• 제목/요약/키워드: Linear matrix inequality technique

검색결과 76건 처리시간 0.03초

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

  • 김창화;정병건;양주호
    • Journal of Advanced Marine Engineering and Technology
    • /
    • 제25권2호
    • /
    • pp.321-330
    • /
    • 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.

  • PDF

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

  • 정종철;허건수
    • 대한기계학회논문집A
    • /
    • 제28권5호
    • /
    • pp.503-510
    • /
    • 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.

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

  • 김택룡;박진배;주영훈
    • 한국지능시스템학회논문지
    • /
    • 제15권3호
    • /
    • pp.324-329
    • /
    • 2005
  • 본 논문에서는 시간 지연을 갖는 이산 시간 비선형 시스템을 $H\infty$ 의미에서 안정하게 하는 정적 출력 제한 퍼지 제어기 설계를 제시한다. 먼저 대상이 되는 비선형 시스템은 Takagi-Sugeno 퍼지 모델로 표현 되어진다. 그리고 parallel distributed compensation technique을 이용하여 퍼지 제어기의 형태를 만든다. 하나의 Lyapunov 함수를 정하여서 폐루프 시스템의 전역 점근적 안정성과 외란에 대한 강인성을 bilinear matrix inequality 형태로 제시한다. 그리고 합동변환법과 동질성 변환법을 통해 이것을 선형 행렬 부등식 (linear matrix inequality) 으로 표현한다. 제안된 방법의 효율성과 가능성을 보여주기 위해 한 예제를 포함한다.

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
    • /
    • 제11권4호
    • /
    • pp.275-279
    • /
    • 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.

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

  • 김준기;양승협;방경호;박홍배
    • 전자공학회논문지
    • /
    • 제49권10호
    • /
    • pp.181-186
    • /
    • 2012
  • 본 논문에서는 변수 불확실성과 필터이득 섭동을 가지는 시스템에 대한 견실비약성 $H_{\infty}$ 칼만형필터 설계기법을 제안한다. 필터가 존재할 충분조건과 견실비약성 $H_{\infty}$ 필터 설계기법을 선형행렬부등식 (LMI: Linear Matrix Inequality 접근법으로 제안하고 시스템과 필터의 불확실성을 매개변수화 선형행렬부등식(PLMI: Parameterized Linear Matrix Inequality)으로 구조화된 불확실성의 형태로 표현한 후 Lyapunov 함수를 통해 시스템의 불확실성과 더불어 필터이득섭동을 고려한 칼만형 $H_{\infty}$ 필터가 존재할 충분조건과 필터설계기법을 PLMI 형태로 보인다. PLMI는 무한개의 LMI의 형태로 나타나므로 완화기법(relaxation technique)을 적용하여 유한개의 LMI의 형태로 변환한 후 견실하고 최적화된 필터이득과 필터섭동범위를 계산하고, 예제와 모의실험을 통해 제시된 필터의 타당성을 검증한다.

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

  • Jang, Seung-Ho;Kim, Sang-Woo
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 제어로봇시스템학회 2005년도 ICCAS
    • /
    • pp.561-565
    • /
    • 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.

  • PDF

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

  • 나원상;진승희;윤태성;박진배
    • 대한전기학회:학술대회논문집
    • /
    • 대한전기학회 1999년도 하계학술대회 논문집 B
    • /
    • pp.592-595
    • /
    • 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.

  • PDF

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

  • 허건수;정종철
    • 한국공작기계학회:학술대회논문집
    • /
    • 한국공작기계학회 2003년도 춘계학술대회 논문집
    • /
    • pp.21-26
    • /
    • 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.

  • PDF

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

  • 김문환;이호재;박진배;차대범;주영훈
    • 한국지능시스템학회:학술대회논문집
    • /
    • 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
    • /
    • pp.141-144
    • /
    • 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.

  • PDF

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

  • Kim, Jong-Hae;Lim, Jong-Seul
    • Journal of applied mathematics & informatics
    • /
    • 제20권1_2호
    • /
    • pp.513-522
    • /
    • 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.