Enhanced passive control of dual-mode systems under extreme seismic loading: An optimal control approach

摘要

Passive protective measures suffer from limited displacement capacities. When the capacity is reached under extreme loading, harsh impacts occur, resulting in spikes in acceleration. Supplemental damping increases the effective displacement capacity at the expense of increasing accelerations, even in the absence of impact, and at the same time altering the normal operation of systems. In this study, a dual-mode system is studied, which improves the performance of these systems under extreme events, without affecting the normal operation, by applying the control action only at some reserved capacity regions. An innovative solution is sought that can more effectively utilize the available displacement capacity while simultaneously seeking to control the sustained accelerations without any prior assumption on force-displacement or force-velocity relationship. Optimal control is used to determine the best possible control force trajectories to achieve both performance objectives. Open-loop solutions are found by solving the Euler-Lagrange equations with the constrained control force. Because finding the solution to this problem requires the knowledge of the future loading, these solutions are not immediately implementable. Therefore, a piecewise optimal control with unknown fixed final times on each excursion is proposed on the reserved capacity regions only, which can be used to find the best control action mechanism that can guide the design of novel dual-mode systems with impact-mitigation mechanisms. Finally, by utilizing the designed curves obtained from the proposed optimal control procedure, a Kelvin-Voigt device is tuned for illustrative purposes. The performance of the system equipped with a tuned Kelvin-Voigt device under an maximum considered earthquake-level event is evaluated, and it is compared with the piecewise optimal solution and a suboptimal solution using the linear quadratic regulator.