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Higher precision in fuel injection can be achieved improving the embedded microcontroller algorithm that is inside the electronic control unit (ECU). This PART I of the present work proposes compare the performance of the PID Aström digital control strategies using the classic analog-digital mapping-rule of Tustin and the new analog-digital mapping rule of Souza-Tredinnick in a same electronic injection system. In future the PART II of the present work we will explore engine performance comparisons using Dahlin control.

We propose in this work, some numerical experiments aiming at the comparison of the performance between two design methods of digital PID (Proportional + Integral + Derivative) control, using two kinds of digital redesign mapping techniques, of a benchmark damped harmonic oscillator as vehicle suspension suffering the fading effect of aliasing due the increasing of the sampling-period of A/D and D/A converters. With a short-pulse input we have used as comparison parameter in transient responses the maximum overshoot and a chaotic behaviour is reported for some cases and the best methodology and mapping is indicated as well as better results are reported with design using the Souza-Tredinnick rule instead of the Tustin rule.

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).

Many interesting phenomena occur when the discrete control is applied over a flexible structure like the aliasing and hidden oscillations. In this work a particular phenomenon called our attention because was a bit strange: increasing the sampling period of a discrete proportional plus derivative closed-loop control (by Tustin or Bilinear method) over a harmonic oscillator (our flexible benchmark plant) we noted that happened regions of stability and instability. Initially we imagined that from some high value of sampling period this control system would instable and it stay instable. This work study analytically this phenomenon and show graphically this bifurcation.