Iterative learning control of bead morphology in Laser Metal Deposition processes

Sammons, Patrick M.; Bristow, Douglas A.; Landers, Robert G.

doi:10.1109/acc.2013.6580770

Cited by 19 publications

(6 citation statements)

References 14 publications

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“…While the more common smooth squared exponential (SE) kernel is used in this article, the Matern class of kernels could be used for systems with sharper features in the frequency response, e.g., for underdamped systems 33) and the approach could be applied to complex-valued kernels in the frequency domain. 36) The concept of model update in the frequency domain proposed here could be used with spatial-domain iterations, e.g., 37), 38) with model identification methods using repetitive trajectories, 39) and with the stable spline kernel for machine learning in the time domain 35) that guarantees bounded-inputbounded-output stability of the resulting models. Finally, the proposed approach can be used to speed up the learning of the different segments in segmented iterative control approaches, e.g.,.…”

Section: )-18)mentioning

confidence: 99%

Iterative Machine Learning for Output Tracking

Devasia

2019

IEEE Trans. Contr. Syst. Technol.

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This article develops iterative machine learning (IML) for output tracking. The inputoutput data generated during iterations to develop the model used in the iterative update. The main contribution of this article to propose the use of kernel-based machine learning to iteratively update both the model and the model-inversion-based input simultaneously. Additionally, augmented inputs with persistency of excitation are proposed to promote learning of the model during the iteration process. The proposed approach is illustrated with a simulation example. §1. IntroductionIterative learning methods, initially developed in e.g.,, 1)-3) improve the outputtracking performance by correcting the input based on the measured tracking error. For example, iterative control has led to some of the highest precision for output tracking, e.g., in scanning probe microscopy as demonstrated in, e.g.,. 4)-10) Note that sets of learned trajectories can be used to enable tracking of other trajectories, e.g., by designing the feedforward control input using pre-specified basis functions e.g., using polynomial functions 11) or rational functions of the reference trajectory. 12) Similarly, new desired output can be generated by considering different combinations of previously-learned output segments 13) and the feedforward can be represented using radial basis functions that can be optimized for a range of task parameters. 14) This article proposes a kernel-based machine learning approach to use augmented inputs to iteratively learn not just the inverse input u d needed to track a specified output y d but to also use the data acquired during the iteration process to to estimate both (i) the modelĝ (and its inverse) for the control update, as well as (ii) the model uncertainty needed to establish bounds on the iteration gain for ensuring trackingerror reduction..Conditions for convergence of iterative methods have been well studied in literature, e.g.,. 15)-24) For example, the need to invert the system g to find the perfect input u d for tracking a desired output y d has motivated the use of the inversê g −1 of the known modelĝ of the system g in early iterative control development. 3) Since convergence depends on the size of modeling error, improvements of the model through parameter adaptation with data acquired during the iteration was studied in, e.g., 25) for robotics application using a discrete-time implementation. Here, for each iteration step, the sampled input vector is mapped to the sampled output vector through a lower triangular matrix map. A stochastic version using such a lower-triangular map has been studied in. 26) Even in the ideal case with no mod- * ) S. Devasia is with the Mechanical Engineering Department, U.

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Section: )-18)mentioning

confidence: 99%

Iterative Machine Learning for Output Tracking

Devasia

2019

IEEE Trans. Contr. Syst. Technol.

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“…Comparatively much less work has been reported on the stability of nonlinear multidi-mensional systems, see, e.g., Pakshin et al (2011b); Kurek (2012); Yeganefar et al (2013) and references therein. Further support for the development of a stability and stabilization theory for nonlinear repetitive processes is supplied by examples such as ILC applied to bead morphology in laser metal deposition processes (Sammons et al, 2013). This paper begins by developing new results on the stability of differential nonlinear repetitive processes using vector Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

Stability and Stabilization of Differential Nonlinear Repetitive Processes with Applications

Emelianov

Pakshin

Gałkowski

et al. 2014

IFAC Proceedings Volumes

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“…In [13,14], the stability of discrete and differential nonlinear repetitive processes was considered and there is a need to extend this work to allow control law design. Among recent possible applications for repetitive process control theory in the nonlinear model setting are metal deposition processes [15] and wind turbine control [16]. This paper starts from the results in [17] and establishes new results on the stabilization of nonlinear differential repetitive processes by a nonstandard application of vector Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

“…Then using the Schur complement lemma, routine calculations and convexity properties, the inequalities (5.14) are reduced to the following coupled set of linear matrix inequalities (LMIs) with respect to these variables: 15) where…”

Section: Introduce the New Variables X(i)mentioning

confidence: 99%

Stabilization of differential repetitive processes

Emelianov¹,

Pakshin²,

Gałkowski

et al. 2015

Autom Remote Control

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Abstract-Differential repetitive processes are a subclass of 2D systems that arise in modeling physical processes with identical repetitions of the same task and in the analysis of other control problems such as the design of iterative learning control laws. These models have proved to be efficient within the framework of linear dynamics, where control laws designed in this setting have been verified experimentally, but there are few results for nonlinear dynamics. This paper develops new results on the stability, stabilization and disturbance attenuation, using an H ∞ norm measure, for nonlinear differential repetitive processes. These results are then applied to design iterative learning control algorithms under model uncertainty and sensor failures described by a homogeneous Markov chain with a finite set of states. The resulting design algorithms can be computed using linear matrix inequalities.

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Iterative learning control of bead morphology in Laser Metal Deposition processes

Cited by 19 publications

References 14 publications

Iterative Machine Learning for Output Tracking

Iterative Machine Learning for Output Tracking

Stability and Stabilization of Differential Nonlinear Repetitive Processes with Applications

Stabilization of differential repetitive processes

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