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    • Control of a nonlinear coupled roll-pitch ship using time-delayed state feedback


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      The work scripted in this paper shows the effectiveness of using time-delayed state feedback to control the vibration of nonlinear coupled roll-pitch motion of a two-degree-of-freedom (2 DOF) system under harmonic excitation. At first, the uncontrolled frequency responses graphs are obtained under various nonresonance and resonance cases, including sub-harmonics and chaos. Next, the same system is investigated for vibration control by time-delayed feedback. The appropriate sets of control gain and delay are selected from the linear stability study of the corresponding linear oscillator. An analytical approach, namely, the Slowly Varying Parameter (SVP) method, is employed for this purpose. Results obtained by the SVP method are validated by the numerical integration (NI) technique at discrete points and they are found to be good in agreement. Moreover, it is seen that using proper control parameters, the nonlinear resonance curves of primary, secondary, subharmonic, simultaneous resonances and chaotic behavior of the system during rolling and pitching can be suppressed considerably, resulting in almost linear frequency responses.

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