Modeling and Control of Towed Seismic Cables
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This doctoral thesis presents new results on modeling and control of towed seismic cables. Nonlinear distributed-parameter mathematical models of the towed cables for large and small deflections are proposed. The equivalent lumped-parameter numerical models are derived. The energy-based passivity properties of the streamer dynamics are established. It is shown that the general and the transversal motion of the streamers are state strictly passive. Similarly, the transversal motion of the cascaded cable system is shown to be state strictly passive. Passive boundary control laws yielding asymptotic and exponential energy decay are proposed to suppress the transversal vibrations in the towed seismic streamers. Asymptotic stabilizing active boundary control laws via backstepping for the towed seismic are proposed. The disturbance propagation along the seismic streamers and the scattering of those disturbances at the actuator locations are considered. The power dissipation at the junctions are investigated where the optimal damping value in terms of cable impedance for maximal energy dissipation is found. The main results of this thesis have been presented at international conferences.