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A Frequency-Domain Approach for Enhanced Performance and Task Flexibility in Finite-Time ILC

Max van Haren, Kentaro Tsurumoto, Masahiro Mae, Lennart Blanken, Wataru Ohnishi, Tom Oomen

TL;DR

This work addresses the dual goals of high tracking performance and task flexibility in iterative learning control (ILC) for repetitive tasks. It develops a hybrid framework that overparameterizes the feedforward as a combination of basis functions and frequency-domain ILC, and derives a norm-optimal representation that enables intuitive, frequency-domain–driven tuning. The key contributions include a norm-optimal representation that recovers finite-time frequency-domain ILC, and a joint optimization scheme that overparameterizes the feedforward to achieve both flexibility and performance, demonstrated on a two-mass system. The results show improved tracking performance and robust task adaptability, offering a practical path for industrial ILC applications with intuitive design procedures.

Abstract

Iterative learning control (ILC) is capable of improving the tracking performance of repetitive control systems by utilizing data from past iterations. The aim of this paper is to achieve both task flexibility, which is often achieved by ILC with basis functions, and the performance of frequency-domain ILC, with an intuitive design procedure. The cost function of norm-optimal ILC is determined that recovers frequency-domain ILC, and consequently, the feedforward signal is parameterized in terms of basis functions and frequency-domain ILC. The resulting method has the performance and design procedure of frequency-domain ILC and the task flexibility of basis functions ILC, and are complimentary to each other. Validation on a benchmark example confirms the capabilities of the framework.

A Frequency-Domain Approach for Enhanced Performance and Task Flexibility in Finite-Time ILC

TL;DR

This work addresses the dual goals of high tracking performance and task flexibility in iterative learning control (ILC) for repetitive tasks. It develops a hybrid framework that overparameterizes the feedforward as a combination of basis functions and frequency-domain ILC, and derives a norm-optimal representation that enables intuitive, frequency-domain–driven tuning. The key contributions include a norm-optimal representation that recovers finite-time frequency-domain ILC, and a joint optimization scheme that overparameterizes the feedforward to achieve both flexibility and performance, demonstrated on a two-mass system. The results show improved tracking performance and robust task adaptability, offering a practical path for industrial ILC applications with intuitive design procedures.

Abstract

Iterative learning control (ILC) is capable of improving the tracking performance of repetitive control systems by utilizing data from past iterations. The aim of this paper is to achieve both task flexibility, which is often achieved by ILC with basis functions, and the performance of frequency-domain ILC, with an intuitive design procedure. The cost function of norm-optimal ILC is determined that recovers frequency-domain ILC, and consequently, the feedforward signal is parameterized in terms of basis functions and frequency-domain ILC. The resulting method has the performance and design procedure of frequency-domain ILC and the task flexibility of basis functions ILC, and are complimentary to each other. Validation on a benchmark example confirms the capabilities of the framework.
Paper Structure (18 sections, 1 theorem, 26 equations, 9 figures, 1 table)

This paper contains 18 sections, 1 theorem, 26 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Problem Setup
  4. Classes of ILC
  5. Norm-Optimal ILC
  6. Basis Functions ILC
  7. Frequency-Domain ILC
  8. Problem Definition
  9. Method
  10. Norm-Optimal Representation of Frequency-Domain ILC
  11. Inclusion of Basis-Function in Frequency-Domain ILC
  12. Procedure
  13. Simulation Example
  14. Simulation Setup and Approach
  15. Basis Function Design
  16. ...and 3 more sections

Key Result

Theorem 1

Let $\hat{J}$ be invertible and $L^f=\hat{J}^{-1}$, then the minimizer of the cost function in eq:fILCOptimization with is equal to finite-time frequency-domain ILC in eq:finiteTimefILC.

Figures (9)

  • Figure 1: Control structure considered.
  • Figure 2: System that is used for validation. The system is discretized with zero-order hold, and has one sample delay.
  • Figure 3: Illustration that norm-optimal ILC with $W_e=I$ and $W_{\Delta f}=0$ converges slowly and non-monotonically for inaccurate models, leading to significantly higher maximum errors $\max_j\left(\|e_j\|_2\right)$.
  • Figure 4: FRF of the system $\mathcal{P}(e^{j\omega})$ ()and of the model available for ILC $\widehat{\mathcal{P}}(e^{j\omega})$ ().
  • Figure 5: The first ()and second ()references that are used during validation.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Example 1
  • Theorem 1
  • Remark 1
  • Remark 2