• Title/Summary/Keyword: Output Feedback Linear Matrix Inequality

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Static Output Feedback Sliding Mode Control Design for Linear Systems with Mismatched Uncertainties (비정합 불확실성을 갖는 선형 시스템을 위한 정적 출력 궤환 슬라이딩 모드 제어기 설계)

  • Choi, Han-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.1
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    • pp.15-18
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    • 2007
  • We consider the problem of designing a static output feedback sliding mode control law for linear dynamical systems with mismatched uncertainties in the state matrix. We assume that an output dependent sliding surface guaranteeing the quadratic stability of the sliding mode dynamics is given, the reachability condition is not required to be satisfied globally, and the output feedback sliding mode control law complises both linear and discontinuous parts. We reduce the problem of designing the linear part of the sliding mode control law to a simple LMI problem which offers design flexibility for combining various useful convex design specifications. Our approach does not require state transformation and it can be applied to mismatched uncertain systems.

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.

Active Vibration Control of a Structure with Output Feedback Based on Simultaneous Optimization Design Method

  • Kim, Young-Bok
    • Journal of Mechanical Science and Technology
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    • v.14 no.1
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    • pp.57-64
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    • 2000
  • Recent advances in the field of control theory have enabled us to design active vibration control systems for various structures. In many studies, the controller used to suppress vibration has been synthesized for the given mathematical model of structure. In these cases, the designer has not been able to utilize the degree of freedom to adjust the structural parameters of the control object. To overcome this problem, so called 'Structure/Control Simultaneous Optimization Method' is used. In this context of view, this paper is concerned with the active vibration control of bridge towers, platforms and ocean vehicles etc. Simultaneous design method is used to achieve optimal system performance. Here, a general framework for the simultaneous design problem of output feedback case is introduced based on LMI (Linear Matrix Inequality). The simulation results show that the proposed design method achieves desirable control performance.

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$H_ {\infty}$ PID Controller Design for an Attraction Type Magnetic Levitation System (흡인식 자기부상시스템의 $H_ {\infty}$ PID 제어기 설계)

  • Kim, Seog-Joo;Kim, Chun-Kyung;Kwon, Soon-Man
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.57 no.9
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    • pp.1624-1627
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    • 2008
  • This paper deals with a linear matrix inequality (LMI) approach to the design of a PID controller for an attraction type magnetic levitation system. First, we convert the $H_ {\infty}$ PID controller problem into a static output feedback problem. We then solve the static output problem by using the recently developed penalty function method. Numerical experiments show the effectiveness of the proposed algorithm.

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.

An LMI-based Decentralized Sliding Mode Static Output Feedback Control Design Method for Large Scale Systems (대규모 시스템을 위한 LMI기반 비집중화 슬라이딩 모드 정적 출력 궤환 제어기 설계)

  • Choi, Han-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.14 no.4
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    • pp.381-384
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    • 2008
  • 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.

Robust Controller Design for Non-square Linear Systems Using a Passivation Approach (수동화 기법에 의한 비정방 선형 시스템의 강인 제어기 설계)

  • 손영익
    • Journal of Institute of Control, Robotics and Systems
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    • v.8 no.11
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    • pp.907-915
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    • 2002
  • We present a state-space approach to design a passivity-based dynamic output feedback control of a finite collection of non-square linear systems. We first determine a squaring gain matrix and an additional dynamics that is connected to the systems in a feedforward way, then a static passivating (i.e. rendering passive) control law is designed. Consequently, the actual feedback controller will be the static control law combined with the feedforward dynamics. A necessary and sufficient condition for the existence of the parallel feedfornward compensator (PFC) is given by the static output feedback fomulation, which enables to utilize linear matrix inequality (LMI). The effectiveness of the proposed method is illustrated by some examples including the systems which can be stabilized by the proprotional-derivative (PD) control law.

Robust H∞ Fuzzy Control for Discrete-Time Nonlinear Systems with Time-Delay (시간 지연을 갖는 이산 시간 비선형 시스템에 대한 H∞ 퍼지 강인 제어기 설계)

  • Kim Taek Ryong;Park Jin Bae;Joo Young Hoon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.15 no.3
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    • pp.324-329
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    • 2005
  • In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time nonlinear systems with time-delay via fuzzy static output feedback is investigated. The Takagj-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear system with time-delayed state. Then, the parallel distributed compensation technique is used for designing of the robust fuzzy controller. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities via similarity transform and congruence transform technique. We have shown the effectiveness and feasibility of the proposed method through the simulation.

Static Output-Feedback-Based Robust Fault Tolerant Controller Design (정적 출력궤환 기반 강인 고장포용 제어기 설계)

  • Jee, Sung Chul;Moon, Ji Hyun;Lee, Ho Jae
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.7
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    • pp.587-591
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    • 2013
  • This paper addresses the robust fault tolerant controller design problems of static output systems with disturbance. The fault is expressed by the abrupt chattering of system parameters. The design conditions are derived in terms of linear matrix inequalities and linear matrix equalities. An illustrative example is provided to verify performances of the proposed controller.

A Robust Pole Placement for Uncertain Linear Systems via Linear Matrix Inequalities (선형행렬부등식에 의한 불확실한 선형시스템의 견실한 극점배치)

  • 류석환
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2000.11a
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    • pp.476-479
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    • 2000
  • This paper deals with a robust pole placement method for uncertain linear systems. For all admissible uncertain parameters, a static output feedback controller is designed such that all the poles of the closed loop system are located within the prespecfied disk. It is shown that the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set guarantees the existence of the output feedback gain matrix for our control problem. By a sequence of convex optimization the aforementioned matrix is obtained. A numerical example is solved in order to illustrate efficacy of our design method.

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