15th Triennial World Congress of the International Federation of Automatic Control
  Barcelona, 21–26 July 2002 
ROBUSTNESS ANALYSIS OF A RELAY OSCILLATOR
Subbarao Varigonda
United Technologies Research Center, East Hartford, CT, USA.
Email: varigos@utrc.utc.com

Relaxation oscillators typically consist of a hysteresis element and a dynamic feedback. The robustness of oscillations in such an interconnection is of interest in many applications. In particular, we seek the robustness margin on the component perturbations in the gap metric so that oscillatory behavior of the closed loop is preserved. A new distance measure for oscillatory signals utilizing time scaling is introduced for this purpose. The robustness of a system consisting of an ideal relay with hysteresis and an integrator has been studied in (Georgiou and Smith 2000). Here analogous results are derived for a system consisting of an integrator and a relay whose branches have non-zero slope. This system resembles the classical van der Pol oscillator more closely than the ideal relay system.
Keywords: Relaxation oscillation, relays, hysteresis, robustness
Session slot T-Th-M08: Oscillations in Nonsmooth Feedback Systems/Area code 2c : Non-linear Systems