• 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 Institute of Control, Robotics and Systems
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• v.8 no.7
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• pp.578-583
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• 2002

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.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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• pp.868-873
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• 2003

$H_{\infty}$ control has been applied to the design of practical control systems widely because of its robustness. It can minimize $H_{\infty}$ norm of the transfer function between the desired output and the disturbances. The SMC(Sliding Mode Control) is more robust and give the better performance than the $H_{\infty}$ control if the matching condition is satisfied. A controller which can have the advantages of $H_{\infty}$ control and the SMC is proposed to add the robustness of the SMC to the $H_{\infty}$ controller. Its design is based on the augmented system of which dynamics have one higher order than that of the original system and has the same dynamic as the desired system in spite of uncertainties. The dynamic of proposed sliding surface is the same dynamic as the system controlled by $H_{\infty}$ controller without the uncertainties which satisfy the matching condition.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.751-753
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• 1996

The $H_{2}$/$H_{\infty}$ robust controller is designed by using polynomial approach. This controller can minimise a $H_{2}$ norm of error under the fixed bound of $H_{\infty}$ norm of mixed sensitivity function by employing the Youla parameterization and using polynomial approach at the same time. It is easy to apply this controller to adaptive system.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.219-222
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• 1998

This paper presents the Mixed H2/H$\infty$ controller design method with the regional pole placements for underwater vehicle. Since the small and light underwater vehicle is sensitive to disturbances and parameter uncertainties, we design the controller which guarantees robustness against time-delays, parameter uncertainties and disturbances. The LMI(linear matrix inequality) formulations for pole placements in specific regions and H2 and H$\infty$ performances are reviewed. The desired controller can be obtained by solving these LMIs.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.6
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• pp.12-22
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• 1996

A numerous designs of PI controllers have been suggested to solve out trade-off between tracing and regulating problems. We constructed the PI controller system with two-degree-of-freedom that is more analytic and a better approach to a practical one. In the conventional H$_{2}$ design of optimal PI controllers, the cost function includes only the plant output terms due to the divergent problems. Since the platn input temr is not considered in PI controller design, occasionally, the plant input thends to be either very large or saturated. To solve the prior mentioned problems, we employed a mixed $H_2/H_{\infty}$ method that combines the H$_{2}$ design method to decide optimal parameters of PI controller and the $H_2/H_{\infty}$ design method to minimize the maximum amplitude of plant input. The calculation time of the H$_{infty}$ norm was considerably reduced by the simple scalar function obtained by the wiener-hopf factorization of non-scalar functions.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.7
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• pp.483-490
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• 2004

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.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.2
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• pp.160-168
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• 1997

A $H_{\infty}$self-tuning control scheme for the tip position of a flexible link robot handling unknown loads is presented here. The scheme essentially comprises a recursive least-squares identification algorithm and $H_{\infty}$self-tunning controller. The $H_{\infty}$control low is designed to be robust to uncertain parameters and the self-tunning action provides adaption to unknown parameters. Through numerical study, the performance comparison of the $H_{\infty}$self-tuning controller with a constant gain $H_{\infty}$controller as well as a LQG self-tuning controller clearly shows its superior ability in handling load changes in quiescent states.nt states.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.620-625
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• 2008

The $H_{\infty}$ entropy in $H_{\infty}$ control theory is discussed based on investigating information transmission in continuous-time linear stochastic systems. It is proved that the stabilizing feedback does not change the time-average information transmission between system input and output, and the $H_{\infty}$ entropies of open- and closed-loop stable transfer functions are bounded by mutual information rate between input and output in the open-loop system. Furthermore, a new $H_2$ upper bound for $H_{\infty}$ entropy is introduced with a numerical example. Thus the $H_{\infty}$ entropy of a stable transfer function is sandwiched between $H_2$ norms of the original system and a static feedback system.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2002.11a
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• pp.339-342
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• 2002

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 H$_{\infty}$ controller was designed. In this paper, H$_{\infty}$ control of 2-mass system using H$_{\infty}$ filter for compensating shaft torque is proposed. Pole-zero maps show the validity of proposed controller.