Derivation of Analytical Setting Formulas for PI Control of Electrical Drives for Active Torque Damping in Deep Drilling Technology

In real drilling processes, nonlinear friction effects can lead to a de-attenuation in the system and thus to increased vibrations that are difficult to control. The goal is to examine the effect of an increasing damping removal on the stability of the open control loop as well as the property of the controller to compensate for possible instabilities. This paper describes the derivation of analytical setting formulas for a PI state control as well as a supplementary state observer of an electrical drive. The mathematical and control engineering considerations are based on the example of deep drilling technology. In this case, the torsional vibrations, induced due to the contact between the drill bit and the rock formation, are modelled using the static friction (Stribeck) model. The friction parameters, on which the model is built, are determined by means of practical tests on an experimental setup in the form of a scaled-down drilling rig. In addition to the state control, a corresponding functionality of the selected state observer is also examined so that the controller can be operated quickly enough.