| In civil engineering, the design of active vibration control systems for structures subjected to earthquake excitation is usually done using linear quadratic optimal control theory. However, when this theory is applied to a system with an external forcing function, the function must be either neglected, known a priori, or treated as white noise. If it is treated as white noise, the control is optimized for steady state response. For seismic analysis of structures, these three assumptions, that the earthquake input is known in advance, neglected, or white noise, are questionable. This represents a defect in using standard methods of linear optimal control for reducing structural vibrations under seismic loading. This study presents a new method of including the earthquake excitation explicitly in the development of control systems, by designing feedback and feed-forward controllers whose gains are optimized by training on an ensemble of earthquakes.; The methodology is first verified on a well known single-degree-of-freedom model and then extended to a more complicated model as part of a benchmark study. The benchmark problem contains significant limitations in the type and amount of feedback information available during the control cycle. The methodology is extended to encompass reduced order and output feedback control.; The development of the control methodology follows the general formalism developed by Kabamba and Longman for the design of optimal controllers of arbitrary prescribed order with quadratic cost functionals. In this formalism, the gradients of the cost functional are obtained in explicit form. The results of this study indicate that inclusion of the forcing function explicitly in the development of the controller provides better structural response than the standard Riccati solution. |
