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This paper discusses fractional-order repetitive control (RC) to advance the quality of periodic energy deposition in laser-based additive manufacturing (AM). It addresses an intrinsic RC limitation when the exogenous signal frequency cannot divide the sampling frequency of the sensor, e.g., in imaging-based control of fast laser-material interaction in AM. Three RC designs are proposed to address such fractional-order repetitive processes. In particular, a new multirate RC provides superior performance gains by generating high-gain control exactly at the fundamental and harmonic frequencies of exogenous signals. Experimentation on a galvo laser scanner in AM validates effectiveness of the designs.
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... In particular, by applying high-precision lasers or electron beams as the energy source, powder bed fusion (PBF) AM has enabled unprecedented fabrication of complex parts from polymeric and metallic powder materials. However, broader adoption of the technology remains challenged by insufficient relia- * Corresponding author bility and in-process variations induced by, for example, uncertain laser-material interactions, environmental vibrations, powder recycling, imperfect interactions of mechanical components, and recursive thermal histories of materials [1][2][3][4][5]. ...
... The input signals fed to the FEM include a pseudorandom binary sequence (PRBS) signal and multiple sinusoidal signals (10~300 Hz), with a magnitude of 20 W and an add-on DC component of q 0 = 60 W. As shown in Fig. 3, the frequency responses of the measured and identified systems match well with each other. From a physics viewpoint, the low-pass dynamics is attributed to the high-density energy deposition of the laser and the first-order temporal dynamics of the temperature evolution in (1). Under the sampling time t s of 0.5 ms, the zero-order-hold equivalent of the plant model is P d (z) = 6.493 × 10 −7 /(z − 0.5901). ...
... is the complementary sensitivity function [1]. ...
Preprint
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Despite the advantages and emerging applications, broader adoption of powder bed fusion (PBF) additive manufacturing is challenged by insufficient reliability and in-process variations. Finite element modeling and control-oriented modeling have been shown to be effective for predicting and engineering part qualities in PBF. This paper first builds a finite element model (FEM) of the thermal fields to look into the convoluted thermal interactions during the PBF process. Using the FEM data, we identify a novel surrogate system model from the laser power to the melt pool width. Linking a linear model with a memoryless nonlinear sub-model, we develop a physics-based Hammerstein model that captures the complex spatiotemporal thermomechanical dynamics. We verify the accuracy of the Hammerstein model using the FEM and prove that the linearized model is only a representation of the Hammerstein model around the equilibrium point. Along the way, we conduct the stability and robustness analyses and formalize the Hammerstein model to facilitate the subsequent control designs.
... In particular, by applying high-precision lasers or electron beams as the energy source, powder bed fusion (PBF) AM has enabled unprecedented fabrication of complex parts from polymeric and metallic powder materials. However, broader adoption of the technology remains challenged by insufficient relia- * Corresponding author bility and in-process variations induced by, for example, uncertain laser-material interactions, environmental vibrations, powder recycling, imperfect interactions of mechanical components, and recursive thermal histories of materials [1][2][3][4][5]. ...
... The input signals fed to the FEM include a pseudorandom binary sequence (PRBS) signal and multiple sinusoidal signals (10~300 Hz), with a magnitude of 20 W and an add-on DC component of q 0 = 60 W. As shown in Fig. 3, the frequency responses of the measured and identified systems match well with each other. From a physics viewpoint, the low-pass dynamics is attributed to the high-density energy deposition of the laser and the first-order temporal dynamics of the temperature evolution in (1). Under the sampling time t s of 0.5 ms, the zero-order-hold equivalent of the plant model is P d (z) = 6.493 × 10 −7 /(z − 0.5901). ...
... is the complementary sensitivity function [1]. ...
Article
Full-text available
Despite the advantages and emerging applications, broader adoption of powder bed fusion (PBF) additive manufacturing is challenged by insufficient reliability and in-process variations. Finite element modeling and control-oriented modeling have been identified fundamental for predicting and engineering part qualities in PBF. This paper first builds a finite element model (FEM) of the thermal fields to look into the convoluted thermal interactions during the PBF process. Using the FEM data, we identify a novel surrogate system model from the laser power to the melt pool width. Linking a linearized model with a memoryless nonlinear submodel, we develop a physics-based Hammerstein model that captures the complex spatiotemporal thermomechanical dynamics. We verify the accuracy of the Hammerstein model using the FEM and prove that the linearized model is only a representation of the Hammerstein model around the equilibrium point. Along the way, we conduct the stability and robustness analyses and formalize the Hammerstein model to facilitate the subsequent control designs.
