Controllability and observability of a damped plate in complex vibration modes

Abstract

In the real world, structural vibrations are complex. Controllability and observability indicators of a structural vibration are significant to the sensor and actuator arrangement in active control systems. We studied the vibration controllability and observability of damping plates based on complex modes. Furthermore, the difference between the real and complex modes was discussed from the angle of controllability and observability. Based on the indicators of controllability and observability in real modes, we discussed the feasibility of its application to the controllability and observability analyses of complex vibration modes. The controllability and observability indicators for the damping plates with various configurations were calculated and analyzed from the real and complex modes. The complexity index of complex modes of the structural vibration was also calculated. Then, we compared and analyzed these indicators. Differences between the real and complex modes in the structural vibration controllability and observability were observed in the results. When the modal shape complexity increases, the changes in the controllability and observability of vibration modes are related to input and output positions. The complex modes can be simplified to real modes in a certain modal shape complexity.