Active Control of Flexible Structures Subject to Distributed and Seismic Disturbances

Abstract

The purpose of this paper is to present a method of active control for suppressing the vibration of a mechanically flexible cantilever beam which is subject to a distributed random disturbance and also a seismic input at the clamped end. First, the mathematical model of the flexible structure is established by a stochastic partial differential equation which describes the Euler-Bernoulli type distributed parameter system with internal viscous damping and subject to the seismic and distributed random inputs. Second, the distributed parameter model, which is considered as an infinite-dimensional system, is reduced to a finite-dimensional one by using the modal expansion, and split into the controlled part and the uncontrolled (residual) one. The principal approach is to regard the observation spillover due to uncontrolled part as a colored observation noise and construct an estimator, and then we construct the optimal control system. Finally, simulation studies are presented by using a real earthquake accelerogram data.

Counteracting moment device for reduction of earthquake-induced excursions of multi-level buildings

“…Active control of flexural structures were discussed by Ohsumi and Sawada. 7 They also discussed a method for computing an optimal control system. Chuang et al showed the LQR control method.…”

Decentralized model reference control of flexible cable-stayed beam structures

“…Among them, the centralized linear active control [2] and decentralized nonlinear active control [31 have received an important attention. In this paper, the dynamic behaviour of this particular type of beam structure is characterized by a nonlinear mathematical model with interconnection terms [31.…”

Partial states feedback two-time scale control of elastic beams subjected to moving vibratory systems

“…Consequently, combining the two reduced-order equations (5-13), (5)(6)(7)(8)(9)(10)(11)(12)(13)(14), and defining Z:=zI, Z:=z,, ly:= w, , w':= w, , the state space form will become 5 = -Bzy[ 4,k + 4,i$ + B2,Z + B,,W + bpS] (5)(6)(7)(8)(9)(10)(11)(12) Substituting (5-12) into (5-9) yields the reduced- …”

“…Therefore, a finite dimensional compensator depending upon only partial states is desired for this family of systems. As pointed out earlier, not all states in (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) are available. Thus assume the available states, that is, the output of the system Furthermore, in many practical cases, only a limited number of modes are excited and the objective of active damping is to stabilize these "effective modes".…”

“…Recently, active vibration absorber (or active damping), have received much attention for the vibration suppression of large flexible structures (Zhang et al 1991, Ohsumi andSawada 1993). Especially, in civil engineering, for the protection of such flexible structures as high-rise buildings or long span bridges against wind and/or seismic input, a number of tuned-mass-damper systems have been installed in the structure.…”