• Journal of Advanced Marine Engineering and Technology
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• 제13권2호
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• pp.78-88
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• 1989

The fundamental objective of this paper has been to develop a means for incoporating the concept of the linear fractional transformation more generally and easily into multivariable feedback design procedure. When we design a continuous system, generally, we are constrained by design methods which arise specifically for the system. Also, in the design of descrete systems, it is the same concept. But the approach developed in this paper is very flexible in the view that in spite of being the continuous or discrete, the design can be done using a well known design method in both cases. That is, when we design a contnuous system or discrete system, the design can be done by a standard design method of continuous systmes or discrete ones, depending on the choice of the linear fractional transformation. Therefore, it is noted that this concept has broken the unflexibility of the conventional design rules for multivariable control system. In essence, the concept shows that if a given system is controllable, some desirable design, for examples, pole assignment within prespecified region, optimal controllers with poles within prespecified region etc., could be done easily by transforming a desirable region into a standard region, such as the complex left-half plane or the unit disk, by the chosen linear fractional transformation, and then by designing the transformed system using the well known standard results.

• 한국정밀공학회지
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• 제8권2호
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• pp.47-56
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• 1991

The specifications needed for the mobile cranes are summarized as the following : 1) there may be not occured the oscillation of the cargo at unloading point. 2)the required time from departure point to destination point may be as short as possible. 3) there may be not a collapse of cargo caused by the oscillation in the course that the crago is mobilling. In this paper, the linear fractional transformation method is adopted as a method in order to improve the above mentioned problems. A design method of servo system is developed by modifying Davison's method for the case that the homogeneous differential equations of reference input and disturbance are different types. The real time control of a mobile crane system is implemented by 16bits microcomputer with A/D and D/A converters to illustrate the application of the adopted method. The experimental results for the three types of the design methods; linear fractional transformation method, servo system design method and optimal control method are shown for the comparison.

• 대한기계학회논문집
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• 제15권2호
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• pp.497-506
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• 1991

In this paper, a new construction for training simulator of R/C helicopter based on two types of servo controller is proposed. Two modified algorithms (algorithm I and II) for servo controller design are presented. Algorithm I is developed by adopting Davison's method in the case that the expressions for the homogeneous differential equations of reference input and disturbance are different types, and algorithm II is done by considering error weighting function for the servo controller of algorithm I . The linear fractional transformation method is incorporated in both design methods in order to assign the closed loop poles of the servo system in a specified region. The helicopter simulator is composed by the gimbals with two freedom of rolling and pitching. The reliability and validity for the design methods of the proposed servo controller are investigated through the practical experiment for the simulator by using 16bits micro-computer with A/D and D/A converters. It can be observered from the experimental results that the proposed servo controller is applicable to practical plants since the simulator is robust for the arbitrary disturbance and it follows to the given reference input without significant steady state error.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.366-370
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• 2003

This paper is on weighted model reduction using structurally balanced truncation. For a given weighted(single or double-sided) transfer function, a state space realization with the linear fractional transformation form is obtained. Then we prove that two block diagonal LMI(linear matrix inequality) solutions always exist, and it is possible to get a reduced order model with guaranteed stability and a priori error bound. Finally, two examples are used to show the validity of proposed weighted reduction method, and the method is compared with other existing methods.

• 전자공학회논문지B
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• 제31B권5호
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• pp.65-72
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• 1994

이산시간 시스템에서 선형분수변환(LPT : linear fractional transformation)으로 표현된 $H^{\infty}$ 제어문제를 체인스케터링표현(CSD : chain scattering description)으로 나타내어 (J,J')-ossless 소인수분해를 이용하여 준최적 $H^{\infty}$ 제어문제를 해결하였다. LFT를 CSD형태로 변환하기 위해서는 표준플랜트의 $P_{21}$의 역행렬이 존재하여야 한다. 본 논문에서는 $P_{21}$의 역행렬이 존재하지 않는 4-블럭문제에서도 LFT를 CSD로 변환하는 방법을 제시하고 이렇게 변환된 행렬을 (J,J')-lossless 소인수분해함으로서 모든 준최적 $H^{\infty}$ 제어기를 매개변수화하였다. 또한 제안한 방법은 단지 두개의 리카티 방정식을 풀므로서 이산시간 시스템의 준최적 $H^{\infty}$ 제어문제를 해결할 수 있음을 보였다.

• 전자공학회논문지S
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• 제35S권3호
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• pp.86-92
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• 1998

This paper deals with an output feedback H control problem for linear time ivariant systems with state delay. The proposed output feedback controller is represented by the lower linear fractional transformation of alinear time invariant system and a delay operator. Sufficient conditions for the existence of the output feedback controller are given in the form of linear matrix inequalities which are less conservative than those for the existence of a rational output feedback controler. We also present a numerical example to demonstrate the efficacy of the proposed method.of the proposed method.

• 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.

• International Journal of Control, Automation, and Systems
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• 제6권2호
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• pp.171-179
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• 2008

This paper addresses the synthesis of an iterative learning controller for a class of linear systems with norm-bounded parameter uncertainties. We take into account an iterative learning algorithm with current cycle feedback in order to achieve both robust convergence and robust stability. The synthesis problem of the developed iterative learning control (ILC) system is reformulated as the ${\gamma}$-suboptimal $H_{\infty}$ control problem via the linear fractional transformation (LFT). A sufficient convergence condition of the ILC system is presented in terms of linear matrix inequalities (LMIs). Furthermore, the ILC system with fast convergence rate is constructed using a convex optimization technique with LMI constraints. The simulation results demonstrate the effectiveness of the proposed method.

• Journal of Power Electronics
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• 제13권5호
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• pp.814-828
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• 2013

The LCL resonant inductive power transfer (IPT) system is increasingly used because of its harmonic filtering capabilities, high efficiency at light load, and unity power factor feature. However, the modeling and controller design of this system become extremely difficult because of parameter uncertainty, high-order property, and switching nonlinear property. This paper proposes a frequency and load uncertainty modeling method for the LCL resonant IPT system. By using the linear fractional transformation method, we detach the uncertain part from the system model. A robust control structure with weighting functions is introduced, and a control method using structured singular values is used to enhance the system performance of perturbation rejection and reference tracking. Analysis of the controller performance is provided. The simulation and experimental results verify the robust control method and analysis results. The control method not only guarantees system stability but also improves performance under perturbation.

• 동력기계공학회지
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• 제5권4호
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• pp.44-52
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• 2001

This paper considers a modeling and identification for the MIMO magnetic bearing system. To obtain the nominal plant transfer functions, we have experimented on the frequency response by a closed-loop identification method because the system is unstable essentially. We suggest a method of curve-fitting for obtaining the transfer function from the frequency responses by using the system's modeling structure and two controllers which are different from each other. From the frequency response results, we found the effects of coupling by opposing controllers. And using this effects and the system's modeling structure, we could obtain the transfer functions of which have the same modularized denominators.