• Title, Summary, Keyword: LMI

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H_{\infty} Control Synthesis for Power System Design using LMI Optimization Method (LMI 최적화기법을 적용한 $H_{\infty}$제어 시스템의 전력계통 안정화장치(PSS) 설계)

  • Jeong, Dae-Won;Ju, Un-Pyo;Kim, Geon-Jung
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.49 no.4
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    • pp.165-174
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    • 2000
  • This paper presents the application of H$\infty$ control synthesis using LMI optimization method to power system stabilizer(PSS) design. Since power system is usually operated under circumstance of unmeasurable uncertainties and external disturbances, the improvement of small signal stability becomes one of the most important issue for securing system stability and preventing low frequency oscillation phenomena. The LMI optimized H$\infty$ PSS provides robust performance and guarantees the internal stability under these operating conditions. The global optimal H$\infty$ norm is found using LMI convex optimization method which is more systematic than standard two Riccati solution method. The design results are simulated for a case study. We verified that the LMI method shows the best performance characteristic smong standard Riccati method and conventional lead/lag method.

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Design of $\gamma$-Suboptimal Reduced-Order Unbiased $H_{\infty}$ Filter Using LMI ($\gamma$-준최적 저차 무편향 $H_{\infty}$ 필터의 LMI를 이용한 설계)

  • Jin, Seung-Hee;Yoon, Tae-Sung;Park, Jin-Bae
    • Proceedings of the KIEE Conference
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    • pp.146-148
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    • 1997
  • An LMI-based parameterization of all $\gamma$-suboptimal reduced-order unbiased $H_{\infty}$ filters is provided in terms of a free matrix, using the unbiasedness condition, bounded real lemma and the general solution of the basic LMI. Also, by sequentially solving the generalized eigenvalue minimization and basic LMI problem, the optimal filter coefficient matrix can be obtained with the best achievable performance.

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An LMI-Based Sliding Mode Observer Design Method for Uncertain Time-Delay Systems (불확실한 시간 지연 시스템을 위한 LMI 기반 슬라이딩 모드 관측기 설계법)

  • Choi Han-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.12 no.10
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    • pp.1018-1021
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    • 2006
  • This paper presents an LMI-based method to design sliding mode observers for a class of uncertain time-delay systems. Using LMIs we derive an existence condition of a sliding mode observer guaranteeing a stable sliding motion. And we give explicit formulas of the observer gain matrices. Finally, we give a simple LMI-based design algorithm, togeter with a numerical design example.

LMI-based Design of Integral Sliding Mode Controllers (적분 슬라이딩 모드 제어기의 LMI 기반 설계)

  • Choi, Han-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.15 no.6
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    • pp.563-566
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    • 2009
  • This paper presents an LMI-based method to design a integral sliding mode controller for a class of uncertain systems. Using LMIs we derive an existence condition of a sliding surface. And we give a switching feedback control law. Our method is a generalization of the previous integral sliding mode control design methods. Since our method is based on LMIs, it gives design flexibility for combining various useful design criteria that can be captured in the LMI-based formulation.

Comparison Study of H-infinity Controller Design Algorithms for Spacecraft Attitude Control (인공위성 자세제어를 위한 H-infinity 제어기 설계 알고리즘 비교 연구)

  • Rhee, Seung-Wu
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.44 no.1
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    • pp.57-69
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    • 2016
  • There are three kinds of algorithms(2-ARE, mu-synthesis, LMI) for controller design using closed-loop shaping method. This paper provides the summary of background theory of three algorithms and $H_{\infty}$ controller design results for spacecraft attitude control using the three controller design tools of Matlab$^{TM}$ Toolbox for comparison. As a result, it reveals that LMI design method is more reliable as well as easier than others for spacecraft attitude control design. Comparison results are as follow: 2-ARE method and LMI method provide almost same results in robust stability, robust performance and control authority level. But 2-ARE method is more sensitive than LMI method with respect to proper design of weighting functions: 2-ARE method is more difficult than LMI method in weighting function design. The design result of mu-synthesis method shows worse performance and requires bigger control authority than others.

