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이동환,주영훈 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.2
For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.
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.
무인 잠수정의 깊이 제어를 위한 T-S 퍼지 모델 기반 ∞ 제어기 설계: 선형 행렬 부등식 접근법
전성우,김도완,이호재 한국지능시스템학회 2012 한국지능시스템학회논문지 Vol.22 No.4
본 논문은 무인 잠수정(Autonomous underwater vehicles: AUVs)의 타카기-수게노 (Takagi-Sugeno: T-S) 퍼지 모델 기반 ∞ 제어기 설계 기법을 제안한다. 설계 기법은 외란을 갖는 무인 잠수정의 깊이 제어 성능을 보장하는 안정성 있는 제어기 설계에 초점을 맞춘다. 비선형 무인 잠수정 시스템은 Sector nonlinearity 기법을 이용하여 T-S 퍼지 시스템으로 모델링된다. 리아푸노프(Lyapunov) 함수를 이용해 제어 성능을 보장하는 선형 행렬 부등식(linear matrix inequality: LMI) 형태의 ∞ 제어기 설계 조건을 유도한다. 성공적인 무인 잠수정의 깊이 제어를 위해 선형 행렬 부등식에 심도각과 피치각의 제한 조건을 고려한다. 시뮬레이션을 통해 제안된 기법의 성능을 검증한다. This paper presents a design technique of a Takagi-Sugeno (T-S) fuzzy-model-based ∞ controller for autonomous underwater vehicles (AUVs). The design procedure aims to render the stabilizing controller which satisfies performance of the diving control for AUVs in the presence of the disturbance. A nonlinear AUV is modeled by the T-S fuzzy system through the sector nonlinearity. By using Lyapunov function, the sufficient conditions are derived to guarantee the performance of robust depth control in the format of linear matrix inequality (LMI). To succeed for diving control of AUV, we add the constraints on the diving and pitch angles in the LMI conditions. Through the simulation, we confirm the effectiveness of the proposed methodology.
대규모 시스템을 위한 LMI기반 비집중화 슬라이딩 모드 정적 출력 궤한 제어기 설계
최환호(Han Ho Choi) 제어로봇시스템학회 2008 제어·로봇·시스템학회 논문지 Vol.14 No.4
In this paper, we consider the problem of designing decentralized sliding mode static output feedback control laws for a class of large scale systems with mismatched uncertainties. We derive a sufficient condition for the existence of a linear switching surface in terms of constrained linear matrix inequalities(LMIs), and we parameterize the linear switching surfaces in terms of the solution matrices to the given constrained LMI existence conditions. We also give an LMI-based algorithm for designing decentralized switching feedback control laws. Finally, we give a design example in order to show the effectiveness of our method.
대규모 시스템을 위한 LMI기반 비집중화 슬라이딩 모드정적 출력 궤환 제어기 설계
최한호 제어·로봇·시스템학회 2008 제어·로봇·시스템학회 논문지 Vol.14 No.4
In this paper, we consider the problem of designing decentralized sliding mode static output feedback control laws for a class of large scale systems with mismatched uncertainties. We derive a sufficient condition for the existence of a linear switching surface in terms of constrained linear matrix inequalities(LMIs), and we parameterize the linear switching surfaces in terms of the solution matrices to the given constrained LMI existence conditions. We also give an LMI-based algorithm for designing decentralized switching feedback control laws. Finally, we give a design example in order to show the effectiveness of our method.
전차수 슬라이딩 모드 관측기를 대체하는 축소차수 관측기의 LMI 기반 설계
최한호(Han Ho Choi) 제어로봇시스템학회 2008 제어·로봇·시스템학회 논문지 Vol.14 No.3
This paper presents an LMI-based method to design reduced order observers by which we can substitute full order sliding mode observers for a class of uncertain time-delay systems. We show that a reduced order observer can be constructed as long as the uncertain system satisfies the previous LMI existence conditions of a full order sliding mode observer. And we give explicit formulas of the reduced order observer gain matrices. Finally, we give a simple LMI-based design algorithm, together with a numerical design example.
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.
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.
비정합 불확실성을 갖는 시스템을 위한 적분 슬라이딩 모드 제어기의 LMI 기반 설계
최한호(Han Ho Choi) 대한전기학회 2010 전기학회논문지 Vol.59 No.8
This paper presents an LMI-based method to design an integral sliding mode controller for for a class of uncertain systems with mismatched unstructured uncertainties. The uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as in the input matrix. Using LMIs we derive an existence condition of a sliding surface. And we give a switching feedback control law. Finally, we give a numerical design example in order to show that the proposed method can be better than the existing results.
LMI를 이용한 Well-Conditioned 관측기 설계
허건수,정종철 한국공작기계학회 2003 한국공작기계학회 춘계학술대회논문집 Vol.2003 No.-
The well-conditioned observer in a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic issues such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic issues such as disturbance and sensor noise. In deterministic perspectives, a small value in the L₂ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic issues and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.