• 제어로봇시스템학회논문지
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• 제4권5호
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• pp.592-599
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• 1998

In this paper, we design a tracking controller which satisfies transient response specifications and maintains tracking error within a tolerable limit for the uncertain track-following system of an optical disk drive. To this end, a robust $H_{\infty}$ control problem with regional stability constraints and sinusoidal disturbance rejection is considered. The internal model principle is used for rejecting the sinusoidal disturbance caused by eccentric rotation of the disk. We show that a condition satisfying the regional stability constraints can be expressed in terms of a linear matrix inequality (LMI) using the Lyapunov theory and S-procedure. Finally, a tracking controller is obtained by solving an LMI optimization problem involving two linear matrix inequalities. The proposed controller design method is evaluated through an experiment.

• 제어로봇시스템학회논문지
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• 제11권11호
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• pp.901-906
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• 2005

The stability robustness problem of continuous linear systems with nominal and delayed time-varying perturbations is considered. In the previous results, the entire bound was derived only for the overall perturbations without separation of the perturbations. In this paper, the sufficient condition for stability of the system with two perturbations, which are nominal and delayed, is expressed as linear matrix inequalities(LMIs). The corresponding stability bounds fer those two perturbations are determined by LMI(Linear Matrix Inequality)-based generalized eigenvalue problem. Numerical examples are given to compare with the previous results and show the effectiveness of the proposed.

• 제어로봇시스템학회논문지
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• 제13권2호
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• pp.147-153
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• 2007

The stability robustness problem of linear discrete-time systems with delayed time-varying perturbations is considered. Compared with continuous time system, little effort has been made for the discrete time system in this area. In the previous results, the bounds were derived for the case of non-delayed perturbations. There are few results for delayed perturbation. Although the results are for the delayed perturbation, they considered only the time-invariant perturbations. In this paper, the sufficient conditions for stability can be expressed as linear matrix inequalities(LMIs). The corresponding stability bounds are determined by LMI(Linear Matrix Inequality)-based algorithms. Numerical examples are given to compare with the previous results and show the effectiveness of the proposed results.

• 제어로봇시스템학회논문지
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• 제13권1호
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• pp.15-18
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• 2007

We consider the problem of designing a static output feedback sliding mode control law for linear dynamical systems with mismatched uncertainties in the state matrix. We assume that an output dependent sliding surface guaranteeing the quadratic stability of the sliding mode dynamics is given, the reachability condition is not required to be satisfied globally, and the output feedback sliding mode control law complises both linear and discontinuous parts. We reduce the problem of designing the linear part of the sliding mode control law to a simple LMI problem which offers design flexibility for combining various useful convex design specifications. Our approach does not require state transformation and it can be applied to mismatched uncertain systems.

• 전기학회논문지
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• 제59권4호
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• pp.797-802
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• 2010

In this paper, a systematic procedure to design a nonlinear controller for nonlinear active magnetic bearing (AMB) systems is presented. To do this, we effectively convert the AMB system into a polytopic quasi-linear parameter varying (LPV) system, which is a representation of nonlinear state-space models and is described by the convex combination of a set of precisely known vertices. Unlike the existing quasi-LPV systems, the nonlinear weighting functions, which construct the polytopic quasi-LPV model of the AMB system by connecting the vertices, include not only state variables but also the input ones. This allows us to treat the input nonlinearity effectively. By means of the derived polytopic quasi-LPV model and linear matrix inequality (LMI) conditions, nonlinear controller that stabilizes the AMB system is obtained. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations.

