Controller Parameters Selection Through Bifurcation Analysis in a Piecewise-Smooth System

Abstract

Classical linear and nonlinear control techniques applied to piecewise-smooth (PWS) systems can be ineffective if an additional bifurcation analysis is not made. Due to the presence of discontinuities, PWS systems present a wide variety of standard and non-standard bifurcations. Safe ranges of system and controller parameters can be established lest these bifurcations appear. This is studied by means of a simplified torsional model of an oilwell drillstring of three degrees of freedom (DOF). A PID-type controller is applied. The bifurcation analysis of the open-loop and the closed-loop systems is used to choose the controller parameters for which non-desired bit sticking situations are avoided. The control goal of driving the rotary velocities to a constant positive value is achieved despite the existence of a sliding motion.