An extrusion printing compensation control system and method for non-newtonian fluid bio-ink

Abstract

The application discloses an extrusion printing compensation control system and method for non-Newtonian fluid biological ink. The system comprises a feedforward control module, a dynamic delay estimation module, an identification feedback module, a pressure relief and back-pulling module, and an upper computer coordination controller. The feedforward module calculates the target extrusion flow rate in real time based on the power-law fluid model; the dynamic delay estimation module determines the total advance to achieve pre-extrusion by combining the communication time delay and the instantaneous thixotropic structural degree evolution equation driven by the kinematics of the robot arm; the feedback module corrects the reference consistency coefficient online by analyzing the explicit inverse rheology model; the back-pulling module calculates the residual elastic internal stress to perform adaptive back-pulling, and based on the hardware execution timestamp, accurately calculates the stress relaxation state of the idle stroke segment, which is used as the initial rheological boundary condition of the next path segment. The application realizes deep cross-domain strong coupling of heterogeneous communication, robot motion control and material rheological state, and improves the forming precision of biological printing.

Description

Technical Field

[0001] This invention belongs to the technical field of bio-3D printing and additive manufacturing, and relates to a compensation control system and method for extrusion printing of non-Newtonian fluid bio-inks. More specifically, it relates to a compensation control system and method for extrusion printing of non-Newtonian fluid bio-inks with deep coupling across multiple cycles, including network communication latency prediction, high-order motion dynamics messages of robotic arms, and internal state machines of fluid microrheology. Background Technology

[0002] With the advancement of bioadditive manufacturing towards high-precision tissue, complex organ scaffolds, and cell assembly, robotic arm bioprinters have found widespread application in tissue engineering due to their multi-degree-of-freedom capabilities and accessibility to complex curved surfaces in three-dimensional space. In a typical distributed intelligent bioprinting architecture, control commands typically need to be asynchronously distributed across heterogeneous network links (e.g., upper-layer industrial Ethernet and lower-layer serial physical buses). Due to varying parsing rates at different bus protocol layers, intermittent jitter in the underlying hardware boards, and concurrent conflicts in heterogeneous network environments, dynamic network communication delays are unavoidable during command issuance and transmission.

[0003] To eliminate this timing misalignment problem, existing technologies have developed control systems based on network timing protocols (such as the IEEE 1588 PTP protocol) for alignment, or employing algorithms such as Kalman filtering to predict communication link delays in real time. These solutions can effectively improve the synchronization and alignment accuracy of multi-axis control commands at both the electronic hardware and network protocol levels, solving the superficial problem of timing alignment from a purely information flow perspective.

[0004] However, bio-inks (such as high-concentration bio-hydrogels, cell-carrier shear fluids, and collagen complexes) are typical non-Newtonian fluids, exhibiting highly complex shear-thinning properties, time-dependent thixotropy, and significant viscoelastic memory effects. In actual printing processes, robotic arms frequently perform high-order kinematic transitions (e.g., transitions from high-speed straight lines to curved paths, abrupt starts and decelerations). During this process, the shear rate experienced by the ink within the flow channel fluctuates dramatically, causing dynamic depolymerization and recovery evolution of its microstructure, resulting in severe material laminar rheological time delays in the macroscopic flow response. Furthermore, the driving pressure differential applied by the front-end feeding mechanism induces non-negligible elastic residual internal stresses within the flow channel, leading to severe material extrusion hysteresis at the start and end points of the printing path, temperature drift in the morphology of long-term continuous printing, and tailing and stringing distortion in the non-printing jump segment.

[0005] The response lag and time memory defects at the material and rheological physics levels are constitutive intrinsic characteristics of fluids and cannot be eliminated simply by improving network communication accuracy or adjusting the timing of pure hardware command issuance. In the current bioprinting control framework, communication latency prediction and material rheological properties are often isolated and operated at different levels, treated as isolated pipelines cascaded together with simple algebraic weighted summation. This technical patchwork prevents the front-end information control layer from proactively sensing the destructive effects of macroscopic high-order trajectory acceleration on the microscopic rheological state of the material. The feedback end also cannot drive the self-evolution of the feedforward underlying model at the mechanistic level, nor can it maintain the viscoelastic time memory characteristics during discontinuous path topology transitions. Ultimately, this results in low edge forming accuracy and poor long-term stability. Therefore, achieving deep and strong cross-domain coupling between heterogeneous network communication, macroscopic high-order motion dynamics, and the material's microscopic rheological state machine is a major technological bottleneck that urgently needs to be overcome in the field of high-precision bioprinting. Summary of the Invention

[0006] The purpose of this invention is to overcome the defects in the prior art, such as the distortion of printing morphology and the drift of long-term operating accuracy caused by the isolated operation of each control level, the lack of deep constitutive coupling between communication synchronization and non-Newtonian rheological properties, and to provide a compensation control system and method for extrusion printing of non-Newtonian fluid bio-inks.

