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With the advancement of actuator engineering, adaptive optic technology has grown considerably over the past couple of decades. Recently, there has been attention in lightweight adaptive optics where piezoelectric sheet actuators are directly attached on the back of optical mirrors to achieve a high precision surface shape with minimum addition weight[C. Kuo, R. Bruno, '90, '92; C. Liu and N. Hagood, '93; R. Kapania, P. Mohan, et al, 1998]. Philen and Wang [2001] investigated the shape control performance of a large flexible circular plate structure having directly attached thin strip piezoelectric sheet actuators placed in the plate's radial and circumferential directions. It was discovered that the performance of the system could be further improved if the piezoelectric actuator was decoupled in direction, meaning that the circumferential (radial) action of the radial (circumferential) actuators is eliminated while the radial (circumferential) action is maintained. To realize the decoupling effect, the performance of an active stiffener concept for high-precision shape and vibration control has been studied [Philen and Wang, 2002]. The active stiffener configuration consists of an insert (stiffener) placed between the host structure and the piezoelectric sheet actuator, which could produce the required decoupling effect. Similar to the active stiffener, the Active Fiber Composite (AFC) possesses a unique orthotropic actuation and has many advantages over the commonly used piezoceramic sheet actuator, thus providing a potential actuation scheme for the control of optical surfaces. In this paper, analytical investigations into several piezoelectric-type actuation methods for shape and vibration control of plate structures are presented. For the study, a performance comparison of the Active Fiber Composite (AFC), the Active Stiffener (AS), and the Direct Attached (DA) actuators for shape and vibration control of a circular plate structure is carried out. The shape control results demonstrate that the AS and the AFC perform much better (more reduction of surface error) than the DA actuator due to the reduced authority in the decoupled direction, and the AS outperforms the AFC for the majority of the deformation modes investigated. While the AFC is able to achieve a greater reduction in the surface error when correcting for certain deformation modes, the required voltages for the AFC are much higher than the AS and DA for all the deformation modes investigated. Due to the reduction of the authority in the decoupled directions, the vibration control results show that the AS and the AFC both have less spillover of the controller's energy into the higher uncontrolled vibration modes than the DA. Similar to the shape control analysis, the AFCs perform comparably to the AS when controlling vibration, but at the cost of much higher voltages.
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