Simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively controlled plate structure is investigated in this paper. The system consists of a clamped-free plate, a H_2 controller and four surface-bonded piezoelectric actuators utilized to suppress the bending and torsional vibrations induced by external disturbances. The plate is represented by a rectangular design domain which is discretized by a regular finite element mesh and for each element the thickness ratio is used as a design variable. A nested solving approach is adopted in which Ricatti-based control syntheses are considered as sub processes and nested into the main optimization process using the method of moving asymptotes to optimize the structural topology and actuator locations. To obtain clear and manufacturable topology, the popular techniques in the topology optimization area including penalization, filtering and perimeter restriction are also employed. Numerical example shows that the approach used in this paper can produce systems with clear structural topology and high control performance.
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