Predictive controlled stiffness devices in MDOF structures

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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).

Original languageEnglish
Pages (from-to)101-115
Number of pages15
JournalJournal of Structural Control
Issue number2
StatePublished - Apr 2003


  • Active control
  • Controlled stiffness devices
  • Semi-active control


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