Actuator topology design using the controllability Gramian

Otávio Augusto Alves da Silveira, Jun Sérgio Ono Fonseca, Ilmar Santos

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This work develops a methodology for the optimal design of actuators for the vibration control of flexible structures. The objective is the maximization of a measure of the controllability Gramian. The test case is the embedding of piezoelectric inserts in elastic structures for vibration control in modal space. A topology optimization was formulated to distribute two material phases in the domain: a passive linear elastic material and an active linear piezoelectric material, with a volume constraint in the latter. The objective function is the trace of the controllability Gramian of a LQR control system. Analytical sensitivities for the finite element model are derived for the objective function and constraints. Results are shown for two dimensional vibration control of a short beam with varying number of electrodes (control inputs) and vibration modes.
Original languageEnglish
JournalStructural and Multidisciplinary Optimization
Pages (from-to)145-157
Publication statusPublished - 2015


  • Actuator placement
  • Controllability Gramian
  • Topology optimization
  • Piezoelectric
  • Vibration control


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