[0007] The core technical solution of this invention lies in breaking away from the traditional unidirectional linear cascaded control pipeline. It constructs a multidimensional mutually feeding mesh closed-loop control network by taking communication delay, macroscopic multi-level kinematic variables, material microstructure state machine, macroscopic geometric tomography, and cross-path viscoelastic relaxation process as input variables.

[0008] To achieve the above objectives, the present invention provides an extrusion printing compensation control system for non-Newtonian fluid bio-inks, the system comprising: The feedforward control module stores a database of bio-ink rheological parameters and uses a power-law fluid model to calculate the target extrusion flow rate that matches the target deposition cross section in real time. The dynamic delay estimation module estimates the total lead time, which is the sum of communication delay and material rheological lag time, in real time, and drives the feeding motor of the extrusion nozzle to start extrusion in advance before the robotic arm actually reaches the target position. The identification feedback module forms a dual-rate closed loop through the near-end wire feeding speed sensor and the far-end thickness sensor, which can suppress extrusion transient disturbances in real time and correct the reference consistency coefficient of the feedforward control module online. The pressure relief and pullback module calculates the residual elastic internal stress based on the historical extrusion flow integral and material viscoelastic parameters before the printing path ends, performs adaptive pullback, and continuously tracks the stress relaxation state in the space between paths, using the incompletely relaxed stress margin as the initial boundary condition when the next path segment starts. The host computer coordinating controller communicates with the robotic arm control system and various functional modules through an industrial real-time communication bus, and is responsible for global process parameter management, path planning and multi-cycle collaborative scheduling of various modules.

[0009] Furthermore, the rheological parameter database includes the power-law rheological exponent n, the baseline consistency coefficient K, the thixotropic structure initialization degree λ0, and the thixotropic structure recovery rate coefficient. Structural failure rate coefficient The feedforward control module uses the power-law fluid model with the driving pressure difference across the effective flow channel of the nozzle, the power-law rheological index, the reference consistency coefficient, the effective flow channel length of the nozzle, and the inner radius of the nozzle as input variables. It receives the reference consistency coefficient, which is corrected online by the identification feedback module, in real time, and calculates the target extrusion flow rate that matches the target deposition cross-section. .

[0010] Furthermore, the dynamic delay estimation module acquires the instantaneous kinematic parameters of the robotic arm control system in real time, and dynamically calculates the instantaneous thixotropic structure degree by combining the thixotropic microstructure evolution equation, thereby determining the total lead time composed of communication delay and dynamic rheological lag time; The dynamic rheological hysteresis time is obtained by dividing the nozzle dead zone volume by the current actual extrusion flow rate and then multiplying it by the thixotropic correction function. The current actual extrusion flow rate is obtained by multiplying the actual feed speed of the near-end wire feed speed sensor by the nozzle cross-sectional area. The thixotropic correction function has the instantaneous thixotropic structuring degree and the current extrusion flow rate as independent variables, and its value increases with the increase of the instantaneous thixotropic structuring degree. The communication delay is constructed by using hardware and software timestamps of the heterogeneous communication link between the bioprinting execution end and the robotic arm control end to build a historical sampling sequence of delay. Based on the real-time calculated delay sampling variance, a sliding window and Kalman filter are used to adaptively and dynamically allocate weights for forward prediction.

[0011] Furthermore, the instantaneous thixotropic structuring degree ranges from fully fluidized to fully structured. The dynamic delay estimation module dynamically updates it through the thixotropic microstructure evolution equation. The thixotropic microstructure evolution equation takes the structure recovery rate coefficient, the structure failure rate coefficient, the instantaneous thixotropic structuring degree, and the equivalent shear rate in the nozzle as independent variables, and outputs the derivative of the instantaneous thixotropic structuring degree with respect to time.

[0012] Furthermore, the equivalent shear rate within the nozzle is obtained by mapping the instantaneous kinematic parameters of the robotic arm control system, which include the translational velocity, acceleration, and jerk of the robotic arm control system.

[0013] Furthermore, the identification feedback module includes a near-end wire feeding speed sensor and a far-end thickness measurement sensor. The near-end wire feeding speed sensor collects the actual wire feeding speed with a short sampling period. The fast-channel error compensation controller outputs an instantaneous control quantity based on the difference between the actual wire feeding speed and the target wire feeding speed to eliminate transient disturbances. The remote thickness sensor collects the actual layer height and linewidth of the deposited material with a long sampling period. When the cumulative geometric deviation exceeds the preset threshold, it is mapped back to the drift amount ΔK of the material consistency coefficient through the explicit inverse rheological identification model. The damping update coefficient η is used to perform progressive correction on the benchmark consistency coefficient K in the database to realize the self-calibration closed-loop update of the feedforward model.

