracking error vector to measure the degree of deviation of the system from the ideal constraint manifold; Using the transpose of the cross-domain constraint matrix in the generalized second-order servo constraint equation as the Jacobian mapping operator, the error vector in the constraint space is projected back to the physical actuation space. Combined with the inverse matrix of the electromechanical joint equivalent inertia matrix, the mathematical error penalty term is mapped to the physical voltage compensation quantity to generate the stable callback control law.

8. The drive motor constraint tracking control method for a heavy-duty friction stir welding robot according to claim 1, characterized in that, Based on the thermomagnetic decay index, the current distribution reconstruction operator dynamically breaks the setting of zero direct-axis current, generating vector control command signals including: When the thermomagnetic decay index is less than or equal to the set decay trigger threshold, the current distribution reconstruction operator outputs the maximum torque current ratio distribution vector, making the stator direct axis reference current command zero. When the thermomagnetic decay index is greater than the set decay trigger threshold, the current distribution reconstruction operator dynamically outputs a vector command to force the direct axis current to be set to zero, injecting negative reactive current into the stator direct axis to generate reluctance torque compensation to share the load of quadrature axis active current.

9. The drive motor constraint tracking control method for a heavy-duty friction stir welding robot according to claim 8, characterized in that, The steps for determining the decay trigger threshold include: Extract the intrinsic thermodynamic limit boundary of the core component of the drive motor, and obtain the maximum safe temperature rise of the system by subtracting the reference temperature of the working environment and the preset calibration error margin from the minimum temperature extreme value in the intrinsic thermodynamic limit boundary. Then, the maximum safe temperature rise is equivalently assigned to the safe demagnetization limit index. The time-domain derivative of the thermomagnetic decay index is extracted as the transient thermal gradient. The transient thermal gradient is smoothed by using an asymmetric low-pass filter to obtain a smooth thermal gradient. The thermal relaxation safety time window determined by the motor's heat transfer hysteresis characteristics and the overload feedforward weight reflecting the ratio of real-time contact resistance torque to physical peak overload torque are combined to calculate the dynamic buffer margin used to prevent thermal inertia overshoot. The decay trigger threshold is obtained by subtracting the dynamic buffer margin from the safe demagnetization limit index.

10. A drive motor constraint tracking control system for a heavy-duty friction stir welding robot, employing the drive motor constraint tracking control method for a heavy-duty friction stir welding robot as described in any one of claims 1 to 9, characterized in that, include: The decay dynamics modeling module is used to construct dynamic decay electromechanical dynamics models; A cross-domain constraint equation construction module is used to construct generalized second-order servo constraint equations; The nominal control torque solver module is used to solve cross-domain nominal constraint control laws; Robust compensation control law generation module, used to generate robust compensation control laws; The instruction generation and output module is used to generate vector control instruction signals to produce underlying inverter drive instructions.

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