Robust Depth and Course Control of AUV Using LMI-based $H_{\infty}$ Servo Control (LMI에 기초한 $H_{\infty}$ 서보제어를 이용한 AUV의 강인한 자동 심도 및 방향제어)

  • 양승윤;김인수;이만형
    • Journal of the Korea Institute of Military Science and Technology
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    • v.3 no.1
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    • pp.38-46
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    • 2000
  • In this paper, robust depth and course controllers of AUV(autonomous underwater vehicles) using LMI-based H$_{\infty}$ servo control are proposed. The $H_{\infty}$ servo problem is modified to an $H_{\infty}$ control problem for the generalized plant that includes a reference input mode, and then a sub-optimal solution that satisfies a given performance criteria is calculated by LMI(Linear Matrix Inequality) approach. The robust depth and course controllers are designed to be satisfied the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under sea wave and tide disturbances. The performances of the designed controllers are evaluated by computer simulations, and these simulation results show the applicability of the proposed robust depth and course controller.

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Active Vibration Control of Structure Using LMI Optimization Design of Robust Saturation Controller (강인 포화 제어기의 LMI 최적 설계를 이용한 구조물의 능동 진동 제어)

  • Park, Young-Jin;Moon, Seok-Jun;Lim, Chae-Wook
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.3
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    • pp.298-306
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    • 2006
  • In our previous paper, we developed a robust saturation controller for the linear time-invariant (LTI) system involving both actuator's saturation and structured real parameter uncertainties. This controller can only guarantee the closed-loop robust stability of the system in the presence of actuator's saturation. But we cannot analytically make any comment on control performance of this controller. In this paper, we suggest a method to use linear matrix inequality (LMI) optimization problem which can analytically explain control performance of this robust saturation controller only in nominal system. The availability of design method using LMI optimization problem for this robust saturation controller is verified through a numerical example for the building with an active mass damper (AMD) system.

Robust Stability of Uncertain Linear Large-scale Systems with Time-delay via LMI Approach (LMI 기법을 이용한 시간지연 대규모 불확정성 선형 시스템의 강인 안정성)

  • Lee, Hee-Song;Kim, Jin-Hoon
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.10
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    • pp.1287-1292
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    • 1999
  • In large-scale systems, we frequently encounter the time-delay and the uncertainty, and these should be considered in the design of controller because these are the source of the degradation of the system performance and instability of system. In this paper, we consider the robust stability of the linear large scale systems with the uncertainties and the time-delays. The considered uncertainties are both structured uncertainty and the unstructured uncertainty. Also, the considered time-delays are time-varying having finite time derivative limits. Based on the Lyapunov theorem and the linear matrix inequality(LMI) technique, we present two sufficient conditions that guarantee the robust stability of the system. The conditions are expressed as the LMI forms which can be easily checked their feasibility by using the well-known LMI control toolbox. Finally, we show by two examples that our results are less conservative than the previous results.

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Robust observer-based $H_{\infty}$ control for singular systems (특이시스템의 강인 관측기 기반 $H_{\infty}$ 제어)

  • Kim, Jong-Hae
    • Proceedings of the KIEE Conference
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    • pp.7-9
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    • 2004
  • This paper provides an observer-based $H_{\infty}$ controller design method for singular systems with and without time-varying delay by just one LMI condition. The sufficient condition for the existence of controller and the controller design method are presented by perfect LMI (linear matrix inequality) approach. The design procedure involves solving an LMI. The observer-based $H_{\infty}$ controller in the existing results can be constructed from the coupled two or more conditions while the proposed controller design method can be obtained from an LMI condition, which can be solved efficiently by convex optimization. Since the obtained condition can be expressed as an LMI form, all variables including feedback gain and observer gain can be calculated simultaneously by Schur complement and changes of variables. An example is given to illustrate the results.

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An LMI-Based Design of Reduced Order Observers Substitutable for Full Order Sliding Mode Observers (전차수 슬라이딩 모드 관측기를 대체하는 축소차수 관측기의 LMI 기반 설계)

  • Choi, Han-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.14 no.3
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    • pp.232-235
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    • 2008
  • This paper presents an LMI-based method to design reduced order observers by which we can substitute full order sliding mode observers for a class of uncertain time-delay systems. We show that a reduced order observer can be constructed as long as the uncertain system satisfies the previous LMI existence conditions of a full order sliding mode observer. And we give explicit formulas of the reduced order observer gain matrices. Finally, we give a simple LMI-based design algorithm, together with a numerical design example.