• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• 호남수학학술지
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• 제43권4호
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• pp.679-689
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• 2021

The first author suggested an exact volume formula of the hypercubes [0, 1]ⁿ clipped by several hyperplanes expressed directly in terms of linear coefficients of the hyperplanes. However, it requires awkward assumptions to apply the formula to various situations. We suggest a concrete method to overcome those restrictions for two or three hyperplanes using 𝜖-perturbation, which gives an exact value applicable for any kind of arrangement of hyperplanes with no consideration.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.35-59
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• 2006

In this paper, we generalized the results of [23, 26], and get the results of the condition number of the W-weighted Drazin-inverse solution of linear system W AW\chi=b, where A is an $m{\times}n$ rank-deficient matrix and the index of A W is $k_1$, the index of W A is $k_2$, b is a real vector of size n in the range of $(WA)^{k_2}$, $\chi$ is a real vector of size m in the range of $(AW)^{k_1}$. Let $\alpha$ and $\beta$ be two positive real numbers, when we consider the weighted Frobenius norm $\|[{\alpha}W\;AW,\;{\beta}b]\|$(equation omitted) on the data we get the formula of condition number of the W-weighted Drazin-inverse solution of linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated.

• International Journal of Control, Automation, and Systems
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• 제6권6호
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• pp.836-844
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• 2008

This paper presents an approach to order reduction of linear parameter varying controller for polytopic model. Feasible solutions which satisfy relevant linear matrix inequalities for constructing full-order parameter varying controller evaluated at each polytopic vertices are first found. Next, sufficient conditions are derived for the existence of a right coprime factorization of parameter varying controller. Furthermore, a singular perturbation approximation for time invariant systems is generalized to reduce full-order parameter varying controller via parameter varying right coprime factorization. This generalization is based on solutions of the parameter varying Lyapunov inequalities. The closed loop performance caused by using the reduced order controller is developed. To examine the performance of the reduced-order parameter varying controller, the proposed method is applied to reduce vibration of flexible structures having the transverse-torsional coupled vibration modes.

• Journal of Mechanical Science and Technology
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• 제20권9호
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• pp.1428-1435
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• 2006

A slightly curved crack with an eigenstrain is considered. Solutions for a slightly curved crack in a linear isotropic material under asymptotic loading as well as for a slightly curved crack in a linear isotropic material with a concentrated force are obtained from perturbation analyses, which are accurate to the first order of the parameter representing the non-straightness. Stress intensity factors for a slightly curved crack with an eigenstrain are obtained from the perturbation solutions by using a body force analogy. Particular attention is given to the crack path stability under mode I loading. A new parameter of crack path stability is proposed for a crack with an eigenstrain. The path stability of a crack with steady state growth in a transforming material and a ferroelectric material is examined.

• 제어로봇시스템학회논문지
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• 제5권4호
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• pp.411-418
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• 1999

Generally PI controller is used in the servo system, But the time response of the system which is designed by the PI control scheme is deviated from the desired time response by the system parameter variation or the perturbation like the torque disturbance. LMFC(Linear Model Following Controller) is used to make the response of the system follow that of the model even though the parameter variation or the perturbation exists. In this paper, the design method which uses auxiliary model to construct the robustness enhancer in LMFC is proposed. And this robustness enhancer is designed by robust control theory. The proposed method has facter convergence time against low frequency torque disturbance than LMFC. The results are verified by SIMULINK simulation and experiments.

• 소음진동
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• 제7권3호
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• pp.387-392
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• 1997

This paper concerns a SCARA robot with the flexible forearm linked to the rigid upper arm. The equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are determined based on the inverse dynamics of the latter. In order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified to have a prescribed degree of stability. The proposed control scheme shows satisfactory performances in experiments as well as in numerical simulations.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.225-228
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• 1996

This paper concerns a SCARA type robot with the second arm flexible. Its equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are first determined based on the inverse dynamics of the latter. Next, in order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified with a prescribed degree of stability. The numerical simulations results show the satisfactory control performance.

• Journal of Mechanical Science and Technology
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• 제14권4호
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• pp.393-400
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• 2000

In this paper, a new algorithm for noninteracting control system design is proposed and applied to ship propulsion system control. For example, if a ship diesel engine is operated by consolidated control with controllable pitch propeller (CPP), the minimum fuel consumption is achieved satisfying the demanded ship speed. For this, it is necessary that the ship is operated on the ideal operating line which satisfies the minimum fuel consumption, and the both pitch angle of CPP and throttle valve angle are controlled simultaneously. In this context of view, this paper gives a controller design method for a ship propulsion system with CPP based on noninteracting control theory. Where, linear matrix inequality (LMI) approach is introduced for the control system design to satisfy the given $H_{\infty}$, constraint in the presence of physical parameter perturbation and disturbance input. To the end, the validity and applicability of this approach are illustrated by the simulation in the all operating ranges.

• 제어로봇시스템학회논문지
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• 제5권7호
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.