Optimal actuator locations for flexible structures with free edges in active vibration control

Locations of actuators greatly influence the effect of active vibration control, thus actuator placement is essential to the design of a control system. In this paper, optimized actuator locations for both beam and plate structures are discussed based on gramian controllability. Apparently various boundary conditions of a structure lead to different difficulties in obtaining the state space equation, especially for a two-dimensional plate. As a result, the flexible structures with free edges which space equations are more complex to obtain are studied. Further, both force actuators and piezoelectric actuators are discussed and the deduced equations show the space equations of which are totally different. Based above, the paper focuses on the optimal actuator locations for piezoelectric actuators and a detailed optimization process is displayed. Finally, the global response of feedforward active vibration control is displayed to validate the optimized result.