• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.1
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• pp.168-175
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• 2010

The issue of rejecting periodic disturbances arises in various applications dealing with rotating machinery. A new method using DIDF (Dual-Input Describing Function) is presented for the rejection of periodic disturbances with uncertain frequency. This can be added to an existing feedback control system without altering the closed-loop system stability. The objective is to design a nonlinear compensator to secure specified oscillation amplitude and frequency which are the same as disturbances. We suggest two procedures to determine coefficients for DIDF's synthesis. The structure of the proposed DIDF is so simple that we can easily synthesize. A number of computer simulations were carried out to demonstrate the salient feature of the proposed DIDF compared to the conventional ones(that is, adaptive algorithms).

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.67.5-67
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• 2001

A closed loop system with a linear plant and nonlinearity in the feedback connection is analyzed for its quasi-static orbital stability by a state-space approach. First a periodic orbit is assumed to exist in the loop which is determined by describing function method for the given nonlinearity. This is possible by selecting a proper nonlinearity and a rigorous justification of the describing function method.[1-3, 18, 20]. Then by introducing residual operator, a linear perturbed model can be formulated. Using various transformations like a modified eigenstructure decomposition, periodic-averaging, charge of variables and coordinate transformation, the stability of the periodic orbit, as a solution of harmonic balance, can be shown by investigating a simple scalar function and result of linear algebra. This is ...

• Journal of the Korean Data and Information Science Society
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• v.19 no.2
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• pp.587-596
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• 2008

This paper develops the optimal periodic preventive maintenance policies following the expiration of warranty: renewing warranty and non-renewing warranty. After the warranty period is expired, the system undergoes the PM periodically and is minimally repaired at each failure between two successive PMs. Firstly, we determine the expected cost rate per unit time and the expected downtime per unit time for the periodic PM model. Then the overall value function suggested by Jiang and Ji(2002) is applied to obtain the optimal PM period and the optimal PM number. Finally, the numerical examples are presented for illustrative purpose.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1415-1432
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• 2013

We consider the value distribution of a class of the functions analytic in the exterior of a disc and their applications to complex oscillation theory of differential equations with periodic coefficients in the complex plane.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.7
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• pp.994-1002
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• 2013

This study suggests a generalized availability and safety evaluation model to evaluate the influences to the system's fault tolerant capabilities depending on automatic fault detection function such as the automatic periodic testings. The conventional evaluation model of automatic fault detection function deals only with the self diagnostics, and supposes that the fault detection coverage of self diagnostics is always constant. But all of the fault detection methods could be degraded. For example, the periodic surveillance test has the potential human errors or test equipment errors, the self diagnostics has the potential degradation of built-in logics, and the automatic periodic testing has the potential degradation of automatic test facilities. The suggested evaluation models have incorporated the loss or erroneous behaviors of the automatic fault detection methods. The availability and the safety of each module of the safety grade platform have been evaluated as they were applied the automatic periodic test methodology and the fault tolerant evaluation models. The availability and safety of the safety grade platform were improved when applied the automatic periodic testing. Especially the fault tolerant capability of the processor module with a weak self-diagnostics and the process parameter input modules were dramatically improved compared to the conventional cases. In addition, as a result of the safety evaluation of the digital reactor protection system, the system safety of the digital parts was improved about 4 times compared to the conventional cases.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.45 no.3
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• pp.78-89
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• 2022

The purpose of this study was to propose useful suggestion by analyzing preventive replacement policy under which there are minor and major failure. Here, major failure is defined as the failure of system which causes the system to stop working, however, the minor failure is defined as the situation in which the system is working but there exists inconvenience for the user to experience the degradation of performance. For this purpose, we formulated an expected cost rate as a function of periodic replacement time and the number of system update cycles. Then, using the probability and differentiation theory, we analyzed the cost rate function to find the optimal points for periodic replacement time and the number of system update cycles. Also, we present a numerical example to show how to apply our model to the real and practical situation in which even under the minor failure, the user of system is not willing to replace or repair the system immediately, instead he/she is willing to defer the repair or replacement until the periodic or preventive replacement time. Optimal preventive replacement timing using two variables, which are periodic replacement time and the number of system update cycles, is provided and the effects of those variables on the cost are analyzed.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.47-56
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• 2003

This note is concerned with some properties of fixed points and periodic points. First, we have constructed a generalized continuous function to give a proof for the fact that, as the reverse of the Sharkovsky theorem[16], for a given positive integer n, there exists a continuous function with a period-n point but no period-m points wherem is a predecessor of n in the Sharkovsky ordering. Also we show that the composition of two transcendental meromorphic functions, one of which has at least three poles, has infinitely many fixed points.

• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.50-61
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• 1996

The breaking phenomenon of regular periodic waves generated by a numerical wave maker is simulated by finite-difference method which can cope with strong interface motions. The air and water flows are simultaneously solved in the time-marching solution procedure for the Navier-Stokes equation. A density-function technique is devised for the implemenation of the interface conditions. The accuracy is examined and applied to the simulation of two-dimensional breaking phenomena of periodic gravity waves.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.751-753
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• 1995

Practical controllers of industrial systems are usually designed and realized in continuous time domain. However, due to the programmable and flexible nature of digital computers and the speed and stability superioity of digital components over analog ones, it seems more effective to adapt digital controllers. When an existing analog controller performs satisfactory, it is often advantageous to use the digital redesign techinque to obtain an equlivalent digital controller which substitutes the analog one. One method of the digital redesign is to use a periodic gain. This method gives a riffle effect on the steady state response, although it's transient response is satisfactory. This paper suggests a method which eliminates or deminishes periodic ripples generated by the periodic function.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.307-315
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• 2014

We investigate an approximation order of a continuous $2{\pi}$-periodic function by periodic neural networks. By using the De La Vall$\acute{e}$e Poussin sum and the modulus of continuity, we obtain a degree of approximation by periodic neural networks.