Additive manufacturing control method based on multi-dimensional constraint nonlinear model predictive control

Abstract

The application discloses an additive manufacturing control method based on a multi-dimensional constraint nonlinear model predictive control, first, setting a target process parameter and obtaining an actual temperature, calculating a mismatch error to introduce a closed-loop feedback; second, constructing a nonlinear differential prediction model coupling heating power and printing speed, and introducing a high-order thermal radiation heat dissipation term; then, constructing a multi-objective cost function, and forcibly applying physical constraints of hardware rated power and motion limits; finally, calling a numerical solver for online rolling optimization, and issuing optimal instructions to the bottom layer execution. The application breaks the single variable control limitation, fundamentally suppresses thermal overshoot, and guarantees the molding quality of soft materials.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of additive manufacturing and advanced process automatic control, and in particular relates to an additive manufacturing control method based on multidimensional constrained nonlinear model predictive control. Background Technology

[0002] In recent years, additive manufacturing (3D printing) technology has demonstrated enormous application potential in fields such as soft robotics, flexible electronics, and biomedicine. For soft materials such as polydimethylsiloxane (PDMS) or thermosetting hydrogels, in the direct extrusion molding process of pure materials without support bath assistance, precise in-situ heating is often highly dependent on accelerating the cross-linking and curing reaction to achieve rapid shaping and continuous layering after liquid resin extrusion. During this process, the temperature field distribution in the molding area directly determines the degree of curing, interlayer bonding force, and mechanical properties of the final part.

[0003] Currently, soft material additive manufacturing systems typically employ a single heat source, such as a bottom-heated constant-temperature heating plate, and generally rely on traditional proportional-integral-derivative (PID) algorithms for single-variable closed-loop temperature control. However, with the deepening of research and industrial applications, existing technologies have revealed the following significant shortcomings: First, single-variable control is highly susceptible to heat accumulation and irreversible thermal degradation. Soft materials generally have extremely low thermal conductivity, and as the number of printed layers increases, heat accumulates rapidly in the bottom layers. Traditional PID controllers can only control heat input unidirectionally by adjusting the power of the heating element; when the system experiences temperature overshoot, the controller can only passively reduce the heating power to zero, relying solely on slow, natural convection for heat dissipation. This asymmetric adjustment mechanism, lacking active cooling capability, is highly prone to causing local temperatures to far exceed the material's safe processing window when faced with printing paths with complex topologies, leading to material scorching, carbonization, or severe thermal stress warping.

[0004] Second, existing control frameworks neglect the multidimensional coupling effect between mechanical motion parameters and thermodynamic evolution. In traditional control strategies, the printing speed of the extruder head is usually treated as a static, purely mechanical process parameter, independent of the temperature control system. In fact, the printing speed directly determines the ratio of heat input to heat dissipation on the extrusion path per unit time. Although some existing process optimization strategies attempt to mitigate heat accumulation by globally reducing the printing speed, this experience-based open-loop feedforward adjustment often comes at the cost of production efficiency. Existing control systems generally lack a mechanism to incorporate "printing speed" and "heating power" as equivalent dynamic control variables into the same multi-objective optimization closed loop, missing the optimal approach to using mechanical motion to collaboratively suppress thermal overshoot.

[0005] Third, traditional linear models and solutions without boundary constraints struggle to handle complex operating conditions. Some existing advanced control strategies (such as conventional linear model predictive control) often simplify the physical model of a system to a first-order linear relationship. However, when soft materials approach the target curing temperature (e.g., 150°C to 250°C), the heat loss from the system increases exponentially according to the Stefan-Boltzmann law (fourth-order law). Existing linear models cannot accurately characterize this high-order nonlinear physical law, easily leading to model mismatch. Furthermore, existing control algorithms generally lack dynamic physical boundary hard constraints on the underlying hardware (such as the upper limit of the rated power of the heating plate and the speed limit for preventing flow interruption in the extrusion mechanism). This can easily lead to dangerous control commands in actual industrial settings, causing hardware damage or printing failures.

