Abstract

The mathematical modeling of dynamic systems is an important task in the design, analysis, and implementation of advanced automotive control systems. Although most vehicle control algorithms tend to use model-free calibration architectures, a need exists to migrate to model-based control algorithms which offer greater operating performance. However, in many instances, the analytical descriptions are too complex for real-time powertrain and chassis model-based control algorithms. Therefore, model reduction strategies may be applied to transform the original model into a simplified lower-order form while preserving the dynamic characteristics of the original high-order system. In this paper, an empirical gramian balanced nonlinear model reduction strategy is examined for the simplification process of dynamic system descriptions. The empirical gramians may be computed using either experimental or simulation data. These gramians are then balanced and unimportant system dynamics truncated. For comparison purposes, a Taylor Series linearization will also be introduced to linearize the original nonlinear system about an equilibrium operating point and then a balanced realization linear reduction strategy will be applied. To demonstrate the functionality of each model reduction strategy, two nonlinear dynamic system models are investigated and respective transient performances compared.

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