Abstract
This paper studies the effects of the time delay on the stability of a finite element method (FEM in short) model of a plate with a self-sensing actuator, in which the controlled voltage is delayed to apply to the piezoelectric actuator. It focuses on the problem how the delay affects the stability of the controlled system as the delay varies. The analysis reveals that even a very small delay can destabilize the smart board controlled by a self-sensing actuator, whereas a board delayed controlled by PD control is insensitive to the displacement gain of mechanical strain voltage. On the other hand, it shows that the feedback gains can be chosen so as to render the system delay-independent stable, namely asymptotically stable for all given delay.
