Fundamental dynamics and control strategies for aseismic structural control

Abstract

This paper introduces fundamental dynamics and control strategies for aseismic structural control, especially focusing on excitation influence and nonlinear effects. Firstly, fundamental structural dynamics with control forces under a seismic excitation are introduced. Then, as a basic strategy for structural control, the effects of linear feedback control laws are reviewed. Next, introducing the least quadratic regulator (LQR) considering excitation influence, the least input energy control and the LQR for short term under given excitation information, roles of the FB, instantaneous counter-reaction and feedforward (FF) terms are clarified. Furthermore, it is inferred that it is difficult to explicitly solve the optimization problems positively considering control force limit, and the Euler equations for the optimal variable-element control become nonlinear. It is also shown that we can construct an extended FB control law assuming a state equation model for excitation information. Then, not only an additional damping effect but also a dissonant effect on a seismic excitation are anticipated. Furthermore, sufficient stability conditions for nonlinear control laws are introduced. Finally, as examples of nonlinear control laws, nonlinear velocity FB laws and nonlinear Maxwell-type control laws are introduced.