Velocity-based closed-loop control in fusion laser cutting for multi-directional and curved geometries

High power laser cutting is an established technology within the current industrial landscape for the processing of metallic sheets and tubes with millimeter-range thicknesses. Despite its widespread use, there is a fundamental interest in improving the productivity and ensuring high qualitative outcomes of process. From this perspective, the use of monitoring sensors to derive information regarding the state of the process is highly appealing to both the scientific and industrial communities. Sensors are typically employed to estimate or predict different defects. Cut quality is typically assessed based on several parameters (as listed in Ref. 1), with dross attachment and roughness of the cut edge being the primary criteria. Critical conditions arise when there is a loss of cut condition, meaning a loss of penetration and failure to separate the material. Sensing devices can capture process related information to inform the user about the qualitative outcome of the process. Among the various monitoring solutions, acoustic sensing was one of the first to be adopted, as shown by De Keuster et al.² and Kurita et al.³ However, photodiodes and camera-based techniques have quickly garnered greater interest. This shift is due to the critical limitations of microphone-based solutions, which are highly influenced by the working environment and exhibit strong directionality, as they are typically implemented in an off-axis configuration. Regarding the usage of photodiodes, Adelmann et al.^4,5 employed InGaAs and Si sensors to identify laser-induced plasma cutting conditions. The authors achieved a high detection rate of cutting tears for both stainless and mild steel by comparing the fluctuation ranges of the two signals. Adelmann et al.⁵ exploited a single InGaAs photodiode to identify loss-of-cut conditions and the end of the piercing phase. Schleier et al.⁶ found a linear correlation between the signal standard deviation and the level of dross attachment during linear cuts. The authors used Si and InGaAs photodiodes to detect loss-of-cut conditions. Although these sensors are a promising solution, there is evidence in the literature that the camera-based monitoring approaches have a strong potential, as they provide spatially resolved information. An off-axis front-view configuration offers insights into the melt flow and spark cone formation along the cut front, while a side-view configuration also reveals the inclination of the cut front, as demonstrated by Sichani et al.⁷ By exploiting information from the off-axis side-view configuration, it is possible to determine a relationship between the spark cone angle and the cutting quality, as shown by Wen et al.⁸ Additionally, this visualization provides indication regarding the risk of plasma formation⁷ and the kerf width.⁹ However, from an industrial perspective, a fixed off-axis side-view configuration significantly limits the sensors’ general applicability, as it may only be useful for evaluating the process in a single direction. For this reason, a coaxial configuration camera-based sensor is preferred for online monitoring and sensing of the process information, despite its intrinsic limitation of the observable field of view. Examples of coaxial camera-based monitoring for reactive fusion cutting can be found in the research by Poprawe¹⁰ and by Sichani et al.¹¹ The spatially resolved information provided by coaxial cameras must be analyzed in real time to provide quantitative information regarding the cut quality and typical process defects. Franceschetti et al.¹² employed a Convolutional Neural Network (CNN) to estimate the dross level in real time during fusion cutting of stainless steel. Similarly, Pacher et al.¹³ showed the potential of a Neural Network (NN) algorithm for the real-time estimation of dross formation. More recently, the same approach has been used to predict in real-time the roughness during reactive fusion cutting of mild steel.¹⁴ Adelmann and Hellman¹⁵ realized a performance comparison of Machine Learning (ML) algorithms to classify dross attachment and loss-of-cut conditions during the cutting of thin electrical sheets. Furthermore, Schleier et al.¹⁶ showed that melt pool geometrical information can be exploited to identify loss of cut conditions,¹⁷ while Levichev et al.¹⁷ correlated such data to quality indicators such as roughness during the cutting of high thickness mild steel plates. It, thus, emerges that coaxial camera-based monitoring approaches can provide reliable information of the cutting state for processing a wide range of materials. This information can be used to estimate the quality of the cut and detect faults, by the complementary use of the collected process data and ML and Artificial Intelligence (AI) techniques. Recently, advanced methods based on ML and AI models are rapidly taken over in the laser cutting framework due to their potential implementation for both real-time and post processing applications, with the goal of improving cut quality and productivity while ensuring process robustness. Schleier et al.¹⁸ exploited a high-speed camera monitoring system to develop a cutting interruption algorithm during fiber laser fusion cutting of stainless steel, zinc-coated steel, and aluminum. The developed algorithm can detect incomplete cuts with an error rate of 2.3%. Furthermore, Santolini et al.¹⁹ proposed an approach aiming at the optimization of the industrial laser cutting process, by adapting three well-known ML algorithms (Gaussian Mixture Models, Recurrent Neural Networks, Convolutional Neural Networks) to estimate cut quality in industrial laser cutting machines. Levichev et al.²⁰ developed a Multilayer Perceptrons (MLPs) algorithm to predict the roughness of materials with different reflectivity behavior, instead of a CNN approach²¹ that requires large training datasets. The authors conducted data augmentation to increase the available training datasets and prediction accuracy, finally quantifying the sample’s roughness. Furthermore, ML and AI techniques can be exploited to derive information about the kerf characteristics,²² which depend on the employed process parameters. Sridarane et al.²³ developed a multilayer Feed-Forward Neural Network (FFNN) to predict the kerf width during CO₂ mild steel laser cutting.

