Global Dynamics, Stability, and Robust Control of Nonlinear Flexible Rotors

Abstract

Rotating machinery such as jet engines, gas turbines, and centrifugal compressors is inherently susceptible to destructive whirling motion caused by mass imbalance, which intensifies near critical speeds and can lead to catastrophic failure. While the nonlinear Jeffcott rotor is the canonical model for studying these dynamics, existing analyses are largely limited to local methods that cannot capture the global structure of coexisting attractors, and most control designs rely on the simplifying assumption of a predefined rotational speed. This dissertation addresses these limitations through three interrelated contributions. First, a unified polynomial stiffness framework is combined with a parallelized Simple Cell Mapping implementation to perform a comprehensive global analysis of the rotor at constant speed, simultaneously identifying all coexisting attractors and their basins of attraction across the four-dimensional state space for linear, cubic, and quintic stiffness cases, and characterizing the influence of damping on the global dynamics. Second, the predefined-speed assumption is relaxed by retaining the full torsional--lateral coupling under a proportional-integral torque controller; rigorous necessary and sufficient stability conditions are derived, and the minimum control effort required to sustain a target speed is quantified. Third, Sliding Mode and Lyapunov Redesign controllers are synthesized for the coupled system subject to bounded parametric uncertainty, with formal proofs of global uniform asymptotic stability under discontinuous switching and uniform ultimate boundedness under continuous approximation. Together, these contributions advance the theoretical foundation for the analysis and robust control of nonlinear rotor systems, providing a pathway toward safer and more reliable rotating machinery designs.