• Journal of Korean Society of Industrial and Systems Engineering
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• v.37 no.1
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• pp.165-171
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• 2014

We develop an optimization algorithm for a periodic review inventory system under a stochastic budget constraint. While most conventional studies on the periodic review inventory system consider a simple budget limit in terms of the inventory investment being less than a fixed budget, this study adopts more realistic assumption in that purchasing costs are paid at the time an order is arrived. Therefore, probability is employed to express the budget constraint. That is, the probability of total inventory investment to be less than budget must be greater than a certain value assuming that purchasing costs are paid at the time an order is arrived. We express the budget constraint in terms of the Lagrange multiplier and suggest a numerical method to obtain optional values of the cycle time and the safety factor to the system. We also perform the sensitivity analysis in order to investigate the dependence of important quantities on the budget constraint. We find that, as the amount of budget increases, the cycle time and the average inventory level increase, whereas the Lagrange multiplier decreases. In addition, as budget increases, the safety factor increases and reaches to a certain level. In particular, we derive the condition for the maximum safety factor.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.147-150
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• 1997

In the study, we consider chua's circuit which is a paradigmatic chaotic system belonging to Lur'e form. It is shown that the dynamic behavior of such a system can be influenced in such a way as to obtain out of chaotic behavior a desired periodic orbit corresponding to an unstable periodic trajectory which exists in the system. This kind of control can be achieved via injection of a single continuous time signal representing the output of the system associated with an unstable periodic orbit embedded in the chaotic attractor We investigate the case when this signal is sampled, i.e. we supply to the system the control signal at discrete time moments only.

• Journal of Astronomy and Space Sciences
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• v.5 no.2
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• pp.129-141
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• 1988

Using the numerical solution in the plane restricted problem of three bodies, abut 490 periodic orbits are computed numerically around the $L_5$ of Sun-Jupiter and about 1600 periodic orbits also be done around the $L_5$ of Sun-Jupiter system. But, in Earth-Moon system, the complex shapes and dents appear around the $L_5$ and periodic orbits intersect one another in the place where dents are shown. And there is a region that three different periodic orbits exist with the same period in this system. The increase of energy is in inverse proportion to that of period in the part of this region. The regions can exist around the $L_5$ of Sun-Jupiter system where periodic orbit can be unstable by perturbation of other force besides the gravitational force of Jupiter. These regions which is close to $L_5$ are a~5.12 AU. The Trojan asteroids that have a small eccentricity and inclination can not exist in this region.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.7
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• pp.795-805
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• 2016

Nonlinear normal modes(NNMs) is a branch of periodic solution of nonlinear dynamic systems. Determination of stable periodic solution is very important in many engineering applications since the stable periodic solution can be an attractor of such nonlinear systems. Periodic solutions of nonlinear system are usually calculated by perturbation methods and numerical methods. In this study, numerical method is used in order to calculate the NNMs. Iteration of the solution is presented by multiple shooting method and continuation of solution is presented by pseudo-arclength continuation method. The stability of the NNMs is analyzed using Floquet multipliers, and bifurcation points are calculated using indirect method. Proposed analyses are applied to two nonlinear numerical models. In the first numerical model nonlinear spring-mass system is analyzed. In the second numerical model Jeffcott rotor system which has unstable equilibria is analyzed. Numerical simulation results show that the multiple shooting method can be applied to self excited system as well as the typical nonlinear system with stable equilibria.

• Journal of Mechanical Science and Technology
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• v.19 no.7
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• pp.1405-1413
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• 2005

Malfunctions or critical fatigue problems often occur in mistuned periodic structural systems since their vibration responses may become much larger than those of perfectly tuned periodic systems. These are called vibration localization phenomena and it is of great importance to accurately predict the localization phenomena for safe and reliable designs of the periodic structural systems. In this study, a simple discrete system which represents periodic structural systems is employed to analyze the vibration localization phenomena. The statistical effects of mistuning, stiffness coupling, and damping on the vibration localization phenomena are investigated through Monte Carlo simulation. It is found that the probability of vibration localization was significantly influenced by the statistical properties except the standard deviation of coupling stiffness.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.99-106
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• 1999

This paper considers an imperfect repair model for which the repairable system is maintained preventively at periodic times and is replaced by a new system when a predetermined number of preventive maintenance has been applied. our main objective of this is to determine the optimal number of preventive maintenances before the system is replaced and the optimal length of interval between two consecutive preventive maintenances under a new repair model which is referred to as an ineffective preventive maintenance. Such a model assumes a periodic preventive maintenance in which the system is effectively maintained with a certain probability. Otherwise the system is not improved at all after each maintenance and thus the failure rate remains the same as before. The criteria to determine the optimal number of preventive maintenances and length of period is the expected cost rate per unit time for an infinite time span. We give the explicit expressions for the expected cost rate per unit time. Some numerical examples are presented for illustrative purposes.

• International Journal of Reliability and Applications
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• v.3 no.3
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• pp.113-124
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• 2002

This paper suggests the optimal periodic preventive maintenance policies after the combination warranty is expired. After the combination warranty is expired, a repairable system undergoes PM periodically and is minimally repaired at each failure. And also the system is replaced by a new system at the N th PM. In this case, we derive the mathematical formula for the expected cost rate per unit time. The optimal number and period for the periodic PM that minimize the expected cost rate per unit time are obtained. Some numerical examples are presented for illustrate purpose.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.3
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• pp.151-167
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• 2012

In this paper, we investigate the dynamic behaviors of a one-prey and two-predator system with Holling-type II functional response and defensive ability by introducing a proportion that is periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for predators at different fixed time. We establish conditions for the local stability and global asymptotic stability of prey-free periodic solutions by using Floquet theory for the impulsive equation, small amplitude perturbation skills. Also, we prove that the system is uniformly bounded and is permanent under some conditions via comparison techniques. By displaying bifurcation diagrams, we show that the system has complex dynamical aspects.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.2
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• pp.139-145
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• 2014

Periodic disturbance compensators are widely used in track following servo systems. They are commonly designed and implemented by adaptive feedforward compensators or internal model based compensators. In track following servo systems, the gains of the compensators should be determined considering the change of the sensitivity transfer function and the implementation methods should be selected considering the system environment. This paper proposes a guide for determining gains of the periodic disturbance compensators. Various simulation and experimental results are presented to see the effect of gains. In addition, this paper introduces the various types of implementation methods and compares their merits and demerits.

• 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).