OPTIMAL STRUCTURAL CONTROL VIA TRAINING ON ENSEMBLE OF EARTHQUAKES

In civil engineering, the design of active vibration control systems f or 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 m ust be either neglected, known a priori, or treated as white noise. If it is treated as white noise, the control is optimized for steady-sta te response. For seismic analyses of structures, these three assumptio ns-that the earthquake input is known in advance, is neglected, or is white noise-are questionable. This represents a serious deficiency in using standard methods of linear optimal control for reducing structur al vibrations under seismic loading. This paper presents a new method of addressing the issue of including the earthquake-type excitation ex plicitly in the development of control systems, by designing feedback and feedforward controllers whose gains are optimized by training on a n ensemble of earthquakes. Two different control strategies are presen ted: in the first, the controller is composed of a state feedback term only (closed loop); in the second, a control term proportional to the external excitation is fed forward (open loop) in addition to the clo sed loop term. The development of the controller follows the general f ormalism developed by Kabamba and Longman (1981, 1983) for the design of optimal controllers of arbitrary prescribed order with quadratic co st functionals. In this formalism, the gradients of the cost functiona l are obtained in explicit form and involve Liapunov equations. The re sults of this study indicate that inclusion of the forcing function ex plicitly in the development of the controller provides better results than the standard Riccati solution and drastically reduces the peak st ructural response.