[0006] In summary, how to break through the limitations of single-variable control, accurately construct a multivariate prediction model that integrates nonlinear heat dissipation laws, and achieve dynamic coordination between heating power and printing speed under strict hardware physical constraints has become a core technical bottleneck that urgently needs to be solved in the current field of soft material additive manufacturing. Summary of the Invention

[0007] To address the problems in existing in-situ curing processes for additive manufacturing of soft materials, such as thermal overshoot caused by a single temperature control variable, neglect of the feedback compensation effect of mechanical motion on thermal evolution, and distortion of linear prediction models under high-temperature conditions, this invention provides an additive manufacturing control method based on multidimensional constrained nonlinear model predictive control. This method breaks through the limitations of single-variable control, fundamentally suppresses thermal overshoot, and ensures the molding quality of soft materials.

[0008] An additive manufacturing control method based on multidimensional constrained nonlinear model predictive control includes the following steps: (1) Obtain process status data for the current control cycle, including the target curing temperature of the soft material, the desired printing speed, and the measured temperature collected by the sensor; and calculate the model mismatch error based on the measured temperature and the predicted temperature. (2) Construct a nonlinear differential prediction model that couples heating power and printing speed, in which printing speed is used as an auxiliary heat dissipation variable to participate in the thermal evolution calculation, and introduce a nonlinear term to characterize higher-order thermal radiation loss in the nonlinear differential prediction model. (3) Set a multi-objective cost function that includes temperature tracking error penalty and printing efficiency deviation penalty, and force dynamic physical boundary constraints on heating power and printing speed; (4) Call the numerical optimization solver within a sampling period to solve for the optimal control command sequence that minimizes the cost function within the physical boundary constraints; (5) Extract the first action combination in the optimal control instruction sequence as the actual control instruction for output execution, and step to the next sampling period after execution.

[0009] Preferably, in step (1), the soft material is a silicone material or hydrogel material with thermosetting properties, and its target curing temperature is set between 150°C and 250°C.

[0010] The specific process of step (1) is as follows: (1-1) At the start of the current control cycle, read the set target curing temperature of the soft material. With expected printing speed ; (1-2) The measured temperature is obtained by sensors deployed in the printing area, and noise reduction is performed using the Kalman filter algorithm to obtain the effective observed temperature at the current moment. ; (1-3) Effective observation temperature Theoretical predicted temperature output from the previous control cycle The model mismatch error is calculated by performing a difference operation. As a closed-loop correction feedback.

[0011] The specific process of step (2) is as follows: (2-1) Determine the control power of the heating plate For active thermal input variables, printhead travel speed To assist in the calculation of heat dissipation variables, a basic state evolution mechanism is constructed by combining linear environmental convective heat dissipation. (2-2) Based on the Stefan-Boltzmann law, a high-order nonlinear thermal radiation loss term is introduced, with the difference between the fourth power of the current temperature and the fourth power of the ambient temperature as the core variable. (2-3) Mismatch error of fusion model A nonlinear differential prediction model with closed-loop feedback characteristics was established.

[0012] The specific formula for the nonlinear difference prediction model is as follows: ; in, For the predicted temperature at the next moment, The effective observed temperature at the current moment. The power gain coefficient, For velocity coupling coefficient, The linear convection heat dissipation coefficient is... For higher-order radiative heat dissipation coefficient, The ambient temperature.

[0013] In step (3), the expression for the multi-objective cost function is as follows: ; in, To predict the time domain, To control the time domain, For temperature tracking weights, Speed ​​efficiency weighting; Indicates in Always looking towards the future Predicted temperature at any given time. Indicates in Always looking towards the future Optimization command value for moment speed.

[0014] In step (3), dynamic physical boundary constraints are forcibly applied to the heating power and printing speed, specifically including: Apply power constraint to the heating plate ,in, The upper limit of heating power set for the system. Set between 400W and 800W; Apply printing speed constraints to the extrusion motor ,in, The maximum printing speed set for the system. Set between 100 mm / min and 500 mm / min.

[0015] In step (4), the numerical optimization solver uses the L-BFGS algorithm or the SQP algorithm (preferably the SLSQP algorithm) with limited memory to complete the online rolling solution of the nonlinear programming problem within each sampling period of 50ms to 100ms.

