Multimode velocity-delayed feedback vibration control of plates using a single sensor and a single actuator

Controlling multimode vibrations using a single actuator and a single sensor is challenging. Most researchers use multiactuators and multisensors to control multimode structural vibrations. In the present work, a multimode delayed feedback control using a single actuator and a single sensor, both attached at the top surface of a simply supported thin plate, is developed. The linear equations of motion of the plate are derived and then discretized using Galerkin's method. The resulting coupled equations are controlled with a velocity-delay feedback control to mitigate multimode structural vibrations. A sensed accelerometer signal is integrated and then filtered to include only the effect of the targeted vibration frequency. A global optimization method is then used by minimizing the root mean square of the total controlled response of the system. Many parameters, such as size, location, and orientation of the sensor/actuator as well as time delay and controller gain, play an essential role in the controller performance. The results showed that the proposed velocity delay feedback controller was efficiently used to control multimode vibrations using a single sensor and a single actuator. The proposed single-input single-output controller is also capable of focusing on a given vibration mode rather than treating them all equally.