Integral Barrier Lyapunov Function-Based Adaptive Event-Triggered Control of Flexible Riser Systems

This paper presents an adaptive boundary control design for flexible riser systems with external disturbances and boundary position constraint. An integral barrier Lyapunov function (iBLF) is used to solve the boundary position constraint problem. Since the iBLF directly constrains the boundary position, this relaxes the conservative restriction on the state constraint of conventional BLF control. A new auxiliary signal is designed to offset the effect of the coupling term that cannot be eliminated. Compared to time triggering, the controller and actuator communicate less when using event triggering. Therefore, an event-triggered control scheme is designed to achieve effective suppression of riser vibration by introducing a relative threshold strategy. The Lyapunov stability theory is used to demonstrate that the flexible riser system is finally constrained. The efficiency of the control strategy is then further verified by numerical simulations
Note to Practitioners
—This paper investigates the control problem of flexible riser systems with external disturbances. Since the riser needs to consider the uninterrupted marine distribution disturbance and external disturbance, the riser will inevitably distort and vibrate. So the stability of the ship is extremely challenging. The riser is regarded as an Euler-Bernoulli beam construction because of its small diameter and lengthy length. Using Hamilton’s principle, the riser is represented as a fourth-order partial differential equation and two ordinary differential equations. In contrast to the logarithmic BLF and tangent BLF, the integral BLF has direct constraints on the boundary positions, which relaxes the conservative restrictions on state constraints imposed by conventional BLF control. Event-triggered control has attracted the interest of many flexible system control researchers due to its benefits in preserving communication, cost and other resources, and is widely used in practical engineering fields. The complexity and uncertainty attributed to the PDE system itself makes the design of event-triggered strategies more difficult. Based on the original ODE event triggering, it discusses the PDE-based event-triggered strategy of flexible riser systems.