Moreover, the collected sensors data, together with ML and AI techniques, can be integrated into feedback control algorithms to regulate process parameters in real time, ensuring iso-quality conditions during the process. Sichani et al. and Duflou et al. explored how using camera-based information could maintain reference quality condition.^11,17,24 Pacher et al., on the other hand, developed an approach to maximize the cutting velocity while maintaining a reference dross level.^13,25,26 Similarly, Wen et al. proposed a velocity regulation algorithm to obtain the best cut quality.⁸ From an industrial perspective, there is evidence that such technological advances are being exploited as demonstrated by Trumpf with the Active Speed Control.²⁷ The current literature review indicates that laser cutting technology has achieved maturity, with a wide range of solutions exploiting process monitoring and feedback control approaches to guarantee high quality cuts. However, one of the most significant limitations of these research works is the applicability of the solutions, which is limited to linear monodirectional cuts. One of the intrinsic characteristics and appreciated advantages of the laser cutting technology is its flexibility in processing a wide range of geometries. Therefore, there is a strong interest in extending feedback control solutions to real-case scenarios involving multidirectional and curved geometries. The present work investigates the possibility of broadening the applicability of the architecture developed by Pacher et al.^13,26 for the fusion laser cutting of multidirectional and variable curvature geometries in processing 5 mm thick stainless steel. First, the research addresses the issues related to multidirectional cuts that impact captured process emission images. By developing a robust supervised ML approach, a predictive model was developed using an NN regression to estimate dross formation. The dross estimation algorithm was validated and tested on both multidirectional cuts and curved geometries. Subsequently, a closed-loop control system was built to regulate the velocity, while maintaining a fixed level of dross. After the testing phase of the controller structure on both linear and curved trajectories, the architecture was validated by cutting a real-case complex geometry, demonstrating the system capability to maximize process productivity while maintaining elevated cut quality conditions.

In the current investigation, 5 mm thick AISI304 stainless steel sheets were used as feedstock material to perform the cutting experiments.

An industrial laser cutting machine [LC5, Adige-SYS S.p.A. BLMGroup, Levico Terme (TN), Italy] was employed to perform the experiments of the presented research activity. The associated laser source (YLS-6000-CUT, IPG Photonics, Oxford, MA) can deliver up to 6 kW of power, with an optical transport having a 100 μm core diameter. The cutting head is equipped with a collimation lens of 75 mm and a focal lens of 155 mm, yielding a beam waist diameter of 207 μm. For monitoring purposes, the cutting head is equipped with an industrial CMOS camera (xiQ MQ013MG-ON, Ximea GmbH, Münster, Germany) providing an image resolution of 6 μm/pixel over a field of view of 320 pixels × 320 pixels. The monitoring system filters the process emission in the NIR wavelength range to capture the process dynamics. The short pass filter and the band pass filter are centered, respectively, at 1000 nm and at 850 ± 10 nm. The main specifications of the laser cutting head and monitoring system are defined in Table I.

Figure 1 illustrates schematically the overall configuration of the cutting head and of the monitoring chain. The camera-based monitoring systems capture spatial information regarding the process emission as well as its intensity. The mentioned setup allows for the extraction of geometrical features from the captured process emission images of the melt pool.