[0014] Furthermore, before the end of each printing path segment, the pressure relief and retraction module calculates the residual elastic internal stress in the nozzle according to Maxwell's viscoelastic constitutive relation based on the historical extrusion flow integral and material viscoelastic parameters within that path segment. It then drives the feed motor to reverse and retract at a speed proportional to the residual internal stress, actively balancing the residual pressure to eliminate end-of-path overflow. The pressure relief and retraction module also continuously tracks the idle time between paths, accurately calculating the idle time consumption using hardware timestamps aligned with a precise time protocol. It continuously calculates the relaxation state of the residual internal stress according to an exponential decay law, using the unrelaxed stress margin at the end of the path as the initial rheological boundary condition for the feedforward control module and dynamic delay estimation module when starting the next printing path segment, thus achieving continuous memorization of the viscoelastic state across paths.

[0015] Furthermore, the host computer coordinating controller establishes a connection with the robotic arm control system and each functional module through an industrial real-time communication bus. It is responsible for broadcasting system-level process parameters, path planning data, and instantaneous kinematic messages of the robotic arm to each functional module, and for synchronizing the communication cycle of each functional module. The message broadcasting cycle is determined based on the real-time requirements of multi-cycle coordination and scheduling of each module.

[0016] Furthermore, the required driving differential pressure of the feedforward control module is obtained according to the different extrusion methods: when configured for pneumatic extrusion, it is obtained by measuring the air pressure at the nozzle inlet in real time by a precision air pressure sensor; when configured for screw or plunger motor extrusion, it is obtained by converting the real-time torque feedback value of the feeding motor with the geometric parameters of the transmission mechanism, without the need to install a separate pressure sensor. The equivalent shear rate within the nozzle is obtained by mapping the higher-order kinematic parameters of the robotic arm, which include the instantaneous translational velocity, instantaneous acceleration, and instantaneous jerk of the robotic arm control system.

[0017] The present invention also provides a printing control method based on the system, which includes the following steps: S1. Before printing, calibrate the power-law rheological parameters, viscoelastic parameters, and thixotropic structure dynamic parameters of the material to construct a rheological parameter database. S2, During the printing process, the host computer coordinating controller captures the communication delay based on timestamp prediction, and simultaneously captures the instantaneous acceleration and instantaneous jerk of the robotic arm. The feedforward control module and the dynamic delay estimation module jointly calculate the dynamic target flow rate and the total lead amount that integrates the instantaneous thixotropic structure evolution, and control the feeding motor to actively respond in advance of the total lead amount. S3, the near-end wire feeding speed sensor performs high-frequency short-cycle instantaneous closed-loop compensation of speed, and the far-end thickness sensor identifies the changes in rheological parameters online through the explicit inverse rheological identification model based on the long-cycle geometric dimension error, and performs progressive correction on the reference consistency coefficient K in the feedforward control module with the damping coefficient η to realize the online self-calibration of the feedforward control model; S4, before the end of the current printing path segment, drives the feeding motor to perform adaptive reverse pressure relief based on the residual elastic internal stress. During the idle period based on the precise time protocol timestamp alignment, it continuously calculates the stress relaxation attenuation value and uses the attenuated stress value as the initial rheological boundary condition for the next path segment to intervene in the feedforward calculation and delay estimation, thereby realizing the cross-path rheological state memory closed loop.

[0018] This invention has significant technical advantages over existing technologies: through deep cross-domain feedback, the high-order dynamic messages of the robotic arm motion and the heterogeneous time delay prediction of the communication layer directly drive the fluid micro-shear history state machine, avoiding over-extrusion or under-material defects at the start and stop of the machine; using an explicit inverse rheological mathematical model, it completes the accurate mapping and overwriting from macroscopic morphology errors to microscopic material constitutive physical quantities K, eliminating the cumulative geometric temperature drift caused by long-term system operation; using a timestamp-based Maxwell stress relaxation memory closed loop, it realizes continuous state chain memory of the idle path state on the time axis, completely breaking the bottleneck of the isolated cascade of the traditional control framework and achieving significant mechanistic collaborative innovation. Attached Figure Description

[0019] Figure 1 This is a mesh-coupled topology diagram of the state variables across multiple cycles of the control system of the present invention.

[0020] Figure 2 This is a timing waveform diagram of the viscoelastic memory and multi-physical quantity linkage control across discontinuous paths according to the present invention.

