Low-Order Controllers

Abstract

This chapter presents some of the most frequently used low-order controllers to regulate the angular velocity and tackle the stick-slip phenomenon. First, a proportional-integral (PI)-like control law to maintain a constant rotary speed is presented. The controller is constructed under the basis of a two degree-of-freedom lumped parameter model; its gains are adjusted by means of the classic two-time-scales separation method. Next, two classic solutions to counteract the stick-slip phenomenon are discussed: the soft torque and the torsional rectification controllers. The torsional rectification control allows the absorption of the energy at the top extremity to avoid the reflection of torsional waves back down to the drillstring. The soft torque is one of the most popular vibration control methods; it has the form of a standard speed controller but includes a high-pass filtered torque signal. Finally, a novel technique to reduce the stick-slip and bit-bounce is introduced. Based on the bifurcation analysis of the drilling system, a pair of low-order controllers aimed at eliminating axial and torsional coupled vibrations are designed: delayed proportional and delayed proportional-integral-derivative. The performances of the proposed control techniques are highlighted through simulations of a proposed drilling model.