• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.35-40
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• 1998

A nonlinear attitude model of a satellite with thrusters, magnetic torquers and a reaction wheel cluster is developed. Then the linearized version of this satellite attitude model is derived far the attitude hold mode. For comparison purpose, various control methods are considered for attitude control of a satellite. We consider a proportional derivative controller which is actually used in the remote sensing satellite, KOMPSAT. Then a comparison is made with an H$_2$controller, an H$\sub$$\infty$/ controller, and a mixed H$_2$/ H$\sub$$\infty$/ controller. The analysis and numerical studies show that the proportional derivative controller's performance is limited in the sense that the pitch angle cannot approach zero. The simulations also show that among three control methods (H$_2$control, H$\sub$$\infty$/ control, and mixed H$_2$/ H$\sub$$\infty$/ control) H$_2$control has the fastest response time, H$\sub$$\infty$/ control has the slowest and mixed H$_2$/ H$\sub$$\infty$/ control comes in between the first two control methods. On the other hand, H$\sub$$\infty$/ control used least amount of control effort while H$_2$control required the most.

• International Journal of Control, Automation, and Systems
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• v.1 no.2
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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.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2599-2601
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• 2000

A helicopter control problem has been researched with many control theory. Especially, study of the hovering flight attitude control of a helicopter has been brisked since 60s with multivariable control theory. In this paper, the modeling is interpreted through the 6-freedom equation. To getting a entire equation, species of parameters and charts are adapted. The $H_2/H_{\infty}$ controller is acquired by mixing the $H_2$ control theory and the $H_{\infty}$ control theory. The $H_2$ control theory is reasonable one to increase the performance of a plant, and the $H_{\infty}$ control theory secures the robust stability. The simulation shows that the helicopter system is being controlled while maintaining performance and robust stability against perturbation.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.5
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• pp.356-366
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• 2000

In this paper, a nonlinear $H_2/H_\infty/LTR$ control for the flexible inverted pendulum of a parallel type with Coulomb friction is presented. The dynamic equation for this system is derived by the Hamilton's principle and assumed-mode method. This hard nonlinear system can be modeled by a the quasi-linear state space model using the REF method. It is shown that the $H_2/H_\infty$ control can be applied to the nonlinear controller design of the system having Coulomb frictions if the proper LTR conditions are satisfied. In order to present the usefulness of the suggested control method, the nonlinear $H_2/H_\infty/LTR$ controller is designed to control the Position of the end point of the flexible inverted pendulum that has Coulomb frictions present in actuator parts. The results are given via computer simulations.

• Journal of Electrical Engineering and information Science
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• v.1 no.1
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• pp.29-38
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• 1996

To improve the reliability of control systems, certain robustness to plant uncertainties and disturbance inputs is required in terms of well founded mathematical basis. Robust control theory was set up and developed until now from this motivation. In this field, H$_2$or H\ulcorner norm performance measures are frequently used nowadays. Moreover a mixed H$_2$/H\ulcorner control problem is introduced to combine the merits of each measure since H$_2$control usually makes more sense for performance while H\ulcorner control is better for robustness to plant perturbations. However only some partial analytic solutions are developed to this problem under certain special cases at this time. In this paper, the mixed H$_2$/H\ulcorner control problem is considered. The analytic(or semi-analytic) solutions of (sub)optimal mixed H$_2$/H\ulcorner state-feedback controller are derived for the scalar plant case and the multivariable plant case, respectively. An illustrative example is given to compare the proposed analytic solution with the existing numerical one.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.1-14
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• 2008

This paper presents a convex optimization method for observer-based mixed $H_2/H_{\infty}$ control design of linear systems with time-varying state, input and output delays. Delay-dependent sufficient conditions for the design of a desired observer-based control are given in terms of linear matrix inequalities (LMIs). An observer-based controller which guarantees asymptotic stability and a mixed $H_2/H_{\infty}$ performance for the closed-loop system of the linear system with time-varying delays is then developed. A Lyapunov-Krasovskii method underlies the observer-based mixed $H_2/H_{\infty}$ control design. A numerical example with simulation results illustrates the effectiveness of the methodology.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.3 no.4
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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.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.529-534
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• 2005

In this paper, a new type of output feedback control, called a $H_2/H_{\infty}$ fnite memory control (FMC), is proposed for deterministic state space systems. Constraints such as linearity, unbiasedness property, and finite memory structure with respect to an input and an output are required in advance to design $H_2/H_{\infty}$ FMC in addition to the performance criteria in both $H_2$ and $H_{\infty}$ sense. It is shown that $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FMC design problems can be converted into convex programming problems written in terms of linear matrix inequalities (LMIs) with some linear equality constraints. Through simulation study, it is illustrated that the proposed $H_2/H_{\infty}$ FMC is more robust against uncertainties and faster in convergence than the existing $H_2/H_{\infty}$ output feedback control schemes.

• Proceedings of the IEEK Conference
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• 2001.06e
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• pp.29-32
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• 2001

This paper presents matrix inequality conditions for H$_2$optimal control of linear time-invariant descriptor systems in continuous and discrete time cases, respectively. First, the necessary and sufficient condition for H$_2$control and H$_2$controller design method are expressed in terms of LMls(linear matrix inequalities) with no equality constraints in continuous time case. Next, the sufficient condition for H$_2$control and H$_2$controller design method are proposed by matrix inequality approach in discrete time case. A numerical example is given in each case.

• 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.