Vibration Control for a Coupled Pitch- roll Ship Model Via a Negative Cubic Velocity Feedback Control

Abstract

One of the most essential ship reactions to waves is roll motion. Due to the intricacy of ship wave interactions and their sensitivity, predicting such a reaction is extremely challenging. Because vibration motion is an undesirable occurrence, it must be removed, decreased, or controlled. A coupled Pitch-roll ship model with negative cubic velocity feedback control subjected to parametric excitations is premeditated and solved in this paper. The method of multiple time scales is applied to scrutinize the response of the two modes of the system neighbouring the simultaneous sub-harmonic, and internal resonance situation. Besides, the steady-state solution is determined through the Rung-Kutta Method (RKM) of fourth order. Stability of the steady state solution near this resonance case is discussed and studied applying Lyapunov's first indirect method and Routh-Hurwitz criterion. The influences of the different parameters on thesteady state solution are reconnoitred and discussed. The controller effects on the stability are clarified. Simulation results are accomplished with the help of MATLAB and Maple software programs.

A vibration analysis of the permanent magnet synchronous motor under the effect of proportional derivative control

“…They have utilized the MATLAB program to examine the efficacy of various parameters and the control of the main system. In order to address the vibration issue of a coupled pitch-roll ship model with a negative cubic velocity feedback control, Amer et al [3] employed the multiple time scales approach and closely examined the behavior of the two system modes that were in close proximity to the internal resonance and simultaneous sub-harmonic scenario. Also, the fourth-order Rung-Kutta Method (RKM) has been used to determine the steady-state solution.…”