The complex oscillations of a nonlinear ocean structural system have been identified in the system model and verified through experiment. The structural system considered is characterized by nonlinear excitation and restoring forces and is modeled as a system of first order ordinary differential equations. The model takes into account a geometric nonlinearity in the restoring force, a viscous drag and periodic excitation. In this paper, a means of actively controlling the nonlinear oscillation is addressed. When applied, the controller is able to drive the dynamical system to periodic oscillations of arbitrary periodicity. The proposed control methodology applies small perturbations to the nonlinear system at prescribed intervals in order to guide a trajectory towards a stable operating state. This is accomplished by creating a locally linear map of the nonlinear system about a desired trajectory and then designing a feedback controller in order to ensure that the linearized system is stable.


Sensitive nonlinear dynamics including, chaotic oscillatory behavior, have been observed in experimental data of a moored, submerged structure (Yim et al, 1993). This phenomenon has been verified through analysis and computer simulations of the governing dynamical system (Gottlieb and Yim, 1990 and Gottlieb and Yim, 1993). This study presents an analysis and control procedure which utilizes the nonlinear, chaotic response of the system to an advantage. By describing the nonlinear response with unstable periodic orbits (UPO"s), a locally linear mapping of the dynamics is obtained. This linear mapping is subsequently employed in a controller design and the controller is applied to the moored structure. An example of a system modeled by the types of nonlinearities considered (e.g. a system characterized by nonlinear excitation and restoring forces) is a mass moored in a fluid medium subject to wave excitations.

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