Topology optimization of piezoelectric sensor and actuator layers for active vibration control

In this work, the layout of piezoelectric transducers is designed using the Topology Optimization Method (TOM). Starting with a finite element model and its modal reduction, a state-space model for a control scheme is built. With this model, two objective functions are formulated, i.e. the maximization of the trace of the controllability gramian matrix and the maximization of the trace of the observability gramian matrix. Each objective function simultaneously seeks an optimized distribution of piezoelectric material over an elastic structure. A SIMP material interpolation model, a spatial filter, and the Sequential Linear Programming (SLP) method with moving limits are used to solve the optimization problem. Moreover, a linear-quadratic-Gaussian controller (LQG) is implemented to verify the structural performance of a cantilever beam exposed to vibration. Finally, numerical results are shown for the transducers' topologies and their control performance.