Robust mixed-sensitivity [formula omitted] control of weight on bit in geological drilling process with parameter uncertainty

Abstract

In this paper, a robust mixed-sensitivity H∞ controller is designed to control surface weight on bit using surface measurement feedback. First, we construct a drill-string longitudinal model with uncertain penetration resistance coefficient based on finite element method, and a reduced-order model is derived for controller synthesis. In order to solve the fixed point tracking problem of weight on bit control with parameter uncertainty, the mixed-sensitivity H∞ control strategy is developed to design on the model with uncertain parameter. The boundary of the uncertain parameter is obtained using field data. A quadratic stability condition of the closed-loop system is derived by using a single Lyapunov function, based on which a suitable dynamic output feedback H∞ controller is obtained. The uncertain penetration resistance coefficient and system’s high-order mode are considered in modeling and control of weight on bit for the first time. Comparison with field data is provided to validate our modeling method. Numerical results are given on a set of models with different penetration resistance coefficient. The integral of time multiplied by the squared error criterion of the closed-loop system with parameters obtained through equidistant sampling are provided. The simulation results demonstrate that the proposed controller can improve the robustness of the system’s tracking performance to parameter uncertainty and suppress the tracking oscillation results from the high-order mode.