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.

使用单个执行器和单个传感器控制多模振动是一项挑战。大多数研究人员使用多执行器和多传感器来控制多模式结构振动。在目前的工作中，开发了一种使用单个致动器和单个传感器的多模式延迟反馈控制，它们都连接在简单支撑的薄板的上表面。推导板的线性运动方程，然后使用Galerkin方法离散化。结果耦合方程由速度延迟反馈控制来控制，以减轻多模结构振动。所感测的加速度计信号被积分，然后被滤波以仅包括目标振动频率的影响。然后通过最小化系统总受控响应的均方根来使用全局优化方法。许多参数（例如传感器/执行器的尺寸，位置和方向以及时间延迟和控制器增益）在控制器性能中起着至关重要的作用。结果表明，提出的速度延迟反馈控制器可有效地用于通过单个传感器和单个执行器控制多模式振动。所提出的单输入单输出控制器还能够专注于给定的振动模式，而不是将它们全部同等对待。