High-gain feedback stability of a nonlinear drivetrain system

The development of modern automotive drivetrain systems has seen a constant increase in complexity over the past years. It is mostly driven by the increasing effort to reduce fuel consumption of passenger cars by optimizing the drivetrain to reduce losses and achieve energy-optimal set points for engine operation. Thus, electronic control units for drivetrain systems, such as automatic transmissions, have become much more complex. This increases the need for more complex control systems that traditionally have to be calibrated in a time-consuming process before production. We propose a new method of designing controllers for the shift procedure in automatic transmissions that have the same capabilities as the traditional control systems, but require less calibration. To this end, we introduce adaptive λ-tracking controllers based on the high-gain feedback principle to replace the current control scheme. In order to ensure high-gain stability, we provide a comprehensive system analysis based on a nonlinear system model and investigate the relative degree and the minimum-phase property in detail.