• Title/Summary/Keyword: matrix inequality approach

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Tracking Control System Design for the Transfer Crane : Design of Full-order Observer with Weighted $H_{\infty}$ Error Bound (트랜스퍼 크레인의 이송위치제어를 위한 서보계 설계 : 가중 $H_{\infty}$ 오차사양을 만족하는 동일차원 관측기 설계)

  • Kim, Y.B.;Jeong, H.H.;Yang, J.H.
    • Journal of Power System Engineering
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    • v.12 no.6
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    • pp.42-49
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    • 2008
  • The most important job in the container terminal area is to handle the cargo effectively in the limited time. To achieve this object, many strategies have been introduced and applied to. If we consider the automated container terminal, it is necessary that the cargo handling equipments are equipped with more intelligent control systems. From the middle of the 1990's, an automated rail-mounted gantry crane(RMGC) and rubber-tired gantry crane(RTG) have been developed and widely used to handle containers in the yards. Recently, in these cranes, the many equipments like CCD cameras and sensors are mounted to cope with the automated terminal environment. In this paper, we try to support the development of more intelligent automated cranes which make the cargo handling be performed effectively in the yards. For this plant, the modelling, tracking control, anti-sway system design, skew motion suppressing and complicated motion control and suppressing problems must be considered. Especially, in this paper, the system modelling and tracking control approach are discussed. And, we design the tracking control system incorporating an observer based on the 2DOF servo system design approach to obtain the desired state informations. In the case of observer design, a weighted $H_{\infty}$ error bound approach for a state estimator is considered. Based on an algebraic Riccati equation(inequality) approach, a necessary and sufficient condition for the existence of a full-order estimator which satisfies the weighted $H_{\infty}$ error bound is introduced. Where, the condition for existence of the estimator is denoted by a Linear Matrix Inequality(LMI) which gives an optimized solution and observer gain. Based on this result, we apply it to the tracking control system design for the transfer crane.

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Dynamic Positioning Control System Design for Surface Vessel: Observer Design Based on H Control Approach (수상선박의 위치 및 자세제어시스템 설계에 관한 연구 : 강인제어기법에 의한 관측기 설계)

  • Kim, Young-Bok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.10
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    • pp.1171-1179
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    • 2012
  • In this study, we consider a dynamic positioning system (DPS) design problem that can be extended to many application fields. Toward this end, tracking and positioning control problems are discussed. In particular, we design a tracking control system that incorporates an observer based on the 2-DOF servo system design approach in order to obtain the desired state information. In the case of observer design, a weighted $H_{\infty}$ error bound approach for a state estimator is considered. Based on an algebraic Riccati equation (inequality) approach, a necessary and sufficient condition for the existence of a full-order estimator that satisfies the weighted $H_{\infty}$ error bound is introduced. The condition for the existence of the estimator is denoted by a linear matrix inequality (LMI) that yields an optimized solution and the observer gain.

Development of Robust Fuzzy Controller with Relaxed Stability Condition: Global Intelligent Digital Redesign Approach (완화된 안정도 조건을 갖는 강인한 디지털 퍼지 제어기 설계: 전역적 디지털 재설계 접근법)

  • Sung, Hwa-Chang;Kim, Jin-Kyu;Joo, Young-Hoon;Park, Jin-Bae
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.5
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    • pp.487-492
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    • 2007
  • This paper presents the development of digital robust fuzzy controller for uncertain nonlinear systems. The proposed approach is based on the intelligent digital redesign(IDR) method with considering the relaxed stability condition of fuzzy control system. The term IDR in the concerned system is to convert an existing analog robust control into an equivalent digital counterpart in the sense of the state-matching. We shows that the IDR problem can be reduced to find the digital fuzzy gains minimizing the norm distance between the closed-loop states of the analog and digital robust control systems. Its constructive conditions are expressed as the linear matrix inequalities(LMIs) and thereby easily tractable by the convex optimization techniques. Based on the nonquadratic Lyapunov function, the robust stabilization conditions are given for the sampled-data fuzzy system, and hence less conservative. A numerical example, chaotic Lorentz system, is demonstrated to visualize the feasibility of the proposed methodology.

Sampled-data Fuzzy Control for Nonlinear Neutral Systems (샘플치 퍼지 제어기 설계를 이용한 비선형 뉴트럴 시스템 제어기 설계)

  • Song, Min-Kook;Joo, Young-Hoon;Park, Jin-Bae
    • Proceedings of the KIEE Conference
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    • 2008.04a
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    • pp.195-196
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    • 2008
  • This paper presents the stability analysis and design for a sampled-data fuzzy control system with neutral type of time delay. The sampling activity and neutral type of time delay will complicate the nonlinear system dynamics. And it make the stability analysis much more difficult than that for a continuous-time fuzzy control system. Based on the fuzzy control approach, linear matrix inequality (LMI)-based stability conditions are derived to guarantee the neutral T-S fuzzy system stability. Finally, an example is provided to illustrate the effectiveness of the proposed approach.

