Predictive controlled stiffness devices in MDOF structures

Abstract

This paper presents a study of a predictive control system used to improve the behavior of a multistorey structure under strong earthquakes. The structure and application of supplemental controlled stiffness devices (CSD) are discussed. Instantaneous optimal control is used to obtain the control forces at each time step during an earthquake according to the predicted values of the displacements and the velocities of each storey. A linear autoregressive model with exogenous input (ARX) is used to predict the displacements and the velocities of the frame in order to overcome the time delay problem in the control system. Control of the forces developed in the CSD is possible, owing to the mechanical structure of the device. This device can be efficiently used as a controller because the forces developed in it are independent of the structure's displacements or velocities. Its efficiency is demonstrated in a numerical simulation of a seven-storey building. The simulation shows that the behavior of a structure with the proposed predictive control system is significantly improved compared with that of an uncontrolled structure subjected to the same earthquakes. In this example, the displacements and velocities in the structure were predicted according to an 'occurring' earthquake by the ARX model and were used to obtain the optimal control forces (predictive control). These forces yielded a response of the structure with CSD that was similar to the response obtained with control forces, which were calculated from a 'known' complete history of the earthquake displacement and velocity values (instantaneous optimal control).

Centralized semi‐active control of post‐tensioned steel frames

“…Semi‐active control of frame structures is an approach that has been progressively developed since the introduction of a semi‐active tuned mass damper . Different approaches have been proposed in the literature, including (a) added semi‐active dampers , (b) stiffness control to avoid resonance of the response , and (c) energy dissipation approach to increase energy dissipation capacity of the frame . These approaches can be centralized or decentralized .…”

“…The main difference between previous stiffness control approaches and the one proposed here is that the control decision (gain) is independent from the structural response (open‐loop control). This control approach does not require monitoring (or prediction) of structural response (displacements or velocities) and can be used not only for PT frames but also for frames with other structural configurations, including variable stiffness devices installed in brace‐frame connections .…”

“…Comparison between Frequency State Feedback and other stiffness control algorithms: active variable stiffness[12] and modal energy transference[13].…”