[0021] Figure 3 This is a schematic diagram of the robotic arm bioprinting hardware system provided in an embodiment of the present invention. Detailed Implementation

[0022] The present invention will now be further analyzed in detail with reference to the accompanying drawings and specific embodiments. Please refer to the accompanying drawings. Figure 1 This invention's control system completely abandons conventional cascaded pipelines in its logical layering. The system as a whole consists of five major functional modules: a host computer coordination controller, a feedforward control module, a dynamic delay estimation module, an identification feedback module, and a pressure relief and pullback module. The host computer coordination controller, as the top-level scheduling unit, communicates bidirectionally with the external robotic arm control system via a data transmission bus, and is responsible for global process parameter management, path planning, and cross-cycle coordination and scheduling of state variables of each module. The external robotic arm control system is placed in... Figure 1 On the left side of the overall topology shown, motion trajectory messages are broadcast in real time via an industrial-grade real-time bus. The bus output is divided into two independent but parallel hardware signal channels: the first channel inputs the instantaneous translational velocity V to the feedforward control module; the second channel broadcasts higher-order dynamic messages containing instantaneous acceleration a and jerk j to the dynamic delay estimation module in real time with a period of no more than 10ms.

[0023] The feedforward control module pre-stores a database of bio-ink rheological parameters, which includes a power-law rheological exponent n, a baseline consistency coefficient K, and an instantaneous thixotropic structuring degree λ. Based on a power-law fluid model, the feedforward control module receives the consistency coefficient K, which is corrected online by the identification feedback module, in real time, and calculates the target extrusion flow rate that matches the target deposition cross-section. The power-law fluid model is expressed as:

[0024] in, Let n be the target extrusion flow rate, n be the power-law rheological exponent, K be the consistency coefficient, ΔP be the driving pressure difference across the effective flow channel of the nozzle, L be the effective flow channel length of the nozzle, and r be the inner radius of the nozzle. The ΔP is obtained as follows: when configured for pneumatic extrusion, it is directly measured using a precision air pressure sensor; when configured for screw or plunger motor extrusion, it is calculated from the real-time torque feedback value of the feeding motor combined with the geometric parameters of the transmission mechanism.

[0025] In the dynamic delay estimation module, the instantaneous kinematic parameters of the robotic arm control system are acquired in real time. The instantaneous thixotropic structure degree λ is dynamically calculated using the thixotropic microstructure evolution equation to determine the impact of communication delay. With dynamic rheological lag time Total lead time The output is then sent to the motor drive unit, ensuring that the extrusion action occurs before the robotic arm actually reaches the target position. Start at any time. The total lead time... The estimation formula is:

[0026]

[0027] in, For dynamically predicted communication latency; The nozzle dead zone volume is calculated by integrating the geometric dimensions of the nozzle cavity. The current actual extrusion flow rate is obtained by multiplying the actual feed rate from the near-end filament feed rate sensor by the nozzle cross-sectional area; λ is the instantaneous thixotropic structuring degree dynamically updated by the thixotropic microstructure evolution equation, with a value ranging from 0 to 1, where 0 represents complete fluidization and 1 represents complete structuring; f(λ) is the thixotropic correction function, in the form of:

[0028] in The structural recovery weighting factor varies with the extrusion flow rate, and β is a calibration coefficient related to the material's structural recovery characteristics. Both the reference flow rate and the communication delay were determined by rheological calibration experiments. It constructs an independent historical delay sampling sequence by using hardware and software timestamps of the heterogeneous communication link between the bioprinting execution end and the robotic arm control end, and performs forward prediction based on the real-time calculated delay sampling variance by using a sliding window and Kalman filter to adaptively and dynamically allocate weights.

[0029] The evolution equation for the instantaneous thixotropic structuring degree λ is defined as follows:

[0030] in, The structural recovery rate coefficient, The structural failure rate coefficient, γ·(a,j), is mapped from the higher-order kinematic parameters of the robotic arm to the equivalent shear rate within the nozzle, and its form is:

[0031] In the formula, v is the current translational speed of the robotic arm. For reference flow rate The corresponding nozzle wall shear rate (calculated from nozzle geometry parameters and reference flow rate). and The coupling effect coefficients of acceleration and jerk on shear rate were determined through rheological calibration experiments. The depolymerization and recovery rates of the material's microstructure are predicted in real time using macroscopic high-order kinematics data from a robotic arm, thereby dynamically adjusting the rheological hysteresis time. .

