• 전기학회논문지
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• 제66권5호
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• pp.819-832
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• 2017

We propose a new switching control scheme for a ball and beam system by utilizing two linearization methods. First, the Jacobian linearization is applied and state observer is developed afterward. Then, motivated [6], the approximate input-output linearization is carried out, and after that, the Jacobian linearization is applied along with the design of state observer. Since the second approach requires two linearizations, it is called a two-step linearization method. The state observer is needed for the estimation of the velocities of ball and motor movement. Since the Jacobian linearization based controller tends to provide faster response at the initial time, and after that, the two-step linearization based controller tends to provide better response in terms of output overshoot and convergence to the origin, it is natural to give a switching control scheme to provide the best overall control response. The validity of our control scheme is shown in both simulation and experimental results.

• 전기학회논문지
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• 제64권4호
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• pp.578-585
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• 2015

Electromagnetic levitation system(EMLS) is one of the well known nonlinear systems. Often, it is not easy to control an EMLS due to its high nonlinearity. In this paper, we first apply two linearization method(jacobian and input-output feedback linearization) to design two feedback controllers for an EMLS. Then, by observing the advantages of each controller, we design a switching control algorithm which engage two controllers depending on the position of the steel ball in order to achieve the improved performance over each controller. The validity of our switching control approach is verified via both simulation and actual experimental results.

• Journal of Electrical Engineering and Technology
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• 제8권6호
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2009년도 정보 및 제어 심포지움 논문집
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• pp.79-81
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• 2009

In this paper, we design a dynamic state feedback smooth stabilizer for a nonlinear system whose Jacobian linearization may have uncontrollable because its eigenvalues are on the right half-plane. After designing an augmented system, a dynamic exponent scaling and backstepping enable one to explicitly design a smooth stabilizer and a continuously differentiable Lyapunov function which is positive definite and proper.

• Journal of Mechanical Science and Technology
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• 제15권1호
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• pp.125-138
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• 2001

An efficient correction storage scheme on a structured grid is applied to a sequence of approximate Jacobian systems arising at each time step from a linearization of the discrete nonlenear system of equations, obtained by the implicit time discretization of the conservation laws for unsteady fluid flows. The contribution of freezing the Jacobian matrix to computing costs is investigated within the correction storage scheme. The performance of the procedure is exhibited by measuring CPU time required to obtain a fully developed laminar vortex shedding flow past a circular cylinder, and is compared with that of a collective iterative method on a single grid. In addition, some computed results of the flow are presented in terms of some functionals along with measured data. The computational test shows that the computing costs may be saved in favor of the correction storage scheme with the frozen Jacobian matrix, to a great extent.

• 전기학회논문지
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• 제66권1호
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• pp.72-81
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• 2017

We propose a switching control scheme for the control of a ball and beam system. It was reported in [4] that a ball and beam system is a nonlinear system which has an ill-defined relative degree. So, the traditional control approaches have been mostly either Jacobian-based control or approximate input-output linearized control in nature. In this paper, motivated by [7], we combine these two traditional control approaches and operate each controller via a pre-designed switching logic so that the improved control result can be obtained without any excessive use of control input. Switching algorithm is developed based on both analysis and actual experimental observation. We verify the effectiveness of our proposed controller via actual experimental results.

• 로봇학회논문지
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• 제7권1호
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• pp.29-34
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• 2012

This paper suggests a new observation model for Extended Kalman Filter based Simultaneous Localization and Mapping (EKF-SLAM). Since the EKF framework linearizes non-linear functions around the current estimate, the conventional line model has large linearization errors when a mobile robot locates faraway from its initial position. On the other hand, the model that we propose yields less linearization error with respect to the landmark position and thus suitable in a large-scale environment. To achieve it, we build up a three-dimensional space by adding a virtual axis to the robot's two-dimensional coordinate system and extract a plane by using a detected line on the two-dimensional space and the virtual axis. Since Jacobian matrix with respect to the landmark position has small value, we can estimate the position of landmarks better than the conventional line model. The simulation results verify that the new model yields less linearization errors than the conventional line model.

• 전자공학회논문지SC
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• 제46권4호
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• pp.1-6
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• 2009

본 논문에서 우리는 비선형 시스템에 대한 다이나믹 스무스 상태 궤환 안정화기를 설계한다. 이 시스템은 우반평면에 고유값이 존재함으로 제어불가능 모드를 가질 수 있다. 이 시스템을 지수적으로 안정화하기 위해서 우리는 추가 다이나믹스를 고려한 다이나믹 제어기를 제안한다. 추가 다이나믹스의 설계 후에 다이나믹 차수 보정법과 역진기법을 이용하여 안정화기와 미분 가능, positive definite, proper인 리아푸노프 함수를 설계한다. 설계된 제어기의 수렴성은 차수 지표자라는 새로운 개념의 도입으로 증명될 것이다.

• 대한전기학회논문지:시스템및제어부문D
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• 제53권9호
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• pp.630-637
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• 2004

In this paper, we present a local reduced-order observer for a class of nonlinear systems that have full robust relative degree. The proposed observer utilizes the coordinate change which transforms a nonlinear system into an approximate normal form. The proposed reduce order observer is applied to a ball and beam system, and simulation results show that substantial improvement in the performance was achieved compared with the jacobian linearization observers.

• 한국지능시스템학회논문지
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• 제21권2호
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• pp.192-197
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• 2011

본 논문은 선형 상태 관측기의 성능 및 실용화 검증을 위하여 도립진자 시스템의 출력 피드백 제어 실험을 수행하였다. 도립진자 시스템으로는 (주)셈웨어의 CEM-IP-01를 실험에 사용하였다. 동역학 해석을 위하여 라그랑지안 방정식 및 자코비안 선형화 방법을 이용하였고, 모의실험을 통하여 일반 상태 피드백 제어기의 출력 응답과 제안된 제어기의 출력 응답을 먼저 비교 분석하였다. 마지막으로 실제 도립진자 시스템에 적용함으로써 제어기 구현에서 발생하는 문제점을 파악하고 해결함으로써 실용화 가능성을 직접 확인하였다.