• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.4
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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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• v.8 no.6
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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.

• Proceedings of the IEEK Conference
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• 2009.05a
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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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• v.15 no.1
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.1
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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.

• The Journal of Korea Robotics Society
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• v.7 no.1
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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.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.4
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• pp.1-6
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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 mode 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. The convergence of the designed controller is proved by the new notion 'degree indicator'.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.9
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.2
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• pp.192-197
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• 2011

In this paper, the output feedback control of inverted pendulum systems is experimented for the practicality verification of the linear state observer. For the experiment, a pendulum system, CEM-IP-01 of Cemware Inc. is used and Lagrange equation and Jacobian linearization are adopted for the dynamic analysis of the pendulum system. In addition, the output responses of the state feedback control and the output feedback control of the pendulum system are compared before the experiment by Matlab. Finally, we directly verify the practical use of the linear state observer by recognizing and solving some real problem to control the inverted pendulum system in practice.