• Title/Summary/Keyword: Diagonal Matrix

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Robust $L_2$Optimization for Uncertain Systems

  • Kim, Kyung-Soo;Park, Youngjin
    • 제어로봇시스템학회:학술대회논문집
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    • 1995.10a
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    • pp.348-351
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    • 1995
  • This note proposes a robust LQR method for systems with structured real parameter uncertainty based on Riccati equation approach. Emphasis is on the reduction of design conservatism in the sense of quadratic performance by utilizing the uncertainty structure. The class of uncertainty treated includes all the form of additive real parameter uncertainty, which has the multiple rank structure. To handle the structure of uncertainty, the scaling matrix with block diagonal structure is introduced. By changing the scaling matrix, all the possible set of uncertainty structures can be represented. Modified algebraic Riccati equation (MARE) is newly proposed to obtain a robust feedback control law, which makes the quadratic cost finite for an arbitrary scaling matrix. The remaining design freedom, that is, the scaling matrix is used for minimizing the upper bound of the quadratic cost for all possible set of uncertainties within the given bounds. A design example is shown to demonstrate the simplicity and the effectiveness of proposed method.

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ADAPTIVE STABILIZATION OF NON NECESSARILY INVERSELY STABLE CONTINUOUS-TIME SYSTEMS BY USING ESTIMATION MODIFICATION WITHOUT USING HYSTERESIS FUNCTION

  • Sen, M.De La
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.29-53
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    • 2001
  • This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.

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Interfacial Evaluation and Microfailure Mechanisms of Carbon Fiber/Bismaleimide (BMI) Composites using Tensile/compressive Fragmentation Tests and Acoustic Emission (인장/압축 Fragmentation 시험법과 음향방출을 이용한 Carbon Fiber/Bismaleimide (BMI) Composites 의 계면 평가와 미세파괴 메커니즘 연구)

  • 김진원;박종만;윤동진
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2000.11a
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    • pp.79-83
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    • 2000
  • Interfacial and microfailure properties of carbon liber/bismaleimide (BMI) composites were evaluated using both tensile fragmentation and compressive Broutman tests with acoustic emission (AE). Since BMI is rather difficult matrix to apply for the conventional fragmentation test because of its too low elongation and too brittle and high modulus properties, dual matrix composite system was applied. After carbon fiber/BMI composite was prepared for rod shape by controlling differing curing stage, composites rod was embedded in toughened epoxy as outer matrix. The typical microfailure modes including fiber break, matrix cracking, and interlayer failure were observed during tensile testing, whereas the diagonal slippage in fiber ends was observed during compressive test. On the other hand, AE amplitudes of BMI matrix fracture were higher than carbon fiber tincture under tensile test because BMI matrix has very brittle and high modulus. The waveform of signals coming from BMI matrix fractures was consistent with AE amplitude result under tensile tests.

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Design Optimization Using Two-Point Diagonal Quadratic Approximation(TDQA) (이점 대각 이차 근사화(TDQA) 기법을 적용한 최적설계)

  • Kim, Min-Soo;Kim, Jong-Rip;Choi, Dong-Hoon
    • Proceedings of the KSME Conference
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    • 2001.06c
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    • pp.386-391
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    • 2001
  • This paper presents a new two-point approximation method based on the exponential intervening variable. To avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables the shifting level into each exponential intervening variable is introduced. Then a new quadratic approximation, whose Hessian matrix has only diagonal elements of different values, is proposed in terms of these intervening variables. These diagonal elements are computed in a closed form, which correct the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the original function at the previous point. Finally, the authors developed a sequential approximate optimizer, solved several typical design problems used in the literature and compared these optimization results with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

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Efficient Mechanical System Optimization Using Two-Point Diagonal Quadratic Approximation in the Nonlinear Intervening Variable Space

  • Park, Dong-Hoon;Kim, Min-Soo;Kim, Jong-Rip;Jeon, Jae-Young
    • Journal of Mechanical Science and Technology
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    • v.15 no.9
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    • pp.1257-1267
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    • 2001
  • For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

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Design Optimization Using Two-Point Diagonal Quadratic Approximation (이점 대각 이차 근사화 기법을 적용한 최적설계)

  • Choe, Dong-Hun;Kim, Min-Su;Kim, Jong-Rip;Jeon, Jae-Yeong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.9
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    • pp.1423-1431
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    • 2001
  • Based on the exponential intervening variable, a new two-point approximation method is presented. This introduces the shifting level into each exponential intervening variable to avoid the lack of def inition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

