General information

Catalog no.: 038806 (graduate)
Credit points: 3
Prerequisites: 035188—Control Theory
Grading policy: Homework (100%, 4 out of 5, provided all solutions are submitted)

Homework solutions to be submitted electronically in PDF format (typeset, not a scan of a handwritten text) to

Lecturer

Leonid Mirkin, 210 D. Dan and Betty Kahn Bld., phone: 3149, email: 

Classes

Wednesday, 14:30-17:20, room 450, Lady Davis Bld.

Syllabus

  1. Introduction
    • time delays in engineering applications
    • system-theoretic preliminaries
  2. Mathematical modeling of time-delay systems
    • frequency domain & modal analyses
    • state space
    • rational approximations
  3. Stability analysis
    • stability notions
    • delay sweeping
    • bilinear transformation
    • Lyapunov's method
  4. Stabilization methods
    • fixed-structure controllers
    • Smith controller & dead-time compensation
    • finite spectrum assignment
    • coprime factorization
  5. Robustness to delay uncertainty
    • unstructured uncertainty embedding
    • Lyapunov-based methods
  6. Performance
    • industrial controllers with dead-time compensation
    • H₂ and H∞ optimizations
  7. Implementation of dead-time compensators
  8. Systems with preview
    • preview tracking and smoothing
  9. Exploiting delays in control (if time permits)
    • repetitive control
    • input shaping
    • PIDD
    • weird loop shaping

Literature:

  1. Course lectures notes last updated 29.8.2024, fixed typos in Ch. 8
  2. J. E. Marshall, H. Górecki, A. Korytowski, and K. Walton, Time-Delay Systems: Stability and Performance Criteria with Applications.  London: Ellis Horwood, 1992.
  3. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems.  Boston: Birkhäuser, 2003.
  4. R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory.  New York: Springer-Verlag, 1995.

Lectures

  1. Introduction and background (in beamer mode)
  2. Delay element, interconnections, Padé approximants (in beamer mode)
  3. I/O stability of delay systems, modal analysis (in beamer mode)
  4. Direct method, Rekašius transformation (in beamer mode)
  5. Lyapunov analysis; stabilization by fixed controllers, historical overview of stabilization methods (in beamer mode)
  6. Stabilization (contd) (in beamer mode)
  7. Stabilization (contd) (in beamer mode)
  8. Delay robustness (in beamer mode)
  9. Delay robustness (Lyapunov-Krasovskii); implementation of FIR elements (in beamer mode) updated 21.08.2024
  10. Effects of delays on standard problems (in beamer mode)
  11. Exploiting delays: closed-loop control (in beamer mode)
  12. Exploiting delays: open-loop control (in beamer mode)

Homework