Symbolic and Numeric Solutions of Modified Bang-Bang Control Strategies for Performance-Based Assessment of Base-Isolated Structures
Symbolic and Numeric Solutions of Modified Bang-Bang Control Strategies for Performance-Based Assessment of Base-Isolated Structures
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Date
2005-04-14
Authors
Sebastianelli, Jr., Robert Richard
Advisor
Austin, Mark A
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Abstract
This work explores symbolic and numeric solutions to
the Lyapunov matrix equation as it applies to performance-based
assessment of base-isolated structures supplemented
by modified bang-bang control.
Traditional studies of this type rely on numeric simulations alone.
This study is the first to use symbolic analysis as a means of identifying key
"cause and effect" relationships existing between
parameters of the active control problem and the
underlying differential equations of motion.
We show that symbolic representations are very lengthy,
even for structures having a small number of degrees of freedom.
However, under certain simplifying assumptions, symbolic
solutions to the Lyapunov matrix equation
assume a greatly simplified form (thereby avoiding the need for computational solutions).
Regarding the behavior of the bang-bang control strategy,
further analysis shows:
(1) for a 1-DOF system, the actuator force acts very nearly in phase,
but in opposite direction to the velocity (90 degrees out of phase
and in opposite direction to the displacement), and
(2) for a wide range of 2-DOF nonlinear base-isolated models,
bang-bang control is insensitive to
nonlinear deformations in the isolator devices.
Through nonlinear time-history analysis,
we see that one- and two-DOF models are good
indicators of behavior in higher DOF models.
An analytical framework for system assessment through energy-
and power-balance analysis is formulated.
Computational experiments on base-isolated systems are conducted to
identify and quantitatively evaluate situations when
constant stiffness bang-bang control can significantly enhance
overall performance, compared to base isolation alone, and
assess the ability of present-day actuator technologies
to deliver actuator power requirements estimated through simulation.