19 June 2000 Measures of modal controllability and observability in balanced coordinates for optimal placement of sensors and actuators: a flexible structure application
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Abstract
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 reducing 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 eigenvector. 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 coordinate system. This paper shows 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 scheme which can take into account for the control effectiveness and the disturbance suppressibility of the closed-loop system simultaneously. These methods are applied to a simply 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.
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Jae Weon Choi, Un Sik Park, Suk B. Lee, "Measures of modal controllability and observability in balanced coordinates for optimal placement of sensors and actuators: a flexible structure application", Proc. SPIE 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures, (19 June 2000); doi: 10.1117/12.388787; https://doi.org/10.1117/12.388787
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