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

Seismic response analysis of structures with velocity-dependent dampers

: 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

Nonlinear elastoplastic dynamic analysis of single-layer reticulated shells subjected to earthquake excitation

SUMMARY

The active control of engineering structures is one of the best methods to reduce structural responses under seismic excitation for the best performance of structures This study presents an effective approach for the optimal control of structures under strong ground motion using the colonial competitive algorithm The colonial competitive algorithm was developed over the last few years in an attempt to overcome the inherent limitations of traditional optimize method The colonial competitive algorithm has been applied due to its ideal performance in optimal control problem The effectiveness and performance of the proposed method have been investigated through two numerical examples for the response control of earthquake-excited structures The obtained results have been compared with the Linear Quadratic Regulator (LQR) control algorithm, and the performance of the proposed control approach has been found to be better than the LQR controller Copyright © 2012 John Wiley & Sons, Ltd

Optimal control of structures under earthquake excitation based on the colonial competitive algorithm

A semi-active control device for structural control implementations is presented and discussed in this paper. Based on two passive control devices, the mass pump and the hydraulic mass system, a new passive control system, the mass damper pump (MDP), is introduced. It is found that the MDP system is more effective in vibration control than the other two passive control systems. It is then shown that the passive control MDP can be modified to be a semi-active control device and is very effective in structural control. Through theoretical analysis and numerical simulations, it is found that the proposed semi-active control device MDP is more suitable for structures with ordinary height or the magnitude of earthquake excitations is not very large (because the control force provided by the semi-active control is limited). Under these situations, the maximum response of a controlled structure can be reduced by one-third to one-half. Also, it is found that multiple MDP is more effective in reducing structural response than a single MDP when they are placed in appropriate locations. Copyright © 2005 John Wiley & Sons, Ltd.

Semi-active control devices in structural control implementation

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.

Suboptimal control strategy in structural control implementation

In this paper, cantilevered tall structures are treated as cantilever bars with varying cross-section for the analysis of their free longitudinal (or axial) vibrations. Using appropriate transformations, exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step non-uniform bar are derived by selecting suitable expressions, such as exponential functions, for the distributions of mass and axial stiffness. The frequency equation of a multi-step bar is established using the approach that combines the transfer matrix procedure or the recurrence formula and the closed-form solutions of one step bars, leading to a single frequency equation for any number of steps. The Ritz method is also applied to determine the natural frequencies and mode shapes in the vertical direction for cantilevered tall structures with variably distributed stiffness and mass. The formulae proposed in this paper are simple and convenient for engineering applications. Numerical example shows that the fundamental longitudinal natural frequency and mode shape of a 27-storey building determined by the proposed methods are in good agreement with the corresponding measured data. It is also shown that the selected expressions are suitable for describing the distributions of axial stiffness and mass of typical tall buildings.

Evaluation of vertical dynamic characteristics of cantilevered tall structures

In this paper, multi-story buildings with shear-wall structures and with narrow rectangular plane configuration are modeled as a multi-step flexural-shear plate with varying cross-section for buckling analysis. The governing differential equation of such a plate is established. Using appropriate transformations, the equation is reduced to analytically solvable equations by selecting suitable expressions of the distribution of stiffness. The exact solutions for buckling of such a one-step flexural-shear plate with variable stiffness are derived for several cases. A new exact approach that combines the transfer matrix method and closed from solution of one-step flexural-shear plate with continuously varying stiffness is presented for stability analysis of multi-step non-uniform flexural-shear plate. A numerical example shows that the present methods are easy to implement and efficient.

J. Y. Xu

Papers

Semi-active control devices in structural control implementation

Suboptimal control strategy in structural control implementation

Evaluation of vertical dynamic characteristics of cantilevered tall structures

Stability of multi-step flexural-shear plates with varying cross-section