• Title/Summary/Keyword: $H_\infty$ 제어

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Design of the multivariable hard nonlinear controller using QLQG/$H_{\infty}$ control (QLQG/$H_{\infty}$ 제어를 이용한 다변수 하드비선형 제어기 설계)

  • 한성익;김종식
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.81-84
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    • 1996
  • We propose the robust nonlinear controller design methodology, the $H_{\infty}$ constrained quasi - linear quadratic Gaussian control (QLQG/ $H_{\infty}$), for the statistically-linearized multivariable system with hard nonlinearties such as Coulomb friction, deadzone, etc. The $H_{\infty}$ performance constraint is involved in the optimization process by replacing the covariance Lyapunov equation with the Riccati equation whose solution leads to an upper bound of the QLQG performance. Because of the system's nonlinearity, however, one equation among three Riccati equations contain the nonlinear correction terms that are very difficult to solve numerically. To treat this problem, we use simple algebraic techniques. With some analytic transformation for Riccati equations, the nonlinear correction terms can be so eliminated that the set of a linear controller to the different operating points are designed. Synthesizing these via inverse random input describing function (IRIDF) technique, the final nonlinear controller can be designed.

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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 Discrete-Time $H_{\infty}$ Controller with Preview Action (예견 기능을 가진 이산시간 $H_{\infty}$ 제어기의 설계)

  • Choi, Jin-Tae;Kim, Jong-Shik
    • Journal of Institute of Control, Robotics and Systems
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    • v.3 no.2
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    • pp.115-123
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    • 1997
  • 이산기간 H/sub .inf./ 제어에 의한 최적 예견제어기를 제안한다. 기존의 H/sub .inf./ 제어기는 미지의 외란만 고려한 것이고, LQ 에 의한 예견제어기는 예견 가능한 외란과 미지의 외란이 동시에 가해지는 동적 시스템의 전달함수 행렬의 infinity 놈의 최소화하는 피드백제어기가 동시에 설계된다. 제어기의 설계는 full-information H/sub .inf./ 제어 이론을 따르나, 그 유도 과정은 LQ 에 기초한 예견제어기와 유사하게 이루어진다. 설계된 H/sub .inf./ 예견 게인 행렬은 LQ 예견 게인 행렬과 유사한 구조를 갖는다. 전달함수 행렬의 infinity 놈이 .inf.로 갈수록 H/sub .inf./ 예견 게인 행렬은 LQ에 의한 것에 접근한다. LQ 예견 게인 행렬은 H/sub .inf./ 예견 게인 행렬의 부분 집합임이 입증한다.

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A Study on the Control of Parallel-Type Inverted Pendulum by $H_\infty$ Control ($H_\infty$제어에 의한 병렬형 도립진자의 제어에 관한 연구)

  • Yang, Joo-Ho;Byun, Jung-Hoan
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.31 no.2
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    • pp.178-189
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    • 1995
  • In this pater, authors derive the state - space equiation about the patallel - type inverted pendulum which is adopted as control object, and constitute the control system by $H_\infty$control theory. The modeling error is unavoidably existed by linearization error, and so on. We regard this modeling error which is determined from the identification through frequency response as unstructured model uncertainty. An augmented state - space equiation with frequency weighting function is constructed for application of the $H_\infty$theory, and the mixed sensitivity problem is considered. The weighting functions are determined in consideration of the model uncertainty and the response of system in frequency region. The $H_\infty$controller is designed by using software package for controller design. From results of response simulation, the control system designed with $H_\infty$theory guarantees low sensitivity for disturbance as well as robustness against the model uncertainties.

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A Robust Controller Design for the Position Control of a Spring-Mass System (탄성-질량시스템의 위치제어를 위한 강건 제어기 설계)

  • 박종우;이상철
    • Journal of the Korean Institute of Telematics and Electronics T
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    • v.36T no.3
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    • pp.41-49
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    • 1999
  • In this paper, we design a controller using the $\mu$-synthesis method and apply it for the spring-mass system with noncollocated sensors and actuators. We assume that the values of the spring stiffness and load mass of the plant are uncertain. The plant is modeled with parametric uncertainty by using the state space equation, especially the descriptor form. The $H_\infty$ controller designed by the $\mu$-synthesis method is compared with the standard $H_\infty$ controller To compare performances of two $H_\infty$ controllers, it is assumed that both controllers were designed with same weighting functions except that the $\mu$-synthesis controller has structured uncertainties. By compared with the standard $H_\infty$ controller, we show that the designed controller has satisfactory robust performance as well as robust stability by simulations and experiments.

