• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.71-77
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• 1995

The control effectiveness and disturbance suppressibility are mainly governed by a left eigenstructure of a system. In this paper, a control algorithm which uses an output feedback eigenstructure assignment scheme is proposed in order that a desired closed-loop system has the specified degree of controllability and/or degree of disturbance suppressibility. To do this, a modal and a gross disturbance suppressibility measures are proposed. A modified version of Hamdan and Nayfeh's modal controllability measure is also presented. The validity and usefulness of the proposed measures and the controller design algorithm are illustrated by designing a controller for a third-order system as an example.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.647-655
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• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.412-419
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• 1993

The transient responses of a linear system having undesired disturbances are dominantly governed by the system's left eigenstructure(eigenvalues/left eigenvectors). In control system design problem of altering the transient response of the system, both the controllability and the disturbance suppressibility, should be considered simultaneously to obtain a robust, effective controller. The controllability of the system may be degraded if the left eigenstructure is chosen to suppress the disturbance, or vice versa. In this paper, first, proposed are a modal disturbance suppressibility measure and an improved version of the modal controllability measure suggested by Hamdan and Nayfeh. Second, a simple and general left eigenstructure assignment scheme, considering both the proposed modal disturbance suppressibility measure and the improved version of modal controllability measure, is suggested. When the previous works are applied to assign the left eigenvectors may differ from the desired ones. But the proposed left eigenstructure assignment scheme makes it possible to achieve the desired colsed-loop eigenvalues exactly, provided the desired left eigenvectors reside in the achievable subspace. In case the desired left eigenvectors do not reside in the achievable subspace, the closed-loop eigenvalues are achieved exactly and the left eigenvectors are assigned to the best possible set of eigenvectors in the least square sense. Finally, a numerical example is included to confirm and demonstrate the usefulness of our propositions and to illustrate the proposed design scheme.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.47-51
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• 1993

A method of finding the optimal actuator location for efficient control of the modes of interest is presented. The proposed approach relies on certain quantitive measure of degree of controllability based on the controllability grammian. This measure proves to be useful for regulating problem of the undamped system and can be extended to cover the tracking problem of the viscous damped system. The example of the uniform cantilever beam is given to verify the effectiveness of the method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.63-70
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• 2008

In this paper, we propose a bearing redundant coordinates and decoupled PD controller for 5-axes active magnetic bearing system, which consists of two bearing parts such as three-pole hybrid active magnetic bearing for stabilize the radial direction and ring-type permanent magnetic bearing stabilizing in axial and tilting motion. Based on derived system equation with decoupled control scheme, we conduct the modal analysis and measure of modal controllability and observability.