An Analytical Approach for Discrete Controllers Design Using a New S-Z Mapping with Two Tuning Parameters

In this work we present a second s-z mapping (ST2) as an extension of a first one, the s-z mapping (ST1), presented in a previous work done by the authors. In that work, the ST1 mapping used only one tuning parameter (csi) ξ to: 1) map the (asymptoticall stable) left half s plane in the interior of the unitary circle in z plane; and 2) attain the asymptotical stabilization of a benchmark harmonic oscillator driven by a PD discrete controller with various sampling periods. In both tests, the ST1 mapping behaved better than other mappings listed in the literature (Tustin, Backward, Shneider-Kaneshige-Groutage, etc.). In this work we use two tuning parameters csil and csi2 in the ST2 mapping to see how both tests behave, including numerical simulations comparing the ST2 mapping with those other mappings ((ST1 and Tustin). Through the numerical results obtained in this work we may perceive that the two new-rules presented are more robust to the fading effects due the increasing of aliasing phenomenon in comparison with the Tustin rule. An analytical description of these new-rules is presented.