잠재전이분석에서의 종단적 측정동일성 검증: 교사-학생 관계 유형 변화의 예

김재욱(Jae Wook Kim),손원숙(Won Sook Sohn) 한국교육학회 2023 敎育學硏究 Vol.61 No.1

본 연구의 목적은 최근 사회과학 분야에서 활발하게 적용되고 있는 잠재전이분석(Latent Transition Analysis: LTA)에서 그동안 소홀하게 다뤄진 종단적 측정동일성(Longitudinal Measurement Invariance: LMI) 검증 절차에 대한 가이드라인을 소개하는 것이다. 이를 위해 LTA 모형을 적용한 국내외 경험연구를 탐색했으며, 중고등학교 전환기 교사-학생 관계를 측정한 종단자료를 대상으로 LTA 모형을 구성하고 LMI 검증과정을 제시했다. 구체적인 연구결과는 다음과 같다. 첫째, 선행연구를 고찰한 결과, LTA 모형을 위한 LMI 검증의 필요성과 구체적 방안에 대한 인식 수준은 국외 연구에 비하여 국내 연구에서 상대적으로 낮은 경향을 보였다. 둘째, LTA 모형에서 검증할 수 있는 LMI 유형을 소개하고, 이와 관련된 구체적 검증 방안이 제시됐다. 셋째, LTA 모형에서의 LMI가 제공하는 통계적이고 개념적 유용성을 논의했다. 마지막으로 본 연구를 논의하고 추후 연구를 위한 제언을 추가했다. Latent transition analysis (LTA) is known to be a powerful tool for exploring change in latent classes of individuals over time. For this reason, applications of LTA have been actively published in the social and behavioral sciences, including education. Although the LTA model does not necessitate longitudinal measurement invariance (LMI), LMI is desirable for model parsimony and interpretation of LTA results. However, the issue of LMI has received relatively less attention in the context of the LTA model. To fill this gap in the literature, we have reviewed previous studies and present guidelines for testing LMI in an LTA framework. We also illustrate the LMI testing procedures for the LTA model with panel data from a sample of 5,439 students ranging from the 9th through 11th grades in South Korea. In addition, we provide the Mplus codes for LMI testing. Finally, practical implications of the results are discussed.

LMI 이론에 의한 삼관성 시스템의 진동억제

최연욱 한국융합신호처리학회 2001 융합신호처리학회 논문지 (JISPS) Vol.2 No.3

일반적으로 관성시스템의 제어 문제는 결국, 시스템 자체에서 발생하는 진동을 최대한 억제하면서 빠른 시간에 출력이 기준입력을 추종하는데 있다. 이 경우 문제로 되는 것은 시스템의 모델링 과정에서 발생하는 플랜트의 불확실성과 parameter 변동이다. 여기서는 일반적인 강인한 제어기 설계 이론의 하나인 H$_{*}$ 이론이 가지는 단점인 제어기의 보수성을 극복하면서, 동시에 출력의 과도응답특성을 개선하기 위한 방법으로 H$_2$이론을 병용하고 이를 LMI 이론으로 해석하였다. 이 과정에서 3 관성시스템에 LMI 이론을 적용하기 위한 일반화플랜트의 모형을 제시하고 이것의 유효성을, 모델의 불화실성과 parameter변동을 동시에 고려한 simulation을 통하여 확인하였다. Generally, it is said that control of the inertia system is to track the reference input quickly while suppressing the vibration due to the system itself. In this case, the difficulty fur designing a controller is caused by modeling uncertainty and parameter variation. The purpose of this paper is to propose a design method to suppress the vibration of three-mass inertia system based on the LMI theory. That is, the generalized plant model by which we can cope with conservativeness of the existing H$_{*}$ theory is proposed and analyzed in terms of LMI. The results of simulation fur the three-mass inertia system show that the proposed design approach is quite effective under the given situations.

LMI를 이용한 불확실시스템에 대한 섭동의 상위경계치해석

김찬용(C. Y. Kim),윤소남(S. Yun),최봉열(B. Y. Choi),박평원(P. W. Park) 한국동력기계공학회 2004 한국동력기계공학회 학술대회 논문집 Vol.- No.-

In this paper, we deal with the upper boundary analysis of perturbation in an uncertain system using LMI. Existing papers used a pole assignment method that locates pole in the specified region to obtain expected performance and the optimal solution of the upper boundary for stable region was got by Lyapunov method. In this study, the method for the upper boundary analysis of perturbation in an uncertain system using LMI for get a stable system characteristics was proposed. And, it was confirmed that the proposed LMI method is more excellent than the Lyapunov method.

계수조건부 LMI를 이용한 다목적 제어기 설계

김석주(Seog-Joo Kim),김종문(Jong-Moon Kim),천종민(Jong-Min Cheon),권순만(Soonman Kwon) 제어로봇시스템학회 2009 제어·로봇·시스템학회 논문지 Vol.15 No.1

This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as H₂/H∞ control. Multi-objective control is formulated as an LMI optimization problem with a nonconvex rank condition, which is imposed on the controller gain matirx not Lyapunov matrices. With this rank-constrained formulation, we can expect to reduce conservatism because we can use separate Lyapunov matrices for different control objectives. An iterative penalty method is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method.

