Ship Parametric Excitation Rolling Motion And Its Robust Control Based On Chaos Analysis

As an important means of transport, the ship can satisfy the stability criteria required by the provisions of international conventions and domestic regulations in the design process, but often may capsize in the wave due to instability. At present, the stability criterion only considers the static stability without considering the dynamic stability and the research for stability loss, the instantaneous movement state and the wave encounter situation during navigating in the sea is lacked. Therefore the research for complex motion characteristics and robust control under the wave excitations has important engineering significance.Parametric excitation rolling can lead to dangerously large rolling motions, endangering the ship, cargo and crew. To decrease the influence caused by parametric resonance, stability of ships in longitudinal waves was then analyzed using Lyapunov characteristic exponents and power spectrum.The mechanism of parametric excitation rolling was explained by chaos theory. Not only the condition of chaos in parametric rolling was discussed, but also the safe and unsafe regions of target ships were then identified. Then the fin stabilizer controller was designed by using backstepping algorithm, closed-loop gain shaping algorithm,Lyapunov stability and simulation tests were carried out under certain disturbances. The simulation results show that the control effects are very effective for the elimination of chaos in the ship parametric rolling system and have satisfactory robust stability.Parametric-forced excitation rolling is more likely to cause dangerously large rolling motions, comparing with parametric excitation rolling, posing a danger to the ship, cargo and crew. In the principal parametric resonance zone, small parametric excitation and forced excitation can still generate large-amplitude roll, or even cause overturning. To decrease the influence caused by parametric and forced resonance, stability of ships in longitudinal waves was then analyzed using Lyapunov characteristic exponents and power spectrum. At the same time, stability and dangerous areas and the relationship between initial motion parameters and rolling movement can be discovered. Then the nonlinear robust controller was designed by using backstepping algorithm,closed-loop gain shaping algorithm,Lyapunov stability and simulation tests were carried out under certain disturbances. The simulation results show that the control effects are very effective for the elimination of chaos in the ship parametric and forced rolling system and have satisfactory robust stability.Under the effects of time-varying metacentric height of the ship, the random longitudinal wave can also a great impact on the ship’s rolling stability. Especially under the condition that the characteristic wavelength is close to the length of ship and the parameters excitation frequency double the rolling natural frequency, the ship will occur large and unstable rolling motion. That is parametric rolling and parametric-forced rolling under the random waves. By obtaining Lyapunov index during principal parametric resonance and analyzing principal parametric resonance stability, the stability domain and unstable domain were found.The influence of ship rolling damping, center frequency of random wave and bandwidth to parametric and parametric-forced excitation was discussed. Then the nonlinear robust controller was designed to reduce ship rolling risk and improve the stability of navigation.