[0016] The present invention also provides an additive manufacturing system based on multidimensional constrained nonlinear model predictive control, comprising: a host computer for storing computer programs and executing the above-described control method; and a low-level execution unit, including a heating plate and a three-axis motion mechanism, for executing control commands issued by the host computer.

[0017] As a further preferred embodiment of the additive manufacturing system, the host computer is a PC, and the underlying execution unit includes a motion control board; the PC and the motion control board communicate via a serial port or bus communication protocol to send the control commands to the motion control board for execution.

[0018] Compared with the prior art, the present invention has the following beneficial effects: 1. Innovative introduction of mechanical variables to regulate the thermal field and suppress thermal degradation. This invention innovatively removes the purely mechanical properties of "printing speed" and endows it with the physical meaning of "active heat dissipation regulation." When faced with the risk of thermal overshoot, through the coupled game of power and speed, the thermal degradation and scorching of soft materials during the in-situ curing process are fundamentally suppressed.

[0019] 2. Introducing a higher-order radiation term to solve the model mismatch problem under high-temperature conditions. This invention introduces a fourth-order higher-order thermal radiation loss term to accurately simulate the real physical evolution of soft materials in high-temperature environments above 150℃, completely correcting the prediction divergence problem caused by neglecting thermal radiation in the traditional linear MPC algorithm.

[0020] 3. A dynamic closed-loop correction mechanism is constructed to improve system robustness. Through the residual feedback between the measured temperature and the predicted value, the system can compensate for disturbances caused by airflow fluctuations or changes in material physical properties in real time, ensuring extremely high steady-state control accuracy.

[0021] 4. Applying hard physical boundary constraints ensures the safe operation of the underlying hardware. This invention directly transforms the physical limits of the hardware into algorithmic constraints, eliminating the generation of abnormal control commands and ensuring the reliable operation of industrial-grade equipment while achieving high-efficiency printing. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a structural diagram of an additive manufacturing system based on multidimensional constrained nonlinear model predictive control, according to an embodiment of the present invention.

[0024] Figure 2 This is a flowchart of an additive manufacturing control method based on multidimensional constrained nonlinear model predictive control, according to an embodiment of the present invention.

[0025] Figure 3 is a temperature tracking curve of the printing process in an embodiment of the present invention.

[0026] Figure 4 is a curve showing the dynamic change of the heating power output by the system in an embodiment of the present invention.

[0027] Figure 5 is a graph showing the dynamic change of printing speed output by the system in an embodiment of the present invention.

[0028] Figure 6 is a schematic diagram of the additive manufacturing in-situ curing experimental device in an embodiment of the present invention.

[0029] In the diagram: 1. Host computer; 2. Motion control board; 3. Mica heating plate; 4. Infrared temperature sensor; 5. Three-axis motion mechanism; 6. Extrusion mechanism; 7. PDMS printed part. Detailed Implementation

[0030] 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.

[0031] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0032] This embodiment uses polydimethylsiloxane (PDMS), specifically the unsupported in-situ curing additive manufacturing process of Sylgard 184 two-component silicone material, as an example. Addressing the engineering challenges of PDMS and other thermosetting soft materials, such as their tendency to flow and collapse during extrusion molding and their extreme sensitivity to thermal history, this embodiment relies on… Figure 1 The control architecture shown is Figure 6 The hardware structure shown illustrates in detail the specific implementation details of the multidimensional constrained nonlinear model predictive control (NMPC) method.

[0033] like Figure 1 and Figure 6 As shown, this embodiment provides an additive manufacturing system based on multidimensional constrained nonlinear model predictive control. Its control link and physical execution structure include the following core components: host computer 1, motion control board 2, mica heating plate 3, infrared temperature sensor 4, three-axis motion mechanism 5, extrusion mechanism 6, and PDMS printed part 7.