The scope of this research was to develop a robust real-time estimation of the dross attachment during the laser cutting of 5 mm thick AISI304. Once the estimation algorithm was validated for its applicability on multidirectional linear cuts and curved geometries, a velocity-based feedback control of the process has been developed for productivity optimization. Previous studies have shown the possibility to correlate dross formation with the geometrical and intensity attributes provided by the camera-based monitoring system using ML algorithms.^12,13 A supervised ML approach must be employed to train the algorithm, where the extracted features are coupled to the dross measured a posteriori on the cut samples. The acquired frames and computed features must be correlated to the measured dross values and then used as a dataset for the training and testing of the ML algorithms. This approach searches for a correlation between the features and the real dross value, considering them as the input and output of an ML model, respectively. In the current research, geometrical feature values were obtained using the previously illustrated image processing procedure. To increase the dimensionality and variability of the data, the geometrical features were expressed in a probabilistic domain by calculating their mean and standard deviation over a lookback time window of 100 ms. Considering the camera acquisition framerate at 740 Hz, the images within the lookback window correspond to 74. To characterize the dross of the cut profile, a high resolution image of the cut profile was acquired through an optical coordinate measurement machine (Mitutoyo QVC-1, Mitutoyo Corporation, Kanagawa, Japan). As previously defined by Pacher et al.,¹³ the dross height profile along the length of the cut was calculated with the optical coordinate measurement machine. Each point-by-point value was then squared and binarized according to a threshold aiming at classifying the presence of a droplet. The resulting data series was converted from the space to the time domain. Finally, it was averaged over a 100 ms moving time window and matched with the input values. The final indicator was a value between 0 and 1, describing the dross as probability of appearance (i.e., where 0 corresponds to a no dross condition and 1 to high dross). The overall methodological approach for the training of the ML algorithm is illustrated in Fig. 3.

The corresponding geometrical features were associated with each of the datapoints of the dross measurement. To produce a complete dataset for the training of the dross estimate algorithm, an experimental design with different levels of cut speed was realized. The starting point of the experimental design corresponded to optimized process parameters where no dross formation occurs (i.e., with a laser power P = 6 kW, nozzle diameter d_noz = 2 mm focal position of the beam at −5.7 mm, stand-off distance of 0.7 mm, and pressure of the N₂ assist gas at 18 bar). This combination of process parameters ensures a conservative condition to prevent dross formation. As the cutting speed increases, dross formation gradually increases as well, until laser-induced plasma starts to form, eventually leading to a loss of cut condition. Hence, cutting speed was selected as one of the variable parameters, with the intention of exploiting this factor as the input of the feedback control loop. The upper limit of the cutting velocity for the experimental design was set to 6400 mm/min, which corresponded to a high level of dross formation while still avoiding plasma cutting condition that would occur at even higher cutting speed. Different cutting directions induced variability on the acquired images, consequently affecting the training of the ML model. Accordingly, cuts were performed exploring a 360° variation in the X–Y plane of the machine, with different levels equally spaced by 45° (from −135° to 180°). In this case, dross formation was not expected to be influenced by the cutting direction. Each condition was replicated three times. Consequently, a full factorial experimental plan was designed with the fixed and variable factors listed in Table II. This approach resulted in a dataset of 1 621 294 points correlating extracted geometrical features to dross measures.

Following the dataset acquisition from the experimental campaign, an NN ML regression model was trained to match the input information (features) to the output (dross). Considering the need of a real-time dross estimation, it is crucial to select the minimum number of independent features to train and compute the ML algorithm. The goal is to achieve sufficient model accuracy while maintaining low computational time. The features selection phase was realized using the Maximum Relevance Minimum Redundancy (MRMR) algorithm, which evaluates the correlation of the features with the output parameter (i.e., dross), indicating the most predictive features. Given their structure, Neural Networks are capable of interpolating nonlinear models. To explore the performance of the NN, the number of hidden layers can be modified. A sensitivity analysis was conducted to evaluate the influence of the number of selected features (5, 7, and 9 features) and the number of hidden layers (n_layer = 1–5). The model performances were evaluated based on statistical and error indicators, such as the R² coefficient and the mean absolute error (MAE) of the model. The aim was to achieve an R² coefficient above 70% with a mean absolute error below 0.05. The models were trained on 67% of the dataset using a K-fold cross-validation approach (with K = 5). The remaining part of the dataset was employed for hold-out model validation to then verify the predictive performance of the algorithm. As a final validation of the algorithm to ensure its applicability to complex geometries, the model was tested to estimate the dross formation during the cutting of circles. The diameter of the circular cuts was set to 20, 40, and 80 mm, representing different levels of curvature (respectively, corresponding to ρ = 0.1, 0.05, and 0.025 mm⁻¹). The cuts were performed at three levels of cutting speed (v = 5200, 5800, and 6400 mm/min). The other parameters were maintained constant as in the previous experimental design, and each condition was replicated two times. The fixed and variable parameters are reported in Table III.

