Optimal Control Design By Adjoint-Based Optimization for Active Mass Damper With Dry Friction

Abstract eng:
The goal of our research is to set up an effective procedure to design control laws of Hybrid Mass Dampers (HMDs) in order to mitigate structural vibration. The system under test is a two-storey frame equipped with an active vibration absorber located on the top of it. The vibration absorber is subjected to dry friction and is driven by a control force. The twostorey frame is subjected to a base excitation whose harmonic content is close to the system natural frequencies. The control actuator is located between the second floor and the mass damper. The control law is obtained using optimal control theory and is calculated solving a constrained minimization problem. The cost function penalizes the control effort and the state deviation from a reference position. Since the system model is non-linear, the optimal control problem is to be solved numerically. The numerical algorithm used in the proposed procedure is an iterative adjoint-based optimization method. This method combines the non-linear conjugate gradient algorithm with adjoint-based gradient computation. In this paper authors propose an analytical model of the dry friction force which describes the interaction between the absorber and structure. Simulations show that the designed control law significantly reduces the structural vibration caused by the base excitation.

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