Nonlinear dynamics of controlled mechanical systems with time delays

Unavoidable time delays in the feedback path of a controlled mechanical system may render the system unstable, and block the development and the application of dynamic control. This paper summarizes the recent work of the authors on the dynamics of controlled mechanical system with time delays. It starts with the dimensional reduction of delayed nonlinear systems composed of stiff and soft substructures and then presents the experimental modeling of linear and nonlinear mechanical systems with the time delays in state feedback taken into account. In the frame of linear controlled systems, this paper outlines the analysis of delay-independent stability and stability switches with the increase of time delay, the stability analysis in the case of short time delay, and the robust stability analysis of the system possessing uncertain parameters. Afterwards, the paper briefly discusses the primary resonance and subharmonic resonance, as well as the corresponding stability analysis, of a kind of harmonically forced Duffing oscillators with lime delay, and the stabilization of periodic motion of nonlinear delayed systems. Finally, the applications of the stability analysis approaches to structure controls and active chassis of ground vehicles are outlined.