Abstract
This chapter introduces key mathematical formulations associated with structural control dynamics. First, the state-space formulation for a linear time-invariant single-degree-of-freedom (SDOF) system is developed and used to generate the free vibration response. This solution provides the basis for establishing a criterion for dynamic stability of a linear SDOF system. Second, the linear SDOF state-space formulation is specialized to deal with discrete time control, where the feedback forces are computed at discrete time points and held constant over time intervals. Stability for discrete time feedback with time delay is examined in detail, and a numerical procedure for determining the time increment corresponding to a stability transition is presented and illustrated with examples. Finally, the state-space formulation is extended to linear multi-degree-of-freedoms systems. The modal properties for an arbitrary damping scheme are derived and used to generate the governing equations expressed in terms of the modal coordinates.
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Bibliography
Agrawal, A., Fujino, Y., & Bhartia, B. (1993). Instability due to time delay and its compensation in active control of structures. Earthquake Engineering & Structural Dynamics, 22(3), 211–224.
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© 2014 Springer International Publishing Switzerland
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Connor, J., Laflamme, S. (2014). Structural Control Dynamics. In: Structural Motion Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-06281-5_8
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DOI: https://doi.org/10.1007/978-3-319-06281-5_8
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-06281-5
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