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 support motion. It is assumed that the support motions are uncertain, time varying, and norm bounded, and that the column itself has no uncertainties associated with it. The control signal is based on Lyapunov theory and noise-free state feedback measurements. The states of the resulting closed-loop system (namely displacement and velocity) are uniformly and ultimately bounded within a neighborhood of the zero state. To illustrate the features of the proposed controller, examples of nonhysteretic and hysteretic columns subjected to combined horizontal and vertical nonstationary seismic excitation are considered. Numerical results for the uncontrolled and controlled responses are obtained and analyzed. Several issues involved in the controller design are examined, and results illustrating the control performance and effectiveness are presented and discussed.