Delay-feedback-based recoil control for deepwater drilling riser systems

This paper deals with the dynamic modelling and pure delayed $ H_{\infty } $ H∞ control for a deepwater drilling riser system in the presence of the friction force of seawater and drilling discharge mud. First, by simplifying a drilling riser system as a spring-mass-damping unit with three degrees of freedom, an increment equation of the riser system subject to friction force of seawater and drilling discharge mud is established. Then, by artificially introducing a time-varying delay with given lower and upper bounds into the control channel, a pure delayed $ H_\infty $ H∞ control scheme is presented to restrain the recoil responses of the riser system. Based on the Lyapunov–Krasovskii functional approach, several new sufficient conditions are derived to design the pure delayed $ H_\infty $ H∞ controller. Finally, comparative simulation results are given to show the effectiveness and merits of the proposed control scheme. It is demonstrated that to mitigate recoil response of the deepwater riser in the event of emergency disconnection, the proposed pure delayed $ H_{\infty } $ H∞ controllers are more economic than the delay-free $ H_\infty $ H∞ controller.