Dynamics of a piecewise linear system subjected to a saturation constraint

The dynamics of a periodically forced single-degree-of-freedom linear system with a proportional feedback control subjected to a saturation constraint is investigated in detail. Emphasis is placed on the determination of a double-entering saturation region per cycle periodic motion. Symmetric period-one solutions are derived analytically and their stability characteristics are determined. Other kinds of solutions such as asymmetric, subharmonic and chaotic solutions as well as multiple-crossing saturation region per cycle periodic solutions, found through numerical simulations, are also presented.