Dynamic Response and Control Nonlinear Coupled Roll-Pitch (2DOF) Motion of Ship Under Harmonic Waves

Abstract

To control vibration and stability of different linear and nonlinear system using various analytical, semi analytical, numerical method, and the time delayed feedback control has been used in the recent past. The present study deals with the complex dynamic behavior of 2DOF coupled roll-pitch system via Numerical Integration based methods (NI). By choice of appropriate of displacement and velocity feedback gain and delay values which may be introduced in the feedback path, the NI based techniques are well suited in stabilizing motion by elimination of undesirable subharmonic, quasiperiodic and chaotic solutions. Therefore, in the present study, a comprehensive numerical schemes based on NI method is developed to analyze the control of nonlinear 2DOF motion under non-linear time-delayed feedback. Time delay feedback control of nonlinear 2DOF roll-pitch coupled motion under harmonic excitations thoroughly investigated by Numerical Integration method. The periodic solutions are obtained by the NI method and compared with the solutions obtained by without time-delay (i.e. uncontrolled) and with time-delay (i.e. controlled) of the system responses. The objective of this paper is to study the efficiency and performance of Numerical Integration Technique for analysis of time delay feedback control of 2DOF coupled roll-pitch motion under harmonic excitations and also study its efficiency in obtaining suppression of various fundamental by choice of appropriate displacement and velocity feedback gain values as well as proper choice of delay.