Multivariable iterative learning control: analysis and designs for engineering applications

Multivariable iterative learning control: analysis and designs for engineering applications

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Iterative learning control (ILC) enables high control performance through learning from measured data using limited model knowledge, typically in the form of a nominal parametric model. Robust stability requires robustness to modeling errors, often due to deliberate undermodeling. The aim of this chapter is to outline a range of design approaches for multivariable ILC that is suited for engineering applications, with specific attention to addressing interaction using limited model knowledge. 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-offbetween modeling requirements, i.e., modeling effort and cost, and achievable performance. This allows control engineers to select the approach that best fits the modeling budget and control requirements. This trade-offis demonstrated in case studies on industrial printers. Additionally, two learning approaches are presented that are compatible with, and provide extensions to, the developed multivariable design framework: model-free iterative learning and ILC for varying tasks.

Chapter Contents:

  • 7.1 Introduction
  • 7.1.1 ILC for complex engineering applications
  • 7.1.2 Design requirements for high-precision applications
  • 7.1.3 Robust multivariable ILC design: the importance of (under) modeling (R1 – R2)
  • 7.1.4 Model-free iterative learning (R2)
  • 7.1.5 ILC for varying tasks (R3)
  • 7.1.6 Contributions
  • 7.1.7 Notation
  • 7.2 System description and problem formulation
  • 7.2.1 ILC framework
  • 7.2.2 Convergence and performance
  • 7.2.3 Design conditions for convergence and performance
  • 7.2.4 Modeling considerations
  • 7.3 ILC design—the SISO case
  • 7.3.1 Manual design in the frequency domain
  • Design of L by inverting
  • Design of Q based on FRF measurements
  • 7.3.2 Design of learning filter: SISO inversion techniques
  • Approximate inversion
  • H∞-optimal synthesis with preview
  • Stable inversion
  • 7.3.3 Toward MIMO ILC design: naive SISO design for MIMO systems
  • 7.4 ILC Design—the MIMO case
  • 7.4.1 Interaction analysis
  • 7.4.2 Decoupling transformations
  • 7.4.3 Robust multi-loop SISO design
  • 7.4.4 Robust decentralized MIMO design
  • 7.4.5 Centralized MIMO design
  • Design of learning filter: MIMO inversion techniques
  • 7.5 Iterative inversion-based control: avoiding the need for parametric models
  • 7.5.1 System description and procedure
  • 7.5.2 Convergence analysis, modeling requirements and design
  • 7.6 ILC with basis functions: enhancing flexibility to varying tasks
  • 7.6.1 Flexibility in ILC—case study on a flatbed printer
  • 7.6.2 Basis functions in ILC
  • 7.6.3 Projection-based MIMO ILC with basis functions: frequency-domain design
  • Basis functions for MIMO ILC
  • Projection step
  • 7.7 Conclusion and ongoing work
  • Acknowledgments
  • References

Inspec keywords: iterative learning control; engineering computing

Other keywords: control performance; Iterative learning control; nominal parametric model; control requirements; Gershgorin bounds; modeling budget; ILC; model-free iterative learning; structured singular value; model knowledge; control engineers

Subjects: Self-adjusting control systems; Interpolation and function approximation (numerical analysis)

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