Weighting Matrix Design for Robust Monotonic Convergence in Norm Optimal Iterative Learning Control

In this paper we examine the robustness of norm optimal ILC with quadratic cost criterion for discrete-time, linear time-invariant, single-input single-output systems. A bounded multiplicative uncertainty model is used to describe the uncertain system and a sufficient condition for robust monotonic convergence is developed. We find that, for sufficiently large uncertainty, the performance weighting can not be selected arbitrarily large, and thus overall performance is limited. To maximize available performance, a time-frequency design methodology is presented to shape the weighting matrix based on the initial tracking error. The design is applied to a nanopositioning system and simulation results are presented

Robustness Analysis of Slow Learning in Iterative Learning Control Systems

This paper examines robust stability and robust transient growth in Iterative Learning Control (ILC). It is well known that small perturbations in system dynamics can result in very large transient growth of some ILC systems. Even larger perturbations can result in instability. One ad hoc technique commonly employed to improve robustness is to slow the learning rate by reducing the learning filter gain or lowpass filtering the error signal. Here, pseudospectra analysis is used to analyze the robustness of ILC algorithms with slow learning. It is found that robustness bounds can be increased and transient growth decreased with decreasing learning gain. This result provides a new theoretical foundation for tuning approaches for improving robustness

Towards Transient Growth Analysis and Design in Iterative Learning Control

In this article the problem of bounding transient growth in iterative learning control (ILC) is examined. While transient growth is not a desirable property, the alternative, robust monotonic convergence, leads to fundamental performance limitations. to circumvent these limitations, this article considers the possibility that some transient growth, if properly limited, is a viable and practical option. Towards this end, this article proposes tools for analysing worst-case transient growth in ILC. the proposed tools are based on pseudospectra analysis, which is extended to apply to ILC of uncertain systems. Two practical problems in norm-optimal ILC weighting parameter design are considered. Using the presented tools, it is demonstrated that successful design in the transient growth regime is possible, i.e. the transient growth is kept small while significantly improving asymptotic performance, despite model uncertainty

Application of a Variable Path Length Repetitive Process Control for Direct Energy Deposition of Thin-Walled Structures

Direct Energy Deposition (DED) Additive Manufacturing is Well Suited to Fabricating Large Thin-Walled Metal Structures Such as Rocket Nozzles but Suffers from Layer-To-Layer Defect Propagation. Propagating Defects May Exhibit as Slumping or a Ripple in Bead Geometry. Recent Works Have Used Repetitive Process Control (RPC) Methods for Additive Manufacturing to Stabilize the Layer-Wise Defect Propagation, But These Methods Require Repetition of the Same Path. However, Typical Thin-Wall DED Applications, Sometimes Referred to as Vase Structures, Have Changing Paths with Each Layer Such as Expanding or Contracting Diameters and Changing Profiles. This Paper Presents an Extension to Optimal RPC that Uses a Geometric Mapping Method in the Learning Algorithm to Project Previous Layer Defects onto the Current Layer, Even When Paths Are of Differing Profile and Length. the Novel Method is Implemented on a DED System and Sample Parts with Layer-Changing Geometry Are Printed. the Experimental Results Demonstrate that the Method is Capable of Stabilizing the Layer-To-Layer Ripple Instability and Producing Parts of Good Quality

Analysis of Transient Growth in Iterative Learning Control Using Pseudospectra

In this paper we examine the problem of transient growth in Iterative Learning Co ntrol (ILC). Transient growth is generally avoided in design by using robust monotonic convergence (RMC) criteria. However, RMC leads to fundamental performance limitations. We consider the possibility of allowing safe transient growth in ILC algorithms as a means to circumvent these limitations. Here the pseudospectra is used for the first time to study transient growth in ILC. Basic properties of the pseudospectra that are relevant to the ILC problem are presented. Two ILC design problems are considered and examined using pseduospectra. The pseudospectra provides new results for these problems and illuminates the oft-misunderstood problem of transient growth

Spatial Transformation of a Layer-To-Layer Control Model for Selective Laser Melting

Selective Laser Melting (SLM) is an Additive Manufacturing (AM) technique with challenges in its complexity of process parameters and lack of control schemes. Traditionally, people tried time-domain or frequency-domain control methods, but the complexity of the process goes beyond these methods. In this paper, a novel spatial transformation of SLM models is proposed, which transforms the time-domain process into a spatial domain model and, thus, allows for state-space layer-to-layer control methods. In a space domain, this also provides the convenience of modelling laser path changes. Finally, a layer-to-layer Iterative Learning Control (ILC) method is designed and demonstrates the methodology of spatial control for SLM. A simulation demonstrates its application and performance

Design of a Linear Time-Varying Cross-Coupled Iterative Learning Controller

In many manufacturing applications contour tracking is more important than individual axis tracking. Many control techniques, including iterative learning control (ILC), target individual axis error. Because individual axis error only indirectly relates to contour error, these approaches may not be very effective for contouring applications. Cross-coupled ILC (CCILC) is a variation on traditional ILC that targets the contour tracking directly. In contour trajectories with rapid changes, high frequency control is necessary in order to meet tracking requirements. This paper presents an improved CCILC that uses a linear time-varying (LTV) filter to provide high frequency control for short durations. The improved CCILC is designed for raster-scan tracking on a Cartesian robotic test platform. Analysis and experimental results are presented

Laser Line Scan Characterization of Geometric Profiles in Laser Metal Deposition

Laser Metal Deposition (LMD) is an additive manufacturing process in which material is deposited by blowing powdered metal into a melt pool formed by a laser beam. When fabricating parts, the substrate is subjected to motion control such that the melt pool traces a prescribed path to form each part layer. Advantages of LMD include relatively efficient powder usage, the ability to create functionally-graded parts and the ability to repair high-value parts. The process, however, is sensitive to variations in process parameters and a need for feedback measurements and closed-loop control has been recognized in the literature [1, 2]. To this end, a laser line scanner is being integrated into an LMD system at the Missouri University of Science and Technology. Measurements from the laser line scanner will provide the feedback data necessary for closed-loop control of the process. The work presented here considers characteristics of the laser line scanner as it relates to scanning LMD depositions. Errors associated with the measurement device are described along with digital processing operations designed to remove them. The parameter bead height is extracted from scans for future use in a closed-loop control strategy

Control-Oriented Modeling and Layer-to-Layer Spatial Control of Powder Bed Fusion Processes

Powder Bed Fusion (PBF) is an important Additive Manufacturing (AM) process that is seeing widespread utilization. However, due to inherent process variability, it is still very costly and time consuming to certify the process and the part. This has led researchers to conduct numerous studies in process modeling, in-situ monitoring and feedback control to better understand the PBF process and decrease variations, thereby making the process more repeatable. In this study, we develop a layer-to-layer, spatial, control-oriented thermal PBF model. This model enables a framework for capturing spatially-driven thermal effects and constructing layer-to-layer spatial controllers that do not suffer from inherent temporal delays. Further, this framework is amenable to voxel-level monitoring and characterization efforts. System output controllability is analyzed and output controllability conditions are determined. A spatial Iterative Learning Controller (ILC), constructed using the spatial modeling framework, is implemented in two experiments, one where the path and part geometry are layer-invariant and another where the path and part geometry change each layer. The results illustrate the ability of the controller to thermally regulate the entire part, even at corners that tend to overheat and even as the path and part geometry change each layer