• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.3
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• pp.33-43
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• 2000

The guarantee of the fast dynamics stability is essential for successful application of singular Perturbation technique to control systems design. Even though the fast dynamics of the control systems is rendered stable by an analog controller, the fast dynamics stability of the control systems resulted from an digital implementation of the analog controller can be impaired severely. In this paper, we first investigate the time sampling effects on singular perturbation based control systems by centering on a design example of recently developed singular perturbation based STT missile autopilot with high performance. The investigation shows that the stability margin the fast dynamics of the STT misile autopilot system decreases rapidly as the sampling interval of discretizing the analog autopilot increases. Under this analysis, we propose a composite digital controller with compensation for the decreasing stability margin of the fast dynamics due to time sampling to achieve better performance with respect to sampling time. The improved performance of the proposed composite digital controller is verified by simulation. This result shows that one needs to investigate time sampling effects in the digital implementation of singular perturbation based controllder, and then can have benefit from the investigation.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.45 no.4
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• pp.276-283
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• 2017

This paper presents position control of multicopter using nonlinear dynamic model inversion in singular perturbation. Multicopter dynamics are developed and separated into the fast time-scale variables, related with the inner-loop design, and the slow time-scale variables, related with the outer-loop design. The final design is evaluated in 6-DOF simulation. The results show accurate position tracking performance.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.7
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• pp.76-82
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• 2004

A method of designing a state feedback gam achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system The present paper extends the previous study to the discrete system and the ${\delta}-operating$ system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.1
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• pp.50-55
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• 2016

This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2224-2226
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• 2004

현재 ATM 망의 ABR 소스에서 불확실한 시간지연에 대한 이산시 모델에 대해, 많은 연구가 진행되고 있다. 이 모델들은 각각의 소스에서의 대역폭(Bandwidth)을 일정하게 보고 있지만, 현실적으로 소스의 네트워크 상황에 따라 각기 할당되는 대역폭은 큰 차이가 있다. 각기 다른 대역폭을 고려할 때 ABR 스위치 모델은 특이 섭동 구조를 갖는다. 본 연구에서는 대역폭 차에 따른 ABR 스위치에서의 특이 섭동 모델을 제안하고 ABR 스위치에서의 체증을 해결하기 위해 합성제어 기법을 이용한 이산시 최적 제어기를 설계한다.

• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2188-2191
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• 2002

MIMO 비최소위상 시스템에 대한 입출력 선형화 제어에 대해서 새로운 접근 방식을 제안한다. 처음에 몇가지 조건 하에서 비선형 궤환과 상태 변환을 하고 또한 magnitude & time scaling을 해서 일반적인 비선형 시스템을 특이 섭동 시스템으로 변환할 수 있다는 것을 보였다. 특히 제안된 방법에 의하여 변환된 특이 섭동 시스템에서 숨겨진 동적 특성이 fast subsystem의 역할을 하게 된다. 그 다음에는 잘 알려진 composite control 기법을 적용하여 시스템이 거의 선형적이고 비간섭적인 I/O 동적 특성을 갖게 하고 내부 상태가 안정화되도록 한다. 기존의 방식 보다 제안된 제어 방법의 가장 큰 이점은 적용될 수 있는 비최소위상 시스템의 범위를 보다 넓히게 되었다는 것이다. 게다가 특이 섭동 방법은 제어기 설계 과정을 단순화시켜 제어기 구현에 있어서 계산 시간을 단축시킨다.

• Proceedings of the KIEE Conference
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• 1984.07a
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• pp.107-110
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• 1984

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.3
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• pp.39-49
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• 2003

The delta operator approach and the singular perturbation technique are introduced. The former reduces the round-off error in the numerical computation. The latter reduces computing time by decoupling the original system into the fast and slow sub-systems. The aircraft dynamics consists of the Phugoid and short-period motions whether its model is longitudinal or lateral. In this paper, an approximated solutions of lateral dynamic model of Beaver obtained by using those two methods in compared with the exact solution. For open-loop system and closed-loop system, and approximated solution gets identical to the exact solution with only one iteration and without iteration, respectively. Therefore, it is shown that implementing those approaches is very effective in the flight dynamic and control.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.5
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• pp.58-64
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• 2004

A new method to obtain approximate solutions by placing the only poles of the slow subsystem for the two-time-scale aircraft dynamic systems. The two kinds of approximate solutions are obtained by a matrix block diagonalization. One is called the uncorrected solution, and the other is called the corrected solution. The former has an error of $O({\varepsilon})$, and the latter has an error of $O({\varepsilon}^2)$. Of course, both solutions are robust enough even though they are reduced solutions. The excellence of the proposed method is illustrated by an numerical example of an aircraft longitudinal dynamics.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.5
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• pp.1-7
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• 2008

This paper presents not only the robust stabilization technique but also robust non-fragile controller design method for discrete-time singular systems and static state feedback controller with multiplicative uncertainty. The condition for the existence of robust stabilization controller, the admissible controller design method, and the measure of non-fragility in controller are proposed via LMI(linear matrix inequality) approach. In order to get the maximum measure of non-fragility, the obtained sufficient condition can be rewritten as LMI optimization form in terms of transformed variable. Therefore, the presented robust non-fragile controller for discrete-time singular systems guarantees robust stability in spite of parameter uncertainty and controller fragility. Finally, a numerical example is given to show the validity of the design method.