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L2 Gain And Passivity Techniques In Nonlinear Control

Iterative Learning Control (ILC) enables high control performance through learning from measured data, using only limited model knowledge in the form of a nominal parametric model. Robust stability requires robustness to modeling errors, often due to deliberate undermodeling. The aim of this paper is to develop a range of approaches for multivariable ILC, where specific attention is given to addressing interaction. The proposed methods either address the interaction in the nominal model, or as uncertainty, i.e., through robust stability. The result is a range of techniques, including the use of the structured singular value (SSV) and Gershgorin bounds, that provide a different trade-off between modeling requirements, i.e., modeling effort and cost, and achievable performance. This allows control engineers to select the approach that fits the modeling budget and control requirements. This trade-off is demonstrated in a case study on an industrial flatbed printer.

Multivariable Iterative Learning Control Design Procedures: from Decentralized to Centralized, Illustrated on an Industrial Printer.

Iterative Learning Control (ILC) can achieve perfect tracking performance for mechatronic systems. The aim of this paper is to present an ILC design tutorial for industrial mechatronic systems. First, a preliminary analysis reveals the potential performance improvement of ILC prior to its actual implementation. Second, a frequency domain approach is presented, where fast learning is achieved through noncausal model inversion, and safe and robust learning is achieved by employing a contraction mapping theorem in conjunction with nonparametric frequency response functions. The approach is demonstrated on a desktop printer. Finally, a detailed analysis of industrial motion systems leads to several shortcomings that obstruct the widespread implementation of ILC algorithms. An overview of recently developed algorithms, including extensions using machine learning algorithms, is outlined that are aimed to facilitate broad industrial deployment.

Learning for Advanced Motion Control

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The print productivity and medium dimensions of wide-format roll-to-roll printing systems are limited by position errors induced by step-wise medium transportation. The aim of this article is to develop a design framework for multivariable repetitive control (RC), that enables improved productivity and accuracy through continuous media flow printing. The developed technical framework for RC explicitly addresses the tradeoff between performance and modeling requirements through decentralized designs. In particular, systematic design approaches are developed that explicitly address unmodeled interaction as uncertainty, i.e., through robustness. The result is a range of solutions, including 1) independent single-input single-output (SISO) designs, and 2) sequential SISO design. Experimental results confirm that the developed RC framework in conjunction with continuous media flow printing outperforms existing approaches.

/pdf/multivariable-repetitive-control-decentralized-designs-with-3r4ih38enb.pdf

Multivariable Repetitive Control: Decentralized Designs With Application to Continuous Media Flow Printing

We analyze the stability, and $\mathcal {L}_{2}$ -gain properties of a class of hybrid systems that exhibit time-varying linear flow dynamics, periodic time-triggered jumps, and arbitrary nonlinear jump maps. This class of hybrid systems encompasses periodic event-triggered control, self-triggered control, and networked control systems including time-varying communication delays. New notions on the stability, and contractivity ( $\mathcal {L}_2$ -gain strictly smaller than 1) from the beginning of the flow, and from the end of the flow are introduced, and formal relationships are derived between these notions, revealing that some are stronger than others. Inspired by ideas from lifting, it is shown that the internal stability, and contractivity in $\mathcal {L}_2$ -sense of a continuous-time hybrid system in the framework is equivalent to the stability, and contractivity in $\ell _2$ -sense (meaning the $\ell _2$ -gain is smaller than 1) of an appropriate time-varying discrete-time nonlinear system. These results recover existing works in the literature as special cases, and indicate that analysing different discrete-time nonlinear systems (of the same level of complexity) than in existing works yield stronger conclusions on the $\mathcal {L}_2$ -gain.

$\mathcal {L}_2$ -Gain Analysis of Periodic Event-Triggered Control and Self-Triggered Control Using Lifting

Neural networks have large potential for motion feedforward because of their ability to approximate a wide range of functions. The aim of this paper is to develop a systematic framework for application of neural networks to motion feedforward, that leads to an intelligent motion feedforward approach in the sense that it achieves both flexibility for varying references and high performance. Iterative learning control is used to generate training data, and a control-relevant performance function is introduced. Non-causal feedforward is enabled through two network configurations that enable respectively finite and infinite preview. The approach is experimentally validated on an industrial flatbed printer.

Control- Relevant Neural Networks for Intelligent Motion Feedforward

Iterative learning control (ILC) and repetitive control (RC) enable high performance for systems that execute repeating tasks. The aim of this paper is to provide an introduction to the design of ILC algorithms for motion systems and to indicate important recent developments. To enforce robust convergence, the design of ILC/RC algorithms often require detailed parametric specifications of the nominal model and its uncertainty. In this paper, a frequency-domain design procedure is outlined that enables robust design through using FRF measurements, which are often inexpensive, accurate and fast to obtain. Application to a consumer electronic printer is reported.

/pdf/frequency-domain-design-of-iterative-learning-control-and-d6afcwi9x5.pdf

Frequency domain design of iterative learning control and repetitive control for complex motion systems

Iterative learning control (ILC) enables highperformance output tracking at sampling instances for systems that perform repetitive tasks. The aim of this paper is to present a state tracking ILC framework that reduces oscillatory intersample behavior often encountered in output tracking ILC. A multirate inversion is performed to achieve state tracking in ILC, which achieves perfect state tracking at every $n$ samples, where $n$ denotes system order. Consequently, this improves the intersample tracking performance. Moreover, convergence criteria based on frequency response data are derived and exploited in a design approach. The approach is successfully applied to a motion system confirming improved intersample tracking accuracy compared to standard frequency domain ILC.

Multirate State Tracking for Improving Intersample Behavior in Iterative Learning Control

Equidistant sampling in control system may lead to quantization errors for certain measurement equipment, e.g., encoders. The aim of this paper is to develop an Iterative Learning Control (ILC) framework that eliminates quantization by exploiting time stamping. The developed ILC framework employs the non-equidistant time stamps in a linear time-varying (LTV) approach. Since the data at the time-stamps does not suffer from quantization, unparalleled performance can be achieved, while the intersample behaviour is bounded by definition. A simulation example confirms superiority of the ILC framework which employs time stamping.

Beyond Quantization in Iterative Learning Control: Exploiting Time-Varying Time-Stamps

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