• Journal of Ocean Engineering and Technology
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• v.22 no.4
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• pp.14-19
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• 2008

This paper proposes a mixed $H_2/H_{\infty}$ optimal PID controller with a genetic algorithm based on the dynamic model of a brushless direct current (BLDC) motor and applies it to speed control. In the dynamic model of the BLDC motor with perturbation, the proposed controller guarantees arobust and optimal tracking performance to the desired speed of the BLDC motor. A genetic algorithm was used to obtain parameters for the PID controller that satisfy the mixed $H_2/H_{\infty}$ constraint. To implement the proposed controller, a control system based on PIC18F4431 was developed. Numerical and experimental results are shown to prove that the performance of the proposed controller was better than that of the optimal PID controller.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.8
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• pp.980-986
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• 1999

In this paper, the optimal controller which decouples a coupled multivariable system and minimizes a quadratic performance index is proposed. Design of the controller is based on the two-degree-of-freedom standard model. The class of all stabilizing and decoupling controllers is parametrized first and the $H^{2}$optimal controller is obtained by using this parametrized form. An illustrative example for a $2{\times}2$ plant is given.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.754-759
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• 1992

In this paper, we proposed a mixed H$_{2}$/H$_{\infty}$ optimal controller design method using the parameterization of H$_{2}$ suboptimal controller. The method is based on the minimization of H$_{2}$ performance measure with an H$_{\infty}$-norm constraint. We also derived the necessary and sufficient conditions for existence of solution from the decoupled Riccati equations. And the designed controller has state-space representation.n.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.10
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• pp.157-165
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• 1995

The new formulation of designing the two degree of freedom(TDF) robust controller is proposed using $H_{\infty}$optimization and model matching method. In this formulation the feedback controller and feedforward controller are designed in a single step using $H_{\infty}$optimization procedure. Roughly speaking, the feedback controller is designed to meet robust stability and disturbance rejection specifications, while the feedforward controller is used to improve the robust model matching properties of the closed loop system. The proposed formulation will be illustrated and evaluated on a seeker scan-loop. And the performances of TDF robust controller are compared with those of the $H_{\infty}$ controller designed using Loop Shaping Design Procedure proposed by McFarlane and Glover.lover.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.3
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• pp.139-145
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• 2001

In this paper, we consider the H$_2$(or guaranteed cost control) and H$_{\infty}$ controller design methods for singular(or descriptor) systems with input time delay. Also, a mixed H$_2$and H$_{\infty}$ controller design algorithm is treated by combination of the proposed H$_2$and H$_{\infty}$ controller design method. The sufficient conditions for the existence of controllers and controller design methods are introduced at each Lemma and Theorem. Furthermore, we present optimization problems to get the upper bound of performance measures. The proposed methods are checked by examples.

• 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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• 2004.08a
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• pp.1754-1757
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• 2004

For the anti-sway control of traveling cranes, there are several solutions, i.e., by fuzzy control, by optimal control theory, etc. Each of them is reported to be effective. And, H infinity control and $H_2$ control can be also used. However, the full order observer which estimates all states in the controlled object is used in these methods. Therefore, the orders of these controllers are apt to be higher than that of the optimal controller, etc. Because the conventional H2 controller which minimizes $H_2$ norm consists of two parts, that is: feedback gains which make the controlled object stable and the full order observer which estimate those states. If the minimal order observer is used instead of the full order one, the order of the controller can be reduced. In this paper, we propose a new method based on the minimalization of $H_2$ norm using the minimal order observer. And, we confirm the effect of a new $H_2$ controller in the experiments of the anti-sway control of a traveling crane.

• Journal of Power System Engineering
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• v.2 no.2
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• pp.67-72
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• 1998

To improve control performance, especially positioning speed, of a pneumatic positioning system, dynamic characteristics of a control valve should be considered. In case we design controller including dynamic characteristics of a control valve, it's not easy to design controller gain using simple state feedback because degree of a control system is increased. This study designed controller using loop shaping of $H_{\infty}$ control theory for a model composed of a pneumatic actuator and a control valve, and positioning experiment using this controller was performed. As a result, it was verified that the controller is useful for high speed positioning of a pneumatic positioning system.