• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1047-1057
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• 2015

In [6], it is proved that the lengths of periods occurring in the ${\beta}$-expansion of a rational series r noted by $Per_{\beta}(r)$ depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic ${\beta}$-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if $r=\frac{P}{Q}$ is written in reduced form with |P| < |Q|, we will generalize the curious property "$Per_{\beta}(\frac{P}{Q})=Per_{\beta}(\frac{1}{Q})$".

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.1
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• pp.16-21
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• 2004

This paper presents an approximation method for simplifying a high-order transfer function to a low-order transfer function. A model reduction is based on minimizing the error function weighted by the numerator polynomial of reduced systems. The proposed methods provide better low frequency fit and a computer aided algorithm that estimates the coefficients vector for the numerator and denominator polynomial on the simplified systems from an overdetermined linear system constructed by frequency responses of the original systems. Two examples are given to illustrate the feasibilities of the suggested schemes.

• Geophysics and Geophysical Exploration
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• v.14 no.1
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• pp.116-120
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• 2011

Radioelement ratios are useful for mapping subtle variations in radiometric signatures in map data. But the conventional method for calculating radioelement ratios has the significant limitation that if just one of the radioelements comprising the ratio has a small spread of concentration estimates relative to its mean, then it will not contribute significantly to the ratio map. However, if both the numerator and denominator are first normalised to approximately the same mean and spread prior to ratioing, then they will contribute equally to the enhancement of the differences between them across the map area.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.127-130
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• 2003

In this paper, a hypothesis in order that the impulse response of a stable linear system does not change sign is suggested. For fixed zeros of the systems, the problem of synthesizing such a system is reduced to the problem of finding a proper denominator polynomial so that the step response of the overall system will not overshoot. The hypothesis is associated with the generalized time constant by Kim[5]. Under the hypothesis, we propose several methods that allow to compose a continuous time LTI systems achieving non-negative impulse response.

• Journal of Electrical Engineering and Technology
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• v.10 no.4
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• pp.1566-1577
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• 2015

A novel high step-up converter is presented herein, which combines the conventional buck-boost converter, the charge pump capacitor and the coupling inductor. By doing so, a quite high voltage conversion ratio due to not only the turns ratio but also the duty cycle, so as to increase design feasibility. It is noted that the denominator of the voltage conversion ratio is the square of one minus duty cycle. Above all, there is no voltage spike across the switch due to the leakage inductance and hence no passive or active snubber is needed, and furthermore, the used switch is driven without isolation and hence the gate driving circuit is relatively simple, thereby upgrading the industrial application capability of this converter. In this paper, the basic operating principles and the associated mathematical deductions are firstly described in detail, and finally some experimental results are provided to demonstrate the effectiveness of the proposed high step-up converter.

• Journal of Advanced Marine Engineering and Technology
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• v.32 no.2
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• pp.336-342
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• 2008

Simple tuning methods of PI, PD and PID controller are proposed for an integrating process with time delay. This is based on matching the coefficients of corresponding powers of s in the numerator and that in the denominator of the closed-loop transfer function. For set-point tracking problem, the derived controller is found to be a PD controller which is shown by Lee's tuning rule based on minimizing the performance indexes (ISE, IAE, ITAE) using a real-coded genetic algorithm. A method can be also proposed PI, PID controllers according to tuning parameter lambda $({\lambda})$ similar to IMC method. Simulation example is given to illustrate the set-point tracking and disturbance rejection performance of the proposed method.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.881-893
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• 1997

E. M. Silvia introduced the class $S^\lambda_\alpha$ of $\alpha$-spirallike functions f(z) satisfying the condition $$ (A) Re[(e^{i\lambda} - \alpha) \frac{zf'(z)}{f(z)} + \alpha \frac{(zf'(z))'}{f'(z)}] > 0, $$ where $\alpha \geq 0, $\mid$\lambda$\mid$ < \frac{\pi}{2}$ and $$\mid$z$\mid$ < 1$. We will generalize Silvia class of functions by formally replacing f(z) in the denominator of (A) by a spirallike function g(z). We denote the new class of functions by $Y(\alpha,\lambda)$. In this note we obtain some results for the class $Y(\alpha,\lambda)$ including integral representation formula, relations between our class $Y(\alpha,\lambda)$ and Ziegler class $Z_\lambda$, the radius of convexity problem, a few coefficient estimates and a covering theorem for the class $Y(\alpha,\lambda)$.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.8
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• pp.584-593
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• 1987

A new combined approximation method using Routh stability array and mean-square error (MSE) method is proposed for deriving reduced-order z-transter functions for discrete time systems. The Routh stability array is used to obtain the reduced-order denominator polynomial, and the numerator polynomial is obtained by minimizing the mean-square error between the unit step responses of the original system and reduced model. The advantages of the new combined approximation method are that the reduced model is always stable provided the original model is stable and the initial and steady-state characteristics of the original model can be preserved in the reduced model.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.660-669
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• 1987

Routh approximation method is the most computationally attractive. But this method may cause time-response error because this method does not match the time-response directly. In this paper a new mixed method for obtaining stable reduced-order models for high-order continuous-time systems is proposed. It makes use of the advantages of the Routh approximation method and the Minimization of Integral Squared Error(MISE) criterion approach. In this mixed method the characteristic polynomial of the reduced-order model is first obtained from that of original system by using the Auxiliary Denominator Polynomial(ADP). The numerator polynomial is then determined so as to minimize the intergral squared-error of unit step responses. The advantages of the propsed method are that the reduced models are always stable if the original system are stable and the frequency domain and time domain characteristic of the original system will be preserved in the reduced models.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.122-124
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• 2005

In this paper, we propose a switching control method for 2nd order nonlinear systems. The main idea behind the method is changing the control law before the trajectory of the solution arrives at the singularities imposed on the denominator of the control law. We show that the control system is asymptotically stable from the fact that the sector consisting of the singular hyperplanes is an invariant set. Illustrative examples are given.