Abstract
In this paper, we deal with a semi-active control of structural systems based on a positive real active control law. It is well known that the range of the phase difference of the positive real controller is limited between ±90 degrees. The phase property of the positive real control is favorable as the reference active control law for the semi-active control because the active control force generated by the positive real active controller can be reproduced with more precision than the case when the reference active control without any phase constraints are used as the reference active control law. The positive real controller with a constraint on the closed-loop H_2 norm can be obtained by solving a sequence of a LMI problem that is an approximation of a BMI problem. The semi-active control law is obtained based on the control force of the output signal of the positive real controller. A simulation study is carried out for the 3-dof structural model of the benchmark building of NCREE in Taiwan. We show that the control force of the semi-active control is close to that of the active control law when the positive real reference control law is adopted. By comparing with the case of sky hook control, the advantage of the proposed semi-active control method is presented.