[0032] In the identification feedback module, the short sampling period of the near-end wire feed speed sensor is used as the fast-channel control period. Based on the difference between the actual wire feed speed and the target wire feed speed, the fast-channel error compensation controller outputs an instantaneous control quantity to eliminate transient disturbances caused by mechanical slippage or localized material blockage. The long sampling period of the far-end thickness sensor is used as the slow-channel control period. When a cumulative deviation in the deposition layer height is detected within M consecutive long periods... or cumulative deviation of line width When the preset threshold is exceeded, the slow channel drift correction controller invokes the embedded explicit reverse rheological identification model. This model is constructed based on the power-law fluid channel extrusion and the conservation law of macroscopic deposition cross-sectional area. The analytical calculation formula for the consistency coefficient drift ΔK is as follows:

[0033] Where K is the baseline consistency coefficient in the current rheological parameter database, and n is the power-law rheological exponent. Design the floor height to the target height. The target linewidth is designed. The slow-channel drift correction controller uses this analytical formula to calculate the actual consistency coefficient drift ΔK of the material in real time, and performs a progressive correction K←K+η·ΔK with a damping update coefficient η to suppress parameter step disturbances introduced by sensor noise. In the pressure relief and back-drawing module, before the end of each printing path segment, the residual elastic internal stress inside the nozzle is calculated based on the historical extrusion flow integral and the material viscoelastic parameters. It also drives the feed motor to reverse and perform adaptive retraction. The adaptive retraction speed at the end of the path... The calculation formula is:

[0034] Where α is the retraction ratio coefficient, calculated by measuring the end overflow volume under different historical extrusion flow conditions and... The residual elastic internal stress was obtained through linear regression fitting and written into the rheological parameter database along with the rheological parameters. Based on Maxwell's viscoelastic constitutive relation, the data consists of the historical extrusion flow integral of the current path segment, the material storage modulus G', and the relaxation time. Joint solution:

[0035] Where, the integration time T is the continuous printing time of the current path segment, and γ·(t) is the shear rate at the nozzle wall at time t, which is obtained by converting the historical actual extrusion flow rate Q(t) through nozzle geometric parameters (γ·=(3n+1) / (4n)×4Q(t) / (πr)). 3 ), G' and Before printing, the parameters are calibrated using a rotating rheometer frequency scan experiment (measuring the changes in storage modulus G' and loss modulus G'' with frequency and fitting a Maxwell model of the unit element), and written into the rheological parameter database along with n and K. When the current printing path segment ends and enters a non-printing idle state, this module performs a hardware-aligned timestamp based on the Precise Time Protocol (PTP). Calculate the absolute difference to accurately determine the idle time period. And continuously calculate the stress relaxation state during this period:

[0036] If the next consecutive print path segment starts, the decayed If the value is greater than zero, the feedforward control module and the dynamic delay estimation module directly use the physical margin as the initial rheological boundary condition and proportionally deduct the initial target extrusion flow rate and pre-extrusion advance at the starting point of the new path segment.

[0037] The logical architecture and operational mechanism of the five functional modules of this invention have been described above. The following, in conjunction with... Figure 3 Explain the deployment method of the above functional modules at the physical hardware level.

[0038] Please see Figure 3 In actual physical deployment, the extrusion execution target of this system is a single-nozzle extrusion nozzle mounted on the end flange of the robotic arm. For example... Figure 3 As shown in the semi-transparent structure within the right frame, the single-nozzle extrusion head comprises, from top to bottom: a feed motor, a reduction gear, a filament / plunger, a square heating / mixing chamber, and a conical nozzle tip at the bottom. To achieve the dual-rate closed-loop sensing required by the aforementioned identification feedback module, the nozzle is precisely configured with a near-end filament feed speed sensor and a far-end thickness sensor in physical space: the near-end filament feed speed sensor is installed below the transmission gear at the nozzle's feed end, on the outside of the filament, directly contacting and monitoring the actual advance speed of the filament or plunger; its output signal is connected to the fast-channel error compensation controller. The far-end thickness sensor is offsetly mounted on the side of the nozzle via a bracket, maintaining a fixed physical offset distance from the nozzle axis. It utilizes its emitted laser / visual physics beam to focus on the deposition lines on the printing platform for non-contact, real-time acquisition of the actual layer height and linewidth deviation signals of the deposited material. Its output signal is connected to the slow-channel drift correction controller. The offset distance of the remote thickness sensor... For fixed mechanical mounting dimensions, the distance between the sensor and the nozzle shaft is obtained through physical measurement and written into the system configuration. A slow drift correction signal is introduced during application based on... Spatial delay compensation, calculated as a ratio to the current printing speed, is used to eliminate errors introduced by measurement position lag. The pressure relief and backflow module is installed before the motor driver, and its output is connected to the drive control terminal of the feed motor.

