• 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.

• 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.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.129-132
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• 1999

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems. The transfer matrix H$_2$and/or H$_{\infty}$ norms are used as criteria in an estimation error sense. In this paper, the mixed $H_2/H_{\infty}$ filtering Problem in lineal discrete-time systems is solved using the LMI approach, yielding a compromise between the H$_2$and H$_{\infty}$ filter designs. This filter design problems we formulated in a convex optimization framework using linear matrix inequalities. A numerical example is presented.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.750-753
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• 1998

This paper gives a simple parameterization of all stable unbiased filters to solve the suboptimal mixed $H_2/H_{\infty}$ filtering problem. Using the central filter, mixed $H_2/H_{\infty}$ filter is designed which minimizes the upper bound for the $H_2$ norm of the transfer matrix from a white noise to the estimation error subject to an $H_{\infty}$ norm constraint on the transfer matrix from an energy-bounded noise to the estimation error. The problem of finding suitable estimator gain can be converted into a convex optimization problem involving linear matrix inequalities.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.401-404
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• 2003

In this paper, $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FIR filters are newly proposed for discrete-time state space signal models. The proposed filters require linearity, unbiased property, FIR structure, and independence of the initial state information in addition to the performance criteria in both $H_2$ and $H_{\infty}$ sense. It is shown that $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FIR filter design problems can be converted into convex programming problems via linear matrix inequalities (LMIs) with a linear equality constraint. Simulation studies illustrat that the proposed FIR filter is more robust against uncertainties and has faster convergence than the conventional IIR filters. the conventional IIR filters.

• 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.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.599-602
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• 1999

In this paper, the genetic algorithm is used to design a mixed $H_2/H{\infty}$ controller. Two kinds of controller forms, Youla's form and the general form are considered to design a mixed $H_2/H{\infty}$ controller Efficient searching methods are sought to minimize the given $H_2$ cost function under the $H{\infty}$ 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.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.4
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• pp.276-284
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• 2000

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.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2006.06a
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• pp.77-78
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• 2006

A mixed method between $H_2\;and\;H_{\infty}$ control are widely applied to systems which has parameter perturbation and uncertain model to obtain an optimal robust controller. Brushless Direct Current (BLDC) motors are widely used for high performance control applications. Conventional PID controller only provides satisfactory performance for set-point regulation. However, with the presence of nonlinearities, uncertainties and perturbations in the system, conventional PID is not sufficient to achieve an optimal robust controller. This paper presents an approach to ease designing a Mixed $H_2/H_{\infty}$ PID controller for controlling speed of Brushless DC motors and the genetic algorithm is used to solve the optimized problems. Numerical results are shown to prove that the performance in the proposed controller is better than that in the optimal PID controller using LQR approach.