In this research, boundary control is developed at the upper end of the riser based on the Lyapanuv’s direct method to reduce top angle and transverse vibration of the riser subjected to time-varying disturbance. First, ocean surface current is assumed to be linearly declined to zero from the ocean surface to the ocean floor and then it is assumed to be exponentially declined to zero. The riser is modeled as a distributed parameter system with one partial differential equation (PDE) coupled with boundary conditions (ODE). Since all of the control signals can be measured by sensors or can be calculated by a backwards difference algorithm, so the boundary control is practical and implementable with existing instrumentation. The Lyapunov’s direct method is applied to stability analysis of the closed-loop system. Finally, efficiency of the controller is verified and results of linear and exponential profiles are compared to each other.

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