[0034] Specifically, the host computer 1, acting as the core algorithm hub of the system, communicates with the underlying motion control board 2 via a serial bus in high-frequency bidirectional real-time. The motion control board 2 cascades downwards and drives the underlying physical execution units, which include: a mica heating plate 3 for providing the forming heat field, a three-axis motion mechanism 5 for controlling spatial displacement, and an extrusion mechanism 6 driven by precision pneumatic pressure. Simultaneously, to construct a control closed loop, the system is equipped with the aforementioned infrared temperature sensor 4. Specifically, to prevent the extrusion mechanism 6 from obstructing the temperature measurement field of view, the infrared temperature sensor 4 is installed at a preset tilt angle, precisely focusing on the currently cured area of ​​the PDMS printed part 7, and feeding back the collected real-time temperature signal to the host computer 1.

[0035] Based on the above hardware architecture, such as Figure 2As shown, the control method of this embodiment of the invention specifically includes the following steps: Step S1: Initialize process parameters and monitor real-time status.

[0036] The sampling control period of this embodiment dt The time limit is set to 50ms. During the system initialization phase, host computer 1 first loads the preset process parameters and hardware physical boundaries.

[0037] The core process parameters of this embodiment are shown in Table 1.

[0038] Table 1 Process Parameter Information

[0039] In the k At the start of each control cycle, infrared temperature sensor 4 collects the raw temperature signal for the current moment. To eliminate electromagnetic high-frequency interference from the stepper motor and heating components, the host computer 1 performs digital filtering and noise reduction on the raw signal to obtain the effective observed temperature for the current moment. Subsequently, the effective observed temperature was... Theoretical predicted temperature output from the previous control cycle By performing subtraction, the model mismatch error can be calculated. Its calculation expression is: ; Step S2: Construct a nonlinear difference prediction model that couples multidimensional variables.

[0040] Unlike conventional solutions that separate temperature and motion control in traditional equipment, this invention innovatively controls the output power of the mica heating plate 3. Defined as an active heat input variable, it controls the moving speed of the extrusion mechanism 6 and the triaxial motion mechanism 5. We introduce an auxiliary heat dissipation variable: the faster the printing speed, the more significant the local heat stripping.

[0041] Furthermore, considering that thermal radiation heat dissipation dominates when PDMS is cured at 220℃, using only linear cooling laws would lead to severe model divergence. Therefore, this invention forcibly introduces a higher-order thermal radiation term based on the Stefan-Boltzmann law into the state-space model. This also incorporates closed-loop feedback errors. e(k) The expression for the constructed nonlinear difference prediction model is: ; in, For the predicted temperature at the next moment, The effective observed temperature at the current moment. The power gain coefficient, For velocity coupling coefficient, The linear convection heat dissipation coefficient is... For higher-order radiative heat dissipation coefficient, The ambient temperature is used. This nonlinear model can accurately predict the future under extreme conditions. The predicted temperature evolution trajectory within the time domain.

[0042] To ensure the accuracy and engineering feasibility of the nonlinear differential prediction model in the in-situ curing process of PDMS soft materials, the various gain coefficients and heat dissipation coefficients in the model need to be identified and calibrated in advance through offline system and experiments. The specific methods are as follows: Power gain coefficient Coupling coefficient with velocity Calibration: Decoupling identification was performed using the standard step response test method. First, with the system in a steady state at ambient temperature, the three-axis motion mechanism 5 was kept stationary while the printing speed was... V =0, apply a fixed amplitude power step signal to the mica heating plate 3, record the temperature rise curve of the printed area using the infrared temperature sensor 4, and obtain the power gain coefficient by fitting the first-order inertial element using the least squares method. Subsequently, after maintaining a constant heating power to bring the system to thermal equilibrium at 220°C, a step velocity signal (e.g., from 0 to 200 mm / min) was applied to the moving mechanism, and the dynamic decrease in local temperature was recorded. Similarly, the coupling equivalent coefficient of mechanical motion to heat dissipation was obtained through fitting. .

[0043] Linear convection heat dissipation coefficient Calibration: Based on Newton's law of cooling, in the low-temperature range below 100℃ (where the thermal radiation effect is weak and can be approximately ignored), the heating power was cut off and the cooling curve of the PDMS printed part 7 under natural convection conditions was recorded. A first-order exponential decay model was used to fit the cooling data, and its time constant was extracted, which was then converted into the linear convection heat dissipation coefficient. .

