도립진자 시스템에 선형 분수 표현법을 이용한 $H_2/ H_\infty$ 제어

곽칠성,최규열 한국정보통신학회 1999 한국정보통신학회논문지 Vol.3 No.4

This paper presents an application of LMI-based techniques to the mixed $H_2/ H_\infty$ control of an inverted pendulum. The linear model of the inverted pendulum represented by an LFR(Linear Fractional Representation) model of uncertainties is derived. Considered uncertainties are three nonlinear components and a parameter uncertainty Augmenting the LFR model by adding weighting functions, we get a generalized plant, for which we design a mixed $H_2/ H_\infty$ controller using the LMI technique. To evaluate control performances and robust stability of the mixed $H_2/ H_\infty$ controller designed, we compare it with the $ H_\infty$controller through the simulation and experiment. The mixed $H_2/ H_\infty$ controller shows the better control performances and robust stability than the $H_\infty$controller in the sense of pendulum angle.

혼합 $H_2/H_{\infty}$제어에 의한 강인한 서보시스템의 설계 -3관성 벤치마크문제의 해법 -

최연욱,Choe, Yeon-Wook The Korea Institute of Convergence Signal Processi 2005 융합신호처리학회 논문지 (JISPS) Vol.6 No.3

본 논문은 혼합 $H_2/H_{\infty}$ 제어를 이용한 강인한 서보시스템의 설계법을 제안하고 이것을 3관성 벤치마크문제에 적용하여 이 방법의 유용성을 확인한다. 먼저 내부모델의 원리를 이용하여 혼합 $H_2/H_{\infty}$ 제어기법을 적용할 수 있는 구조를 제안하고 이 구조의 타당성을 검토한다. 다음에 강인한 서보시스템의 설계조건을 각각 $H_2$ 및 $H_{\infty}$의 설계사양으로 분리한 뒤 제안된 혼합 $H_2/H_{\infty}$ 설계법에 적용하여 설계를 LMI이론에 의하여 실행한다. 마지막으로 3관성벤치마크 문제에서 부가된 몇 가지의 사양을 제안된 혼합 $H_2/H_{\infty}$법에 맞도록 수정한 뒤 제어기의 설계를 통한 설계사양의 만족도를 확인한다. The purpose of this paper is to propose an approach to design a robust servo controller based on the mixed $H_2/H_{\infty}$ theory, and confirm its validity by applying to a benchmark problem. First, the existing $H_{\infty}$ servo problem is modified to a structure for the mixed $H_2/H_{\infty}$ control problem by virtue of the internal model principle. By making use of proposed structure, we can divide specifications required in the robust servo system design into $H_2$ and $H_{\infty}$ performance criteria, respectively. It is shown that the proposed design approach is quite effective through an application to a three inertia benchmark problem.

$H_2$/H$\infty$와 $\mu$이론을 이용한 유연 빔의 위치제어

최연욱 한국융합신호처리학회 2001 융합신호처리학회 논문지 (JISPS) Vol.2 No.1

본 연구는 유연한 빔의 위치를 제어하기 위한 강인한 제어기 설계를 위한 하나의 방법으로서 혼합 $H_2/H_{\infty}$과 $\mu$이론을 이용한 하나의 방법을 제시하고 있다. 먼저 제어기의 설계를 위한 유연한 빔의 수식모델을 얻기 위해 해석적인 방법과 실험을 통한 방법을 적용하였다. 이 결과로서 강인한 제어기의 설계를 위해 필요한 불확실성의 영역에 대한 정확한 정보를 얻을 수 있다. 다음, 혼합 $H_2/H_{\infty}$ 이론을 상기모델에 적용하여 강인한 제어기를 설계하고, 여기에 $\mu$이론을 적용하여 일반적으로 혼합 $H_{\infty}$ 제어기가 가질 수 있는 보수성을 완화시킨다 마지막으로 Simulation과 실험을 통하여 설계된 제어기의 유효성을 보인다. The objective of this paper is to present a method for designing robust positioning control systems of a flexible arm using mixed $H_2/H_{\infty}$ and $\mu$ theory. We begin with a description of the flexible arm based on the model identification method and discuss the derivation of the model uncertainty. The validity of the obtained model is confirmed experimentally. Next, a robust controller is designed based on the mixed $H_2/H_{\infty}$ and $\mu$ theory by which we can improve robustness of the entire system. On this occasion, we also propose a general plant formation suitable to mixed $H_2/H_{\infty}$ control and $\mu$-theory. Finally, the effectiveness of the proposed design method is verified through experimentation.

시간지연을 갖는 비선형 시스템의 퍼지 H₂H_∞ 제어기 설계

조희수,이갑래,박홍배,Jo, Hui-Su,Lee, Gap-Rae,Park, Hong-Bae 제어로봇시스템학회 2002 제어·로봇·시스템학회 논문지 Vol.8 No.7

This paper presents a method for designing fuzzy $H_2/H_{\infty}$ controllers of nonlinear systems with time varying delay. Takagi-Sugeno fuzzy model is employed to represent nonlinear systems with time varying delay. Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. A sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is then presented in terms of linear matrix inequalities(LMls). The proposed fuzzy $H_2/H_{\infty}$ controllers minimizes the upper bound on the linear quadratic performance measure.

