Fast Air-Path Modeling for Stiff Components 2022-01-0410

Development of propulsion 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 shaped 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 for other stiff air-path components. A simple impedance calibration method is further presented. When applying the impedance method and forward-Euler discretization to a diesel mean-value engine model, transient simulations ran roughly five-times faster compared to more computationally-expensive solvers, including an implicit solver for stiff systems, without degrading the root-mean-square model accuracy.