Recoil attenuation for deepwater drilling riser systems via delayed H∞ control

This paper deals with the recoil suppression problem of a deepwater drilling riser system via active H∞ control using both current and delayed states. First, based on the three degrees of freedom spring-mass-damping model of the riser system, an incremental dynamic equation of the system subject to the platform heave motion and the friction force induced by drilling discharge mud and seawater is established. Then, to reject recoil movements of the riser, a delayed state feedback H∞ controller with delayed states as well as current states is designed. The existence conditions and the design method of the delayed H∞ recoil controllers are presented. Third, the effects of the introduced time-delays on the recoil control of the riser are analyzed, and the design of optimal artificial time-delays is formulated as the minimum value problem of a series of quintic algebraic polynomials, which are related to the weights of average response amplitudes, steady-state errors, and the control force. Lastly, simulation results are provided to demonstrate the effectiveness of delay-free and delayed H∞ recoil control schemes for the riser. It is shown that (i) under the delayed H∞ controllers, the recoil responses of the riser can be controlled significantly; (ii) the decay rate of the recoil response under the delay-free H∞ controller is slightly faster than the one under the delayed H∞ controllers. However, the former requires more control cost than the latter; (iii) compared with the delayed H∞ controller with the existing linear quadratic optimal controller, the control cost by the former is larger than that by the latter. However, the steady-state errors of the riser under the latter are slightly smaller than that under the former; (iv) the introduced time-delays with proper size play positive role of suppressing recoil response of the system, and the corresponding delayed H∞ controller series provide more options for recoil control of the riser.