[0044] Higher-order radiative heat dissipation coefficient Calibration: Since this embodiment involves a high-temperature curing range of 150°C to 250°C, the radiation terms must be accurately calibrated based on the Stefan-Boltzmann law. Based on this, the natural cooling curve of the system in the target high-temperature range was measured. The slope of the total heat loss was subtracted from the curve of the system under natural cooling. The determined linear part is the remaining nonlinear heat dissipation and the fourth-order variance term of the current temperature. Regression fitting is performed to extract the higher-order radiative heat dissipation coefficient applicable to the surface of PDMS materials. .

[0045] Step S3: Set the multi-objective cost function and apply hard constraints to the physical boundaries.

[0046] In the optimization module of host computer 1, a multi-objective cost function that balances temperature tracking accuracy and printing motion efficiency is constructed. J : ; In the formula, In this embodiment, the temperature tracking weight is set to 100 to compensate for the difference in dimensions between temperature and speed, and to ensure extremely high thermal sensitivity. As a speed efficiency weight, this embodiment sets it to 1 to release the control degree of the speed variable, allowing it to participate in flexible optimization as an auxiliary temperature control method.

[0047] Before performing the optimization solution, the algorithm forcibly imposes the hardware's rated limits as explicit hard constraints: based on the rated power limit setting of the mica heating plate 3. (This embodiment uses 600W); Rheological flow interruption limit setting based on pneumatic extrusion. (In this embodiment, the speed is 300 mm / min). This measure eliminates the risk of integral saturation and dangerous command output from the algorithm's underlying layer.

[0048] Step S4: Online rolling optimization solution.

[0049] Within a very short sampling period of 50ms, the SLSQP (Sequential Least Squares Programming) solver deployed on host computer 1 is activated. This solver is specifically designed to handle nonlinear optimization problems with multidimensional hard boundary constraints. It solves the nonlinear cost function within the multidimensional feasible region space formed by these hard constraints. J A high-speed iterative optimization is performed to find a set of optimal future control command sequences that minimize the overall cost.

[0050] Step S5: Instruction output and time-domain advancement.

[0051] Following the rolling time-domain principle of model predictive control, the system only extracts the first action combination from the optimal sequence. The host computer 1 sends the command to the motion control board 2, which then drives the mica heating plate 3 to execute the corresponding power at the physical layer, and simultaneously drives the three-axis motion mechanism 5 to run at the corresponding speed. After execution, the system time is recorded. Then return to step S1 for the next round of closed-loop rolling optimization.

[0052] Experimental results and verification of physical mechanisms: To verify the dynamic control performance of this embodiment in in-situ curing of soft materials, Figures 3 to 5The measured data response of the system was demonstrated over 100 consecutive sampling cycles (a total of 5 seconds of ultra-fast transient control).

[0053] Combination Figure 3 and Figure 4 It is evident that during the initial startup phase, facing a significant temperature potential difference of up to 70°C between the initial system temperature (150°C) and the target temperature (220°C), the NMPC solver accurately and decisively addresses the hard constraints of the physical boundary, outputting a full-load saturated heating power of 600W for several consecutive cycles. This maximization-driven boundary optimization strategy allows the actual observed temperature to rise rapidly with a steep, hysteresis-free slope, significantly shortening the system's cold start-up and interlayer curing waiting time. When the measured temperature approaches the 220°C target temperature, the nonlinear prediction model anticipates the system's thermal inertia in advance. Figure 4 The heating power experienced a sharp, step-like drop, eventually settling into a stable, slightly oscillating range around 160W. This physical phenomenon fully demonstrates the algorithm's superior resistance to integral saturation and its ability to compensate for steady-state heat dissipation. The 160W power maintained in steady state precisely offsets the combined heat loss from linear convection and high-order nonlinear thermal radiation, effectively suppressing temperature overshoot and pyrolysis carbonization phenomena commonly encountered in traditional PID control during soft material printing.

