Predictive Hold with Error Correction Techniques that Maintain Signal Continuity in Co-Simulation Environments

• Published in: SAE International Journal of Aerospace 2012-10, Vol.5 (2), p.481-493, Article 2012-01-2205
• Main Authors: Wells, Jason, Hasan, Maher, Lucas, Charles
• Format: Article
• Language: English
• Subjects: Aerospace engineering; Aerospace industry; Discontinuity; Dynamic models; Environment models; Error correction; Functions (mathematics); Interpolation; Polynomials; Schedules; Simulation; Subsystems
• ISSN: 1946-3855; 1946-3901; 1946-3901
• DOI: 10.4271/2012-01-2205

The combination of increasing performance demands, increasing system complexity, and the need for reduced program development schedule and budget costs in the aerospace industry is driving engineers to increasingly rely upon modeling, simulation, and analysis (MS&A) in the platform development cycle. One approach to ensuring that such integrated system simulations remain computationally tractable is co-simulation utilizing technology found in commercially available packages, such as PC Krause and Associates, Inc.'s (PCKA's) Distributed Heterogeneous Simulation (DHS) / FastSim software. In such co-simulation environments, dynamic models are executed in independent model spaces, with coupling between subsystems achieved by exchanging a minimal set of required data typically found at subsystem boundaries. In such environments, an important challenge that must be overcome is the estimation of communicated signals whose true values may only be updated at some reduced rate compared to the model in which they are used. This estimation has traditionally been achieved with simple sample/hold techniques, wherein the communicated signals are sampled at the discrete communication intervals, and interpolation (most often utilizing polynomial functions) is used to reconstruct the signal in between samples. While conceptually simple, this approach often gives rise to step discontinuities in the communicated signals due to the difference between the interpolating function used and the signal itself. In certain models, such step discontinuities are undesirable, as they may give rise to spurious high-frequency dynamics, resulting in slower simulation speeds and potentially inaccurate solutions. In this paper, the problem of signal estimation and reconstruction is recast in a generalized framework based on notions of prediction and error correction. Abstracting the problem in this form allows for describing different signal estimation schemes in a unified manner, as application of different prediction and error correction formulas, including the sample/hold techniques commonly used in co-simulation tools. Based on this framework, a new prediction and error correction scheme is derived which allows for maintaining various levels of continuity in the estimated signal and in its derivatives, ensuring that smoothness is retained and step discontinuities associated with traditional sample/hold approaches are eliminated. This paper presents a detailed comparison of the proposed te