Fast Air-Path Modeling for Stiff Components
2022-01-0494
03/29/2022
- Event
- Content
- Development of powertrain control systems frequently involves large-scale transient simulations, e.g. Monte Carlo simulations or drive-cycle optimizations, which require fast dynamic plant models. Models of the air-path—for internal combustion engines or fuel cells—can exhibit stiff behavior, though, causing slow numerical simulations due to either using an implicit solver or sampling much faster than the bandwidth of interest to maintain stability. This paper proposes a method to reduce air-path model stiffness by adding an impedance in series with potentially stiff components, e.g. throttles, valves, compressors, and turbines, thereby allowing the use of a fast-explicit solver. An impedance, by electrical analogy, is a frequency-dependent resistance to flow, which is used to suppress the high-frequency dynamics causing air-path stiffness, while maintaining model accuracy in the bandwidth of interest. The proposed impedance method is demonstrated for a simple two-state incompressible-flow throttle model, then generalized to other stiff air-path components. An automated impedance calibration method is further presented. Using the impedance method and forward-Euler discretization, transient simulations of a 6.7-liter diesel mean-value engine model achieved runtimes three-times faster than using an implicit solver for stiff systems, without degrading the root-mean-square model accuracy in the bandwidth of interest.
- Citation
- Brewbaker, T., and Vigild, C., "Fast Air-Path Modeling for Stiff Components," SAE Technical Paper 2022-01-0494, 2022, .