Optimal Placement of Piezoelectric Actuators for Active Structural Acoustic Control

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Abstract
This paper presents a general formulation of the optimization problem for the place ment and sizing of piezoelectric actuators in adaptive LMS control systems. The selection of objec tive function, design variables and physical constraints are separately discussed. A case study for the optimal placement of multiple fixed size piezoelectric actuators in sound radiation control is pre sented. A solution strategy is proposed to calculate the applied voltages to piezoelectric actuators with the use of linear quadratic optimal control theory which is to simulate the LMS feedforward control algorithm. The location of piezoelectric actuators is then determined by minimizing the ob jective function, which is defined as the sum of the mean square sound pressure measured by a number of error microphones. The optimal location of piezoelectric actuators for sound radiation control is determined and shown to be dependent on the excitation frequency. Particularly, the opti mal placement of multiple piezoelectric actuators for on-resonance and off-resonance excitation is presented. The results show that the optimally located piezoelectric actuators perform far better sound radiation control than arbitrarily selected ones. This work leads to a design methodology for adaptive or intelligent material systems with highly integrated actuators and sensors. The optimiza tion procedure also leads to a reduction in the number of control transducers.