Model Order Reduction for x-In the Loop (xIL) Simulation of Automotive Transmissions

Increasing complexity of automotive systems along with growing safety and performance requirements, is causing development cycle costs to swell. A common solution is to use a Model-Based Design (MBD) approach, particularly using x-In the Loop (xIL) simulation methods for Validation and Verification (V&V). MBD allows efficient workflow from offline control design using high-fidelity models to real time V&V using Hardware-in-the-Loop (HIL) simulations. It is very challenging to reduce the complex non-linear high-fidelity models to real-time capable models for HIL simulation. Current literature does not provide a standard approach for obtaining the HIL-capable reduced model for complex non-linear systems. In this paper we present an approach to perform model reduction in light of HIL-level requirements. The approach is presented using an example of a 10-speed automatic transmission. The system constitutes three subsystems - the hydraulic network, mechanical gearbox, and torque converter. In the first step, a high-fidelity model for each subsystem is built up from the component level using one-dimensional mechanics and zero-dimensional hydraulic fluid flow. Secondly, the model is reduced gradually to meet the real-time requirements while achieving the performance requirements. In order to be able to compare the different models for simulation time and performance, metrics are defined for each subsystem. In the second step, the model is reduced by removing higher-order derivatives and states with faster eigenvalues. A parametric sensitivity analysis is done to quantify the effect of parameters on system response. Lastly, a full automatic transmission model with hydraulic actuation circuit and dynamic torque converter has been implemented on a dSpace HIL simulator for real-time testing without control hardware in the loop. The step-by-step approach used for model order reduction results in a real-time capable model which meets the performance requirements.