Optimal Placement and Shape Morphing Of Thin Plates Using Dynamic Inversion Design

This paper presents active vibration control and morphing of thin plates using an array of piezoelectric actuator-sensor system whose locations are determined by optimization. The sudden application of control input for morphing leads to unwanted vibrations which are suppressed using the piezoelectric actuator-sensor couples, which form a feedback control loop. Dynamic Inversion technique is used to determine the control inputs to morph the plate and to suppress the vibrations in the process. The Dynamic Inversion controlled system is compared to uncontrolled system and as a reference, the results are compared with that of Linear Quadratic Controller. The partial differential equations governing the behaviour of plate and piezoelectric actuation are solved using lower dimensional projection method, following Design-then-Approximate (DTA) method, which will reduce spillover effects. Two reference configurations are considered to perform simulations. The actuators are designed for both vibration control and morphing since thin plates have poor damping characteristics and need external damping. The displacement, velocity and error norm time histories are analysed and the configuration achieved by the system by both controllers are compared.