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Mixed $H_2/H_{\infty}$ Control of Two-wheel Mobile Robot

  • Roh, Chi-Won;Lee, Ja-Sung;Lee, Kwang-Won
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.438-443
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    • 2003
  • In this paper, we propose a control algorithm for two-wheel mobile robot that can move the rider to his or her command and autonomously keep its balance. The control algorithm is based on a mixed $H_2/H_{\infty}$ control scheme. In this control problem the main issue is to move the rider while keeping its balance in the presence of disturbances and parameter uncertainties. The disturbance force caused by uneven road surfaces and the uncertainty due to different rider's heights are considered. To this end we first consider a state feedback controller as a basic framework. Secondly, we obtain the state feedback gain $K_2$ minimizing the $H_2$ norm and the state feedback gain $K_{\infty}$ minimizing the $H_{\infty}$ norm over the whole range of parameter uncertainty. Finally, we select mixed $H_2$/$H_{\infty}$ state feedback controller K as the geometric mean of $K_2$ and $K_{\infty}$. Simulation results show that the mixed $H_2/H_{\infty}$ state feedback controller combines the effects of the optimal $H_2$ state feedback controller and robust $H_{\infty}$ controller state feedback controller efficiently in the presence of disturbance and parameter uncertainty.

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The Design of Multi-Objective $H_2/H_{\infty}$ Controllers for multiple linear Time-invariant models (다중 선형 시불변 모델에 대한 다목적 $H_2/H_{\infty}$ 제어기 설계)

  • Cho, Do-Hyeoun;Won, Young-Jin;Lee, Jong-Yong
    • Journal of the Institute of Electronics Engineers of Korea TE
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    • v.42 no.3
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    • pp.13-18
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    • 2005
  • This paper presents a design of a multi-objective $H_2/H_{\infty}$ controller of an inverted pendulum with polytopic model by the stabilizing regulator and tracking performances. Multi-objective controllers are designed for polytopic models by the LMI design technique with convex algorithms. It is observed that the inverted pendulum controlled by any controller designed for each polytopic model is stably restored to the vertical angle position for initial values of larger tilt angles.

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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A Study on the $H_{\infty}$ Robust Controller for Adaptive Control-polynomial approach (적응제어를 위한 $H_{\infty}$ 강인제어기의 설계-다항식 접근방법)

  • Park, Seung-Kyu
    • Proceedings of the KIEE Conference
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    • 1996.07b
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    • pp.936-938
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    • 1996
  • The $H_{\infty}$ robust controller is designed for on-line adaptive control application by using polynomial approach. The $H_{\infty}$ robust controllers for adaptive system were designed first by Grimble. But they have a problem that two minimum costs can exist and did not minimize the conventional $H_{\infty}$ cost function which is the $H_{\infty}$ sum of weighted sensitivity and complementary sensitivity terms. In this paper, the two minimum costs problem can be avoided and the conventional $H_{\infty}$ cost function is minimized by employing the Youla parameterization and polynomial approach at the same time. In addition pole placement is possible without any relation with weighting function.

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$H_{\infty}$ Control of Seeker Scan-Loop using LSDP (LSDP를 이용한 탐색기 주사루프의 $H_{\infty}$ 제어)

  • Lee, Ho-Pyeong;Song, Chang-Seop
    • Journal of the Korean Society for Precision Engineering
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    • v.12 no.1
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    • pp.78-86
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    • 1995
  • $H_{\infty}$ Controller of seeker scan-loop is designed using LSDP proposed by McFarlane. The performance and robustness of $H_{\infty}$ controller are analyzed using robustness theorems by Lehtomaki and compared with those of the LQG/LTR controller. Especially, structured singular value .mu. -test of Doyle is used to evaluate robust performance of seeker scan-loop. It is demonstated that seeker scan-loop by $H_{\infty}$ controller is very robust to model uncertainties described by additive and multiplicative perturbations.

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