MISO Control System for Noise Reduction in 3-D Enclosures Using PZT Actuators

The low-frequency, high-level blade passage noise in aircraft and helicopter cabins deems passive noise reduction techniques ineffective. Most of the research on active techniques have focused on single input single output (SISO) control. The present work presents a multi-input single output (MISO) linear quadratic Gaussian (LQG) control system to actively reduce acoustic pressure inside a 3-D enclosure, representing a helicopter cabin, using piezoelectric actuators. The enclosure has five walls that are acoustically rigid and is covered with a simply supported flexible plate, to which piezoelectric actuators are symmetrically bonded. External noise is modeled with a time-dependent, spatially bounded Heaviside function simulating vibrations from helicopter rotor impinging disturbance on the upper surface of the cabin. First, the governing equations describing the distribution of plate displacements, piezoelectric actuator response, and acoustic pressure within the cavity are presented and combined to develop the state-space model of the coupled structural-acoustic system. Optimal design of a LQG controller is developed for the case of MISO control. The model is validated by comparison of its results with available published numerical and experimental results. The frequency response of the output due to input from each input channel is then determined and studied. Results demonstrate that significant attenuation is obtained for the desired low-frequency range compared to the uncontrolled system and to SISO control.