Characterizing the Dynamics of the Watt Governor System Under Harmonic Perturbation and Gaussian Noise

Abstract

We investigate the disturbance on the dynamics of a Watt governor system model due to the addition of a harmonic perturbation and a Gaussian noise, by analyzing the numerical results using two distinct methods for the nonlinear dynamics characterization: (i) the well-known Lyapunov spectrum, and (ii) the 0-1 test for chaos. The results clearly show that for tiny harmonic perturbations only the smallest stable periodic structures (SPSs) immersed in chaotic domains are destroyed, whereas for intermediate harmonic perturbation amplitudes there is the emergence of quasiperiodic motion, with the existence of typical Arnold tongues and, the consequent distortion of the SPSs embedded in the chaotic region. For large enough harmonic perturbations, the SPSs immersed in chaotic domains are suppressed and the dynamics becomes essentially chaotic. Regarding the noise perturbations, it is able to suppress periodic motion even if tiny noise intensities are considered, as analyzed by a periodic attractor subject to different noise intensities. The threshold of noise amplitude for chaos generation in periodic structures is reported by both methods. Additionally, we investigate the robustness of the 0-1 test for chaos characterization in both noiseless and noise cases, and for the first time, we compare the Lyapunov exponents and 0-1 test methods in the parameter-planes. Our findings are generic due to their remarkable agreement with results previously reported for dynamical systems in other contexts.

Two-Parameter Dynamics of An Autonomous Mechanical Governor System With Time Delay

“…Owing to the simple yet effective characteristics, the centrifugal governor devices have been widely used in many rotating machines to avoid potential damage, such as in the internal combustion engines, fueled turbines, modern striking clocks and so on. Induced by the inherent nonlinearities, many dynamical phenomena have been observed and reported in such systems, including periodic oscillations [28,29], chaotic motions [30,31], hyperchaotic behavior [32], multistability [15,33], fractal and mode-locking structures [34,35]. To avoid the damages caused by the undesired system response, various control schemes have been proposed to stabilize the system.…”

Two-parameter dynamics of an autonomous mechanical governor system with time delay

“…Owing to the simple yet effective characteristics, the centrifugal governor devices have been widely used in many rotating machines to avoid potential damage, such as in the internal combustion engines, fueled turbines, modern striking clocks and so on. Induced by the inherent nonlinearities, many dynamical phenomena have been observed and reported in such systems, including periodic oscillations [28,29], chaotic motions [30,31], hyperchaotic behavior [32], multistability [15,33], fractal and mode-locking structures [34,35]. To avoid the damages caused by the undesired system response, various control schemes have been proposed to stabilize the system.…”