Bifurcation analysis of a two-DoF mechanical system subject to digital position control. Part II. Effects of asymmetry and transition to chaos

Abstract

Considering a two DoF system subject to digital position control, of interest for robotic application, we analyze the dynamics of the system at the intersection of two loci of Neimark–Sacker bifurcations, where a double Neimark–Sacker bifurcation is taking place. In the system, the saturation of the control force is the only nonlinear term considered, other than this, the system is piecewise linear. Starting from the analytical investigation already performed in Part I (Habib et al. in Nonlin. Dyn., under review, 2013), in this paper the effects of an asymmetry of the saturation of the control force are investigated, both analytically and numerically. The results show the increasing complexity of the dynamics for a more and more asymmetric system. First, the asymmetry is making the bifurcation transit from supercritical to subcritical, then it generates a stable torus that breaks down into a strange attractor, associated with a chaotic motion. In the last part of the paper, the torus breakdown and the onset of chaos are investigated, furthermore the evolution of complex dynamics through regions of phase locking and higher-dimensional chaos is outlined.