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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]. ...
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]. ...
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.
... While PBF has revolutionized the fabrication of complex parts, there are still challenges to its wider adoption. These challenges include issues with reliability and inprocess variations caused by uncertain laser-material interactions, environmental vibrations, powder recycling, imperfect interactions of mechanical components, and the recursive thermal histories of materials [1][2][3][4][5]. ...
... In controloriented modeling, [9][10][11][12] employ the low-order system models and further build the nonlinear submodels to cover more process dynamics. Based on these models, subsequent control algorithms such as PID control [13], sliding mode control [11], predictive control [9], repetitive control [2,14], iterative learning-based control [15], and iterative simulation-based control [4,16] have proven effective in improving the dimensional accuracy of printed parts. This paper presents a novel approach to modeling and examining PBF by combining finite element modeling and control-oriented modeling. ...
While powder bed fusion (PBF) additive manufacturing offers many advantages and exciting applications, its broader adoption is hindered by issues with reliability and variations during the manufacturing process. To address this, researchers have identified the importance of using both finite element modeling and control-oriented modeling to predict and improve the quality of printed parts. In this paper, we propose a novel control-oriented multi-track melt pool width model that utilizes the superposition principle to account for the complex thermal interactions that occur during PBF. We validate the effectiveness of the model by applying a finite element model of the thermal fields in PBF.
... 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 ...
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.
... To overcome this limitation, there are three main approaches: (i) Rounding-off the fractional delay to the nearest integer delay [24], which is simple but would definitely induce residual errors. (ii) Using the frequency adaptive RC approach [25]. The errors could be decreased in theory but the computational burden and implementation complexity would increase inevitably. ...
... 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. ...
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.
The so-called Stefan system describes the dynamical model of the liquid–solid phase change in materials ranging from water and ice in the polar caps to metal casting and additive manufacturing (3D printing). The mathematical structure is given by a partial differential equation (PDE) with a moving boundary governed by a scalar ordinary differential equation. Because of the system's moving-boundary nature, control of the Stefan model is unconventional even within the class of otherwise challenging PDE control problems. The second decade of the twenty-first century has witnessed remarkable advances in control design for the Stefan system. Such advances carry significant potential in several areas of technology. In this article, we briefly review the principal literature on control of the Stefan model, along with the associated basics of the PDE analysis of the model and select applications. Principal ideas from our work on control design, stability analysis, and the maintenance of physical phase constraints are given sufficient attention and tutorial treatment so that the article can serve as a self-contained point of entry into the growing subject of boundary control of the Stefan system using the method of PDE backstepping.
Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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.
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.
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.
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.
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.
While most loads on wind turbines are originated from wind speed fluctuations, they show a periodic nature with a time-varying frequency proportional to the turbine rotation. This paper exploits this relation and proposes a modified Resonant Controller able to attenuate these frequency-varying periodic disturbances. The resulting controller is designed for both partial and full load wind speed conditions, therefore, it is able to reject periodic loads even when the wind turbine system is subject to changes in the operating rotation speed. Furthermore, a novel piecewise linear representation of the system is presented allowing a systematic design procedure, based on Linear Matrix Inequalities, in order to compute the control parameters. Simulation results in a 2.5MW large scale three-bladed wind turbine illustrate the proposed method, which is able to reduce the root mean value of blade load up to 12 times when compared to a traditional LPV controller.
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.
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.
In situ experimental measurements of the laser powder bed fusion build process are completed with the goal gaining insight into the evolution of distortion in the powder bed fusion build process. Utilizing a novel enclosed instrumented system, five experimental builds are performed. Experimental builds compare materials: Ti-6Al-4V and Inconel® 718, differing build geometries, and manufacturing machines: EOS M280 and Renishaw AM250. A combination of in situ measurements of distortion and temperature and post-build measurements of final part geometry are used to compare and contrast the different experiments. Experimental results show that builds completed using Inconel® 718 distort between 50%-80% more relative to Ti-6Al-4V depending on substrate size and build geometry. The experimental build completed on the Renishaw AM250 distorted 10.6% more in the Z direction when compared with the identical build completed on the EOS M280 machine. Comparisons of post-build XY cross-sectional area show a 0.3% contraction from the predefined build geometry for the Renishaw AM250 as compared with the 4.5% contraction for the part built using the EOS M280. Recommendations and future work are also discussed.