• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.327-344
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• 2005

The first part of the paper deals with a brief introduction of the plant-herbivore model system along with deterministic analysis of local stability and Hopf-bifurcations. The second part consists of stability analysis of the limit cycle arising from Hopf-bifurcation and uniqueness of limit cycle. The third part deals with the study of global stability of the model system under consideration.

• 전자공학회논문지 IE
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• 제46권3호
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• pp.33-41
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• 2009

본 논문에서는 Limit-cycle 항법의 안정성을 분석하고 path follwer를 제안한다. Limit-cycle 항법은 2차 비선형 함수의 특징을 이용하며, 빠른 이동로봇의 움직임을 제어하기 위해 제안되어졌다. Limit-cycle의 수렴반경과 방향을 조절하여 충돌 없이 장애물을 회피하고, 목표점에 도달할 수 있다. 하지만 지금까지 Limit-cycle 항법의 안정성은 연구되어지지 않았다. 따라서 본 논문에서는 이러한 안정성을 분석하고, Limit-cycle 항법을 로봇축구에 적용하여, 시뮬레이션과 실제 실험에서 제안된 방법을 검증한다.

• Journal of Electrical Engineering and Technology
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• 제6권5호
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• pp.697-705
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• 2011

In this paper, a closed-loop system constructed with a linear plant and nonlinearity in the feedback connection is considered to argue against its planar orbital stability. Through a state space approach, a main result that presents a sufficient stability criterion of the limit cycle predicted by solving the harmonic balance equation is given. Preliminarily, the harmonic balance of the nonlinear feedback loop is assumed to have a solution that determines the characteristics of the limit cycle. Using a state-space approach, the nonlinear loop equation is reformulated into a linear perturbed model through the introduction of a residual operator. By considering a series of transformations, such as a modified eigenstructure decomposition, periodic averaging, change of variables, and coordinate transformation, the stability of the limit cycle can be simply tested via a scalar function and matrix. Finally, the stability criterion is addressed by constructing a composite Lyapunov function of the transformed system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.507-507
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• 2000

In this paper, a kind of limit cycle of an inverted pendulum system is discussed. We propose a stabilization control law for such a limit cycle of an inverted pendulum system that the pendulum rotates periodically. Besides, the stabilization control law is extended so as to ensure not only stability of the limit cycle but also an L$_2$-gain disturbance attenuation in the presence of modeling error and viscosity friction.

• 대한기계학회논문집
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• 제19권6호
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• pp.1469-1478
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• 1995

PWM control is a kind of nonlinear control. The merits of PWM control of hydraulic equipment are the robustness of the high speed on-off valve and its low price. And it is easily implemented to hydraulic equipments with microcomputer. The high speed on-off valve is directly digitally controlled without any D/A converter. The objectives of this study is to analyze the limit cycle which regularly appear in the position control system using high speed on-off valve, and to give a criterion for the stability of this system. To do this, the nonlinear characteristics of PWM and cylinder friction of this system are described by harmonic linearization and the effects of parameter variations to the system stability are examined theoretically and experimentally. Consequently, the availability of the proposed method is confirmed well.

• 한국소음진동공학회논문집
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• 제13권12호
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• pp.903-910
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• 2003

A two-degree-of-freedom model is suggested to describe basic dynamical behaviors of the interaction between the pad and the disc of a disc brake system. Although a pad (and a disc) has many modes of vibration in practice, only one mode of each component Is considered. In this paper, a linear analysis is performed by means of the stability analysis to show various conditions for the system to become unstable, and is based on the assumption that the existence of limit cycle (this corresponds to an unstable equilibrium point inside the limit cycle) represents the squeal state of the disc brake system. The results of the stability analysis show that the damping of the disc is as much Important as that of the pad, whereas the damping of the pad only is considered In most practical situations.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.299-304
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• 1991

A novel approach based on a nonlinear compensator is proposed to prevent 'windup', which is caused by the saturation of the actuator and the integration action of the controller. The anti-windup compensator is located between the conventional linear controller, designed neglecting the saturation, and the actuator. It was proven based on the describing function method that, if the closed loop control systems are stable assuming no saturation, then there exist a range of compensator gain which prevents any limit-cycle and hence, guarantees the system stability. The computer simulation results show that the compensator proposed in the manuscript can eliminate unstable limit cycle and improve the transient response.

• 한국소음진동공학회논문집
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• 제21권6호
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• pp.562-569
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• 2011

In this study linear and nonlinear dynamic stability characteristics of a medium-size high-speed turbocharger, whose rotor is supported by two 3-lobe journal bearings, are analyzed to evaluate and identify the effects of its bearing design variables. The rotor has the rated speed of 40,500 rpm and maximum continuous speed of 45,000 rpm. At first, utilizing the linear stability analysis method, bearing designs of yielding stable or unstable LogDecs as small as possible are searched by manipulating with machined bearing clearances and preloads. As next, utilizing the nonlinear analysis method, limit cycles of the rotor responses at the rated and maximum continuous speeds are simulated to check their acceptances. Results have shown that for the turbocharger rotor-bearing system considered, the 3-lobe journal bearing design with a smaller machined clearance and a larger preload are preferred for the stable rotor responses. More importantly, since there exists a good correlation between the linear and nonlinear stability analysis results, it is concluded that firstly the linear stability analysis method may be applied to screen quickly the ranges of bearing designs for stable or least unstable solutions and then, lastly the nonlinear stability analysis method may be deployed to check an absolute motion stability in terms of the limit cycle.

• 충청수학회지
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• 제28권3호
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• pp.465-472
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• 2015

In this paper, we study the existence and the stability of equilibria of predator-prey models with Ivlev's functional response. We give a simple proof for the uniqueness of limit cycles of the predator-prey system. The existence and the stability at the origin and a boundary equilibrium point(including the positive equilibrium point) are also investigated.

• 한국군사과학기술학회지
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• 제11권4호
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• pp.159-165
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• 2008

The purpose of this paper is to study the impact of concentrated nonlinearities, freeplays, on the aeroelastic behaviors of single- and double-folded control fins. The nonlinearities may cause limit cycle oscillation(LCO) below the linear flutter boundary. The effects of nonlinear hinges on LCO characteristics of the fins are examined as flight condition changes. Nonlinear time-domain flutter analyses are performed, using ZAERO. The results show that the aeroelastic stability boundaries of double-folded fin(DF) are higher than those of the single-folded fin(SF) and the lower hinge freeplay impact more critically on the stability than the upper hinge freeplay of the DF.