RESPONSE CONTROL IN NONLINEAR SYSTEMS WITH NOISE

Abstract

Noise is unavoidable and/or present in a wide variety of engineering systems. Although considered to be undesirable from certain viewpoints, it can play a useful role in influencing the behavior of nonlinear mechanical and structural systems that have multiple solutions in the form of equilibrium points, periodic solutions, and aperiodic (including chaotic) solutions. The aim of this dissertation work is to discover clues related to noise enabled steering or control for engendering desirable changes in system behavior.

A combination of experimental, analytical, and numerical studies have been undertaken on the following: i) shifting of jump-up and jump-down frequencies leading to an eventual collapse of hysteresis observed in the response of a nonlinear oscillator, ii) influence of noise on the chaotic response of a nonlinear system, and iii) noise-induced escape route from a chaotic-attractor. Furthermore, a combination of analytical and numerical studies have been undertaken to understand an extended Jeffcott rotor-stator system and the influence of noise on the system dynamics.

Additionally, this dissertation includes work on partial control of chaotic systems under the influence of noise, wherein the trajectories are confined inside a particular region (chaotic attractor) despite the presence of white noise. Maintaining chaotic behavior in systems in the presence of an external disturbance may be desirable and important for the dynamics of certain systems. The proposed algorithm has been shown to be effective for systems with different dimensions.

The dissertation outcomes provide answers to the following fundamental questions: i) how can noise influence the long-time responses of mechanical and structural systems and ii) how can noise be used to steer a system response to avoid an undesirable dynamical state. These answers can serve as an important foundation for many industrial applications (e.g., applications with rotor-stator systems) as well.