... If the nearest integer of is used in RC, the tracking performance is deteriorated significantly. To address this problem, multirate RC is proposed so that RC is implemented with a variable sampling rate to make an integer [24,25]. However, the implementation of varied control structure is complex and may result in destabilization. ...
... Z. Feng et al. Substituting (25) into (24), it is obtained that ...
Article
The development of nanotechnology requires a precision tracking of periodic signals in order to complete repetitive industrial or scientific tasks. Although repetitive control is an intuitive choice to realize precisely periodic signal’s tracking, an integer number should match the period of signals for a digital control system otherwise the performance would be deteriorated significantly. Thus, in this paper, a fractional delay filter based repetitive control (FDFRC) is developed to achieve precision signal tracking with arbitrary periods. According to the internal model principle, a fractional delay filter with the spectrum-selection property is designed by using of a Farrow structure to address integer/non-integer delays. The stability of FDFRC is also given and analyzed in frequency domain to facilitate controller implementation. The proposed FDFRC allows an easy, simple and practical realization with only one parameter to be adjusted for different integer/non-integer delays. Comparative experiments with different frequencies of triangular waves for x axis and Lissajous scanning for x–y plane on a piezoelectric nanopositioning stage are conducted to further verify the significant improvements on the tracking performance of the proposed controller.
... However, broader adoption of the technology remains challenged by insufficient reliability and in-process variations. These variations are induced by, for example, uncertain laser-material interactions, environmental vibrations, powder recycling, imperfect interactions * Corresponding author of mechanical components, and complex thermal histories of materials [1][2][3]. ...
... Besides the bidirectional scan, other scan patterns yield similar repetitive disturbances (see, e.g., experimental results in [32]). To deal with these undesired repetitive spectra, we develop the closed-loop simulation in Section 2 to bring automatic control algorithms [1,33] into FEM. More results and analyses will be elaborated in Section 5. ...
Article
Full-text available
A high-precision additive manufacturing process, powder bed fusion (PBF) has enabled unmatched agile manufacturing of a wide range of products from engine components to medical implants. While finite element modeling and closed-loop control have been identified key for predicting and engineering part qualities in PBF, existing results in each realm are developed in opposite computational architectures wildly different in time scale. This paper builds a first-instance closed-loop simulation framework by integrating high-fidelity finite element modeling with feedback controls originally developed for general mechatronics systems. By utilizing the output signals (e.g., melt pool width) retrieved from the finite element model (FEM) to update directly the control signals (e.g., laser power) sent to the model, the proposed closed-loop framework enables testing the limits of advanced controls in PBF and surveying the parameter space fully to generate more predictable part qualities. Along the course of formulating the framework, we verify the FEM by comparing its results with experimental and analytical solutions and then use the FEM to understand the melt-pool evolution induced by the in- and cross-layer thermomechanical interactions. From there, we build a repetitive control algorithm to attenuate variations of the melt pool width.
... However, broader adoption of the technology remains challenged by insufficient reliability and in-process variations. These variations are induced by, for example, uncertain laser-material interactions, environmental vibrations, powder recycling, imperfect interactions * Corresponding author of mechanical components, and complex thermal histories of materials [1][2][3]. ...
... Besides the bidirectional scan, other scan patterns yield similar repetitive disturbances (see, e.g., experimental results in [32]). To deal with these undesired repetitive spectra, we develop the closed-loop simulation in Section 2 to bring automatic control algorithms [1,33] into FEM. More results and analyses will be elaborated in Section 5. ...
Preprint
Full-text available
A high-precision additive manufacturing process, powder bed fusion (PBF) has enabled unmatched agile manufacturing of a wide range of products from engine components to medical implants. While finite element modeling and closed-loop control have been identified key for predicting and engineering part qualities in PBF, existing results in each realm are developed in opposite computational architectures wildly different in time scale. This paper builds a first-instance closed-loop simulation framework by integrating high-fidelity finite element modeling with feedback controls originally developed for general mechatronics systems. By utilizing the output signals (e.g., melt pool width) retrieved from the finite element model (FEM) to update directly the control signals (e.g., laser power) sent to the model, the proposed closed-loop framework enables testing the limits of advanced controls in PBF and surveying the parameter space fully to generate more predictable part qualities. Along the course of formulating the framework, we verify the FEM by comparing its results with experimental and analytical solutions and then use the FEM to understand the melt-pool evolution induced by the in-and cross-layer thermomechan-ical interactions. From there, we build a repetitive control algorithm to attenuate variations of the melt pool width.