LMI 제어를 적용한 트레일러 차동 브레이킹 제어를 통한 주행 안전성 개선

강래청(Raecheong Kang),장은영(Eunyoung Jang),임묘택(Myotaek Lim) 한국자동차공학회 2023 한국자동차공학회 학술대회 및 전시회 Vol.2023 No.11

This study proposes a control methodology using Linear Matrix Inequality (LMI) techniques to minimize lateral oscillations during trailer steering in electric buses equipped with fuel cell systems. The trailers examined have a shorter length, making them more susceptible to lateral oscillations caused by sudden steering changes. The objective is to enhance driving safety and stability by minimizing these oscillations. The research focuses on the safety aspects of the trailers components, particularly the independent control of brakes installed on both sides of the trailers wheels. LMI control techniques, known for their applicability to multivariable systems and relatively simple mathematical computations, are employed. The study conducts system modeling incorporating electric buses and trailers, analyzes the influence of sudden steering maneuvers on lateral oscillations, and defines state-space models and performance objectives for LMI control design. Simulations using dSPACEs ASM model are performed to evaluate the proposed approach. Overall, this research aims to present an LMI-based control method for minimizing lateral oscillations during trailer steering in fuel cell-equipped trailers integrated into electric bus systems, thereby enhancing driving safety and stability.

Dynamic Characteristic Analysis and LMI-based H_ Controller Design for a Line of Sight Stabilization System

Lee, Won-Gu,Kim, In-Soo,Keh, Joong-Eup,Lee, Man-Hyung The Korean Society of Mechanical Engineers 2002 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.16 No.10

This paper is concerned with the design or an LMI (Linear Matrix Inequality) -based H$\infty$ controller for a line of sight (LOS) stabilization system and with its robustness performance. The linearization of the system is necessary to analyze various nonlinear characteristics, but the linearization entails modeling uncertainties which reduce its performance. In addition, the stability of the LOS can be adversely affected by angular velocity disturbances while the vehicle is moving. As the vehicle accelerates, all the factors that are Ignored and simplified for the linearization tend to Inhibit the performance of the system. The robustness in the face of these uncertainties needs to be assured. This paper employs H$\infty$ control theory to address these problems and the LMI method to provide a suitable controller with minimal constraints for the system. Even though the system matrix does not have a full rank, the proposed method makes it possible to design a H$\infty$ controller and to deal with R and S matrices for reducing the system order. It can be also shown that the proposed robust controller has a better disturbance attenuation and tracking performance. The LMI method is also used to enhance the applicability of the proposed reduced-order H$\infty$ controller for the system given. The LMI-based H$\infty$ controller has superior disturbance attenuation and reference input tracking performance, compared with that of the conventional controller under real disturbances.

시간 지연 시스템을 위한 적분 슬라이딩 모드 제어기의 LMI 기반 설계

최한호(Han Ho Choi) 대한전기학회 2009 전기학회논문지 Vol.58 No.12

This paper presents an LMI-based method to design a integral sliding mode controller for a class of uncertain time-delay systems. Using LMIs we derive an existence condition of a sliding surface guaranteeing the asymptotic stability of the sliding mode dynamics. And we give a switching feedback control law. Our method is a generalization of the previous integral sliding mode control design methods. Since our method is based on LMIs, it gives design flexibility for combining various useful design criteria that can be captured in the LMI-based formulation. We also give LMI existence conditions of sliding surfaces guaranteeing -stability or LQ performance constraint. Finally, we give a numerical design example to show the effectiveness of the proposed method.

LMI를 이용한 공기압 구동장치의 제어기 설계

지상원(S. W. Ji),김영복(Y. B. Kim),장지성(J. S. Jang) 한국동력기계공학회 2007 한국동력기계공학회 학술대회 논문집 Vol.- No.-

Pneumatic driving systems have a hard non-linear characteristics and a large friction force compared with driving power. Hence, it can not be robust against parameter uncertainties, modelling error, disturbance and noise. In this study, we apply a mixed H₂/H∞ control to the generalized plant for a pneumatic driving apparatus system involved parameter uncertainty and disturbance. In order to design the H₂/H∞ controller, we use the LMI technique. To evaluate control performance and robust stability of designed controller, we compare it with the conventional controller(PVA controller) using the simulation results. As a result, it can be know that designed controller shows the better robust stability than the conventional controller.

LMI를 이용한 불확실한 퍼지 시스템의 슬라이딩 모드 관측기 설계

송민국,주영훈,박진배 한국지능시스템학회 2006 한국지능시스템학회 학술발표 논문집 Vol.16 No.1

본 논문에서는 비선형 시스템의 슬라이딩 모드 관측기 설계에 대해서 논의한다. 제어 대상인 비선형 시스템을 모델링 하는데 있어서 Takagi-Sugeno(T-S) 퍼지 모델 기법을 이용하였고, 이때 발생할 수 있는 모델 불확실성과 외란에 대해 그것의 최대 최소 범위를 안다고 가정하였다. 제안된 시스템의 LMI (Linear Matrix Inequality)를 기반으로 한 슬라이딩 모드 관측기 설계 방법에서는 관측기와 시스템의 차이를 슬라이딩 표면으로 설정한다. 안정한 슬라이딩 표면을 갖는 슬라이딩 관측기의 존재 가능성을 선형 행렬 부등식의 형태로 표현한다. 슬라이딩 모드 관측기 이득은 LMI 존재 조건의 해를 이용하여 구한다.

LMI에 기초한 $H_{\infty}$ 서보제어를 이용한 AUV의 강인한 자동 심도 및 방향제어

양승윤,김인수,이만형 한국군사과학기술학회 2000 한국군사과학기술학회지 Vol.3 No.1

In this paper, robust depth and course controllers of AUV(autonomous underwater vehicles) using LMI-based H$_{\infty}$ servo control are proposed. The $H_{\infty}$ servo problem is modified to an $H_{\infty}$ control problem for the generalized plant that includes a reference input mode, and then a sub-optimal solution that satisfies a given performance criteria is calculated by LMI(Linear Matrix Inequality) approach. The robust depth and course controllers are designed to be satisfied the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under sea wave and tide disturbances. The performances of the designed controllers are evaluated by computer simulations, and these simulation results show the applicability of the proposed robust depth and course controller.