• Structural Engineering and Mechanics
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• 제67권1호
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• pp.33-43
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• 2018

The dynamic output-feedback robust control method based on linear matrix inequality (LMI) method is presented for suppressing vibration response of a functionally graded material (FGM) beam with piezoelectric actuator/sensor layers in this paper. Based on the reduced model obtained by using direct mode truncation, the linear fractional state space representation of a piezoelectric FGM beam with material properties varying through the thickness is developed by considering both the inherent uncertainties in constitution material properties as well as material distribution and the model error due to mode truncation. The dynamic output-feedback robust H-infinity control law is implemented to suppress the vibration response of the piezoelectric FGM beam and the LMI method is utilized to convert control problem into convex optimization problem for efficient computation. In numerical studies, the flexural vibration control of a cantilever piezoelectric FGM beam is considered to investigate the accuracy and efficiency of the proposed control method. Compared with the efficient linear quadratic regulator (LQR) widely employed in literatures, the proposed robust control method requires less control voltage applied to the piezoelectric actuator in the case of same control performance for the controlled closed-loop system.

• 전기학회논문지
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• 제66권2호
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• pp.387-393
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• 2017

This paper focuses on a horizontal waypoint tracking and a speed control of large diameter unmanned underwater vehicles (LDUUVs) with X-stern configuration plane. The concerned design problem is converted into an asymptotic stabilization of the error dynamics with respect to the desired yaw angle and surge speed. It is proved that the error dynamics under the proposed control scheme based on the linear control and the feedback linearization can be considered as a cascade system; the cascade system is asymptotically stable if its nominal systems are so. This stability connection enables to separately deal with the waypoint tracking problem and the speed control one. By using the sector nonlinearity, the nominal system with nonlinearities is modeled as a polytopic linear parameter varying (LPV) system with parametric uncertainties. Then, sufficient linear matrix inequality (LMI) conditions for its asymptotic stabilizability are derived in the sense of Lyapunov stability criterion. An example is given to show the validity of the proposed methodology.

• International Journal of Control, Automation, and Systems
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• 제3권2호
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• pp.143-151
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• 2005

This paper considers a robust decentralized $H_\infty$ control problem for uncertain large-scale interconnected systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in subsystems. A design method based on the bounded real lemma is developed for a dynamic output feedback controller, which is reduced to a feasibility problem for a nonlinear matrix inequality (NMI). It is proposed to solve the NMI iteratively by the idea of homotopy, where some of the variables are fixed alternately on each iteration to reduce the NMI to a linear matrix inequality (LMI). A decentralized controller for the nominal system is computed first by imposing structural constraints on the coefficient matrices gradually. Then, the decentralized controller is modified again gradually to cope with the uncertainties. A given example shows the efficiency of this method.

• 전자공학회논문지
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• 제50권3호
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• pp.155-159
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• 2013

본 연구에서는 정적 출력 되먹임 제어기를 구하기 위한 비선형 행렬 부등식 조건과 비선형 최적화 문제를 제안한다. 제안된 최적화 문제는 선형 행렬부등식 제약 조건과 비선형 목적함수를 가지며, 구조적인 제약이 있는 제어기 설계에도 적용할 수 있음을 보인다. 비선형 목적함수를 선형화시키고, 선형화된 최적화 문제를 반복적으로 푸는 방법으로 제안된 비선형 최적화 문제를 풀어 정적 출력 되먹임 제어기를 구할 수 있다. 제안된 방법을 실제 문제에 적용하여 그 유효성을 보인다.

• 정보처리학회논문지:소프트웨어 및 데이터공학
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• 제1권3호
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• pp.195-200
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• 2012

카메라의 시선을 조정하기 위해서는 비전 시스템의 시스템 파라미터를 사용해야 한다. 하지만 이러한 시스템 파라미터는 측정 당시와 사용중이 달라 질 수 있다. 이 경우 원하는 카메라의 시선 조정이 이루어지기 어렵다. 이 문제를 보완하기 위한 방법으로서 본 연구에서는 LMI(Linear Matrix Inequality)에 기반한 비전 시스템의 시스템 파라미터의 변화에 강건한 시선 고정 방법을 제안한다. 시뮬레이션 검증 결과는 제안하는 방법이 기존의 선형 알고리즘에 비해 더 적은 시선 추적 에러를 보이고, 기존의 비선형 알고리즘에 비해 더 안정적인 시선 추적 에러를 보인다. 또한 제안하는 방법은 속도가 빨라서 실시간 사용이 가능하다.