Linear quadratic AMD controller with an observer for buildings under seismic ground motion

Performance Studies of Linear Quadratic AMD Controller for Civil Engineering

“…Fig. 1 A structural dynamic system implemented with an active mass damper system Where: x is the (6×1) displacement vector, M is the (6×6) mass matrix, C is the (6×6) damping matrix, K is (6×6) stiffness matrix, ( ) t u is the control force, B is the (6×1) location matrix of the control forces, ( ) t x g is the earthquake ground acceleration, E is the (6×1) location matrix of the earthquake ground acceleration The control force, ( ) t u , can be further expressed in terms of the torque, Γ , of the servomotor [10]. As the servomotor rotates one revolution, the mass block is advanced one pitch of the ball screw.…”

“…After further calculations, the equation of motion of the dynamic system implemented with the AMD system driven by the servomotor, can be expressed as [10]:…”

“…Optimal control algorithms are based on the minimization of a quadratic performance index whose objective is to maintain the desired system state while minimizing the control effort [6,12]. For a linear system, this performance index can be defined as [10]:…”

“…By minimizing the criterium of the equation ( 4) and after using optimal calculation we obtain at infinite time duration [10]:…”

Generalized Minimum Variance Control for MDOF Structures under Earthquake Excitation

“…Several structural models have been investigated in the literature for an active control perspective. Indeed, many researchers have used an active control strategy based on state-space model to develop and design a controller for structural vibration [1][2][3][4][5][6]. Nonlinear model has been used and presented for Stochastic Optimal Control of Structural Systems [1,7].…”