[0039] The robotic arm control system and the host computer coordination controller are connected via an industrial real-time communication bus. Its instantaneous motion trajectory and dynamic messages are sent to the dynamic delay estimation module and the feedforward control module in a short broadcast cycle to meet the requirements of real-time capture of high-order kinematic parameters. The principle for determining this cycle is that its time scale should be much smaller than the characteristic time required for a significant change in the degree of thixotropic structure of the material.

[0040] Having clarified the above logical architecture and physical deployment, the following combines... Figure 2 This section describes the cross-domain multi-physical quantity coupling and linkage mechanism of this system when crossing discontinuous printing path segments. On the same shared global time axis, when the robotic arm finishes printing path 1, it transitions from a constant-speed printing state to a non-printing state, executes an idle trajectory in space, and after experiencing a physical time consumption of Δt_jump, reaches the starting point of the new path 2, and then transitions back to the printing state.

[0041] Correspondingly, the residual elastic internal stress σ_residual inside the nozzle exhibits a highly time-dependent characteristic. During continuous printing on path 1, the internal stress remains high due to flow integral and viscoelastic energy storage. When the end command is triggered at the end of path 1, the feed motor responds rapidly by performing an adaptive reverse pullback dynamically determined by the magnitude of the internal stress, resulting in a sharp drop on the stress curve. Subsequently, within the spatial jump segment Δt_jump across the path, due to the cessation of feed drive, the residual elastic internal stress exhibits a typical exponential decay curve according to Maxwell's relaxation constitutive equation.

[0042] Due to the complex and varied spatial trajectories of the distributed printing process, when the robotic arm actually arrives at the starting point of path 2 carrying the printhead and triggers the start command, the system's Precision Time Protocol (PTP) hardware execution timestamp is used. The difference of absolute values ​​indicates the current The extremely short duration means that the residual stress inside has not yet been fully relaxed and released, i.e., at this point... Figure 2 The initial residual stress shown It is still significantly greater than zero.

[0043] At this point, the cross-path topological viscoelastic memory chain of the present invention is activated, and the stress residual greater than zero directly serves as the physical initial rheological boundary condition for the starting segment of path 2. For example... Figure 2 The bottom feed motor controls the target flow rate. As shown in the curve, the feedforward control module and the dynamic delay estimation module automatically compensate for the initial extrusion flow rate and pre-extrusion advance at the starting point of path 2 by proportionally reducing the peaks and depressions by receiving the stress residual. The starting current and flow curves of the feeding motor at the starting point of the new path are no longer the steep steps of the conventional system, but instead exhibit a concave deformation with dynamic buffering. The material utilizes the elastic residual pressure that has not been fully released to coordinate the discharge, perfectly avoiding the common defects of material accumulation, overflow, or large head at the breakpoint jump. This enables the multi-segment discontinuous trajectory to achieve a complete viscoelastic continuum memory closed loop at the physical rheological level.

[0044] The following section, using a specific scenario of continuously decelerating curve printing, elaborates on the details of cross-cycle data feedback and fusion in the formulas of each module in this invention: When the front-end host computer coordinating controller plans a printing trajectory that rapidly decelerates from a high-speed straight section into a high-curvature composite concentric circular arc, the heterogeneous communication bus, through a sliding window with dual hardware and software timestamps and Kalman filtering, combined with its real-time calculated delay sampling variance, adaptively adjusts the weights and predicts the current system's network communication latency with high precision and forward-looking accuracy. .

[0045] Meanwhile, the dynamic delay estimation module periodically captures the instantaneous high-order dynamic messages broadcast by the robotic arm to meet the requirements of real-time capture of high-order kinematic parameters. At the junction of the abruptly decelerated incision arc, acceleration *a* and jerk *j* change abruptly. The module directly injects this high-order motion variable into the microstructure evolution differential equation of the instantaneous thixotropic structuring degree λ. Due to the long-term high-speed, high-shear conditions before deceleration, the historical shear rate integral value γ·(a,j) in the equation is at a high cumulative level. The system solution shows that the microstructure of the ink is severely disintegrated at the moment of entering the curve, and the instantaneous thixotropic structuring degree λ is at an extremely low fluidization value.

[0046] At this point, the delay estimation module substitutes this dynamic λ into the thixotropic correction function f(λ), and f(λ) decreases accordingly. This is due to the deceleration affecting the current actual flow rate. Reduce dead zone volume The system is constant, and the time delay equation of the rheological response is used. Dynamically update the rheological response time and compare it with the network's predicted latency. Cross-domain cascaded addition outputs the most accurate dynamic total lead. .

[0047] In the slow-channel operation of the feedback loop, the remote thickness sensor continuously detects the single-line geometry of the current deposition over a long period. Due to the increased ambient temperature during long-term operation, the viscosity decreases, resulting in a cumulative deviation in layer height. Cumulative deviation of line width (This manifests as material thinning and increased size). The slow-channel drift correction controller captures this dimensional variation and immediately invokes the explicit inverse rheological identification model. Since the actual denominator area is larger than the target numerator area, the algebraic formula accurately and quantitatively outputs a negative consistency coefficient true drift ΔK.

