BIFURCATION ANALYSIS OF A TWO-DOF SYSTEM SUBJECT TO DIGITAL POSITION CONTROL

This paper analyzes the stability of a two-DoF system, subject to PD digital position control. In the model the control force is considered piecewise constant. Introducing the nonlinearity related to the saturation of the control force, the bifurcations occurring in the system are analyzed. The system is generally loosing stability through Neimark-Sacker bifurcations, with a relatively simple dynamics. However; the interaction of two different Neimark-Sacker bifurcations steers the system to much more complicated behaviors. About this kind of bifurcation, namely double Neimark-Sacker bifurcation, there are very few studies in the literature. Our analysis is carried out using the method proposed by Kuznetsov. The performed investigation shows the appearance of quasiperiodic motions and the existence of regions with coexisting periodic stable attractors, in the space of the control gains. Numerical simulations validate the results obtained analytically.