Optimal semi-active control and non-linear dynamic response of variable stiffness structures

In this paper we study the semi-active control of structural systems by means of variable stiffness devices, and the resulting non-linear dynamics of the controlled system. In particular, the study is applied to base-excited single-degree-of-freedom systems, controlled by variable ON-OFF elastic devices and subjected to simple motion conditions: free vibrations following initial conditions and stationary response to harmonic input. A performance index, which, in the case of base-excited structures, assumes an original dual formulation following the relative or absolute approaches, has been proposed for instantaneous optimal control. The Study includes both the optimal control design and the observation of the resulting non-linear dynamics of the controlled system. The dynamic behavior of the controlled non-linear system is studied with respect to the parameters which characterize the algorithms, the control device, and the input. In this way, also by means of significant (and original) analytical solutions of the equations of motion, the optimal formulation of the algorithms, some particular behaviors of the controlled systems, and the performances of the control approach are shown and explained for the different control strategies.