Nonlinear Model Reduction for Dynamic and Automotive System Descriptions

Abstract

The mathematical modeling of dynamic systems is an important task in the design, analysis, and implementation of advanced 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 may offer greater operating performance. However, in many instances, the analytical descriptions are too complex for real-time powertrain and chassis model-based control algorithms. Thus, 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. The controllability gramian represents the energy needed to transport the system between states, while the observability gramian denotes the output energy transmitted. These gramians are then balanced and select 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 applied to reduce the linearized model. To demonstrate the functionality of each model reduction strategy, a vehicle suspension system and exhaust gas recirculation valve are investigated, and respective transient performances are compared.