• Title/Summary/Keyword: 행렬부등식

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Structural Damage Detection Method Using Sensitivity Matrices (민감도행렬을 사용한 구조물의 손상추정법)

  • 윤정방;김두기
    • Computational Structural Engineering
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    • v.9 no.4
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    • pp.117-126
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    • 1996
  • Damage detection methods using structural tests can be divided into two methods, i.e., static and dynamic. The static methods which use the stiffness properties of the structure are simpler than the dynamic methods. However, static approaches are very sensitive to the displacement measurement noises and modeling errors. The dynamic methods also have limitations in acquiring the natural frequencies and mode shapes of the high frequencies. In this study, a method for the structural damage assessment using sensitivity matrices is developed, in which the drawbacks of the static and dynamic methods can be compensated. Based on the measurement data for the static displacements and dynamic modal properties, the damage locations and the degree of damage are determined using the presented sensitivity matrix method. The efficiency of the proposed method has been examined through numerical simulation studies on truss type structures.

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(Robust Non-fragile $H^\infty$ Controller Design for Parameter Uncertain Systems) (파라미터 불확실성 시스템에 대한 견실 비약성 $H^\infty$ 제어기 설계)

  • Jo, Sang-Hyeon;Kim, Gi-Tae;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.39 no.3
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    • pp.183-190
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    • 2002
  • This paper describes the synthesis of robust and non-fragile H$\infty$ state feedback controllers for linear varying systems with affine parameter uncertainties, and static state feedback controller with structured uncertainty. The sufficient condition of controller existence, the design method of robust and non-fragile H$\infty$ static state feedback controller, and the set of controllers which satisfies non-fragility are presented. The obtained condition can be rewritten as parameterized Linear Matrix Inequalities(PLMls), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. However, in contrast to LMIs, PLMIs feasibility problems involve infinitely many LMIs hence are inherently difficult to solve numerically. Therefore PLMls are transformed into standard LMI problems using relaxation techniques relying on separated convexity concepts. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a degree.

Development of Robust Intelligent Digital Controller for Smart Space (스마트 스페이스 구축을 위한 강인 지능형 디지털 제어기 개발)

  • Joo, Young-Hoon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.1
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    • pp.60-65
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    • 2008
  • In this paper, we concern the stability of smart space by using the robust digital controller. The proposed methodologies are based on the intelligent digital redesign (IDR). More precisely, we represent the nonlinear and uncertain analog system as the Takaki-Sugeno (T-S) fuzzy model. Then the IDR problem can be reduced to find the digital gains minimizing the norm distance between the closed-loop states of the analog and digital control. Its constructive conditions are expressed as the linear matrix inequalities (LMIs). At last, a numerical example, HVAC system, is demonstrated to visualize the feasibility of the proposed methodology.

A Derivation of the Representative Unit Hydrograph from Multiperiod Complex Storm by Linear Programming (선형계획법(線型計劃法)에 의한 대표단위도(代表單位圖) 유도(誘導))

  • Kwon, Oh Hun;Ryu, Tae Sang;Yoo, Ju Hwan
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.13 no.2
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    • pp.173-182
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    • 1993
  • This paper presents an algorithm to derive the representative unit hydrograph for the real environment of a watershed. For a given watershed, the conventional methods give several different unit hydrographs by storm events. In this study the LP model is somewhat modified based on the previous study by Mays et also as follows: the objective function is designed to minimize the sum of weighted residuals. An additional constraint of moving average is added to prevent the unit hydrograph from the occurence of oscillation which was not active in Mays's paper. Configuration of rainfall matrix was improved to reduce its dimension in accordance with Diskin's review point. In spite of the superiority of LP approach in terms of representativeness, all the methods were very sensitive to the validity of baseflow separation and rainfall-loss. Several methods of the separations for rainfall excesses and direct runoffs were applied and no preferred methods were identified. This is the matter of judgement considering catchment and rainfall characteristics. This algorithm was applied to a real watershed of the Wi stream in the Nak-dong river. Compared with the IHP results by conventional methods, this optimized representative unit hydrograph demonstrated relatively smaller and shorter values in terms of the peak discharge and the basin lag respectively, and the oscillation of its falling limb successfully eliminated owing to the additional constraints of moving averages.

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Stability Condition of Discrete System with Time-varying Delay and Unstructured Uncertainty (비구조화된 불확실성과 시변 지연을 갖는 이산 시스템의 안정 조건)

  • Han, Hyung-seok
    • Journal of Advanced Navigation Technology
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    • v.22 no.6
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    • pp.630-635
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    • 2018
  • In this paper, we consider the stability condition for the linear discrete systems with time-varying delay and unstructured uncertainty. The considered system has time invariant system matrices for non-delayed and delayed state variables, but its delay time is time-varying within certain interval and it is subjected to nonlinear unstructured uncertainty which only gives information on uncertainty magnitude. In the many previous literatures, the time-varying delay and unstructured uncertainty can not be dealt in simultaneously but separately. In the paper, new stability conditions are derived for the case to which two factors are subjected together and compared with the existing results considering only one factor. The new stability conditions improving many previous results are proposed as very effective inequality equations without complex numerical algorithms such as LMI(Linear Matrix Inequality) or Lyapunov equation. By numerical examples, it is shown that the proposed conditions are able to include the many existing results and have better performances in the aspects of expandability and effectiveness.

