Aseismic Hybrid Control of Nonlinear and Hysteretic Structures II

Abstract

Instantaneous optimal control for nonlinear and inelastic systems is formulated incorporating the specific hysteretic model of the sytem. The resulting optimal control vector is obtained as a function of the total deformation, velocity, and the hysteretic component of the structural response. The hysteretic component of the response can be estimated from the measured structural response and the hysteretic model used. It is shown that the optimal control vector satisfies not only the necessary conditions, but also the sufficient condition of optimality. Specific applications of the optimal algorithm to two types of hybrid control systems are demonstrated. These include: (1) Active control of base‐isolated buildings using frictional‐type sliding base isolators; and (2) active control of base‐isolated buildings using lead‐core rubber bearings. Numerical examples are worked out to demonstrate the appplications of the proposed control algorithm. It is shown that the performance of such an optimal algorithm is an improvement over that of the algorithm that does not consider the hysteretic components in the determination of the control vector.