Measures of modal controllability and observability in balanced coordinates for optimal placement of sensors/actuators: a flexible structure application

摘要

In general, it is well known that the measures of controllability and observability are variant under a coordinates transformation. In particular, the balanced realization of a system which is useful for reducting the order of a model and for implementing filters has some valuable properties, for example, that a system is equally controllable and observable and has a symmetric relation between a left and the corresponding right eighenvector. In this paper, we present a method for optimal placement of sensors and actuators by using the proposed measures of modal controllability and observability which are defined in a balanced coordingate system. This paper shown that these measures are more pertinent and useful in practical engineering problem such as the selection of the optimal number and location of sensors and actuators, and they are more accurate than the earlier results of Hamdan and Nayfeh in a viewpoint that they can reflect the effects of the norm of eigenvectors on the magnitude of measures. In addition, the optimal placement method using the additional measures is presented. For the vibration suppression of a flexible structure, a state feedback controller is designed by using the left eigenstructure assignment sceme which can take into account for the control effectiveness and the disturbance suppressibility of the closed-loop system simulataneously. These methods are applied to a simploy supported flexible beam which is modeled to have six vibration modes, and the results of the simulations for optimal placement of sensors and actuators and vibration control of a flexible structure are presented for the validity of the proposed measures and the optimal placement method.