Optimal placement of actuators and sensors for gyroelastic body from the controllability and observability perspective

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