Moving toward the industrial applicability of the described approach, a closed-loop control system was developed. The real-time dross estimation algorithm was employed to design a control architecture where the control variable is the cutting speed v, while a properly designed Proportional Integral (PI) regulator aims at tracking the reference value of dross y_r. This value is set by the user to achieve a desired cut quality. The system response ŷ corresponds to the dross estimated by the ML regression model. The architecture of the control loop is illustrated in Fig. 4.

The feedback output error e is the difference between the reference dross value y_r and the estimated dross ŷ, respectively. The error feeds the regulator R(s) to compute the cutting speed v. This allows the laser cutting system to operate at the highest value of velocity while maintaining iso-quality conditions of the cut components (thus maximizing process productivity). The proportional and integral coefficients of the controller must be tuned based on the dynamic relationship between input and output. Therefore, a system identification phase is necessary to describe this dynamic behavior with a Transfer Function (TF) G(s) in the Laplace domain. A system identification was performed by evaluating the system response ŷ to sinusoidal inputs oscillating at fixed amplitude between v = 5400 mm/min and v = 6400 mm/min and at different frequencies (0.25–10 Hz). From each of these cuts, the amplitude ratio and phase shift between the input v and output ŷ were obtained. Following the system identification, an appropriate regulator R(s) was designed to meet performance requirements, including a step response rise time lower than 0.3 s, zero steady-state error and phase margin greater than 60°. These parameters ensure that the control action guarantees accuracy and stability to the closed-loop system, thanks to the properly tuned regulator. The developed controller architecture was tested on linear cuts in different directions, circular trajectories and finally in a case study representative of a generic geometry (i.e., the logo of the Politecnico di Milano).

The amount of dross formed during the laser cutting process is strongly influenced by the cutting speed. Figure 5 shows the cut profile on different samples obtained at increasing levels of velocity (at a fixed direction θ = 0°), where it is possible to observe that the attachment of metal droplets tends to increase for higher cutting speeds. On the other hand, the cut direction did not show significant variations in terms of dross formation from the acquired profiles.

Moreover, Figs. 6(a) and 6(b) show the boxplot with respect to the cutting speed of the mean of the LengthLag at 45 binarization threshold and of the mean of the Length at 210 binarization threshold value (at a fixed direction θ = 0°). As it can be observed, the geometrical features of the melt pool are visibly influenced by the cutting speed. This is a fundamental aspect as it suggests the possibility of correlating these features with variations in the dross formation.

Furthermore, Fig. 7 illustrates representative process emission images captured in various cutting directions. Qualitative analysis indicates that the melt pool region is significantly influenced by the cutting direction. This effect is likely caused by the alignment between the imaging chain and the laser beam axis. Although the imaging system is centered on the process beam, a slight misalignment may affect the portion of observable kerf.

The qualitative trends observed in the dross formation together with the ones found on the extracted features are depicted in Fig. 8. Figure 8(a) presents the main effects plot of the average dross as a function of the cutting speed and direction. This confirms that the dross formation is highly influenced by the velocity, whereas the orientation does not impact on defect formation. Figure 8(b) shows the variation of the average value of intensity at 225 binarization threshold value. In this case, image intensity is significantly affected by both the cutting speed and the direction, with the former displaying a linear relationship and the latter an almost sinusoidal variation. Similar trends could be observed for other geometrical features indicating a dependence of the vision system on both the speed and cutting direction.

