• Journal of the Korea Computer Graphics Society
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• v.7 no.3
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• pp.1-7
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• 2001

We present an efficient and robust algorithm to parametrize a perspective silhouette curve of a canal surface. We also detect each connected component of the silhouette. A canal surface is an envelope surface of a moving sphere with varying radii, which is defined by the center trajectory C(t) and radius function r(t) of the moving sphere. A canal surface can be decomposed to a set of characteristic circles. We derive the equations for the silhouette points on each characteristic circle, then parameterize the silhouette curve by using the equation. The sphere $S(t_*)$ with center point $C(t_*)$ and radius $r(t_*)$ intersects with the canal surface at a characteristic circle $K(t_*)$. The perspective silhouette of the sphere $S(t_*)$ from given view point consists of a circle $Q(t_*)$. By finding the values of t at which K(t) and Q(t) tangentially intersect, we detect each connected component of the silhouette curve.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.278-285
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• 1999

This paper utilizes the method of Q-parameterization control to design a controller which solves the problem of imbalance in magnetic bearing systems. There are two methods to solve this problem using feedback controal. The first method is to compensate for the imbalance forces by generating opposing forces on the bearing surface (imbalance compensation). The second method is to make the rotor rotate around its axis of inertia (automatic balancing);in this case no imbalance forces will be generated. In this paper we deal with only imbalance compensation. The free parameter of the Q-parameterization controller is chosen such that these goals are achieved. After the introduction of a model of the magnetic bearing system, we explain the Q-parameterization controller design of the magnetic bearing system with emphasis on the rejection of sinusoidal disturbance for imbalance compensation design. The design objectives are formulated as a linear equations in the controller free paramete Q. Finally, simulation and experimental results are presented and showed the robustness and effectiveness of the proposed controllers.

• Journal of KSNVE
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• v.8 no.5
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• pp.964-973
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• 1998

In this paper we propose a levitation and imbalance compensation controller design methodology of magnetic bearing system. In order to achieve levitation and elimination of unbalance vibartion in some operation speed we use the discrete-time Q-parameterization control. When rotor speed p = 0 there are no rotor unbalance, with frequency equals to the rotational speed. So in order to make levitatiom we choose the Q-parameterization controller free parameter Q such that the controller has poles on the unit circle at z = 1. However, when rotor speed p $\neq$ 0 there exist sinusoidal disturbance forces, with frequency equals to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has poles on the unit circle at z = $exp^{ipTs}$ for a certain speed of rotation p ( $T_s$ is the sampling period). First, we introduce the experimental setup employed in this research. Second, we give a mathematical model for the magnetic bearing in difference equation form. Third, we explain the proposed discrete-time Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function. Fourth, we show that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. Finally, several simulation and experimental results are obtained to evaluate the proposed controller. The results obtained show the effectiveness of the proposed controller in eliminating the unbalance vibrations at the design speed of rotation.