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$H_{\infty}$ Fuzzy State-Feedback Control Design for Uncertain Nonlinear Descriptor Systems;An LMI Approach

  • Assawinchaichote, W.;Nguang, S.K.
    • 제어로봇시스템학회:학술대회논문집
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    • 2004.08a
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    • pp.1037-1041
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    • 2004
  • This paper examines the problem of designing an $H_{\infty}$ fuzzy state-feedback controller for a class of uncertain nonlinear descriptor systems which is described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an $H_{\infty}$ state-feedback controller which guarantees the $L_2$-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of systems. A numerical example is provided to illustrate the design developed in this paper.

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Sampled-data Fuzzy Observer Design for an Attitude and Heading Reference System and Its Experimental Validation

  • Kim, Han Sol;Park, Jin Bae;Joo, Young Hoon
    • Journal of Electrical Engineering and Technology
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    • v.12 no.6
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    • pp.2399-2410
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    • 2017
  • In this paper, a linear matrix inequality-based sampled-data fuzzy observer design method is proposed based on the exact discretization approach. In the proposed design technique, a numerically relaxed observer design condition is obtained by using the discrete-time fuzzy Lyapunov function. Unlike the existing studies, the designed observer is robust to the uncertain premise variable because the fuzzy observer is designed under the imperfect premise matching condition, in which the membership functions of the system and observer are mismatched. In addition, we apply the proposed method to the state estimation problem of the attitude and heading reference system (AHRS). To do this, we derive a Takagi-Sugeno fuzzy model for the AHRS system, and validate the proposed method through the hardware experiment.

High Performance of Self Scheduled Linear Parameter Varying Control with Flux Observer of Induction Motor

  • Khamari, Dalila;Makouf, Abdesslam;Drid, Said;Chrifi-Alaoui, Larbi
    • Journal of Electrical Engineering and Technology
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    • v.8 no.5
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    • pp.1202-1211
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    • 2013
  • This paper deals with a robust controller for an induction motor (IM) which is represented as a linear parameter varying systems. To do so linear matrix inequality (LMI) based approach and robust Lyapunov feedback are associated. This approach is related to the fact that the synthesis of a linear parameter varying (LPV) feedback controller for the inner loop take into account rotor resistance and mechanical speed as varying parameter. An LPV flux observer is also synthesized to estimate rotor flux providing reference to cited above regulator. The induction motor is described as a polytopic LPV system because of speed and rotor resistance affine dependence. Their values can be estimated on line during systems operations. The simulation and experimental results largely confirm the effectiveness of the proposed control.

Stability of Interval Time-delayed Linear Systems using a Switched System Approach (전환 시스템 접근법을 이용한 구간 시간지연 선형 시스템의 안정성)

  • Kim, Joo-Kyeong;Kim, Jin-Hoon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.5
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    • pp.673-678
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    • 2013
  • This paper considers the stability of linear systems having an interval time-varying delay using a switched system approach. The time-delay system is converted to the switched system equivalently, and then a stability criterion in the form of linear matrix inequality(LMI) is derived by using a parameter dependent Lyapunov-Krosovskii function(PD-LKF). In constructing a PD-LKF, the decomposition is employed for delay free intervals, and the reduction of conservatism is shown analytically as the number of decomposition increases. Finally, two well-known numerical examples are given to show the reduction of conservatism compared to the recent results.

Networked $H_{\infty}$ Approach and Power System Stabilization (Networked $H_{\infty}$ Approach에 의한 전력계통안정화)

  • Lee, Sang-Seung
    • Proceedings of the KIEE Conference
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    • 2005.07a
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    • pp.226-228
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    • 2005
  • This paper deals with power system stabilization problem using a network control system in which the control is applied through a communication channel in feedback form. Analysis and synthesis issues are investigated by modeling the packet delivery characteristics of the network as a Bernoulli random variable, which is described by a two state Markov chain. This model assumption yields an overall system which is described by a discrete-time Markov jump linear system. These employ the norm to measure the performance of the system, and they compute the norm via a necessary and sufficient matrix inequality condition.

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Takagi-Sugeno Fuzzy Model-based Iterative Learning Control Systems: A Two-dimensional System Theory Approach

  • Chu, Jun-Uk;Lee, Yun-Jung
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.169.3-169
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    • 2001
  • This paper introduces a new approach to analysis of error convergence for a class of iterative learning control systems. First, a nonlinear plant is represented using a Takagi-Sugeno(T-S) fuzzy model. Then each iterative learning controller is designed for each linear plant in the T-S fuzzy model. From the view point of two-dimensional(2-D) system theory, we transform the proposed learning systems to a 2-D error equation, which is also established in the form of T-S fuzzy model. We analysis the error convergence in the sense of induced 2 L -norm, where the effects of disturbances and initial conditions on 2-D error are considered. The iterative learning controller design problem to guarantee the error convergence can be reduced to linear matrix inequality problems. In comparison with others, our learning algorithm ...

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