• Title/Summary/Keyword: LMI Optimization

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Active Vibration Control of Structure Using LMI Optimization Design of Robust Saturation Controller (강인 포화 제어기의 LMI 최적 설계를 이용한 구조물의 능동 진동 제어)

  • Park, Young-Jin;Moon, Seok-Jun;Lim, Chae-Wook
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.3 s.108
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    • pp.298-306
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    • 2006
  • In our previous paper, we developed a robust saturation controller for the linear time-invariant (LTI) system involving both actuator's saturation and structured real parameter uncertainties. This controller can only guarantee the closed-loop robust stability of the system in the presence of actuator's saturation. But we cannot analytically make any comment on control performance of this controller. In this paper, we suggest a method to use linear matrix inequality (LMI) optimization problem which can analytically explain control performance of this robust saturation controller only in nominal system. The availability of design method using LMI optimization problem for this robust saturation controller is verified through a numerical example for the building with an active mass damper (AMD) system.

H_{\infty} Control Synthesis for Power System Design using LMI Optimization Method (LMI 최적화기법을 적용한 $H_{\infty}$제어 시스템의 전력계통 안정화장치(PSS) 설계)

  • Jeong, Dae-Won;Ju, Un-Pyo;Kim, Geon-Jung
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.49 no.4
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    • pp.165-174
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    • 2000
  • This paper presents the application of H$\infty$ control synthesis using LMI optimization method to power system stabilizer(PSS) design. Since power system is usually operated under circumstance of unmeasurable uncertainties and external disturbances, the improvement of small signal stability becomes one of the most important issue for securing system stability and preventing low frequency oscillation phenomena. The LMI optimized H$\infty$ PSS provides robust performance and guarantees the internal stability under these operating conditions. The global optimal H$\infty$ norm is found using LMI convex optimization method which is more systematic than standard two Riccati solution method. The design results are simulated for a case study. We verified that the LMI method shows the best performance characteristic smong standard Riccati method and conventional lead/lag method.

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Rank-constrained LMI Approach to Simultaneous Linear Quadratic Optimal Control Design (계수조건부 LMI를 이용한 동시안정화 LQ 최적제어기 설계)

  • Kim, Seog-Joo;Cheon, Jong-Min;Kim, Jong-Moon;Kim, Chun-Kyung;Lee, Jong-Moo;Kwon, Soom-Nam
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.11
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    • pp.1048-1052
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    • 2007
  • This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.

Multi-Objective Controller Design using a Rank-Constrained Linear Matrix Inequality Method (계수조건부 LMI를 이용한 다목적 제어기 설계)

  • Kim, Seog-Joo;Kim, Jong-Moon;Cheon, Jong-Min;Kwon, Soon-Mam
    • Journal of Institute of Control, Robotics and Systems
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    • v.15 no.1
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    • pp.67-71
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    • 2009
  • This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as $H_2/H_{\infty}$ 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.

Structured Static Output Feedback Stabilization of Discrete Time Linear Systems (구조적인 제약이 있는 이산시간 선형시스템의 정적출력 되먹임 안정화 제어기 설계)

  • Lee, Joonhwa
    • Journal of Institute of Control, Robotics and Systems
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    • v.21 no.3
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    • pp.233-236
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    • 2015
  • In this paper, a nonlinear optimization problem is proposed to obtain a structured static output feedback controller for discrete time linear systems. The proposed optimization problem has LMI (Linear Matrix Inequality) constraints and a non-convex objective function. Using the conditional gradient method, we can obtain suboptimal solutions of the proposed optimization problem. Numerical examples show the effectives of the proposed approach.

Robust Control of Two-axes Precise Stage Using LMI Optimization (LMI 최적화를 이용한 2축 정밀 스테이지의 강인제어)

  • Kim, Yeung-Shik;Park, Heung-Seok;Kim, In-Soo
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.22 no.5
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    • pp.845-851
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    • 2013
  • In this paper, a robust optimization approach is applied to the two-axes stage using a piezoelectric actuator for precise motion tracking. Robust control is based on LQG/LTR (linear quadratic Gaussian control with loop transfer recovery) control. Further, an LMI (linear matrix inequality) is used to find the optimal parameter in the loop transfer recovery step, instead of a trial and error method. A decoupler in the shape of FIR filter is added to reduce the coupling effect between the motions of the two axes, and hence, the feedback control loop is designed independently for each axis motion. The experimental result shows that the proposed control scheme can be applied effectively for motion control of the two-axes stage.

Design of a reduced-order $H_{\infty}$ controller using an LMI method (LMI를 이용한 축소차수 $H_{\infty}$ 제어기 설계)

  • Kim, Seog-Joo;Chung, Soon-Hyun;Cheon, Jong-Min;Kim, Chun-Kyung;Lee, Jong-Moo;Kwon, Soon-Man
    • Proceedings of the KIEE Conference
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    • 2004.11c
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    • pp.729-731
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    • 2004
  • This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

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ON GLOBAL EXPONENTIAL STABILITY FOR CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Kwon, O.M.;Park, Ju-H.;Lee, S.M.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.961-972
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    • 2008
  • In this paper, we consider the global exponential stability of cellular neural networks with time-varying delays. Based on the Lyapunov function method and convex optimization approach, a novel delay-dependent criterion of the system is derived in terms of LMI (linear matrix inequality). In order to solve effectively the LMI convex optimization problem, the interior point algorithm is utilized in this work. Two numerical examples are given to show the effectiveness of our results.

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Structured Controller Synthesis Using a Penalized LMI Method (페널티화된 LMI를 이용한 구조적 제약이 있는 제어기 설계)

  • Kim Seog-Joo;KWon Soonman Kwon;Cheon Jong-Min;Moon Young-Hyun
    • Journal of Institute of Control, Robotics and Systems
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    • v.11 no.8
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    • pp.656-661
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    • 2005
  • This paper is concerned with an iterative linear matrix inequality (LMI) approach to the design of a structurally constrained output feedback controller such as decentralized control. The structured synthesis is formulated as a novel rank-constrained LMI optimization problem, where the controller parameters are explicitly described so as to impose structural constraints on the parameter matrices. An iterative penalty method is applied to solve the rank-constrained LMI problem. Numerical experiments are performed to illustrate the effectiveness of the proposed method.

Robust observer-based $H_{\infty}$ control for singular systems (특이시스템의 강인 관측기 기반 $H_{\infty}$ 제어)

  • Kim, Jong-Hae
    • Proceedings of the KIEE Conference
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    • 2004.05a
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    • pp.7-9
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    • 2004
  • This paper provides an observer-based $H_{\infty}$ controller design method for singular systems with and without time-varying delay by just one LMI condition. The sufficient condition for the existence of controller and the controller design method are presented by perfect LMI (linear matrix inequality) approach. The design procedure involves solving an LMI. The observer-based $H_{\infty}$ controller in the existing results can be constructed from the coupled two or more conditions while the proposed controller design method can be obtained from an LMI condition, which can be solved efficiently by convex optimization. Since the obtained condition can be expressed as an LMI form, all variables including feedback gain and observer gain can be calculated simultaneously by Schur complement and changes of variables. An example is given to illustrate the results.

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