• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.597-607
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• 2019

In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.43-51
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• 2022

The aim of this paper is to obtain a Radau type quadrature formula for a rational interpolation process satisfying the almost quasi Hermite Fejér interpolatory conditions on the zeros of Chebyshev Markov sine fraction on [-1, 1).

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.708-713
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• 1994

A new flux observer based vector control system of an induction motor is constructed by using an observer in which the commanded stator currents are used to estimate the rotor flux. In this system, the flux observer is formulated by using a model of induction motor in a stationary coordinate system. By considering an observer of induction motor in a fixed co-ordinate system located on its secondary flux, a slip frequency controlled type of vector control system is also proposed. From these control schemes, the relation between the conventional slip frequency controlled type system and the observer based one is clarified. The steady-state error of the developed torque which is caused by the parameter change of induction motor is analyzed and discussed for the selection of observer gains. The poles of the observer error dynamics and those of the observer based vector control system are calculated analytically by neglecting the machine parameter change. In order to analyze the robust stability, a linear model of the observer based vector control system is proposed taking into account the machine parameter change. By using this model, the trajectories of the poles and zeros of the torque transfer function are computed and discussed. To test validity of the theoretical analysis, experiments are conducted by using a digital signal processor (TMS320C30) and a current controlled voltage source PWM inverter.

• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.76-82
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• 2003

This paper establishes some integral equalities formulated by zeros located in the convergence region of a Laplace transformable function. Using the definition of the Laplace transform, it shows that Laplace transformable functions have to satisfy the integral equalities in the time-domain, which can be applied to the understanding of the fundamental limitations on the control system represented by the transfer function. In the unity-feedback control scheme, another integral equality is derived on the output response of the system with open-loop poles located in the convergence region of the output function. From these integral equalities, two sufficient conditions related to undershoot and overshoot phenomena in the step response, respectively, are investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.855-860
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• 2005

For the accurate measurement of acoustic properties of a surface, efforts have been made to reduce errors caused by external disturbance. If the reflection coefficient is considered as a transfer function between reflected wave and incident wave, causality is required between them and the reflection coefficient should be of minimum phase. In this thesis, the minimum phase condition is applied to measure correct reflection coefficient. The reflection coefficient is approximated as a rational function in the Z domain by minimizing the sum square error. Then the minimum phase reflection coefficient is reconstructed using the distribution of poles and zeros of the reflection coefficient model. The incident wave, the reflected wave and the impulse response function of causality are recalculated from the minimum phase reflection coefficient for further applications.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.6
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• pp.85-93
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• 1997

This paper analyzes the steady-state and dynamic characteristics of the watkings-johnson converter. the major contributions of this paper includ identification of the following characteristics unique to the watkins-johnson converter: (1) The output voltage of the converter is nearly constant at the continous conduction mode (CCM), and at discontinousou conduction mode (DCM) it decreses linerly as the output curretn increases. (2) The control-to-output transfer function is a second-order one with a left-half-plane (LHP) zero determined by the combination of the output capacitor and equivalent series resistor of the converter. This LHP zero signinificantly improves the stability of the converter. (3) The control-to-output transfer function reduces to a first-order one, as the converter moves from CCM to DCM. (4) The parastic resistance of the inductor does not cause any significant influence on poles and zeros of the transfer function.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.247-260
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• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1131-1136
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• 2005

For the accurate measurement of acoustic properties of a surface, efforts have been made to reduce errors caused by external disturbance. If the reflection coefficient is considered as a transfer function between reflected wane and incident wave, the causality is required between them and the reflection coefficient should be of minimum phase. In this thesis, the minimum phase condition is applied to measure correct reflection coefficient. The reflection coefficient is approximated as a rational function In the Z domain by minimizing the sum square error. Then the minimum phase reflection coefficient is reconstructed using the distribution of poles and zeros of the reflection coefficient model.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.95-98
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• 1995

In this paper, an unknown-input proportional integral (PI) observer is presented and its applicability to the design of exact loop transfer recovery (Exact LTR) is shown. First, a sufficient condition for the PI observer to estimate the states of systems without knowledge of unknown input is derived. A simple existence condition of the observer is given. Under the conditions, the Exact LTR with specified observer's poles is achieved by the unknown-input PI observer.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1303-1314
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• 2011

We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.