Previous studies conducted the training and testing phases of the ML algorithms solely on linear trajectories. However, the information provided in Fig. 8 suggests that an additional challenge must be addressed to achieve a truly direction independent solution. Therefore, the feature selection stage was crucial in choosing indicators, which were not influenced by the cutting direction. The training of the ML model relied on the selection of features that were statistically relevant in describing the defect formation (according to the MRMR approach), while leveraging the complexity of the Neural Network to establish direction independent relationships. The Neural Network model was trained using a subset of geometrical features and its performance in terms of the R² fitting coefficient and mean absolute error is reported in Fig. 9.

The results indicate that the most performing NN that meets the performance and computational time requirements comprises three hidden layers and utilizes nine features selected by the MRMR algorithm. The selected and employed features are represented by Intensity60_Mean, LenghtLag45_Mean, Compactness15_Mean, Circularity45_Std, Lenght45_Std, LenghtLag15_Std, Compactness30_Mean, Lenght210_Mean, and Width120_Mean, where Mean and Std, respectively, indicate the mean and standard deviation over the previously mentioned lookback window of 100 ms. This configuration meets the requirements imposed in terms of MAE and R². The highest obtained R² score, around 73%, is lower than the one obtained from the model trained and tested with monodirectional cuts (above 90%).¹³ Therefore, it can be stated that high fitting performance must be sacrificed in favor of estimation robustness with respect to the cutting direction. Moreover, as the number of features increases, the predictive accuracy of the model improves due to the larger available data. However, this also implies an increase of the computational time that could affect the real-time implementation of the dross estimation.

The optimal number of layers of the ML model is lower than the one employed by Pacher et al.¹³ for the one-direction linear cuts model. This may be related to the different generated dataset and extracted features during the dross estimation training phase. Furthermore, as the number of layers of the ML model increases, the computational time increases as well, possibly affecting the real-time implementation of the dross estimation. For this reason, the authors opted for a restricted number of layers in the NN model, reducing simultaneously the computational effort and time.

The ML model developed to estimate the dross formation was tested on the hold-out validation dataset of linear cuts. To evaluate the prediction performance, the estimated dross (ŷ) was compared to the measured dross (y). The results of the hold-out validation phase of the model are reported in Fig. 10.

Data from two representative directions and different cut velocities are reported in Fig. 10. Figure 10(a) shows data from linear cuts at θ = −90° and Fig. 10(b) shows data from cuts at θ = −45°. The measured dross displays the same trend (i.e., increasing with velocity) as depicted in the main effects plot of Fig. 8(a). The estimated dross value consistently follows the trend of the measured dross, indicating the robustness of the model. Overall, the hold-out validation exhibited an R² value of 73.2% and a mean absolute error of 0.049 mm, confirming the predictive capability of the ML model. Moreover, the model robustness was tested on circular cuts with varying curvature levels. Figure 11 shows the model performance in estimating the dross for three different curvature values at three cutting speed values. In this case, the estimated dross could not be compared to the measured value given the geometry of the sample, which could not be measured with the optical microscope on a curved surface.

However, the expected level of dross is indicated based on the average value of dross measured in the previous training experimental campaign. The model demonstrates robust performances, correctly identifying low, mid, and high dross formation conditions (corresponding to v = 5200, 5800, and 6400 mm/min, respectively). Additionally, the dross estimation algorithm predicts the defect at different levels of curvature. The most critical condition in terms of error occurs at ρ = 0.1 mm⁻¹ and v = 5800 mm/min. This aspect requires further investigation; nevertheless, the data indicate that the estimated dross eventually aligns with the expected value at the center of the cut, possibly indicating a transient behavior in the dross formation for such geometry. Overall, the ML-based dross estimation algorithm provides a robust indication of the defect formation and it can consequently be used to develop a real-time control architecture.

The computed TF presents a static gain of 0.59 × 10⁻³, two poles at 3.14 Hz and a time delay of 0.04 s. Figure 12 shows the magnitude and phase logarithmic plot of the G(s) fitting over the experimental points.

Finally, the complete control architecture was tested on linear cuts in different directions and circular trajectories. The starting cutting speed was set to a high value corresponding to high dross formation (i.e., v = 6600 mm/min), with the target dross level set at y_r = 0.02 mm (indicating low or negligible dross presence). During the cutting process, the control action was activated after an arbitrary delay, as shown in Fig. 13.