$H_\infty$ Controller Design for Discrete-time Linear Systems with Time-varying Delays in States using S-procedure (S-procedure를 이용한 상태에 시변 시간지연을 가지는 이산 선형 시스템에 대한 $H_\infty$ 제어기 설계)

  • Kim, Ki-Tae;Cho, Sang-Hyun;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.39 no.2
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    • pp.95-103
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    • 2002
  • This paper deals with the H$_{\infty}$ control problems for discrete-time linear systems with time-varying delays in states. The existence condition and the design method of the H$_{\infty}$ state feedback controller are given. In this paper, the H$_{\infty}$ control law is assumed to be a memoryless state feedback, and the upper-bound of time-varying delay and S-procedure are used. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

A Study on the Robust Control of Horizontal-Shaft Magnetic Bearing System Considering Perturbation (불확실성을 고려한 횡축형 자기 베어링 시스템의 로버스트 제어에 관한 연구)

  • Kim, Chang-Hwa;Jung, Byung-Gun;Yang, Joo-Ho
    • Journal of Advanced Marine Engineering and Technology
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    • v.34 no.1
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    • pp.92-101
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    • 2010
  • Recently, the magnetic bearings which have many advantages such as no noise, less mechanical friction are widely applied to the suspension of rotors on the rotary machineries. However, the magnetic bearing system is inherently unstable, nonlinear and MIMO(multi-input-multi-output) system as well. In this paper, we design a state feedback controller using linear matrix inequality(LMI) to the multi-objective synthesis, for the magnetic bearing system with integral type servo system. The design objectives include $H_{\infty}$ performance, asymptotic disturbance rejection, and time-domain constraints on the closed-loop pole location. The results of computer simulation show the validity of the designed controller.

Stochastic Stabilization of TS Fuzzy System with Markovian Input Delay (마코프 입력 지연을 갖는 TS 퍼지 시스템의 확률전 안정화)

  • 이호재;주영훈;이상윤;박진배
    • Journal of the Korean Institute of Intelligent Systems
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    • v.11 no.6
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    • pp.459-464
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    • 2001
  • This paper discusses a stochastic stabilization of Takagi-Sugeno(TS) fuzzy system with Markovian input delay. The finite Markovian process is adopted to model the input delary of the overall control system. It is assumed that the zero and hold devices are used for control input. The continuous-time TS fuzzy system with the Markovian input delay is discretized for easy handling delay, according, the discretized TS fuzzy system is represented by a discrete-time TS fuzzy system with jumping parameters. The stochastic stabilizibility of the jump TS fuzzy system is derived and formulated in terms of linear matrix inequalities (LNIS)

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Repetitive Control for Track-Following Servo of an Optical Disk Drive Using Linear Matrix Inequalities (선형 행렬 부등식을 이용한 광 디스크 드라이브의 트랙 추종 서보를 위한 반복 제어)

  • 도태용;문정호
    • Journal of Institute of Control, Robotics and Systems
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    • v.9 no.2
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    • pp.117-123
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    • 2003
  • Rotational machines such as optical disk drives, hard disk drives, and so on are subject to periodic disturbances caused by their mechanical characteristics. In the meanwhile, it is well known that repetitive control rejects periodic disturbance effectively. This paper presents a practical application of repetitive control to the track-following servo of an optical disk drive. The repetitive control system is composed of two repetitive controllers which compensate for periodic disturbances generated by track geometry and eccentric rotation of disk and a feedback controller stabilizing the feedback loop. A robust stability for all plant uncertainties is proved using linear matrix inequalities (LMIs). In the controller design, a weighting function is introduced for the feedback controller to ensure a minimum loop gain and a sufficient phase margin. The repetitive controllers and the feedback controller are designed by solving an optimization problem which can consider the robust stability condition and the system performance. The developed repetitive control system is implemented in the digital control system with a 16-bit fixed-point digital signal processor (DSP). Through simulation and experiment. The feasibility of the proposed repetitive control system is verified.

Delay-dependent $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays (다중 상태 시간지연을 가지는 연속시간 특이시스템의 지연종속 $H_{\infty}$ 필터링)

  • Kim, Jong-Hae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.46 no.5
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    • pp.22-28
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    • 2009
  • In this paper, we consider the problem of $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays. The aim of designed filter is to guarantee regularity, impulse-free, asymptotic stability and $H_{\infty}$ norm bound of filtering error singular system. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent BRL (bounded real lemma) for singular systems with multiple state-delays is derived. Based on the result, the existence condition of $H_{\infty}$ filter and filter design method are proposed in terms of LMI (linear matrix inequality). Finally, a numerical example is provided to show the validity of the design methods.