• Title/Summary/Keyword: linear matrix inequality(LMI)

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A new approach to deal with sensor errors in structural controls with MR damper

  • Wang, Han;Li, Luyu;Song, Gangbing;Dabney, James B.;Harman, Thomas L.
    • Smart Structures and Systems
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    • v.16 no.2
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    • pp.329-345
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    • 2015
  • As commonly known, sensor errors and faulty signals may potentially lead structures in vibration to catastrophic failures. This paper presents a new approach to deal with sensor errors/faults in vibration control of structures by using the Fault detection and isolation (FDI) technique. To demonstrate the effectiveness of the approach, a space truss structure with semi-active devices such as Magneto-Rheological (MR) damper is used as an example. To address the problem, a Linear Matrix Inequality (LMI) based fixed-order $H_{\infty}$ FDI filter is introduced and designed. Modeling errors are treated as uncertainties in the FDI filter design to verify the robustness of the proposed FDI filter. Furthermore, an innovative Fuzzy Fault Tolerant Controller (FFTC) has been developed for this space truss structure model to preserve the pre-specified performance in the presence of sensor errors or faults. Simulation results have demonstrated that the proposed FDI filter is capable of detecting and isolating sensor errors/faults and actuator faults e.g., accelerometers and MR dampers, and the proposed FFTC can maintain the structural vibration suppression in faulty conditions.

$H_{\infty}$ Depth and Course Controllers Design for Autonomous Underwater Vehicles (무인 수중운동체의 $H_{\infty}$ 심도 및 방향 제어기 설계)

  • Yang, Seung-Yun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.12
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    • pp.2980-2988
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    • 2000
  • In this paper, H(sub)$\infty$ depth and course controllers of autonomous underwater vehicles using H(sub)$\infty$ servo control are proposed. An H(sub)$\infty$ servo problem is foumulated to design the controllers satisfying a robust tracking property with modeling errors and disturbances. The solution of the H(sub)$\infty$servo problem is as follows; firest, this problem is modified as an H(sub)$\infty$ control problem for the generalized plant that includes a reference input mode, and than a sub-optimal solution that satisfies a given performance criteria is calculated by LMI(Linear Matrix Inequality) approach, The H(sub)$\infty$depth and course controllers are designed to satisfy the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under disturbances(was force, wave moment, tide). The performances(the robustness to the uncertainties, depth and course tracking properties) of the designed controlled are evaluated with computer simulations, and finally these simulation results show the usefulness and applicability of the propose H(sub)$\infty$ depth and course control systems.

Autopilot Design of an Autonomous Underwater Vehicle Using Robust Control

  • Jung, Keum-Young;Kim, In-Soo;Yang, Seung-Yun;Lee, Man-Hyung
    • Transactions on Control, Automation and Systems Engineering
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    • v.4 no.4
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    • pp.264-269
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    • 2002
  • In this paper, Η$_{\infty}$ depth and course controller of an AUV(Autonomous Underwater Vehicle) using Η$_{\infty}$ servo control is proposed. The Η$_{\infty}$ servo problem is formulated to design the controllers satisfying a robust tracking property with modeling errors and disturbances. The solution of the Η$_{\infty}$ servo problem is as fellows: first, this problem is modified as an Η$_{\infty}$ 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 Η$_{\infty}$ depth and course controller are designed to satisfy with the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under disturbances(wave force, wave moment, tide). The performances of the designed controllers are evaluated with computer simulations, and finally these simulation results show the usefulness and application of the proposed Η$_{\infty}$ depth and course control system.

Depth and Course Controller Design of Autonomous Underwater Vehicles using H$_\infty$ Servo Control (H$_\infty$ 서보제어를 이용한 무인 수중운동체의 심도 및 방향제어기 설계)

  • 김인수;정금영;양승윤;조상훈;정찬희;이만형
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.215-215
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    • 2000
  • In this paper, depth and course controllers of autonomous underwater vehicles using H$_{\infty}$ servo control are proposed. An H$_{\infty}$ servo problem is formulated to design the controllers satisfying a robust tracking property with modeling errors and disturbances. The solution of the H$_{\infty}$ servo problem is as follows: first, this problem is modified as 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 H$_{\infty}$ depth and course controllers ate designed to satisfy with the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under disturbances(wave force, wave moment, tide). The performances(the robustness to the uncertainties, depth and course tracking properties) of the designed controllers are evaluated with computer simulations, and finally these simulation results show the usefulness and application of the proposed H$_{\infty}$ depth and course control systems.

