• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 추계학술대회 논문집 학회본부
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• pp.195-198
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• 1995

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is the most well-known and provides precise and rigorous theoretical backgrounds. However, tile conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, it is required to consider the damping effects. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations. This method tan be utilized as a powerful tool to determine the region of attraction.

• 한국지진공학회논문집
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• 제6권6호
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• pp.49-53
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• 2002

가중행렬은 일반적인 최적 제어 설계에서 우선적으로 필요하지만 일반적으로 제어 설계자들 이 경험적 지식에 의존하고 있다. 이 논문은 구조물의 에너지를 고려한 최적제어기의 가중행렬을 결정하는 체계적인 절차를 제시하였다. 최적제어기는 LQR과 ILQR로 구분될 수 있다. 구조물의 총에너지를 고려한 Lyapunov 함수를 적용하고, 이로부터 유도된 식이 음수라는 상태를 이용하면 가중행렬을 어렵지 않게 구할 수 있다. 이러한 방법으로 산정된 가중행렬을 이용하여 LQR과 ILQR제어기를 설계하고 제어효율을 입증하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.77-80
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• 1996

In this paper a nonlinear control strategy via feedback linearization and energy based Lyapunov function for underactuated mechanical systems is investigated. Underactuated mechanical system is a system of which the number of actuators is less than the number of degrees of freedom. Developed algorithm is applied to a crane system of grab operation. Positioning of the trolley as well as swing-up of the pendulum to the up-right position including maintaining the sway angle at some desired degree are demonstrated. Simulations are provided.

• 제어로봇시스템학회논문지
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• 제7권6호
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• pp.477-486
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• 2001

Many physical systems can be modeled by incorporating continuous and discrete event nature together. Such hybrid systems contain both continuous and discrete states that influence the dynamic be-havior of the systems. There has been an increasing interest in thers types of systems during the last dec-ade, mostly due to the growing usage of computers in the control of physical plants but also as a result of the hybrid nature of physical processes. The stability theory for hybrid systems is considered as extension of Lyapunov theory where the existence of an abstract energy function satisfying certain properties verifies stability, called multiple Lyapunov theory. In this paper, a hybrid stabilizing controller is proposed using the control Lyapunov function method and multiple Lyapunov theory, and the proposed method is applied to lon-gitudinal spacing control in a vehicle platoon for intelligent transportation systems(ITS).

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제12권2호
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• pp.131-136
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• 2012

If one can find a control Lyapunov function (CLF) for a given nonlinear system, the control input stabilizing the system can be easily obtained. To find a CLF, the time derivative of an energy function should be negative definite. This procedure frequently requires a control input which is a rational function or includes an inverse function. The control input is not defined on the specific state-space where the denominator of the rational function is equal to 0 or the inverse function does not exist. In this region with singularities, the trajectory of the control system cannot be generated, which is one of the most important reasons why it is hard to make the origin of a nonlinear system be globally asymptotically stable. In this paper, we propose a smooth control law ensuring the globally asymptotic stability by means of cancelling the singularity in the control input.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.47-55
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• 2003

This paper Presents active control algorithm using probability density function of structural energy. It is assumed that the structural energy under excitation has Rayleigh probability distribution. This assumption is based on the fact that Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of control force is determined by Lyapunov controller design method. Proposed control algorithm shows much reduction of peak responses under seismic excitation compared to LQR controller, and it can consider control force limit in the controller design. Also, chattering problem which sometimes occurs in Lyapunov controller can be avoided.

• International Journal of Aeronautical and Space Sciences
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• 제4권1호
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• pp.99-109
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• 2003

Attitude control law synthesis for the three-axis attitude maneuver of a flexible spacecraft model is presented in this study. The basic idea is motivated by previous works for the extension into a more general case. The new case includes gravitational gradient torque which has significant effect on a wide range of low earth orbit missions. As the first step, the fully nonlinear dynamic equations of motion are derived including gravitational gradient. The control law design based upon the Lyapunov approach is attempted. The Lyapunov function consists of a weighted combination of system kinetic and potential energy. Then, a set of stabilizing control law is derived from the basic Lyapunov stability theory. The new control law is therefore in a general form partially validating the previous work in some sense.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
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• pp.133-134
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• 2007

A swing-up control strategy is suggested for a rotary inverted pendulum with restricted rotation range. In order to take the rotation range limitation into account, a new Lyapunov function used for energy-based control is proposed a control strategy is derived from the Lyapunov function. Futhermore, optimization-base parameter estimation is adopted to get an exact mathematical model for the pendulum. Simulation results show that the proposed control strategy swings up the rotary inverted pendulum efficiently.

• 제어로봇시스템학회논문지
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• 제14권6호
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• pp.548-553
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• 2008

In this paper, we propose a new swing-up control strategy for rotary inverted pendulums with restricted rotation range. The control law is derived from a Lyapunov function. The Lyapunov function is defined as the square of the sum of the absolute value of the total mechanical energy and weighted squares of the arm's angular displacement and velocity. By adjusting the weighting parameters in the Lyapunov function, we can affect the swing-up strategy such that the restriction on rotation range can be satisfied. Finally, we verify the performance of the proposed control law through simulation and experiments.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.2474-2479
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• 2005

The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving nonlinear string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton's principle. The Lyapunov function method is used in deriving a boundary control law, in which the Lyapunov function candidate is introduced from the total mechanical energy of the system. The performance of the proposed control law is compared with other two control algorithms available in the literature. Experimental results are given.