Deterministic control of column under horizontal-vertical excitation

A control methodology is presented for a column, modeled as a single-degree -of-freedom system subjected to simultaneous horizontal and vertical suppor t motion. It is assumed that the support motions are uncertain, time varyin g, and norm bounded, and that the column itself has no uncertainties associ ated with it. The control signal is based on Lyapunov theory and noise-free state feedback measurements. The states of the resulting closed-loop syste m (namely displacement and velocity) are uniformly and ultimately bounded w ithin a neighborhood of the zero state. Td illustrate the features of the p roposed controller, examples of nonhysteretic and hysteretic columns subjec ted to combined horizontal and vertical nonstationary seismic excitation ar e considered. Numerical results for the uncontrolled and controlled respons es are obtained and analyzed. Several issues involved in the controller des ign are examined, and results illustrating the control performance and effe ctiveness are presented and discussed.