Placement optimization of actuators and sensors for gyroelastic body

Gyroelastic body refers to a flexible structure with a distribution of stored angular momentum provided by fly wheels or control moment gyroscopes. The angular momentum devices can exert active torques to the structure for vibration suppression or shape control. This article mainly focuses on the placement optimization issue of the actuators and sensors on the gyroelastic body. The control moment gyroscopes and angular rate sensors are adopted as actuators and sensors, respectively. The equations of motion of the gyroelastic body incorporating the detailed actuator dynamics are linearized to a loosely coupled state-space model. Two optimization approaches are developed for both constrained and unconstrained gyroelastic bodies. The first is based on the controllability and observability matrices of the system. It is only applicable to the collocated actuator and sensor pairs. The second criterion is formulated from the concept of controllable and observable subspaces. It is capable of handling the cases of both collocated and noncollocated actuator and sensor pairs. The illustrative examples of a cantilevered beam and an unconstrained plate demonstrate the clear physical meaning and rationality of the two proposed methods.