Figure 13 shows the results of the real-time control experiments. Figures 13(a) and 13(b) display the estimated dross and velocity profile for straight cuts with direction θ = 135° and θ = 0°, respectively, while Fig. 13(c) shows the controlled cut on a circular trajectory with curvature ρ = 0.05 mm⁻¹. In all of these conditions, when the control action is activated (after a small transient delay), the cutting speed is adjusted accordingly. Concurrently, the estimated dross rapidly decreases from a high dross condition (in the 0.3–0.4 mm range) to the required target level y_r = 0.02 mm. Interestingly, the cut velocity needed to achieve dross-free cuts varies between linear and circular paths. This difference may be correlated to heat propagation effects or other uncontrolled variables, requiring a slower cutting speed on the circular cut path to achieve a low dross cut, while higher velocities may be utilized on straight paths. The rise time of the control action is less than 0.3 s and the reference dross is tracked accurately and without oscillations. This demonstrates the applicability of the velocity-based closed-loop control for different directions and curved geometries cases.

In an industrial scenario, a custom geometry might simultaneously include segments with different directions and curvature levels. To demonstrate the functionality and applicability of the developed closed-loop control in an industrial environment, the architecture was tested on a complex geometry (i.e., the logo of the Politecnico di Milano). The dross reference level was set to y_r = 0.02 mm, aiming for a defect free result. The performance of the velocity regulation control is compared with a cut performed with the current industrial best practice, where speed is set at a constant velocity to ensure low dross formation (v = 5200 mm/min). Figure 14(a) shows the cut logo, while Fig. 14(b) presents the ratio between the cut velocity imposed by the active speed control and the fixed level of cutting speed.

An important consideration is that the feedback control architecture may be activated only once the cutting head has finished its transient behavior. The machine dynamics inherently impact on the speed profile, particularly during abrupt changes of direction. In such cases, the control action is deactivated. However, when a stationary cutting regime is achieved, the control action can be reactivated to improve the process productivity while maintaining iso-quality conditions. Figure 14(c) shows the dross level when the feedback control system is activated, while Fig. 14(d) compares the cut velocity imposed by the control action to the reference constant speed level. During the processing of the demonstrator geometry, the ratio reaches a maximum value of 1.24, implying a peak performance improvement of 24%, with an overall decrease in execution time of 10%. Further investigations are required to characterize the system performance across a wider range of geometries and industrial case studies. However, the feedback control approach represents a promising solution for improving process productivity, while ensuring part quality.

The present work establishes a methodological approach to develop a velocity-based feedback control architecture. A coaxial camera monitoring system was utilized to retrieve process relevant information, allowing for the correlation of the geometrical features of the melt pool with dross formation. The main results can be summarized as follows:

• A Neural Network regression model was implemented to compute a real-time estimate of the dross formation.

• A closed-loop speed regulating control action was developed employing the mentioned dross estimate. The control action was then tested and validated across a wide range of cuts on linear trajectories in different directions and circular paths, demonstrating robust predictive capabilities.

• The control architecture was tested on an industrial case scenario demonstrating the capability of the presented solution to improve process productivity while maintaining the desired cut quality levels.

• To achieve industrial applicability, further investigations are required to characterize the system performance across a wider range of geometries and industrial cases. Moreover, the implemented control action should be extended to prevent the formation of other process defects, such as loss of cut or laser-induced plasma cutting.

The Italian Ministry of Education, University and Research is acknowledged for the support provided through the National Plan of Recovery and Resilience (PNRR).

The authors have no conflicts to disclose.

Sofia Guerra: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Luca Vazzola: Conceptualization (equal); Data curation (equal); Writing – original draft (equal); Writing – review & editing (equal). Leonardo Caprio: Conceptualization (equal); Data curation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Matteo Pacher: Conceptualization (equal); Methodology (equal); Validation (equal). Davide Gandolfi: Conceptualization (equal); Supervision (equal); Validation (equal). Mara Tanelli: Supervision (equal); Writing – review & editing (equal). Sergio M. Savaresi: Supervision (equal); Writing – review & editing (equal). Barbara Previtali: Supervision (equal); Writing – review & editing (equal).