Parameter-Estimation-Based Gain-Scheduling Control of Weight on Bit in Drilling Process With Uncertain Penetration Resistance Coefficient

It is inevitable to encounter through different formations in the drilling process for deep exploration, and the penetration resistance coefficient (PRC) is an uncertain parameter related to lithology. In this article, a parameter-estimation-based gain-scheduling controller is developed to eliminate undesired system performance deterioration due to the uncertain parameter. First, a drill-string axial finite element model with the uncertain PRC is established, and a control-oriented low-order model is derived via mode selection. A gain-scheduling controller is computed based on the quadratic stability condition of the closed-loop system, which can cope with the system’s parameter uncertainty using variable low-frequency gain. An adaptive observer is designed to estimate the unmeasurable scheduling variable. Field data from a geothermal drilling well is obtained to validate our model. According to this drilling well scenario, both numerical and experimental results illustrate the effectiveness of our method. The explicit relationship between the controller gain and the uncertain parameter is presented. It is found that the performance of the closed-loop system is more sensitive to the controller gain when drilling in soft formations, requiring more attention in such scenarios.