• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.482-485
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• 1993

This paper deals with structured singular value and mixed sensitivity problem for robust performance. We derive the sufficient condition that mixed sensitivity problem satisfies structured singular value in robust performance problem. And we show the bound of perturbation between structured singular value and norm of mixed sensitivity functions.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.83.6-83
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• 2002

$\textbullet$ Disturbance observer $\textbullet$ Performance enhancement $\textbullet$ LFT formulation $\textbullet$ Structured singular value $\textbullet$ Maximum bandwidth of DOB $\textbullet$ DVD experiments $\textbullet$ Robust stable disturbance observer

• ICROS
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• v.10 no.3
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• pp.21-26
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• 2004

Structured singular value (SSV)는 robust stability와 robust performance를 매우 엄밀하게 다루기 위해 고안되었다 (Doyle, 1982; Safonov, 1982). 이 엄밀성으로 제어시스템의 설계 및 분석에 광범위하게 사용되고 있다. 강건제어의 단초를 이루었으며 loop failure tolerance, decentralized integral controllability (Campo and Morari. 1994), D-stability (Lee and Edgar, 2001) 등에 SSY가 사용되고 있다. SSV의 중요성이 알려짐에 따라 이것에 관한 많은 연구가 있었다(Fan et at., 1991 ; Pacltard and Pander, 1993), 그러나 이 값의 계산은 매우 어려운 NP-hard인 것으로 판명되었으며 (Braatz et al.. 1994). 실수 불확실 변수에 대한 SSV의 경우 원하는 오차범위 내로 근사 값을 구하는 것도 마찬가지 인 것으로 밝혀졌다(Fu, 1997).(중략)

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.5
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• pp.17-24
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• 1996

In this paper, we present a robust performance improvement method for the NLCF(normalized left coprime factor) uncertain structure using loop shaping and the structure singular value. For this, we select weighting functions for a loop shaping considering condition numer, and transform the NLCF uncertain structure into the 4-block structure. However, we can't get a good performance on account of the restriction of weighting functions. To cope with this, we motivate the use of structured singular vlaue in the robust performance improvement procedure. After all, the robust performance improvement can be obtained by a factor W$_{a}$ and a scaling factor of D-K iteration.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.1
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• pp.13-19
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• 1995

In this paper, generalized singular value is defined. Using the generalized singular value, robust stability conditions and robust pole placement conditions of structured uncertain systems with star shaped uncertainties are derived. Especially, norm bounded and polytopic uncertainty regions are considered as star shaped uncertainty regions. Linear matrix inequality problems are proposed in order to compute the upper bound of the generalized singular value. The proposed linear matrix inequality problems can be solved by using the convex optimization method.

• International Journal of Precision Engineering and Manufacturing
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• v.1 no.2
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• pp.76-83
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• 2000

A study on the robust control of a composite beam with a distributed PVDF sensor and piezo-ceramic actuator is presented in this paper. $1^{st}$ and $2^{nd}$ natural frequencies are considered in the modeling, because robust control theory which has robustness to structured uncertainty is adopted to suppress the vibration. If the controllers designed by $H_{\infty}$ theory do not satisfy control performance, it is improved by $\mu$-synthesis method with D-K iteration so that the $\mu$-controller based on the structured singular value satisfies the nominal performance and robust performance. Simulation and experiment were carried out with the designed controller and the verification of the robust control properties was presented by results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.6
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• pp.2634-2648
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• 2020

In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.301-305
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• 1996

$\mu$ theory can handle the parametric uncertainty and produces more non-conservative controller than H$_{\infty}$ control theory. However an existing solution of the theory, D-K iteration, creates a controller of huge order and cannot handle the real or mixed real-complex perturbation sets. In this paper, we use genetic algorithms to solve these problems of the D-K iteration method. The Youla parameterization is used to obtain all stabilizing controllers and the genetic algorithms determines the values of the state feedback gain, the observer gain, and Q parameter to minimize $\mu$, the structured singular value, of given system. From an example, we show that this method produces lower order controller which controls a real parameter-perturbed plant than D-K iteration method.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.1
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• pp.77-82
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• 2010

An analytical method for robust design of the multi-loop proportional-integral (PI) controller is proposed for various types of multi-delay processes. On the basis of the direct synthesis and generalized IMC-PID approach, the analytical tuning rules of the multi-loop PI controller are firstly derived for achieving the desired closed-loop response, and the structured singular value synthesis is then utilized for the tradeoffs between the robust stability and performance by adjusting only one design parameter (i.e., the closed-loop time constant). To verify the superiority of the proposed method, the simulation studies have been conducted on a wide variety of multivariable processes. The multi-loop PI controller designed by the proposed method shows a fast, well-balanced and robust response with the minimum integral absolute error (IAE) in compared with other renowned methods.

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.1
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• pp.35-44
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• 1996

A design method for a teleoperator robot system is presented in this paper. The control system consists of two phases; approach phase and contact one. The end-effector position of the estimated slave robot and the contact force between the end-effector and wall are displayed on the monitors at control site, using which the operator controls the teleoperator system. The approach phase controller is designed using Smith's principle and the contact one designed based upon the structured singular value ${\mu}$ in order to increase the robustness of the system. The uncertainatices such as communication time delay and the variations of system parameters are considered as a muliplicative pertubation. Computer simulations are conducted in order to evaluate the performance of the proposed design method. It is found that desirable control performance, especially in the contact phase, is obtained if the control mode is switched into contact phase when the estimated position of the slave robot end-effector is in front of the wall.