... Instead of applying ILC, several studies have proposed using repetitive control (RC) for quick adaption of online reference variations in galvanometer-based raster scanning, such as the fraction-order RC (Wang & Chen, 2018) and local loop-shaping RC (Jiang, Xiao, Tang, Sun, & Chen, 2019). The structure of RC is the same as that of noreset ILC. ...
Article
Data-driven repetitive control (RC) is proposed in this work to track online, dynamical raster trajectories in galvanometer-based scanning. To remove the requirement of a plant model in conventional model-based RC, we use model-free iterative learning control (ILC) to synthesize the data-driven repetitive controllers. Specifically, the frequency-domain plant-inversion and loop-shaping methods are both converted into time-domain trajectory tracking problems. The ILC is then applied to solve the trajectory tracking problems and subsequently derive the repetitive controllers from data. The stability conditions of both methods are analyzed and used to guide the data-driven control design. Experimental results on a commercially available galvanometer scanner demonstrate that the proposed methods improve the tracking error of a predefined raster scan by more than 30 times, as the conventional ILC does. Moreover, after applying data-driven RC, users can online assign various center positions and magnitudes of the raster trajectory. Once assigning a new reference in this continuous mode, the tracking error rapidly converges to the steady-state within ten periods.
... This hybrid control system was able to stabilize layer growth by avoiding over-building and compensating under-building through control of the process heat input. Wang and Chen [105] proposed to use fractional-order repetitive control (RC) to advance the quality of laser based AM. In this work, three RC designs were proposed to address fractional-order repetitive processes. ...
Article
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Wire arc additive manufacturing technology (WAAM) has become a very promising alternative to high-value large metal components in many manufacturing industries. Due to its long process cycle time and arc-based deposition, defect monitoring, process stability and control are critical for the WAAM system to be used in the industry. Although major progress has been made in process development, path slicing and programming, and material analysis, a comprehensive process monitoring, and control system are yet to be developed. This paper aims to provide an in-depth review of sensing and control design suitable for a WAAM system, including technologies developed for the generic Arc Welding process, the Wire Arc Additive Manufacturing process and laser Additive Manufacturing. Particular focus is given to the integration of sensor-based feedback control, and how they could be implemented into the WAAM process to improve its accuracy, reliability, and efficiency. The paper concludes by proposing a framework for sensor-based monitoring and control system for the GMAW based WAAM process. This framework provides a blueprint for the monitoring and control strategies during the WAAM process and aims to identify and reduce defects using information fusion techniques.
Chapter
Metal Additive Manufacturing (AM) is a state-of-the-art manufacturing technology which has emerged rapidly in the last decade as observed from the growth in its global market. AM’s impact relies on products and supply chains in numerous industries such as automobiles, consumer electronics, aerospace, and medical devices. While industrial AM systems for polymer materials can produce reasonable quality for customers, AM for metallic materials still has room for quality improvement.
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Metal additive manufacturing (AM) has been intensively advanced due to numerous industrial applications, such as automobiles, aerospace, consumer electronics, and medical devices. The dynamics of the melt pool via laser sintering for metal AM has been studied by means of the thermodynamic phase change model known as the "Stefan problem". In this article, we develop a control design for the laser power to drive the depth of the melt pool to the desired set point. The governing equation is described by a partial differential equation (PDE) defined on a time-varying spatial domain, which is dependent on the PDE state, and the optical penetration of the laser energy affects the PDE dynamics in the domain as well as at the surface boundary. First, we design the full-state feedback control law utilizing the entire spatial profile of the temperature in the melt pool and the moving interface position. The closed-loop system is proven to satisfy some conditions to validate the physical model, and its origin is shown to be exponentially stable. Next, we propose an observer-based output feedback control law by reconstructing the temperature profile with the availability of only the measured interface position and prove the analogous properties of the closed-loop system. Numerical simulation for a controller designed on a single-phase Stefan model is conducted on a more complex and realistic two-phase Stefan model, which incorporates the cooling effect from the solid phase. In addition, a bias in the interface location measurement is considered. The numerical results illustrate the robustness of the proposed feedback. By lowering the initial temperature in the solid and by increasing the interface sensor bias to more extreme levels, which leads to the controller's failure (where the failure is exhibited through the entire metal freezing and the melt pool disappearing), we explore the limits of how much uncertainty our control law can handle.
