Actuator topology design using the controllability Gramian

作者：Alves da Silveira Otavio Augusto; Ono Fonseca Jun Sergio; Santos Ilmar Ferreira

来源：Structural and Multidisciplinary Optimization, 2015, 51(1): 145-157.

DOI：10.1007/s00158-014-1121-z

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

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.

• 出版日期2015-1