• International Journal of Control, Automation, and Systems
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• 제1권2호
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• pp.206-209
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• 2003

An $H_2$/$H_{\infty}$ -controller realization is carried out by considering an entropy integral. Using J-spectral factorization, the parametrizations of all $H_{\infty}$ stabilizing controllers are derived. By the relation of a mixed $H_2$/$H_{\infty}$ control problem and a minimum entropy/$H_{\infty}$ control problem, the mixed $H_2$/$H_{\infty}$-controller state-space realization is presented.

• 한국정보통신학회논문지
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• 제3권4호
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• pp.875-885
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• 1999

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.

• 한국통신학회논문지
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• 제25권7A호
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• pp.967-977
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• 2000

본 논문은 도립전자 시스템을 LFR(Linear Fractional Representation)로 표현하여 얻어진 일반화 제어대상에 대하여 혼합 ${H_2}/H_{\infty}$ 제어기법을 적용한다. 먼저, 일반화 제어대상을 얻기 위하여, LFR로 표현한 도립진자의 선형 모델을 유도한다. LFR에서 고려한 구체적인 불확실성은 3개의 비선형 성분과 1개의 진자질량 불확실성이다. 유도된 선형모델에 하중함수를 더하여 LFR 모델을 확대함으로써 일반화된 제어대상을 얻는다. 다음으로, 이 일반화 제어대상에 대하여 혼합 ${H_2}/H_{\infty}$ 제어기를 설계한다. 혼합 ${H_2}/H_{\infty}$ 제어기 설계를 위해서 LMI(Linear Matrix Inequalities) 기법을 이요한다. 설계된 혼합 ${H_2}/H_{\infty}$ 제어기의 제어성능과 강건 안정성을 평가하기 위해서 모의실험과 실물실험을 통하여 $H_{\infty}$ 제어기와 비교한다. 실험결과, $H_{\infty}$ 제어때 보다 적은 피드백 정보만으로도 혼합 ${H_2}/H_{\infty}$ 제어기는 도립진자의 진자각도 측면에서 $H_{\infty}$ 제어기보다 나은 강건 안정성과 제어 성능을 보인다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.888-891
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• 1996

The objective of a mixed H$_{2}$/H$_{\infty}$ controller of active suspension system is to achieve not only the general performance improvement(H$_{2}$) but also the worst case disturbance rejection(H$_{\infty}$). In this paper, a mixed H$_{2}$/H$_{\infty}$ controller for an active suspension system, comparing the performance with that of an H$_{2}$ controller and of an H$_{\infty}$ controller.ler.EX> controller.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.560-564
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• 1996

A mixed H$^{2}$/$H^{\infty}$ controller design method for linear systems with time delay in all variables and parameter uncertainties in all system matrices is proposed. Robust $H^{\infty}$ performance and H$^{2}$ performance condition that accounts for model-matching of closed loop system and disturbance rejection is also derived. With expressing uncertain system with linear fractional transformation form, we transform the robust stability and performance problem to the H$^{2}$/$H^{\infty}$ optimization problem and design a mixed H$^{2}$/$H^{\infty}$ controller. Using the proposed method, mixed H$^{2}$/$H^{\infty}$ controller for underwater vehicle with time delay and parameter variations are designed. Simulations of a design example with hydrodynamic parameter variations and disturbance are presented to demonstrate the achievement of good robust performance.t performance.ance.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 B
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• pp.999-1001
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• 1996

In this paper, we represented the relation of minimum entropy/$H_{\infty}$-controller and mixed $H_2/H_{\infty}$-controller. An $H_2$ controller design problem involving a constraint on $H_{\infty}$ disturbance attenuation is considered. By the equivalence of the mixed $H_2/H_{\infty}$ control problem and the minimum entropy/$H_{\infty}$-control problem, we presented the controller state-space realization. Decentralized case was illustrated briefly.

• 제어로봇시스템학회논문지
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• 제7권11호
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• pp.896-903
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• 2001

This study investigates the use of mixed $H_2/H_{$\infty}$ and $\mu$-synthesis to construct a robust controller for the benchmark problem. The model treated in the problem is a coupled three-inertial system that reflects the dynamics of mechanical vibrations. This kind of problem requires to be satisfied the robust performance (both in the time and frequency-domain specifications). We, first, adopt the mixed $H_2/H_{$\infty}$ theory to design a feedback controller K(s). Next, $\mu$-synthesis method is applied to the overall system to make use of structured parametric uncertainty. This process permits higher levels of controller authority and reduces the conservativeness of the controller. Finally, the feedforward controller is also used to improve the transient response of the output. We confirm that all design specifications except a complementary sensitivity condition can be achieved.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.331-331
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• 2000

This paper presents the mixed $H_2/H_{\infty}$ output feedback controIler design method for linear systems with delayed state. The objective is to design the output feedback controller which minimizes the H$_2$-norm of one transfer function while ensuring the H$_{\infty}$-norm of the other is held below a chosen level. When objective is tormulated in terms of a common Lyapunov function, the sufficient conditions of existence of mixed $H_2/H_{\infty}$ controller are given in terms of LMIs. terms of LMIs.