Stabilizing and Improving the Active Vibration Damping by a New S-Z Mapping for Digital Control

This paper presents an analytical and simulation study of the stabilization and improvement of the active vibration damping of a system modeled by a simple analog harmonic oscillator driven by discrete time control. Initially, this control is the Bilinear (or Tustin) s-z mapping equivalent of a continuous-time asymptotically stable Proportional plus Derivative (PD) control. It is tested with high values of the sampling period. It is shown that all classical mappings (Tustin, Schneider, etc.) tested may instabilize the system. To circumvent this, we propose and use a new (ST1) mapping that behaves better than the classical ones tested under the same conditions. We also model an active discrete control of a suspension of a vehicle, and compare the performance between the PD controllers designed by Bilinear and by the new (ST1) S-Z mappings, for this example.