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Sampled-data Fuzzy Controller for Network-based Systems with Neutral Type Delays (뉴트럴 타입 시간 지연을 갖는 네트워크 기반 시스템의 샘플치 퍼지 제어기 설계)

  • Joo, Young-Hoon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.2
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    • pp.151-156
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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, which is formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampling activity and neutral type of time delay will complicate the system dynamics and make the stability analysis much more difficult than that for a pure continuous-time fuzzy control system. Based on the fuzzy-model-based control approach, LMI(linear matrix inequality)-based stability conditions are derived to guarantee the nonlinear networked system stability. An application example will be given to show the merits and design a procedure of the proposed approach.

The Finite Control Set Model Predictive Torque Control Method for Surface Mounted Permanent Magnetic Synchronous Motor of Electric Vehicle (전기자동차용 표면 부착형 영구자석 동기 전동기의 토크제어를 위한 유한 제어 요소 모델 예측제어(FCS-MPC) 기법)

  • Park, Seong Hwan;Lee, Young Il
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.6
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    • pp.453-462
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    • 2016
  • This paper proposes a torque control method for surface mounted permanent magnetic synchronous motor (PMSM) driven by a 2-level voltage source driven inverter, which has fast torque response and small torque ripple. The proposed torque control method follows the finite control set model predictive control (FCS-MPC) strategy. A reference state is derived at each time step for the given time varying torque reference and the cost index is defined so that the tracking error for this reference state should be penalized. The choice of an optimal output voltage vector is made first from the 6 possible active voltage vectors of the 2-level voltage source inverter. Then a modulation factor for the chosen optimal voltage vector is obtained so that the torque ripple can be reduced further. It is shown that the proposed FCS-MPC control method yields fast torque tracking response and small torque ripple through simulation and experiments.

A novel smart criterion of grey-prediction control for practical applications

  • Z.Y. Chen;Ruei-yuan Wang;Yahui Meng;Timothy Chen
    • Smart Structures and Systems
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    • v.31 no.1
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    • pp.69-78
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    • 2023
  • The purpose of this paper is to develop a scalable grey predictive controller with unavoidable random delays. Grey prediction is proposed to solve problems caused by incorrect parameter selection and to eliminate the effects of dynamic coupling between degrees of freedom (DOFs) in nonlinear systems. To address the stability problem, this study develops an improved gray-predictive adaptive fuzzy controller, which can not only solve the implementation problem by determining the stability of the system, but also apply the Linear Matrix Inequality (LMI) law to calculate Fuzzy change parameters. Fuzzy logic controllers manipulate robotic systems to improve their control performance. The stability is proved using Lyapunov stability theorem. In this article, the authors compare different controllers and the proposed predictive controller can significantly reduce the vibration of offshore platforms while keeping the required control force within an ideal small range. This paper presents a robust fuzzy control design that uses a model-based approach to overcome the effects of modeling errors. To guarantee the asymptotic stability of large nonlinear systems with multiple lags, the stability criterion is derived from the direct Lyapunov method. Based on this criterion and a distributed control system, a set of model-based fuzzy controllers is synthesized to stabilize large-scale nonlinear systems with multiple delays.

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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Robust and Non-fragile $H_{\infty}$ Decentralized Fuzzy Model Control Method for Nonlinear Interconnected System with Time Delay (시간지연을 가지는 비선형 상호연결시스템의 견실비약성 $H_{\infty}$ 분산 퍼지모델 제어기법)

  • Kim, Joon-Ki;Yang, Seung-Hyeop;Kwon, Yeong-Sin;Bang, Kyung-Ho;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.47 no.6
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    • pp.64-72
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    • 2010
  • In general, due to the interactions among subsystems, it is difficult to design an decentralized controller for nonlinear interconnected systems. In this study, the model of nonlinear interconnected systems is studied via decentralized fuzzy control method with time delay and polytopic uncertainty. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. And the represented model can be rewritten as Parameterized Linear Matrix Inequalities(PLMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. We show that the resulting fuzzy controller guarantees the asymptotic stability and disturbance attenuation of the closed-loop system in spite of controller gain variations within a resulted polytopic region by example and simulations.

Robust Position Control of a Reaction Wheel Inverted Pendulum (원판의 반작용을 이용한 역진자의 강인 자세 제어)

  • Park, Sang-Hyung;Lee, Hae-Chang;Lim, Seong-Muk;Kim, Jung-Su
    • Journal of the Korean Institute of Intelligent Systems
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    • v.26 no.2
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    • pp.127-134
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    • 2016
  • This paper presents a robust control of a reaction wheel inverted pendulum. To this end, a mathematical model is derived using physical laws, and then parameters in the model are identified as well. Based on the model, a robust position control is designed, which consists of two parts: swing-up control using passivity and robust stabilization control using LMI (Linear Matrix Inequality). When the pendulum starts to move, the swing-up control is applied. If the position of the pendulum is near the desired upright position, the control is switched to the robust stabilization control. This robust control is employed in order to deal with the uncertainties in the inertia of the pendulum dynamics. The performance of the proposed control scheme is validated not only simulation but also real experiment.