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stiffness or coefficient of viscous damping, has recently drawn more attention [Kamopp, D., 1995, Dyke, S.
J., Spencer, Jr., B. R, 1997, Yoshida. S. and Yoshida. K., 1997, Fujio. T. and Yoshida. K., 1999] than the
active control methodology which needs much power. Semi-active control is characteristic of less power then
active control and higher performance than passive control. Especially, variable dampers have already been
put into practice in the field of automobile, and a skyhook damper is approximately realized by using variable
damper. Since the suppression of actuator power is an important issue for active structural control, in this
stud\, a new semi-active control method for vibration base isolation is presented by a sliding mode using the
switching hyperplane designed by disturbance-accommodating bilinear control.
One of the authors proposed an bilinear potimal control with feedforward link for a semi-active dynamic
vibration absorber and then applied it to a base isolation problem [Fujio. T. and Yoshida. K., 1999]. This
study presents a sliding mode controller using the switching hyperplane designed by disturbance-accommodating
bilinear control. In order to investigate the performance and the effectiveness of the proposed method
by numerical calculation and computer simulation, it is applied to a model of an actual structure with 10 degree-of-freedom.
CONTROLLER DSEIGN
Fundamental Model for Controller Design
hi this study, a ten-storied structural model with semi-active base isolator subjected to seismic excitation is
treated as a control object A variable damper is installed between the base and the first story of structure. As a
result of the eigenvalueanalysis, first natural frequency of system is 0.25Hz and damping ratio is 2%, respectively.
Then this control object is represented by the following bilinear equation.
V" ;r Y" •' • A TC TC V • • • T I
l A 0 A 10 "hj
"S L A 10
where .r is state variable vector and z is disturbance vector, u denotes the vector of the control input, that is, the
damping coefficient of damper given by the semi-active control.
Controller with Feedforwrad Link
In this stud}, it is assumed that there is a disturbance with flat spectral density at the controlled frequency
range in order to adapt to various earthquakes. Accordingly, by restricting the frequency range of disturbance,
we assume that the characteristic of power sepectal density is the same as white noise within the restricted
frequency range. Then, we assume that the disturbance is such a colored noise that has the transfer function of the
characteristic of a low pass filter as shown in Fig. 1, whose transfer function is give by