• Title/Summary/Keyword: $H_\infty$-norm

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H$\infty$ Kalman Filter 설계

  • 박재삼
    • Proceedings of the Korea Society for Industrial Systems Conference
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    • 1998.10a
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    • pp.757-764
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    • 1998
  • 본 논문에서는 Glover-Doyle의 H$\infty$ 설계기법을 이용하여 H$\infty$ 성능경계를 만족하는 Kalman 필터를 설계하는 방법을 제시한다. 제시한 방법을 사용하면, kalman 필터의 성능 강인성과 안정화 강인성 문제와의 관계를 설계변수의 설정으로 설계자가 적절하게 선택함으로써 구조적 불확실성에 대하여 비교적 강인한 H$\infty$ -norm Kalman 필터를 설계할 수 있도록 한다. 설계의 예를 통하여 H$\infty$ -norm Kalman 필터의 설게방법을 보이고, H2-norm Kalman 필터와 비교함으로써 제시된 방법이 특성을 보인다.

Robust and Reliable $H_\infty$ Control for Linear Systems with Parameter Uncertainty (파라메타 불확실성을 갖는 선형시스템에 대한 강한 신뢰 $H_\infty$제어)

  • 서창준;김병국
    • 제어로봇시스템학회:학술대회논문집
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    • 1993.10a
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    • pp.498-503
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    • 1993
  • In this paper, a robust and reliable H$_{\infty}$ control problem is considered for linear uncertain systems with time-varying norm-bounded uncertainty in the state matrix, which performs well despite of actuator outages. Using linear static state feedback and the quadratic stabilization with H$_{\infty}$-norm bound, a robust and reliable H$_{\infty}$ controller is obtained that stabilizes the plant and guarantees an H$_{\infty}$-norm bound constraint on disturbance attenuation for all admissible uncertainties and normal state as well as faulty state of actuators. It provides a sufficient condition for robust and reliable stabilization with H$_{\infty}$-norm bound. Reliability is guaranteed provided actuator outages only occur within a prespecified subset of actuators.tors.

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Robust H$_\infty$ Control for Discrete Time-delay Linear Systems with Frobenius Norm-bounded Uncertainties (파라미터 불확실성을 가지는 이산 시간지연 시스템에 대한 견실 H$_\infty$ 제어)

  • 김기태;이형호;이상경;박홍배
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.23-23
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    • 2000
  • In this paper, we proposed the problems of robust stability and 개bust H$_{\infty}$ control of discrete time-delay linear st.stems with Frobenius norm-bounded uncertainties. The existence condition and the design method of robust H$_{\infty}$ state feedback control]or are given. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

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A robust generalized predictive control which guarantees $H_{\infty}$ norm bounds ($H_{\infty}$노옴조건을 만족하는 강인한 일반형예측제어기)

  • 이영일;김용호;권욱현
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.556-559
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    • 1996
  • In this paper, we suggest a H center .inf. generalized predictive control(H center GPC) which guarantees $H_{\infty}$-norm bounds. THe suggested control is obtained by solving the min-max problem in nonrecursive forms. The stability conditions of the suggested control are derived in a somewhat simple form and it is not required for the derived solution to be a saddle point solution. It is also shown that the suggested control guarantees the $H_{\infty}$-norm bounds under the same conditions of stability.

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Design of a Model-based Controller for a 6-DOF Precision Positioning Stage using $H_{\infty}$ norm ($H_{\infty}$ norm을 이용한 6 자유도 정밀스테이지의 모델기반 제어기 설계)

  • Moon, Jun-Hee;Lee, Bong-Gu
    • Journal of the Korean Society for Precision Engineering
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    • v.27 no.12
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    • pp.59-66
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    • 2010
  • We developed a model-based controller for 6-DOF micropositioning of a precision stage using $H_{\infty}$ norm, For the design, a state-space system of the mathematical model of the stage is derived In developing the controller, weighting functions are effectively designed in consideration of upper bounds of the sensitivity of the control loop and control input. Step responses in open and closed loop control are provided to verify the micropositioning performance of the stage. By applying the developed controller we prove that the inverse of the weighting function forms the upper bound of the control loop. It is also found that the controller makes the same sensitivity shape with all the DOFs due to the use of $H_{\infty}$ norm. The developed controller is expected to be applied successfully for industrial use.

