Optimal Control of Seismic Response of Structures

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We developed a new closed-open-loop optimal control law that has been derived by minimizing the sum of the quadratic time-dependent performance index and the dynamic energy input to the structural system. Three types of input energy are considered that are the seismic energy, control force energy and the sum of both energy. This control law is simple and reliable for on-line control operations because control force does not depend on the rigidity of structural system. The control efficiency affected by two weighting matrices included in the performance index is investigated in detail. Using the concept of neural network we have developed an algorithm to implement the developed control law into structural system for controlling seismic response of structures. The algorithm consists of two parts. One is an identification mode in which the back propagation learning process is applied to identify the structural parameters such as mass, damping and stiffness matrices. The other is a controller mode in which the time-dependent performance index consisting of response and control force vectors as well as the seismic energy input to the structure system is minimized. To realize a practical control device of active mass damper (AMD) type for high-rise buildings we also implemented this new algorithm into an eight story building model with AMD system and checked feasibility to control seismic response of the structure. Numerical examples are worked out to demonstrate the control efficiency of the proposed algorithms.