Suppressing Coupled Axial–Torsional Vibration of Drill-String System Considering Regenerative Cutting Induced Delay and Actuator Saturation
Chengda Lu, Zhaoqing He, Luefeng Chen, Quanxin Li, Min Wu
Abstract
This article is concerned with suppression of coupled axial–torsional vibration of drill-string system, taking into account the state-dependent delay inherited from regenerative cutting of drill-bit on rock and actuator saturation of drill-rig. Note that, in practice, the measurement and saturated control input could only be applied at the surface side of drill-string, while a nonlinearity of time-delay is introduced due to the bit-rock interaction at the downhole side. The main contribution of this article lies in three points. First, to capture the rich dynamics of drill-string, a multi-degree-of-freedom lumped parameter model of two differential equations is established for the axial and torsional motions of drill-string. A bit-rock interaction model for coupled cutting-frictional contact process is employed, resulting in a constraint on current and delayed states of drill-bit. Second, combining the drill-string and bit-rock interaction models, the dimensionless dynamic of coupled axial–torsional vibration of drill-string is described by a state-space equation of time-delay system with saturation nonlinearity. Third, using a second-order Bessel-Legendre integral inequality and a reciprocally convex inequality, delay-dependent sufficient conditions are provided to design a proper dynamic output-feedback controller with an antiwindup compensator for vibration suppression, using surface measurement and control only. The effectiveness of the approach is demonstrated through a case study of real data and an experiment based on a laboratory drill-rig.