Reinitialization of a class of nonlinear systems under impulse inputs: treatment of impulse–discontinuous state products with a CSTR application

Abstract

Impulse response analysis is an effective and extensively utilized technique in chemical engineering, especially for residence time distribution analysis, dynamic characterization, and system identification. However, the strong nonlinearity of these systems, coupled with intractable terms involving products of impulses and discontinuous states, poses significant computational challenges to capture state reinitialization and evolution after discontinuities. In this work, an approach based on singularity analysis is proposed. Singularity analysis is performed to get the model’s singular component, and various strategies are employed to derive the reinitializations, which are then applied to initialize the regular component of the model and numerically compute the state trajectories. Choosing continuous stirred-tank reactor as a case study, the accuracy of these strategies is assessed across a broad range of operational parameters. The results obtained from these strategies are compared for robustness, and their relative precision and applicable ranges are systematically evaluated.