Conference Paper
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This paper studies repetitive control (RC) algorithms to advance the quality of repetitive energy deposition in laser-based additive manufacturing (AM). An intrinsic limitation appears in discrete-time RC when the period of the exogenous signal is not an integer multiple of the sampling time. Such a challenge hampers high-performance applications of RC to laser-based AM because periodicity of the exogenous signal has no guarantees to comply with the sampling rate of molten-pool sensors. This paper investigates three RC algorithms to address such fractional-order RC cases. A wide-band RC and a quasi RC apply the nearest integer approximation of the period, yielding overdetermined and partial attenuation of the periodic disturbance. A new multirate RC generates high-gain control signals exactly at the fundamental frequency and its harmonics. Experimentation on a dual-axis galvo scanner in laser-based AM compares the effectiveness of different algorithms and reveals fundamental benefits of the proposed multirate RC.
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Many servo systems require micro/nano-level positioning accuracy. This requirement sets a number of challenges from the viewpoint of sensing, actuation, and control algorithms. This article considers control algorithms for precision positioning. We examine how prior knowledge about the parameterization of control structure and the disturbance spectrum should be utilized in the design of control algorithms. An outer-loop inverse-based Youla–Kucera parameterization is built in the article. The presented algorithms are evaluated on a tutorial example of a galvo scanner system.
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Repetitive control (RC) with linear phase lead compensation provides a simple but very effective control solution for any periodic signal with a known period. Multirate repetitive control (MRC) with a downsampling rate can reduce the need of memory size and computational cost, and then leads to a more feasible design of the plug-in repetitive control systems in practical applications. However, with fixed sampling rate, both MRC and its linear phase lead compensator are sensitive to the ratio of the sampling frequency to the frequency of interested periodic signals: (1) MRC might fails to exactly compensate the periodic signal in the case of a fractional ratio; (2) linear phase lead compensation might fail to enable MRC to achieve satisfactory performance in the case of a low ratio. In this paper, a universal fractional-order design of linear phase lead compensation MRC is proposed to tackle periodic signals with high accuracy, fast dynamic response, good robustness, and cost-effective implementation regardless of the frequency ratio, which offers a unified framework for housing various RC schemes in extensive engineering application. An application example of programmable AC power supply is explored to comprehensively testify the effectiveness of the proposed control scheme.
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A linear feedback control is applied in high accuracy tracking of a periodic reference input. Asymptotic tracking of an input with a given period is achieved by locating the imaginary poles of the controller's transfer function to suit the period of the input. A frequency-domain analysis of the transient and noise characteristics leads to a simple controller design principle. The method was applied to the computer control of the 27-MVA thyristor power supply to the three main ring magnets of a proton synchrotron. The 10⁻⁴ tracking accuracy required of the exciting current control was achieved after 16 cycles of a pulsed operation.
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Additive manufacturing (AM) is pushing towards industrial applications. But despite good sales of AM machines, there are still several challenges hindering a broad economic use of AM. This keynote paper starts with an overview over laser based additive manufacturing with comments on the main steps necessary to build parts to introduce the complexity of the whole process chain. Then from a manufacturing process oriented viewpoint it identifies these barriers for Laser Beam Melting (LBM) using results of a round robin test inside CIRP and the work of other research groups. It shows how those barriers may be overcome and points out research topics necessary to be addressed in the near future.
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Iterative learning control (ILC) is a method for improving the performance of stable, repetitive systems. Standard ILC is constructed in the temporal domain, with performance improvements achieved through iterative updates to the control signal. Recent ILC research focuses on reformulating temporal ILC into the spatial domain, where 2D convolution accounts for spatial closeness. This work expands spatial ILC to include optimization of multiple performance metrics. Performance objectives are classified into primary, complementary, competing, and domain specific objectives. New robustness and convergence criteria are provided. Simulation results validate flexibility of the spatial framework on a high-fidelity additive manufacturing system model.
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