| A critical review of classical optimal control algorithms is made with respect to the specific application of structural control under seismic loads. It is shown that the classical optimal open-loop and closed-open-loop control laws are not applicable to seismic control of structures, because the future earthquake ground motions are not known a priori. Furthermore, with the seismic ground acceleration being the major source of continuous external disturbances, the Riccati closed-loop control does not satisfy the optimal condition. While the future earthquake ground acceleration is not known a priori, it can be measured in real-time on-line by installing sensors on the basement floor. Such measured information along with a quadratic time-dependent performance index are used to establish three new control algorithms, referred to as the instantaneous optimal closed-loop control, instantaneous optimal open-loop control, and instantaneous optimal closed-open-loop control. The control efficiency of these three instantaneous optimal control algorithms are identical under ideal operational environments. Numerical examples using active tendon and active mass damper control systems are worked out to demonstrate the effectiveness of the newly proposed control algorithms. It is shown that the practical implementation for instantaneous optimal control algorithms is much easier than the Riccati closed-loop control.; Several important problems associated with the practical implementation of an active control system are investigated. These include the system time delay, the truncation of small control forces, and the uncertainty involved in identifying the structural parameters. It is shown that the effects of the time delay, the uncertainty in structural identification, and the truncation of small control forces on the control system depend heavily on the control algorithm used. |
