Affiliations: Institute for Systems Research, University of
Maryland, College Park, MD 20742, USA | Department of Civil and Environmental Engineering,
University of Maryland, College Park, MD 20742, USA
Abstract: In the performance-based design of earthquake-resistant structures,
researchers have recently proposed protection systems where base isolation
devices are supplemented by active control mechanisms. Established approaches
to understanding this problem domain rely on numerical and experimental
analyses, which have the disadvantage of obscuring potential insight into
cause-and-effect relationships existing between parameters of sub-optimal
control and their affect on linear and nonlinear system response. As a first
step toward mitigating this limitation, this paper explores the role of
symbolic analysis in understanding how sub-optimal bang-bang control mechanisms
depend on design objectives and their impact on performance of base isolated
structures. New results are obtained through three avenues of investigation:
(1) Single- and two-degree-of-freedom systems, (2) Restricted classes of
multi-degree-of-freedom systems, and (3) Sensitivity of parameters in modified
bang-bang control to localized nonlinear deformations in the base isolation
devices. The principle outcome is matrices of symbolic expressions for
bang-bang control expressed in terms of the structural system parameters and
state. We identify modeling constraints and limits (e.g., perfect isolation)
where lengthy symbolic expressions simplify to the point where relationships
between the inner workings of the bang-bang control strategy and specific
design objectives become evident.
Keywords: Base isolation, symbolic analysis, sub-optimal bang-bang control
