• 제어로봇시스템학회논문지
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• 제7권11호
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• pp.896-903
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• 2001

This study investigates the use of mixed $H_2/H_{$\infty}$ and $\mu$-synthesis to construct a robust controller for the benchmark problem. The model treated in the problem is a coupled three-inertial system that reflects the dynamics of mechanical vibrations. This kind of problem requires to be satisfied the robust performance (both in the time and frequency-domain specifications). We, first, adopt the mixed $H_2/H_{$\infty}$ theory to design a feedback controller K(s). Next, $\mu$-synthesis method is applied to the overall system to make use of structured parametric uncertainty. This process permits higher levels of controller authority and reduces the conservativeness of the controller. Finally, the feedforward controller is also used to improve the transient response of the output. We confirm that all design specifications except a complementary sensitivity condition can be achieved.

• 전자공학회논문지
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• 제52권12호
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• pp.89-98
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• 2015

본 논문에서는 임의적으로 발생하는 폴리토프 불확실성과 외란을 고려한 시간지연시스템의 강인비약성 $H_{\infty}$ 제어기설계 알고리듬을 다룬다. 먼저 임의적으로 발생하는 불확실성과 외란을 가지는 시간지연시스템을 설계하고, Lyapunov 안정성 분석과 $H_{\infty}$ 성능지수를 기반으로 강인비약성 $H_{\infty}$ 제어기가 존재하기 위한 충분조건을 선형행렬부등식(LMI, linear matrix inequality)의 형태로 제시한다. 구한 충분조건은 변수치환과 슈어 여수(Schur complement) 정리를 바탕으로 파라미터의 함수를 포함한 파라미터화 선형행렬부등식(PLMI, parameterized linear matrix inequality)으로 표현할 수 있으므로 PLMI의 모든 해로부터 제어기이득과 비약성을 만족하는 제어기 섭동영역 및 $H_{\infty}$ 성능을 만족하는 노옴 한계치 ${\gamma}$를 한번에 구할 수 있다. 마지막으로 예제와 모의실험에서 제안한 강인비약성 $H_{\infty}$ 제어기가 임의적으로 발생하는 불확실성 및 외란, 시간지연이 있더라도 폐루프시스템을 안정화시키고 $H_{\infty}$ 성능을 보장함을 확인하고 확정적인 불확실성을 기반으로 설계한 제어기와 성능을 비교한다.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.699-717
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• 2012

In this paper, we deal with the robust mixed $H_2/H_{\infty}$ guaranteed-cost control problem involving uncertain neutral stochastic distributed delay systems. More precisely, the aim of this problem is to design a robust mixed $H_2/H_{\infty}$ guaranteed-cost controller such that the close-loop system is stochastic mean-square exponentially stable, and an $H_2$ performance measure upper bound is guaranteed, for a prescribed $H_{\infty}$ attenuation level ${\gamma}$. Therefore, the fast convergence can be fulfilled and the proposed controller is more appealing in engineering practice. Based on the Lyapunov-Krasovskii functional theory, new delay-dependent sufficient criteria are proposed to guarantee the existence of a desired robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which are derived in terms of linear matrix inequalities(LMIs). Furthermore, the design problem of the optimal robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which minimized an $H_2$ performance measure upper bound, is transformed into a convex optimization problem with LMIs constraints. Finally, two simulation examples illustrate the design procedure and verify the expected control performance.

• 대한기계학회논문집A
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• 제24권4호
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• pp.1065-1074
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• 2000

A robust nonlinear $H_2$/$H_{\infty}$ control method for a parallel inverted pendulum with structured perturbation and dry friction is proposed. By the random input describing function techniques, the nonlinear dry friction is approximated into the quasi-linear system. Introducing the quadratic robustness theorem, the robust $H_2$/$H_{\infty}$ control system is constructed for the quasi-linear perturbed system. But it is difficult to design a controller due to the nonlinear correction term in Riccati equation. With some transformations on the Riccati equation containing nonlinear correction term, the design of the robust nonlinear controller can be done easily. Hence when the stiffness and mass of the parallel inverted pendulum vary in certain ranges, the proposed control scheme has the robustness for both the structured perturbation and dry friction. The results of computer simulation show the effectiveness of our proposed control method.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 V
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• pp.2589-2592
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• 2003

In this paper, a robust mixed H$_2$/H$\_$$\infty$/ output feedback control method is applied to the design of loop filter for PLL carrier phase tracking. The proposed method successfully copes with large S-curve slope uncertainty and a significant decision delay in the closed-loop that may exist In modern receivers due to a convolutional decoder or an equalizer. The objective is to design an output feedback controller which minimizes the H$_2$performance while satisfying the H$\_$$\infty$/ performance to guarantee the gain margin and phase margin for linear time invariant(LTI) polytopic uncertain systems. LMIs based approach is given to solve this problem. We can verify the H$\_$$\infty$/ performance satisfaction and minimize the phase detector error through the simulation result.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.858-863
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• 1990

A synthesis of feedback control-law with combined H$_{2}$/H$_{\infty}$ perfoemance criteria is proposed for discrete-time systems, under the assumption that the state is available for feedback. An auxiliary minimization problem is defined to enforce the H$_{\infty}$ disturbance attenuation constrain while minimizing the H$_{2}$ performance bound. The design equation is presented in terms of a modified Riccati equation which leads to the standard LQ solution when the H$_{\infty}$ constraint is completely relaxed. The results of the paper clarity the correspondences between H$_{2}$/H$_{\infty}$ results in discrete-time systems and their continuous-time counter-parts.rts.

