Robust Control of Feeding Speed in Coal Seam Drilling Process Considering Borehole Friction

During the coal seam drilling process, the drill string is subject to compressive deformation, compounded by unpredictable variations in formation hardness and borehole wall friction, leading to challenges in maintaining a stable feeding speed. This paper presents a novel approach by introducing uncertain parameters to describe the effects of formation hardness and borehole wall friction. Drill string axial movement model is modeled as a polyhedral system based on a lumped parameter representation. To meet industrial performance requirements, we design a robust <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> controller to achieve consistent feeding speed control. Our simulation results demonstrate the controller's effectiveness in ensuring system stability despite fluctuations in formation hardness and drill string friction.