Receding Horizon $H_{\infty}$ Predictive Control for Linear State-delay Systems

  • Lee, Young-Sam
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.2081-2086
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    • 2005
  • This paper proposes the receding horizon $H_{\infty}$ predictive control (RHHPC) for systems with a state-delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terns, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHPC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the well-known nonincreasing monotonicity. Finally, we shows the asymptotic stability and $H_{\infty}$-norm boundedness of the closed-loop system controlled by the proposed RHHPC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon $H_{\infty}$-norm bound.

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A study on the design of $H_{2}$/$H_{\infty}$ robust controller-polynomial approach ($H_{2}$/$H_{\infty}$ 강인제어기 설계에 관한 연구-다항식 접근방법)

  • 박승규;송대원
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.751-753
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    • 1996
  • The $H_{2}$/$H_{\infty}$ robust controller is designed by using polynomial approach. This controller can minimise a $H_{2}$ norm of error under the fixed bound of $H_{\infty}$ norm of mixed sensitivity function by employing the Youla parameterization and using polynomial approach at the same time. It is easy to apply this controller to adaptive system.

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On the Properties of $\gamma$-.$\varepsilon$ for $H_\infty$ Control by State Feedback and Computation of the Infimum of $H_\infty$ Norm

  • Tian, Dong;Ohta, Michio
    • 제어로봇시스템학회:학술대회논문집
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    • 1993.10b
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    • pp.562-565
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    • 1993
  • It is well known that H$_{\infty}$ control problem involves solving an algebraic Riccati equation which includes a pair of parameters (.gamma., .epsilon.). Focusing on .epsilon. the maximum of .epsilon.. We discuss in this paper about the properties between the H$_{\infty}$ norm of a trnsfer function matrix and the parameters(.gamma., .epsilon.). We can change the algebraic relattion between .gamma. and .epsilon. by the similarity transformation of a considered system and we can find a proper transformation to get a simple quadratic algebraic equation between .gamma. and .epsilon.. This relation provide the H$_{\infty}$ norm of a transfer function.on.

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A Synthesis for Robust Servo System Based on Mixed $H_2/H_{\infty}$ Control

  • Park, Yeon-Wook;Lee, Kum-Won
    • 제어로봇시스템학회:학술대회논문집
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    • 1999.10a
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    • pp.88-91
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    • 1999
  • The purpose of this paper is to propose an approach to design a robust servo controller based on the Mixed H$_2$/H$\sub$$\infty$/ theory. In order to do this, we first modify the generalized plant for the usual H$\sub$$\infty$/ servo problem to a structure of the Mixed H$_2$/H$\sub$$\infty$/ minimization problem by virtue of the internal model principle. By doing this, we can divide specifications adopted for robust servo system design into H$_2$and H$\sub$$\infty$/ performance criteria, respectively. Then, the mixed H$_2$/H$\sub$$\infty$/ problem is solved in order to find the best solution, by which we can minimize H$_2$-norm of the transfer function under the condition of H$\sub$$\infty$/-norm value, through Linear Matrix Equality (LMI).

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Descriptor and Non-Descriptor Controllers in Mixed $H_2/H_{\infty}$ Control of Descriptor Systems

  • Choe, Yeon-Wook;Ahn, Young-Ju
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.892-897
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    • 2003
  • This paper considers the design of mixed $H_2/\;H_{\infty}$ controllers for linear time-invariant descriptor systems. Firstly, an $H_{\infty}$ and $H_2$ synthesis problem for a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, the existence of a mixed $H_2/\;H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_{\infty}$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables. In addition, we show the procedure by which a obtained descriptor controller can be transformed to a non-descriptor one.

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