• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.5
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• pp.19-27
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• 2004

A delay dependent fuzzy $H_2/H_{\infty}$ controller design method for delayed fuzzy dynamic systems is considered. Using delay-dependent Lyapunov function, the asymptotical stability and $H_2/H_{\infty}$ performance problem are discussed. A sufficient condition for the existence of fuzzy controller is presented in terms of linear matrix inequalities(LMIs). A simulation example is given to illustrate the design procedures and performances of the proposed methods.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.239-245
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• 2002

In this Paper, we present a method for designing fuzzy $H_2/H_{\infty}$ controllers of delayed nonlinear systems with saturating input. Takagi-Sugeno fuzzy model is employed to represent delayed nonlinear systems with saturating input. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. And a sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is given in terms of linear matrix inequalities(LMIs). The designing fuzzy $H_2/H_{\infty}$ controllers minimize an upper bound on a linear quadratic performance measure. Finally, a design example of fuzzy $H_2/H_{\infty}$ controller for uncertain delayed nonlinear systems with saturating input.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.7A
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• pp.967-977
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• 2000

In this paper, we apply a mixed $H_2/H_{\infty}$ control to a generalized plant of inverted pendulum system represented by an LFR(Linear Fractional Representation). First, in order to obtain the generalized plant, the linear model of the inverted pendulum represented by an LFR(Linear fractional Representation) is derived. In LFR, we consider system uncertainties as three nonlinear components and a pendulum mass uncertainty. Augmenting the LFR model by adding weighting functions, we get a generalized plant. And then, we design a mixed $H_2/H_{\infty}$ controller for the generalized plant. In order to design the mixed $H_2/H_{\infty}$ controller, we use 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. In the result, with the fewer feedback information, 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.

• Journal of the Institute of Convergence Signal Processing
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• v.2 no.1
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• pp.101-107
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• 2001

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.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.43 no.2 s.308
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• pp.1-10
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• 2006

This paper is concerned with $H_2$ control design for active vibration control of a plate vibration system. We construct a plate vibration system with a plate, PZT ceramics actuators and sensors. The plate titration system is MIMO system and its transfer matrix is obtained by system identification experiments. We design a $H_2$ controller using the state space model obtained from system identification. Effectiveness and performance of the designed controller are verified by both simulation and experiment results.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.5
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• pp.1111-1116
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• 2000

The mixed $H_2/ H_\infty$ control method is one of positive approaches to design a controller having both the$H_2$-performance and the $H_\infty$-robust stability. In this paper, Firstly, The tracking Performance to be designed has been represented as $H_2$-norms for the plants with uncertainties. Secondly, $H_\infty$-norm have been set up in order to ensure the robust stabilities. The mixed digital controllers have been designed for an inverted system. The mixed $H_2/ H_\infty$digital controller for the inverted pendulum system was intended to stabilize the unstability of the plant together with the good tracking Performance.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.11
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• pp.1311-1318
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• 2012

Vehicle systems are frequently exposed to parameter uncertainties such as vehicle speed and height of center of gravity. If a controller is designed to be robust against these parameter uncertainties, the rollover prevention capability can be considerably enhanced. In this study, robust controllers $H_2$ and $H_{\infty}$ are designed by using LMI for vehicle rollover prevention control in the discrete time domain. Some simulations using CarSim, a reliable simulation tool, are performed to validate the proposed controllers.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.1
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• pp.57-69
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• 2016

There are three kinds of algorithms(2-ARE, mu-synthesis, LMI) for controller design using closed-loop shaping method. This paper provides the summary of background theory of three algorithms and $H_{\infty}$ controller design results for spacecraft attitude control using the three controller design tools of Matlab$^{TM}$ Toolbox for comparison. As a result, it reveals that LMI design method is more reliable as well as easier than others for spacecraft attitude control design. Comparison results are as follow: 2-ARE method and LMI method provide almost same results in robust stability, robust performance and control authority level. But 2-ARE method is more sensitive than LMI method with respect to proper design of weighting functions: 2-ARE method is more difficult than LMI method in weighting function design. The design result of mu-synthesis method shows worse performance and requires bigger control authority than others.

• 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.