• 전자공학회논문지SC
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• 제48권1호
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• pp.55-60
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• 2011

이동로봇의 동시 위치인식 및 지도작성 (Simultaneous Localization And Mapping, SLAM) 에서 가장 기본이 되는 알고리즘은 확장 칼만 필터 SLAM(Extended Kalman Filter SLAM, EKF-SLAM)이다. 하지만 칼만 필터를 사용할 때, 시스템 설계자는 외부 입력에 대한 시스템적 특성과 외부 노이즈의 확률적 모델을 알고 있어야 하나, 실제 환경에서는 이를 정확히 파악할 수 없는 한계가 있다. 이에, 칼만 필터를 불확실성이 심한 실제 환경에 적용할 경우 내부 변수의 변화에 민감하게 반응하거나, 필터의 수학적 일관성이 지켜지지 않거나 또는 부정확한 상태 변수값을 추정하기도 한다. 이에 비해 $H_{\infty}$ 필터는 외부 모델에 대한 상세한 정보가 없을지라도 강인하게 상태를 예측할 수 있다는 장점을 가지고 있다. 본 논문에서는 이러한 $H_{\infty}$ 필터의 특성이 이용로봇의 SLAM 알고리즘의 성능 향상에 도움이 될 것이라는 아이디어에 착안하여 $H_{\infty}$ 필터에 가번한 SLAM 알고리즘을 제안하고 이를 모의 실험에 적용해 보았다. 이를 통해 불확실성이 큰 환경에서는 제안된 알고리즘이 기존의 EKF-SLAM에 비해 다소 우수한 예측 성능을 보임을 확인할 수 있었다.

• Journal of Advanced Marine Engineering and Technology
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• 제24권3호
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• pp.88-98
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• 2000

In this paper, a robust controller using $H_{\infty}$ control theory has been designed for the load frequency control of interconnected 2-area power system. The main advantage of the proposed $H_{\infty}$ controller is that uncertainties of power system can be included at the stage of controller design. Representation of uncertainties is modeled by multiplicative uncertainly. In the mixed sensitivity problems, disturbance attenuation and uncertainty of the system is treated simultaneously. The robust stability and the performance of model uncertainties are represented by frequency weighted transfer function. The design of load frequency controller for each area was based on state-space approach. The comparative computer simulation results for the proposed controller and the conventional techniques such as the optimal control and the PID one were analyzed at the additions of various disturbances. Their deviation magnitude of frequency and tie line power flow at each area were mainly evaluated. Also the testing results of robustness for the cases that the perturbations of the all parameters of power system were amounted to about 20% were introduced. It was approved that the resultant performances of the proposed $H_{\infty}$ controller with mixed sensitivity were more robust and stable than the one of conventional controllers.

• 대한수학회지
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• 제51권2호
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• pp.345-362
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• 2014

We describe the Haagerup tensor product ${\ell}^{\infty}{\otimes}_h{\ell}^{\infty}$ and the extended Haagerup tensor product ${\ell}^{\infty}{\otimes}_{eh}{\ell}^{\infty}$ in terms of Schur product maps, and show that ${\ell}^{\infty}{\otimes}_h{\ell}^{\infty}{\cap}\mathbb{B}({\ell}^2)$(resp. ${\ell}^{\infty}{\otimes}_{eh}{\ell}^{\infty}{\cap}\mathbb{B}({\ell}^2)$) coincides with $c_0{\otimes}_hc_0{\cap}\mathbb{B}({\ell}^2)$(resp. $c_0{\otimes}_{eh}c_0{\cap}\mathbb{B}({\ell}^2)$). For $C^*2$-algebras A, B, it is shown that $A{\otimes}_hB=A{\otimes}_{eh}B$ if and only if A or B is finite-dimensional.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.696-698
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• 2004

In this paper we design $H_{\infty}$ infinity controller for Induction motor with low speed operation. $H_{\infty}$ controller is applied in order to design a state feedback static controller for field oriented control of an induction motor. $H_{\infty}$ controller are linear plant can be set up using the same assumptions that are at the basis of field oriented control. Thus, $H_{\infty}$ control theory can be successfully used to set up a state feedback controller for field oriented control of an induction motor. The performances of the $H_{\infty}$ controller is numerically analysed and experimentally verified to prove the validity of the design procedure. In this paper show that performances with high robustness to variations of system parameter.