An Efficient Overlapped LDPC Decoder with a Upper Dual-diagonal Structure

  • Byun, Yong Ki;Park, Jong Kang;Kwon, Soongyu;Kim, Jong Tae
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.13 no.1
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    • pp.8-14
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    • 2013
  • A low density parity check (LDPC) decoder provides a most powerful error control capability for mobile communication devices and storage systems, due to its performance being close to Shannon's limit. In this paper, we introduce an efficient overlapped LDPC decoding algorithm using a upper dual-diagonal parity check matrix structure. By means of this algorithm, the LDPC decoder can concurrently execute parts of the check node update and variable node update in the sum-product algorithm. In this way, we can reduce the number of clock cycles per iteration as well as reduce the total latency. The proposed decoding structure offers a very simple control and is very flexible in terms of the variable bit length and variable code rate. The experiment results show that the proposed decoder can complete the decoding of codewords within 70% of the number of clock cycles required for a conventional non-overlapped decoder. The proposed design also reduces the power consumption by 33% when compared to the non-overlapped design.

Comparison of Misalignment and Retardation Errors of Dual Rotating Quarter-Wave Plates in Muller-Matrix Ellipsometry (타원편광 분석기에서 정렬오차와 사분파장판의 지연오차로 인한 뮬러 매트릭스 오차 분석)

  • Cheong, Hai Du;Kim, Dukhyeon
    • Korean Journal of Optics and Photonics
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    • v.25 no.5
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    • pp.262-272
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    • 2014
  • Using an ellipsometer with dual rotating quarter-wave plates, we have analyzed the relationship between Fourier coefficients and Mueller matrices in the cases of an error-free optical system and of five systematic errors (alignment errors and retardation errors in the quarter-wave plates, and alignment error in the analyzer). In the case with five systematic errors, simulation results show that retardation errors cause more error in the diagonal elements of the Mueller matrix than do alignment errors. We have found that errors in the Mueller matrix caused by initial misalignment of the dual quarter-wave plates were the same. We have chosen the rotation rates of two quarter-wave plates such that the rotational frequencies ${\omega}_1$ and ${\omega}_2$ differ by a factor of 5, i.e. ${\omega}_2=5{\omega}_1$. The simulation results show 0.18% relative error in the diagonal elements ($m_{22}$ and $m_{33}$) and 200% relative error in the off-diagonal elements ($m_{23}$ and $m_{32}$), when we compare errors caused by misalignment of the analyzer to those caused by initial misalignment of the quarter-wave plates. We can use these results in measuring accurate Mueller matrices of optical materials.

Sequential Loop Closing Identification of Hammerstein Models for Multiple-Input Multiple-Output Processes (다변수 Hammerstein 공정의 순차 확인법)

  • Park Ho Cheol;Koo Doe Gyoon;Lee Moon Yong;Lee Jietae
    • Journal of Institute of Control, Robotics and Systems
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    • v.10 no.12
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    • pp.1280-1286
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    • 2004
  • A lot of industrial chemical processes contain certain input nonlinearities even though they are controlled by several linear controllers. Here we investigate a sequential loop closing identification method for MIMO Hammerstein nonlinear processes with diagonal nonlinearities. The proposed method separates the identification of the nonlinear static function from that of the linear subsystem by using a relay feedback test and a triangular type signal test. From 2 n activations for n n MIMO nonlinear processes, we sequentially identify the whole range of the nonlinear static function as well as the transfer function matrix of the linear subsystem.

Experiments on a Visual Servoing Approach using Disturbance Observer (외란 관측기를 이용한 시각구동 방법의 구현)

  • Lee, Joon-Soo;Suh, Il-Hong
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.10
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    • pp.1311-1316
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    • 1999
  • A visual servoing method has been proposed based on disturbance observer to eliminate the effect of the off-diagonal component of image feature Jacobian, since performance indices such as measurement sensitivity of visual features, sensitivity of the control to noise and controllability could be improved when an image feature Jacobian was given as a block diagonal matrix. In this paper, experimental results of disturbance observer-based visual servoing are discussed where Samsung FARAMAN-AS1 6-axis industrial robot manipulator is employed. Also, the feature saturator is proposed to stabilize the disturbance observer loop by saturating the differential changes of the image features.

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