Feedback-feedforward control of structures under seismic excitation

While the base acceleration resulting from a seismic activity on a civil engineering structure is not known a priori, it can be measured in real time. In this paper, it is shown that this extra information can be used for achieving a better control of the structure with little additional effort. The approach taken is to augment the equations of motion for the structural system with an appropriate model of the earthquake excitation based on filtering a Gaussian white noise process. The augmented equations of motion are used to determine a control which utilizes both feedback and feedforward compensation. The feedback loop incorporates measurements of the response of the structure into the control law. The information from both the structure and the earthquake excitation model is utilized in the feedforward control law with an observer designed to estimate the states of the eartquake model based upon the base acceleration measurements. A quadratic performance index is used as a measure of optimality of the control algorithms. Results are given which indicate that the proposed method offers advantages in performance over the control method employing only state feedback and that it is also able to improve upon results of the recently develped instntaneous control algorithms. It is also shown that the nostationarity in the earthquake excitation can often be neglected in practical design of linear systems. Finally, a discussion is given of how the method might be coupled with equivalent linearization techniques and extended for use with nonlinear structures.