[0054] At the same time, such as Figure 5 As shown, under extreme conditions where the heating power changes drastically by several times in the early stages to mitigate thermal field errors, thanks to the algorithm's multi-dimensional decoupling mechanism, the final output optimized speed command... The speed consistently converges precisely to the desired setpoint of 200 mm / min. This demonstrates that the present invention successfully achieves the highly challenging thermo-mechanical dual-field coordinated control without sacrificing mechanical forming stability.

[0055] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An additive manufacturing control method based on multidimensional constrained nonlinear model predictive control, characterized in that, Includes the following steps: (1) Obtain the process status data of the current control cycle, including the target curing temperature of the soft material, the expected printing speed, and the measured temperature collected by the sensor; and calculate the model mismatch error based on the measured temperature and the predicted temperature; the specific process is as follows: (1-1) At the start of the current control cycle, read the set target curing temperature of the soft material. With expected printing speed ; (1-2) The measured temperature is obtained by sensors deployed in the printing area, and noise reduction is performed using the Kalman filter algorithm to obtain the effective observed temperature at the current moment. ; (1-3) Effective observation temperature Theoretical predicted temperature output from the previous control cycle The model mismatch error is calculated by performing a difference operation. As closed-loop correction feedback; (2) Construct a nonlinear differential prediction model that couples heating power and printing speed, in which printing speed is used as an auxiliary heat dissipation variable to participate in the thermal evolution calculation, and introduce a nonlinear term to characterize higher-order thermal radiation loss in the nonlinear differential prediction model. The specific process is as follows: (2-1) Determine the control power of the heating plate For active thermal input variables, printhead travel speed To assist in the calculation of heat dissipation variables, a basic state evolution mechanism is constructed by combining linear environmental convective heat dissipation. (2-2) Based on the Stefan-Boltzmann law, a high-order nonlinear thermal radiation loss term is introduced, with the difference between the fourth power of the current temperature and the fourth power of the ambient temperature as the core variable. (2-3) Mismatch error of fusion model A nonlinear differential prediction model with closed-loop feedback characteristics was established. (3) Set a multi-objective cost function that includes temperature tracking error penalty and printing efficiency deviation penalty, and force dynamic physical boundary constraints on heating power and printing speed; the expression of the multi-objective cost function is as follows: ； in, To predict the time domain, To control the time domain, For temperature tracking weights, Speed ​​efficiency weighting; Indicates in Always looking towards the future Predicted temperature at any given time. Indicates in Always looking towards the future Optimization command value for moment-to-moment speed; (4) Call the numerical optimization solver within a sampling period to solve for the optimal control command sequence that minimizes the cost function within the physical boundary constraints; (5) Extract the first action combination in the optimal control instruction sequence as the actual control instruction for output execution, and step to the next sampling period after execution.

2. The additive manufacturing control method based on multidimensional constrained nonlinear model predictive control according to claim 1, characterized in that, In step (1), the soft material is a silicone material or hydrogel material with thermosetting properties, and its target curing temperature is set between 150°C and 250°C.

3. The additive manufacturing control method based on multidimensional constrained nonlinear model predictive control according to claim 1, characterized in that, The specific formula for the nonlinear difference prediction model is as follows: ； in, For the predicted temperature at the next moment, The effective observed temperature at the current moment. The power gain coefficient, For velocity coupling coefficient, The linear convection heat dissipation coefficient is... For higher-order radiative heat dissipation coefficient, The ambient temperature.

4. The additive manufacturing control method based on multidimensional constrained nonlinear model predictive control according to claim 1, characterized in that, In step (3), dynamic physical boundary constraints are forcibly applied to the heating power and printing speed, specifically including: Apply power constraint to the heating plate ,in, The upper limit of heating power set for the system. Set between 400W and 800W; Apply printing speed constraints to the extrusion motor ,in, The maximum printing speed set for the system. Set between 100 mm / min and 500 mm / min.

5. The additive manufacturing control method based on multidimensional constrained nonlinear model predictive control according to claim 1, characterized in that, In step (4), the numerical optimization solver uses the L-BFGS algorithm or the SQP algorithm with limited memory to complete the online rolling solution of the nonlinear programming problem within each sampling period of 50ms to 100ms.

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