• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.658-662
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• 2004

This paper develops a stability analysis and controller synthesis methodology for a continuous-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties. Affine T-S fuzzy system can be an advantage because it may be able to approximate nonlinear functions to high accuracy with fewer rules than the homogeneous T-S fuzzy systems with linear consequents only. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of bilinear matrix inequalities (BMIs). A simulation example is given to illustrate the application of the proposed method.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1022-1027
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• 2004

In this study, the shape of plate-fin type heat sink is numerically optimized to acquire the minimum pressure drop under the required temperature rise. To do this, a new sequential approximate optimization (SAO) is proposed and it is integrated with the computational fluid dynamics (CFD). In thermal/fluid systems for constrained nonlinear optimization problems, three fundamental difficulties such as high cost for function evaluations (i.e., pressure drop and thermal resistance), the absence of design sensitivity information, and the occurrence of numerical noise are confronted. To overcome these problems, the progressive quadratic response surface method (PQRSM), which is one of the sequential approximate optimization algorithms, is proposed and the heat sink is optimize by means of the PQRSM.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.7
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• pp.578-583
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• 2002

This paper presents a method for designing fuzzy $H_2/H_{\infty}$ controllers of nonlinear systems with time varying delay. Takagi-Sugeno fuzzy model is employed to represent nonlinear systems with time varying delay. Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. A sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is then presented in terms of linear matrix inequalities(LMls). The proposed fuzzy $H_2/H_{\infty}$ controllers minimizes the upper bound on the linear quadratic performance measure.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.371-376
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• 2008

In this paper, it is shown that if f satisfies the following functional inequality (0.1) $${\parallel}\sum\limits_{i,j=1}^3\;f{(xi,yj)}{\parallel}{\leq}{\parallel}f(x_1+x_2+x_3,\;y_1+y_2+y_3){\parallel}$$ then f is a bi-additive mapping. We moreover prove that if f satisfies the following functional inequality (0.2) $${\parallel}2\sum\limits_{j=1}^3\;f{(x_j,\;z)}+2\sum\limits_{j=1}^3\;f{(x_j,\;w)-f(\sum\limits_{j=1}^3\;xj,\;z-w)}{\parallel}{\leq}f(\sum\limits_{j=1}^3\;xj,\;z+w){\parallel}$$ then f is an additive-quadratic mapping.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.7
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• pp.655-660
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• 2009

In many real applications, the discrepancy problem between controller outputs and plant inputs or the abrupt variation problem of controller outputs can occur. These problems have a negative effect on control performance and stability. It is well-known that two phenomena called 'windup' and 'bump' cause these problems. So far these problems have been studied separately in each side of the anti-windup and the bumpless transfer. This paper proposes a new unified method combines the anti-windup and the bumpless transfer method using the linear quadratic minimization and a proper state space model representation for the anti-windup controller. The proposed method has a feature that it takes account of both the anti-windup and the bumpless transfer in one formula. Finally, we exemplify the performance of the proposed method via numerical examples using the controller switching between the anti-windup PID controller and the anti-windup LQ controller.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2312-2321
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• 1994

In this work the dynamics of an electromagnetic levitation system is described by a set of three first order nonlinear ordinary differential equations. The objective is to design a digital linear controller which takes the inherent instability of the uncontrolled system and the disturbing force into consideration. The controller is made by employing digital linear quadratic(LQ) design methodology and the unknown state variables are estimated by the kalman filter. The state estimation is performed using not only an air gap sensor but also both an air gap sensor and a piezoelectric accelerometer. The design scheme resulted in a digital linear controller having good stability and performance robustness in spite of various modelling errors. In case of using both a gap sensor and an accelerometer for the state estimation, the control input was rather stable than that in a system with gap sensor only and the controller dealt with the disturbing force more effectively.

• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.170-183
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• 2007

This paper presents a delay-dependent approach to robust filtering for linear parameter-varying (LPV) systems with discrete and distributed time-invariant delays in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. Some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs) such that the filtering process remains asymptotically stable and satisfies a prescribed $H_{\infty}$ performance level. Using polynomially parameter-dependent quadratic (PPDQ) functions and some Lagrange multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust $H_{\infty}$ filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.

• Journal of the Korean Society of Industry Convergence
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• v.12 no.3
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• pp.149-155
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• 2009

A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

• 전기의세계
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• v.49 no.9
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• pp.9-16
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• 2000

A receding horizon $H_{\infty}$ predictive control method is derived by solving a min-max problem in non-recursive forms. The min-max cost index is converted to a quadratic form which for systems with input saturation can be minimized using QP. Through the use of closed-loop prediction the prediction of states the use of closed-loop prediction the prediction of states in the presence of disturbances are made non-conservative and it become possible to get a tighter $H_{\infty}$ norm bound. Stability conditions and $H_{\infty}$ norm bounds on disturbance rejection are obtained in infinite horizon sence. Polyhedral types of feasible sets for sets and disturbances are adopted to deal with the input constraints. The weight selection procedures are given in terms of LMIs and the algorithm is formulated so that it can be solved via QP. This work is a modified version of an earlier work which was based on ellipsoidal type feasible sets[15].

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1335-1364
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• 2023

The aim of this paper is to investigate the spectral instability of roll waves bifurcating from an equilibrium in the 2-dimensional generalized Swift-Hohenberg equation. We characterize unstable Bloch wave vectors to prove that the rolls are spectrally unstable in the whole parameter region where the rolls exist, while they are Eckhaus stable in 1 dimension [13]. As compared to [18], showing that the stability of the rolls in the 2-dimensional Swift-Hohenberg equation without a quadratic nonlinearity is determined by Eckhaus and zigzag curves, our result says that the quadratic nonlinearity of the equation is the cause of such instability of the rolls.