• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2001년도 ICCAS
• /
• pp.38.1-38
• /
• 2001

In this paper, the vibration suppression problem of an axially moving power transmission belt is investigated. The equations of motion of the moving belt is first derived by using Hamilton´s principle for systems with changing mass. The total mechanical energy of the belt system is considered as a Lyapunov function candidate. Using the Lyapunov second method, a nonlinear boundary control law that guarantees the uniform asymptotic stability is derived. The control performance with the proposed control law is simulated. It is shown that a boundary control can still achieve the uniform stabilization for belt systems.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
• /
• pp.52-54
• /
• 1991

In this paper, the robust stability, and the quadratic performance of linear uncertain systems are studied. A quadratic Lyapunov function candidate with time-varying matrix is derived to provide robust stability bounds. Also upper bounds of a quadratic performance is given under the assumption that the uncertain system is stable. Both the robust stability bounds and the upper bounds of a quadratic performance are obtained as solutions of a class of modified Lyapunov equations.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2005년도 ICCAS
• /
• pp.700-705
• /
• 2005

The purpose of this project is the derivation and development of techniques for the new estimation of robustness for the systems having uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. Bounded means the uncertainties are with same positive/negative range. The number of uncertainties will be the degree of freedoms in the calculation of the stability region. This is so called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, the selection of Lyapunov candidate function is of various forms. In this paper, the quadratic form is selected. this generated techniques has been demonstrated by recent research interest in the area of robust control design and confirms that estimation of robustness bounds will be improved upon those obtained by results of the original Lyapunov method. In this paper, the symbolic algebraic procedures are utilized and the calculating errors are reduced in the numerical procedures. The application of numerical procedures can prove the improvements in estimations of robustness for one-and more structured perturbations. The applicable systems is assumed to be linear with time-varying with nonlinear bounded perturbations. This new techniques will be extended to other nonlinear systems with various forms of uncertainties, especially in the nonlinear case of the unstructured perturbations and also with various control method.

• 동력기계공학회지
• /
• 제21권4호
• /
• pp.18-25
• /
• 2017

This paper deals with vibration control of a small mount with MR(Magneto-Rheological) fluid as a functional fluid mount for precision equipment of automobiles. Damping and stiffness coefficients of the mount with MR fluid are changed by variations of the applied magnetic field strength. We present the robust control scheme, based on a conventional sliding mode control theory, for the design of a stable controller that is capable of vibration control due to various disturbances such as impact and periodic excitations, and is insensitive to dynamic properties of the mount. We got stable controller by using Lyapunov stability theory. The controller is then realized by using a semi-active control condition in simulations. Chattering problem of the sliding mode control is eliminated by saturation function instead of signum function. The sliding mode control with Lyapunov stability theory is superior to passive and Sky-Hook control in performance.

• Journal of Mechanical Science and Technology
• /
• 제18권8호
• /
• pp.1288-1296
• /
• 2004

Wall-following control problem for a mobile robot is to move it along a wall at a constant speed and keep a specified distance to the wall. This paper proposes wall-following controllers based on Lyapunov function candidate for a two-wheeled mobile robot (MR) to follow an unknown wall. The mobile robot is considered in terms of kinematic model in Cartesian coordinate system. Two wall-following feedback controllers are designed: full state feedback controller and observer-based controller. To design the former controller, the errors of distance and orientation of the mobile robot to the wall are defined, and the feedback controller based on Lyapunov function candidate is designed to guarantee that the errors converge to zero asymptotically. The latter controller is designed based on Busawon's observer as only the distance error is measured. Additionally, the simulation and experimental results are included to illustrate the effectiveness of the proposed controllers.

• 한국산학기술학회논문지
• /
• 제5권3호
• /
• pp.266-272
• /
• 2004

본 논문에서는 주행 차량의 직진운동 제어를 위하여 관측자를 이용한 적응제어기를 제안한다. 차체중량, 시정수 등의 차량 파라미터들을 추정하기 위해 표준형 적응칙을 이용한다. 차량의 구동력 입력에서 가속도 까지의 비선형 모델을 이용하여 차량주행 속도 및 가속도 관측자를 설계한다. 제안한 관측자의 지수함수적인 안정도 및 관측자에 의거하여 설계한 적응제어기의 안정도를 리아프노브 함수 후보에 의해 입증한다. 전체 시스템의 안정도 및 차차간 상대거리/속도/가속도 오차들의 점근적인 수렴성도 수학적으로 입증하며, 제안한 방법의 타당성 및 효율성을 시뮬레이션을 통해 검증한다.

• 한국정밀공학회지
• /
• 제11권6호
• /
• pp.20-27
• /
• 1994

This paper presents a controller design to coordinate a robot manipulator under unknown system parameters and bounded disturbance inputs. To control the motion of the manipulator, an inverse dynamics control scheme is applied. Since parameters of the robot manipulators such as mass and inertia are not perfectly known, the difference between the actual and estimated parameters works as a disturbance force. To identify the unknown parameters, an improved adaptive control algorithm is directly derived from a chosen Lyapunov's function candidate based on the Lyapunov's Second Method. A robust control algorithm is devised to counteract the bounded disturbance inputs such as contact forces and disturbing forces coming from the difference between the actual and the estimated system parameters. Numerical examples are shown using three degree-of-freedom planar arm.

• International Journal of Aeronautical and Space Sciences
• /
• 제7권2호
• /
• pp.1-13
• /
• 2006

The Lyapunov stability theory has been known inadequate to prove capturability of guidance laws because the equations of motion resulted from the guidance laws do not have the equilibrium point. By introducing a proper transformation of the range state, the original equations of motion for a stationary target can be converted into nonlinear equations with a specified equilibrium subspace. Physically, the equilibrium subspace denotes the direction of missile velocity to the target. By using a single Lyapunov function candidate, capturability of several PN laws for a stationary target is then proved for examples. In this approach, there is no assumption of the constant speed missile. The proposed method is expected to provide a unified and simplified scheme to prove the capturability of various kinds of guidance laws.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1998년도 하계학술대회 논문집 C
• /
• pp.982-984
• /
• 1998

In this paper, a stability proof of the closed-loop stability for the nonlinear feedback linearization-$H_\infty$/sliding mode controller (NFL-$H_\infty$/SMC) is done by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1998년도 하계학술대회 논문집 C
• /
• pp.994-996
• /
• 1998

In this paper, the standard Dole, Glover, Khargoneker, and Francis (abbr. : DGKF 1989) $H_{\infty}$ controller $(H_{\infty}C)$ is extended to the nonlinear feedback linearization-$H_\infty$-based sliding mode controller (NFL-$H_\infty$-based SMC). A stability proof of the closed-loop stability is done by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.