Effective reduction of drill-string vibration is still a major problem in drilling industry and therefore robust predictive tools need to be developed. In this paper we study two low dimensional nonlinear models. The first is a 1-DOF torsional model of the botom-hole assembly (BHA). The second model is a 3-DOF torsional system having in addition to the BHA a rotary table, which allows simulation of interactions for which there is experimental evidence. Three different friction models with increasing levels of complexity are applied to determine their influence in the dynamical responses. Comparison between the dynamic responses for three friction models shows that the dangerous stick-slip limit-cycles do not change qualitatively. Simulations show that, if appropriately controlled, large amplitude stick-slip limit-cycles can change to small amplitude limit-cycles in Model 2. In Model 1, with constant velocity of the rotary table, it goes from a large amplitude stick-slip limit-cycle to a fixed point. Bifurcation diagrams confirm the existence of a set of parameters in which the system operates without stick-slip vibration.