<p>In the deep-sea suspension cable system, controlling cable oscillation is crucial. The elasticity of cables, disturbances from sea breezes, and finite end-drive energy pose unavoidable challenges in practical applications. The extant studies on cable oscillation control addresses only one or two of the above three characteristics, and the final control effect is only bounded, far from the requirements of high-precision control. However, this article explores the design of a controller when all three characteristics coexist, successfully achieving the ultimate convergence of vibration to zero. Initially, the time-varying-length deep-sea suspension cable system is formulated as nonlinear partial differential equations. Subsequently, a nonlinear observer was established to estimate the unknown boundary disturbance. In order to deal with the effects of input saturation and distributed disturbance, an auxiliary system has been constructed. Compared with previous research, the breakthrough of this article is the introduction of dynamic compensation for cable disturbances in auxiliary control systems, achieving convergence of cable vibration. Ultimately, utilizing the observer and auxiliary system, a boundary controller was devised at the bottom end of the suspended cable. Under this control scheme, it was demonstrated that the lateral amplitude of the control system ultimately converges to zero. The comparison of methods and simulation results validate the superiority of the proposed control scheme in ensuring the stability performance of the deep-sea suspension cable system.</p>