Optimal semiactive control of structures with isolated base

Abstract

The paper investigates the benefits of implementing the semiactive control systems in relation to passive viscous damping in the context of seismically isolated structures. Frequency response functions are compiled from the computed time history response to pulse-like seismic excitation. A simple semiactive control policy is evaluated in regard to passive linear viscous damping and an optimal non-causal semiactive control strategy. The optimal control strategy minimizes the integral of the squared absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied. The optimization procedure involves a numerical solution to the Euler-Lagrange equations Keywords: optimal control, Euler-Lagrange equations, nonlinear systems Introduction. Passive and active control techniques have been studied in various engineering fields [4, 5, 8, 9, 11-13, 15, 17]. Application of various techniques to civil engineering has been the subject of considerable research since the pioneer work of Yao [16]. Now, the trend in practice for passive isolation systems is toward very large isolators incorporating large viscous dampers. Recent studies show that the use of supplemental dampers in seismic isolation to increase the isolation damping reduce displacements, but at the expense of increases in interstory displacements and accelerations at high frequencies in the superstructure [7]. An increase in the interstory drifts and superstructure accelerations is counter to the primary goal of isolation systems: to protect the sensitive internal equipment and non-structural elements.Semiactive control systems, on the other hand, are a class of control systems in which the control actions are applied by changing the mechanical properties (i.e., stiffness and damping) of the control device [10]. Civil engineering structures incorporating semiactive devices exhibit nonlinear behavior and this motivates the development of nonlinear control strategies that can be practically implemented, which is a challenging task. As is well known, optimal control problem of a linear system with respect to a quadratic performance index has a flexible solution, which leads to the construction of a linear state regulator when there are no constraints on admissible controls [1][2][3]. It is known to the control community that except for relatively few special cases, the mathematical theory of nonlinear oscillations provides little help for practical nonlinear vibration control problems [6]. Therefore, the difficulties in synthesizing optimal feedback controls for nonlinear non-autonomous dynamical systems have motivated many researchers to use the formalism of optimal control theory to derive sub-optimal feedback controllers by obtaining approximate solutions to either the two-point boundary-value problem or to the Hamilton-JacobiBellman equations. Numerical solution to the two-point boundary-value problem for nonlinear non-autonomous dynamical systems can also be found using numerical optimization techniques. The resulting optimal c...

Optimal Semiactive Control of Elevated Highway Bridges: An Upper Bound on Performance via a Dynamic Programming Approach

“…Alhan et al (2006) used the same deterministic optimization approach to find optimal semiactive control forces for a single degree of freedom (SDOF) structure subjected to pulse-like ground motion. Aldemir and Gavin (2006) used a similar approach to study the effectiveness of different semiactive control strategies for structural base isolation by comparing them to the optimal semiactive control. In this paper, the same optimization procedure is used to investigate semiactive control of elevated highway bridges with an emphasis on minimizing the bridge pier response.…”

Nonlinear dynamics of a system of rigid bodies with controlled electromagnetic dampers

“…These mechanisms are designed to weaken the constraint between the structure and the buried portion of its foundation and to intensify the dissipation of seismic energy. Recent developments are models and designs of controlled damping devices with liquid electro-and magneto-rheological materials (suspensions) for SIMs [13][14][15][16][17]. A possible way to improve the dissipative properties of seismic-protection devices is to use frictional electromagnetic dampers without magnetorheological suspensions.…”

Vibrations of a rigid body with a controlled frictional electromagnetic seismic damper: nonlinear model

“…The possibility of damping vibrations by controlling the absolute velocity and acceleration is established Keywords: gravitational vibratory system, electromagnetic seismic damper, nonlinear model, feedback circuit, least-squares method, multifrequency inertial excitation Introduction. Seismic isolation mechanisms (SIMs) have been used for earthquake protection since the second half of the 20th century [5,6,11,[14][15][16][17][20][21][22][23]. Such mechanisms are designed to weaken the coupling between protected structures and ground and to dissipate the energy of seismic disturbances.…”