Integrated optimization of actuator placement and vibration control for piezoelectric adaptive trusses

In this paper, the integrated optimization of actuator placement and vibration control for piezoelectric adaptive truss is studied. Based on the dynamic finite element (FE) model and a linear-quadratic-Gaussian (LQG) model of vibration control for an adaptive truss, an integrated optimization model is built in which an improved quadratic performance index is adopted as the objective function and the mode closed-loop damping ratio, modal controllability and actuator number are selected as the constraints. A layered optimization strategy is implemented to address this optimization problem with discrete-continuous design variable. To prevent the optimization process from converging to the local optimal solution, the genetic algorithm (GA) for outside-layer optimization is extended with an improved penalty function. Numerical examples and the vibration control experiments for piezoelectric adaptive truss were used to validate the efficiency of the proposed method. The following conclusions were drawn from the results. (1) The improved penalty function can orient the optimization process to the global optimal solution. (2) Although the number of struts on the truss is large, the optimization computation time is short because of the high efficiency of the proposed method. (3) In the experiment, the quadratic performance index, modal response and sensor signals for the present paperʹs optimal actuator placement scheme are better than those described in the literature, but the placement requires more energy, which is consistent with the numerical results.