Deterministic Approaches to Transient Trajectory Generation

This chapter studies a deterministic approach to transient trajectory generation and control as applied to the forced Van der Pol oscillatory system. This type of system tends towards a strongly nonlinear system, which can be considered chaotic. A classical tuning method, targeted exponential weighting, and isolated trajectory fractionalization trajectory generation methods are examined. Illustrating the given deterministic approach via the Van der Pol system highlights the potentially iterative nature of deterministic methods, and that traditional optimal linear time-invariant control techniques are unable to perform as desired whereas even an idealized nonlinear feedforward control significantly outperforms at the steady-state. It will be shown that utilizing a-priori knowledge of the system dynamics will enable the isolated trajectory fractionalization method to minimize the nonlinear transient effects due to miss-modeled or unmodeled plant dynamics, and that this benefit can be coupled with the targeted exponential weighting approach for greatly decreased trajectory tracking error on the order of a 92% reduction of the objective cost function in the presented case study based on the forced Van der Pol system.

Reference-Free Breathing Crack Identification of Beam-Like Structures Using an Enhanced Spatial Fourier Power Spectrum with Exponential Weighting Functions

Detection of incipient damage of structures at the earliest possible stage is desirable for successful implementation of any health monitoring system. In this paper, we focus on breathing crack problem and present a new reference-free algorithm for fatigue crack detection, localization, and characterization for beam-like structures. We use the spatial curvature of the Fourier power spectrum as a damage sensitive feature for fatigue crack identification. An exponential weighting function that takes into account nonlinear dynamic signatures, such as sub- and superharmonics, is proposed in the Fourier power spectrum in order to enrich the damage-sensitive features of the structure. Both numerical and experimental studies have been carried out to test and verify the proposed algorithm.