Control of Hysteretic System Using Velocity and Acceleration Feedbacks

Optimal control algorithms usually involve a state feedback including displacements and velocities. For control of building structures subjected to strong earthquake ground motions, it is much easier to measure the acceleration response than the displacement response. In this paper, a version of the instantaneous optimal algorithm, using velocity and acceleration feedbacks, for nonlinear or hysteretic structural systems is presented. Stable controllers are obtained using the Lyapunov direct method. The Lyapunov function for the controlled nonlinear structure is obtained through an appropriate transformation. The optimal algorithm is applied to control of a hysteretic building structure equipped with an aseismic hybrid control system. It is demonstrated numerically that for the particular hybrid control system considered, the performance of the present control algorithm is as good as the previous algorithm, which uses the displacement response of the structure for the determination of the control vector.