PhD Seminar Course on

Frequency domain methods of analysis of oscillations and sliding-mode systems

Cagliari, July 22, 2008



Instructor: Prof. Igor Boiko
University of Calgary, Canada
Duration: 2 hours
Schedule: Tue Jul 22 16-18
Venue: Sala Riunioni, Padiglione B
Topics: At this seminar, the frequency-domain theory of discontinuous control systems will be reviewed. In particular, the describing function method and the locus of a perturbed relay system method will be considered. The theory considered is illustrated by the examples of a relay pneumatic servomechanism design and modified relay feedback test application to PID controller tuning.
  1. Introduction:
    Frequency domain linear theory and extension of the ideas to nonlinear systems
  2. Describing function method (DF):
    Fourier series representation of the nonlinear block output
    Open-loop definitions and ideas
    Oscillations and harmonic balance
    Application to relay system analysis
    Chattering analysis in classical sliding mode (SM)
    Second order SM - Twisting
    Asymmetric oscillations
    Slow inputs propagation, the idea of equivalent gain
  3. The locus of a perturbed relay system (LPRS)
    Transformation of the DF ideas
    State space description
    Transfer function description
    Partial fraction description
    Non-reduced order model of a SM system and disturbance rejection analysis
  4. Example of pneumatic servomechanism analysis and compensating filter design
  5. Modified relay feedback test application to non-parametric tuning of PID controllers
  6. Implementation of modified relay feedback test within industrial loop tuner on Honeywell TPS distributed control system
Organizer: Prof. Elio Usai
Dep. of Electrical and Electronic Engineering
University of Cagliari, Italy
Email: eusai@diee.unica.it