다중 선형 시불변 모델에 대한 다목적 $H_2/H_{\infty}$ 제어기 설계

조도현,원영진,이종용,Cho, Do-Hyeoun,Won, Young-Jin,Lee, Jong-Yong 대한전자공학회 2005 電子工學會論文誌 IE (Industry electronics) Vol.42 No.3

본 논문은 안정화 조절기와 추종 성능을 확보하기 위하여 폴리도프 모델를 갖는 도립진자 시스템의 다목적 $H_2/H_{\infty}$ 제어기를 설계를 나타낸다. 꼭지점 기법을 갖는 LMI 설계 기법에 의하여 폴리토프 모델에 대한 다목적 제어기를 설계한다. 각 폴리포프 모델에 대하여 설계된 제어기에 의해 제어된 도립진자를 경사각의 초기값에 대한 수직 각을 안정하게 연직 위치로 복원시키는 곳을 관찰한다. 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.

부분적인 상태궤환과 공진비제어를 이용한 2관성계의 H_∞제어

김진수,유상봉 한국조명전기설비학회 2003 조명·전기설비학회논문지 Vol.17 No.4

전동기와 부하가 강성이 작은 축으로 연결되는 산업용 전동기 구동시스템에 있어서 전동기의 관성과 부하의 관성에 의해 축에 비틀림 진동이 발생한다. 이러한 문제를 해결하기 위하여 기존에 2자유도 H$_{\infty}$제어기가 제안되었다. 그러나 이 제어기는 구현하는데 어려움이 있다. 본 논문에서는 부분적인 상태궤환과 공진비제어를 이용한 2관성계의 H$_{\infty}$제어가 제안되었다. 제안된 제어기는 간단하면서도 외란 및 진동억제 성능을 만족한다.어기는 간단하면서도 외란 및 진동억제 성능을 만족한다. In the industrial motor drive system which is composed of a motor and load connected with a flexible shaft, a torsional vibration is often generated because of the elastic elements in torque transmission. To solve this problem, the two degrees of freedom H$_{\infty}$ controller was designed. But it is difficult to realize that controller. In this paper, H$_{\infty}$ control of 2-mass system using partial state feedback and resonance ratio control is proposed. Proposed controller has simple structure but satisfies the attenuation of disturbances and vibrations.

Structure-Control Combined Design with Structure Intensity

Park, Jung-Hyen,Kim, Soon-Ho Korean Society of Ocean Engineers 2003 International journal of ocean engineering and tec Vol.6 No.1

This paper proposes an optimum design method of structural and control systems, using a 2-D truss structure as an example. The structure is subjected to initial static loads and disturbances. For the structure, a FEM model is formed. Using modal transformation, the equation of motion is transformed into modal coordinates, in order to decrease D.O.F. of the FEM model. To suppress the effect of the disturbances, the structure is controlled by an output feedback $H_{\infty}$ controller. The design variables of the combined optimal design of the control-structure systems are the cross sectional areas of truss members. The structural objective function is the structural weight. The control objective function is the $H_{\infty}$ norm, the performance index of control. The second structural objective function is the energy of the response related to the initial state, which is derived from the time integration of the quadratic form of the state in the closed-loop system. In a numerical example, simulations have been perform. Through the consideration of structural weight and $H_{\infty}$ norm, an advantage of the combined optimum design of structural and control systems is shown. Moreover, since the performance index of control is almost nearly optimiz, we can acquire better design of structural strength.

Mixed $H_{2}/H_{\infty}$ Controller Design for Descriptor Systems

Choe, Yeon-Wook The Korean Institute of Electrical Engineers 2004 전기학회논문지 D Vol.53 No.7

The descriptor system model has a high ability in representing dynamical systems. It can preserve physical parameters in the coefficient matrices, and describe the dynamic part, static part, and even the improper part of the system in the same form. The design of mixed $H_{2}/H_{\infty}$ controllers for linear time-invariant descriptor systems is considered in this paper. Firstly, an $H_2$ and $H_{\infty}$ synthesis problems fur a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, we show that 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 $H_2$ 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.

H∞제어기법에 의한 다층 층상 구조물의 진동제어에 관한 연구

정해종,김창화,변정환,양주호 한국소음진동공학회 1997 소음 진동 Vol.7 No.5

This paper is concerned with the vibration control of multi-layer structure for ultra-tall buildings and main tower of large bridge etc. We have modeled the multi-layer structure with the distributed mass system as the lumped mass system of two-degree-of-freedom structure and made experimental equipment. The $H_\infty$control theory was applied to the design of the control system. The designed control system was simulated by computer. As a result, the designed $H_\infty$controller showed the good vibration control performance to impulse response and frequency response.

유전 알고리즘을 이용한 $H_2 / H_\infty$ 혼합 제어기 설계

이종성,강기원,박기헌,Lee, Jong-Sung,Kang, Ki-Won,Park, Ki-Heon 제어로봇시스템학회 2000 제어·로봇·시스템학회 논문지 Vol.6 No.4

In this paper, the genetic algorithm is used to design a mixed H₂/ H/sub ∞/ controller Two kinds of controller forms, Youla's form and the general form, are considered to design a mixed H₂/ H/sub ∞/ controller. Efficient searching methods are sought to minimize the given H₂cost function under the H∞ constraint. It is verified by an example that the developed algorithm can provide stable results in the region where unstable results are shown by the conventional gradient method.