• Title/Summary/Keyword: Linear matrix inequality technique

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A Robust Control of Horizontal-Shaft Magnetic Bearing System Using Linear Matrix Inequality Technique (선형행렬부등식 기법을 이용한 횡축형 자기 베어링 시스템의 로버스트 제어)

  • 김창화;정병건;양주호
    • Journal of Advanced Marine Engineering and Technology
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    • v.25 no.2
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    • pp.321-330
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    • 2001
  • Magnetic bearing system is frequently used for high-speed rotating machines because of its frictionless property. But the magnetic bearing system needs feedback controller for stabilization. This paper presents a robust controller design by using linear matrix inequality for magnetic bearing system which shows the control performance and robust stability under the physical parameter perturbations. To the end, the validity of the designed controller is investigated through computer simulation.

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Design of the Well-Conditioned Observer - A Linear Matrix Inequality Approach - (Well-Conditioned 관측기 설계 - A Linear Matrix Inequality Approach -)

  • Jung, Jong-Chul;Huh, Kun-Soo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.28 no.5
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    • pp.503-510
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    • 2004
  • In this paper, the well-conditioned observer for a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic uncertainties such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic uncertainties such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_{2}$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic uncertainties. In stochastic viewpoints, the estimation variance represents the robustness to the stochastic uncertainties and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.

Robust H∞ Fuzzy Control for Discrete-Time Nonlinear Systems with Time-Delay (시간 지연을 갖는 이산 시간 비선형 시스템에 대한 H∞ 퍼지 강인 제어기 설계)

  • Kim Taek Ryong;Park Jin Bae;Joo Young Hoon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.15 no.3
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    • pp.324-329
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    • 2005
  • In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time nonlinear systems with time-delay via fuzzy static output feedback is investigated. The Takagj-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear system with time-delayed state. Then, the parallel distributed compensation technique is used for designing of the robust fuzzy controller. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities via similarity transform and congruence transform technique. We have shown the effectiveness and feasibility of the proposed method through the simulation.

Observer-based sampled-data controller of linear system for the wave energy converter

  • Koo, Geun-Bum;Park, Jin-Bae;Joo, Young-Hoon
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.4
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    • pp.275-279
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    • 2011
  • In this paper, an observer-based sampled-data controller of linear system is proposed for the wave energy converter. Based on the sampled-data observer, the controller is design. In the closed-loop system with controller, it obtains the norm inequality between the continuous-time state variable and the discrete-time one. Using the norm inequality, sufficient condition is derived for the asymptotic stability of the closed-loop system and formulated in terms of linear matrix inequality. Finally, the wave energy converter simulation is provided to verify the effectiveness of the proposed technique.

Design of Robust and Non-fragile $H_{\infty}$ Kalman-type Filter for System with Parameter Uncertainties: PLMI Approach (변수 불확실성을 가지는 시스템에 대한 견실비약성 $H_{\infty}$ 칼만형필터 설계: PLMI 접근법)

  • Kim, Joon Ki;Yang, Seung Hyeop;Bang, Kyung Ho;Park, Hong Bae
    • Journal of the Institute of Electronics and Information Engineers
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    • v.49 no.10
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    • pp.181-186
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    • 2012
  • In this paper, we describe the synthesis of robust and non-fragile Kalman filter design for a class of uncertain linear system with polytopic uncertainties and filter gain variations. The sufficient condition of filter existence, the design method of robust non-fragile filter, and the measure of non-fragility in filter are presented via LMIs(Linear Matrix Inequality) technique. And the obtained sufficient condition can be represented as PLMIs(parameterized linear matrix inequalities) that is, coefficients of LMIs are functions of a parameter confined to a compact set. Since PLMIs generate infinite LMIs, we use relaxation technique, find the finite solution for robust non-fragile filter, and show that the resulting filter guarantees the asymptotic stability with parameter uncertainties and filter fragility. Finally, a numerical example will be shown.

A Sliding Surface Design for Linear Systems with Mismatched Uncertainties based on Linear Matrix Inequality

  • Jang, Seung-Ho;Kim, Sang-Woo
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.561-565
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    • 2005
  • Sliding mode control (SMC) is an effective method of controlling systems with uncertainties which satisfy the so-called matching condition. However, how to effectively handle mismatched uncertainties of systems is still an ongoing research issue in SMC. Several methods have been proposed to design a stable sliding surface even if mismatched uncertainties exist in a system. Especially, it is presented that robustness and efficiency of SMC for linear systems with mismatched uncertainties can be improved by reducing mismatched uncertainties in the reduced-order system. The reduction method needs a new sliding surface with an additional component based on Lyapunov redesign technique. In this paper, a stable sliding surface which contains additional component to reduce the influence of mismatched uncertainties, is introduced. It is designed by using linear matrix inequalities that guarantees the stability of the system. A numerical example demonstrates the validity of the proposed scheme.

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A Unified Approach to Discrete Time Robust Filtering Problem (이산시간 강인 필터링 문제를 위한 통합 설계기법)

  • Ra, Won-Sang;Jin, Seung-Hee;Yoon, Tae-Sung;Park, Jin-Bae
    • Proceedings of the KIEE Conference
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    • 1999.07b
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    • pp.592-595
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    • 1999
  • In this paper, we propose a unified method to solve the various robust filtering problem for a class of uncertain discrete time systems. Generally, to solve the robust filtering problem, we must convert the convex optimization problem with uncertainty blocks to the uncertainty free convex optimization problem. To do this, we derive the robust matrix inequality problem. This technique involves using constant scaling parameter which can be optimized by solving a linear matrix inequality problem. Therefore, the robust matrix inequality problem does not conservative. The robust filter can be designed by using this robust matrix inequality problem and by considering its solvability conditions.

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Well-Conditioned Observer Design via LMI (LMI를 이용한 Well-Conditioned 관측기 설계)

  • 허건수;정종철
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2003.04a
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    • pp.21-26
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    • 2003
  • The well-conditioned observer in a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic issues such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic issues such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_2$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic issues and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.

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A Decentralized Fuzzy Controller for Experimental Nonlinear Helicopter Systems (헬리콥터 시스템의 퍼지 분산 제어기 설계)

  • 김문환;이호재;박진배;차대범;주영훈
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2001.12a
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    • pp.141-144
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    • 2001
  • This paper proposes a decentralized control technique for 2-dimensional experimental helicopter systems. The decentralized control technique is especially suitable in large-scale control systems. We derive the stabilization condition for the interconnected Takagi-Sugeno (75) fuzzy system using the rigorous tool - Lyapunov stability criterion and formulate the controller design condition in terms of linear matrix inequality (LMI). To demonstrate the feasibility of the proposed method, we include the experiment result as well as a computer simulation one, which strongly convinces us the applicability to the industry.

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ROBUST OUTPUT FEEDBACK $H\infty$ CONTROL FOR UNCERTAIN DELAYED SINGULAR SYSTEMS

  • Kim, Jong-Hae;Lim, Jong-Seul
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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    • pp.513-522
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    • 2006
  • This paper considers a robust output feedback $H\infty$ controller design method for singular systems with time-varying delay in state and parameter uncertainty in system matrix by an LMI approach and observer based technique, which can be solved efficiently by convex optimization. The sufficient condition for the existence of controller and the controller design method are presented by strict LMI(linear matrix inequality) approach. 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.