A new active control performance index for vibration control of three-dimensional structures

A Short Review on the Active Control Approaches in Earthquake Engineering at the Last 10 Years (2008-2018)

“…For numerical validation of their algorithm they used simple eight story shear frame structures. A new performance index for active vibration control of three-dimensional structures was presented in [17]. To analytically validate the proposed performance index, a six story three-dimensional structure was considered as an example with a fully active tendon controller system.…”

“…This example is shown in Fig. 10 and the resulting control law from their study is given in (8) [17]. In (8) Z 3D is the three dimensional state vector, t  is the sampling interval of the simulation and the other parameters are defined above.…”

Data‐driven optimal predictive control of seismic induced vibrations in frame structures

“…It allows to define the optimal control force gains able to minimize a performance index appropriately weighted on the controlled state and control force. Moreover, in civil engineering, a different target can be pursued like reduction of displacement, velocity or absolute accelerations, and interstory drifts . LQR design is based on a cost function that has to be minimized through a reasonable trade‐off between the control cost and the achievable reduction of structural vibrations.…”

“…Moreover, in civil engineering, a different target can be pursued like reduction of displacement, velocity or absolute accelerations, and interstory drifts. 15 LQR design is based on a cost function that has to be minimized through a reasonable trade-off between the control cost and the achievable reduction of structural vibrations. However, this approach requires measurements of all the state variables, which in real applications is often impossible.…”

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