This study firstly proposes some representative simple methods to obtain the suboptimal passive damping and stiffness parameters from the optimal control gain matrix since it is not possible to add the exact optimal damping and stiffness parameters to the structure in practice. It is shown numerically that modifying the structural damping and the stiffness in the proposed suboptimal ways may suppress the uncontrolled vibrations while the performance levels depend on the seismic inputs. Since the proposed approach is intrinsically passive and has no adaptive property against changing dynamic effects, this study secondly proposes a new performance index so that the mechanical energy of the structure, control and the seismic energies are considered simultaneously in the minimization procedure. The implementation of the resulting closed-loop control algorithm does not require both a priori knowledge of the seismic excitation and the solution of the nonlinear matrix Riccati equation. The performance of the proposed approach is investigated, e.g., structures subjected to three seismic inputs and compared to the performance of the uncontrolled, the classical linear optimal control, and the passive cases. It is shown by the numerical simulation results that the proposed algorithm is capable of suppressing the uncontrolled seismic structural displacements and the absolute accelerations simultaneously and performs almost as well as the classical linear optimal control in reducing the displacements with comparable control effort and performs better than the classical linear optimal control in reducing the absolute accelerations. The results show that while the proposed active approach has similar performance to the classical linear optimal control, the classical linear optimal control increases the absolute accelerations slightly compared to the proposed active approach in regulating displacements, while the proposed active approach regulates and reduces both displacements and absolute accelerations. The proposed approach is promising in protecting both the structural and non-structural members from the seismic forces since a simultaneous reduction both in the displacements and the absolute accelerations is achieved.

Control of Structural Response Under Earthquake Excitation

: A simple integral type quadratic functional is proposed as the performance index so that the optimal control policy is derived based on the minimization of the proposed performance index between the successive control instants by using the method of calculus of variations. The resulting optimal control law is applied to seismically excited linear buildings modeled as lumped mass shear frame structures. Active tendon actuators are considered as control devices. The performance of the proposed control (PC) is investigated when the example structure is subjected to three different seismic inputs and compared to the uncontrolled case and the classical linear optimal control (CLOC), which requires the solution of nonlinear matrix Riccati equation. It is shown by numerical simulation results that the PC is capable of suppressing the uncontrolled seismic vibrations of the linear structures and performs better than the CLOC.

A Simple Active Control Algorithm for Earthquake Excited Structures

The development, experimental testing, and analytical modeling of an intelligent seismic response control system is described in this paper. The control system is in the form of semiactive fluid damping devices which may be installed within the lateral bracing system of buildings or as part of a seismic isolation system for bridges or buildings. The dampers have mechanical properties which can be modified through a closed-loop feedback control system which utilizes the measured earthquake excitation and/or the response of the structural system. Further, the dampers exhibit fail-safe characteristics in that, in the event of failure to operate as semi-active devices, the dampers convert to passive high-damping devices. The dampers were extensively tested to determine the mechanical properties and the dynamic behavior of the devices. Furthermore, mathematical models for describing the damper behavior were developed and utilized for analytically predicting experimental results.

Experimental testing and analytical modeling of semi-active fluid dampers for seismic protection

The suboptimal control rule is introduced in structural control implementation as an alternative over the optimal control because the optimal control may require large amount of processing time when applied to complex structural control problems. It is well known that any time delay in structural control implementation will cause un-synchronized application of the control forces, which not only reduce the effectiveness of an active control system, but also cause instability of the control system. The effect of time delay on the displacement and acceleration responses of building structures is studied when the suboptimal control rule is adopted. Two examples are given to show the effectiveness of the suboptimal control rule. It is shown through the examples that the present method is easy in implementation and high in efficiency and it can significantly reduce the time delay in structural control implementation without significant loss of performance.

J. Tang

Papers

Suboptimal control strategy in structural control implementation