[0048] The ΔK is weighted by the damping coefficient η and progressively corrected to the reference consistency coefficient K (K←K+η·ΔK) in the rheological parameter database, thus achieving smooth calibration of K. The updated K value, along with the total lead t_lead calculated in the above linkage, is directly injected into the power-law formula of the feedforward control module. Based on the new material constitutive state, the feedforward module recalculates the most accurate target extrusion flow rate for the curved section. Under the combined command of this underlying constitutive self-evolutionary feedforward and cross-domain delay advance, the motor drive unit ensures that the robotic arm enters the circular curve before... The feeding motor speed can be precisely controlled at any time.

[0049] In the entire control process, five core physical state variables—network communication latency, macroscopic mechanical dynamics messages, fluid microscopic thixotropic structuring degree, macroscopic deposition geometry reverse identification, and cross-path viscoelastic relaxation memory—are interconnected, mutually causal and input variables, and interwoven into a network under multi-cycle collaborative scheduling. At the level of physical rheology and cross-domain control, the coupling relationship of these five state variables forms a closed loop in the control logic. The output of each module directly serves as the input variable for other modules, achieving cross-domain state linkage under multi-cycle collaborative scheduling, resulting in high boundary forming accuracy and full-lifecycle printing stability.

Claims

1. A compensation control system for extrusion printing of non-Newtonian fluid bio-inks, characterized in that, The system includes: The feedforward control module stores a database of bio-ink rheological parameters and uses a power-law fluid model to calculate the target extrusion flow rate that matches the target deposition cross section in real time. The dynamic delay estimation module estimates the total lead time, which is the sum of communication delay and material rheological lag time, in real time, and drives the feeding motor of the extrusion nozzle to start extrusion in advance before the robotic arm actually reaches the target position. The identification feedback module forms a dual-rate closed loop through the near-end wire feeding speed sensor and the far-end thickness measurement sensor, which can suppress extrusion transient disturbances in real time and correct the reference consistency coefficient of the feedforward control module online. The pressure relief and pullback module calculates the residual elastic internal stress based on the historical extrusion flow integral and material viscoelastic parameters before the printing path ends, performs adaptive pullback, and continuously tracks the stress relaxation state in the space between paths, using the incompletely relaxed stress margin as the initial boundary condition when the next path segment starts. The host computer coordinating controller communicates with the robotic arm control system and various functional modules through an industrial real-time communication bus, and is responsible for global process parameter management, path planning and multi-cycle collaborative scheduling of various modules.

2. The system according to claim 1, characterized in that, The rheological parameter database includes the power-law rheological index n, the baseline consistency coefficient K, the thixotropic structure initialization degree λ0, and the thixotropic structure recovery rate coefficient. Structural failure rate coefficient The feedforward control module uses the power-law fluid model with the driving pressure difference across the effective flow channel of the nozzle, the power-law rheological index, the reference consistency coefficient, the effective flow channel length of the nozzle, and the inner radius of the nozzle as input variables. It receives the reference consistency coefficient, which is corrected online by the identification feedback module, in real time, and calculates the target extrusion flow rate that matches the target deposition cross-section. .

3. The system according to claim 1, characterized in that, The dynamic delay estimation module acquires the instantaneous kinematic parameters of the robotic arm control system in real time, and dynamically calculates the instantaneous thixotropic structure degree by combining the thixotropic microstructure evolution equation, thereby determining the total lead time composed of communication delay and dynamic rheological lag time; The dynamic rheological hysteresis time is obtained by dividing the nozzle dead zone volume by the current actual extrusion flow rate and then multiplying it by the thixotropic correction function. The current actual extrusion flow rate is obtained by multiplying the actual feed speed of the near-end wire feed speed sensor by the nozzle cross-sectional area. The thixotropic correction function has the instantaneous thixotropic structuring degree and the current extrusion flow rate as independent variables, and its value increases with the increase of the instantaneous thixotropic structuring degree. The communication delay is constructed by using hardware and software timestamps of the heterogeneous communication link between the bioprinting execution end and the robotic arm control end to build a historical sampling sequence of delay. Based on the real-time calculated delay sampling variance, a sliding window and Kalman filter are used to adaptively and dynamically allocate weights for forward prediction.

