• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.987-1004
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• 2018

In this paper, we get several centroaffine invariant properties for a ruled surface in ${\mathbb{R}}^4$ with centroaffine theories of codimension two. Then by solving certain partial differential equations and studying a centroaffine surface with some centroaffine invariant properties in ${\mathbb{R}}^4$, we obtain such a surface is centroaffinely equivalent to a ruled surface or one of the flat centered cyclic surfaces. Furthermore, some centroaffine invariant properties for centered cyclic surfaces are considered.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1847-1852
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• 2004

This article provides the connection between feedback stabilization and interpolation conditions for n-D linear systems (n > 1). In addition to internal stability, if one demands performance as a design goal, then there results an n-D matrix Nevanlinna-Pick interpolation problem. Application of recent work on Nevanlinna-Pick interpolation on the polydisk yields a solution of the problem for the 2-D case. The same analysis applies in the n-D case (n > 2), but leads to solutions which are contractive in a norm (the "Schur-Agler norm") somewhat stronger than the $H^{\infty}$ norm. This is an analogous version of the connection between the standard $H^{\infty}$ control problem and an interpolation problem of Nevanlinna-Pick type in the classical 1-D linear time-invariant systems.

• Journal of KSNVE
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• v.6 no.4
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• pp.521-528
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• 1996

Recently, higher speed optical disk drives including computer CD-ROM drives tend to be increasingly demanded to read or write the enormous volume of digital data. To this end, both structure and controller designs of the optical pick-ups should be improved concurrently. In this paper, the pick-up during auto-focusing motion is mathematically modelled retaining all its peculiar features. The model turns out a linear time invariant system suitable for a control design namedH${\infty}$ which ensures robust stability in the presence of system uncertainties. Numerical simulations are performed to demonstrate the robustness with appropriate performance specifications being satisfied. In addition, as the implementation issue of it, procedures of temporal discretization as well as model reduction of the controller are also addressed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.119-124
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• 1996

Recently, high speed optical disk drives are increasingly demanded to read or write data fastly enough. To this end, both structure and controller designs of their optical pick-ups should be improved concurrently. In this paper, the pick-up during auto-focusing motion is mathematically modelled retaining all its peculiar features. The model turns out a linear time invariant system suitable for a control design method named H$_{\infty}$ which ensures robust stability in the presence of system uncertainties. Numerical simulation are performed to demonstrate the controller robustness with appropriate performance specifications being satisfied..

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.12
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• pp.1903-1910
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• 2012

This paper presents a data based low-order controller design algorithm for a linear time-invariant process with a time delay. The algorithm is composed by combining an identification step based on open loop pulse test with a low-order controller design step to obtain the entire set of controllers achieving multiple performance specifications. The initial information necessary for this algorithm are merely the width and amplitude of a rectangular pulse, a controller of four types (PI, PD, PID, first-order), and design objectives. Various parametric approaches that have been developed are merged in the controller design algorithm. The resulting controller set satisfying the design objectives are displayed on the 2D and 3D graphics and thus it is very easy for us to pick a controller inside the admissible set because we can check the corresponding closed-loop performances visually.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.5
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• pp.462-466
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• 2008

This paper proposes a stable gain scheduling method of linear time invariant controllers for tracking servo system. In order to read and write the data on the optical disc, the pick-up head should be moved to the exact track quickly and follow the track immediately. Two different controllers are used for each moving and track-following. In pull-in period, a transition period from moving to track-following, the head might slip and miss the target track. This brings on another searching process and increases the total time. One way to avoid slipping is to extend the bandwidth of the track-following controller. But, extending the bandwidth could degrade the following performance. More prevalent way is to use one more controller in this pull-in period and switch to the following controller. In general, however, switching or scheduling of stable controllers cannot guarantee the stability. This paper suggests an scheduling method guaranteeing the overall stability not only in a generalized form but also in special form for SISO system. The sufficient condition is derived from the fact that Q factor of a stable controller should be stay in $RH_{\infty}$ space. In the experiment, the proposed method shows better performance than the switching method such as shorter time and lower current consumption.