4. The system according to claim 3, characterized in that, The instantaneous thixotropic structuring degree ranges from fully fluidized to fully structured. The dynamic delay estimation module dynamically updates it through the thixotropic microstructure evolution equation. The thixotropic microstructure evolution equation takes the structure recovery rate coefficient, the structure failure rate coefficient, the instantaneous thixotropic structuring degree, and the equivalent shear rate in the nozzle as independent variables, and outputs the derivative of the instantaneous thixotropic structuring degree with respect to time.

5. The system according to claim 4, characterized in that, The equivalent shear rate within the nozzle is obtained by mapping the instantaneous kinematic parameters of the robotic arm control system, which include the translational velocity, acceleration, and jerk of the robotic arm control system.

6. The system according to claim 1, characterized in that, The identification feedback module includes a near-end wire feeding speed sensor and a far-end thickness measurement sensor. The near-end wire feeding speed sensor collects the actual wire feeding speed with a short sampling period. The fast-channel error compensation controller outputs an instantaneous control quantity based on the difference between the actual wire feeding speed and the target wire feeding speed to eliminate transient disturbances. The remote thickness sensor collects the actual layer height and linewidth of the deposited material with a long sampling period. When the cumulative geometric deviation exceeds the preset threshold, it is mapped back to the drift amount ΔK of the material consistency coefficient through the explicit inverse rheological identification model. The damping update coefficient η is used to perform progressive correction on the benchmark consistency coefficient K in the database to realize the self-calibration closed-loop update of the feedforward model.

7. The system according to claim 1, characterized in that, Before the end of each printing path segment, the pressure relief and retraction module calculates the residual elastic internal stress in the nozzle according to Maxwell's viscoelastic constitutive relation based on the historical extrusion flow integral and material viscoelastic parameters within that path segment. It then drives the feed motor to reverse and retract at a speed proportional to the residual internal stress, actively balancing the residual pressure to eliminate end-of-path overflow. The pressure relief and retraction module also continuously tracks the idle time between paths, accurately calculating the idle time consumption using hardware timestamps aligned with a precise time protocol. It continuously calculates the relaxation state of the residual internal stress according to an exponential decay law, using the unrelaxed stress margin at the end of the path as the initial rheological boundary condition for the feedforward control module and dynamic delay estimation module when starting the next printing path segment, thus achieving continuous memorization of the viscoelastic state across paths.

8. The system according to claim 1, characterized in that, The host computer coordinating controller establishes a connection with the robotic arm control system and each functional module through an industrial real-time communication bus. It is responsible for broadcasting system-level process parameters, path planning data, and instantaneous kinematic messages of the robotic arm to each functional module, and for synchronizing the communication cycle of each functional module. The message broadcasting cycle is determined based on the real-time requirements of multi-cycle coordination and scheduling of each module.

9. The system according to claim 2, characterized in that, The required driving differential pressure for the feedforward control module is obtained according to the different extrusion methods: when configured for pneumatic extrusion, it is obtained by measuring the air pressure at the nozzle inlet in real time by a precision air pressure sensor; when configured for screw or plunger motor extrusion, it is obtained by converting the real-time torque feedback value of the feeding motor with the geometric parameters of the transmission mechanism, without the need to install a separate pressure sensor. The equivalent shear rate within the nozzle is obtained by mapping the higher-order kinematic parameters of the robotic arm, which include the instantaneous translational velocity, instantaneous acceleration, and instantaneous jerk of the robotic arm control system.

10. A printing control method based on the system according to any one of claims 1-9, characterized in that, Includes the following steps: S1. Before printing, calibrate the power-law rheological parameters, viscoelastic parameters, and thixotropic structure dynamic parameters of the material to construct a rheological parameter database. S2, During the printing process, the host computer coordinating controller captures the communication delay based on timestamp prediction, and simultaneously captures the instantaneous acceleration and instantaneous jerk of the robotic arm. The feedforward control module and the dynamic delay estimation module jointly calculate the dynamic target flow rate and the total lead amount that integrates the instantaneous thixotropic structure evolution, and control the feeding motor to actively respond in advance of the total lead amount. S3, the near-end wire feeding speed sensor performs high-frequency short-cycle instantaneous closed-loop compensation of speed, and the far-end thickness sensor identifies the changes in rheological parameters online through the explicit inverse rheological identification model based on the long-cycle geometric dimension error, and performs progressive correction on the reference consistency coefficient K in the feedforward control module with the damping coefficient η to realize the online self-calibration of the feedforward control model; S4, before the end of the current printing path segment, drives the feeding motor to perform adaptive reverse pressure relief based on the residual elastic internal stress. During the idle period based on the precise time protocol timestamp alignment, it continuously calculates the stress relaxation attenuation value and uses the attenuated stress value as the initial rheological boundary condition for the next path segment to intervene in the feedforward calculation and delay estimation, thereby realizing the cross-path rheological state memory closed loop.

Images