• Journal of Mechanical Science and Technology
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• 제19권5호
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• pp.1138-1147
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• 2005

This paper aims at demonstrating the feasibility of active control of beams with a multiobjective state-feedback control technique. The multiobjective state-feedback controller is de­signed on a linear matrix inequality (LMI) approach for the multiobjective synthesis. The design objectives are to achieve a mix of Hoo performance and H2 performance satisfying constraints on the closed-loop pole locations in the face of model uncertainties. The controller is also designed to reject the effects of the noise and external of disturbances. For the theoretical analysis, the governing equation of motion is derived by Hamilton's principle to describe the dynamics of a smart structural system. Numerical examples are presented to demonstrate the effectiveness of the integrated robust controller in damping out the multiple vibration modes of the piezo/beam system.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.828-833
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• 2004

The performance of a mixed $H_{\infty}/H_2$ design with pole placement constraints based on robust vibration control for a piezo/beam system is investigated. The governing equation of motion for the piezo/beam system is derived by Hamilton's principle. The assumed mode method is used to discretize the governing equation into a set of ordinary differential equation. A robust controller is designed by $H_{\infty}/H_2$ feedback control law that satisfies additional constraints on the closed-loop pole location in the face of model uncertainties, which are derived for a general class of convex regions of the complex plane. These constraints are expressed in terms of linear matrix inequalities (LMIs) approach for the multiobjective synthesis. The validity and applicability of this approach for vibration suppressions of SMART structural systems are discussed by damping out the multiple vibrational modes of the piezo/beam system.

• Transactions on Control, Automation and Systems Engineering
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• 제2권1호
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• pp.31-39
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• 2000

We present a robust and reliable H$\infty$ state-feedback controller design for linear uncertain systems, which have norm-bounded time-varying uncertainty in the state matrix, and their prespecified sets of actuators are susceptible to failure. These controllers should guarantee robust stability of the systems and H$\infty$ norm bound against parameter uncertainty and/or actuator failures. Based on the linear matrix inequality (LMI) approach, two state-feedback controller design methods are constructed by formulating to a set of LMIs corresponding to all failure cases or a single LMI that covers all failure cases, with an additional costraint. Effectiveness and geometrical property of these controllers are validated via several numerical examples. Furthermore, the proposed LMI frameworks can be applied to multiobjective problems with additional constraints.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.452-458
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• 2003

This paper presents a robust vibration control methodology of smart structural systems. The governing equations and associated boundary conditions are derived by Hamilton's principle. A robust controller is designed using a linear matrix inequality (LMI) approach to the multiobjective synthesis. The design objectives are to achieve a mix of H$\sub$$\infty$/ performance and H$_2$ performance satisfying constraints on the closed-loop pole locations in the face of model uncertainties. Numerical examples are presented to demonstrate the effectiveness of LMI approach in damping out the multiple modes of vibration of the piezo/beam system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.21-21
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• 2000

In this paper, we design the state feedback gain using linear matrix inequality(LMI) to the multiobjective synthesis, in the magnetic bearing system with integral type servo system. The design objectives can be a H$\_$$\infty$/ performance, asymptotic disturbance rejection, time-domain constraints, on the closed-lnp pole location. To the end, we investigated the validity of the designed controller through results of simulation.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.100-104
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• 1993

In Part 1, we derived robust stability conditions for an LTI interconnected to time-varying nonlinear perturbations belonging to several classes of nonlinearities. These conditions were presented in terms of positive definite solutions to LMI. In this paper we address a problem of synthesizing feedback controllers for linear time-invariant systems under structured time-varying uncertainties, combined with a worst-case H$_{2}$ performance. This problem is introduced in [7, 8, 15, 35] in case of time-invariant uncertainties, where the necessary conditions involve highly coupled linear and nonlinear matrix equations. Such coupled equations are in general difficult to solve. A convex optimization approach will be employed in this synthesis problem in order to avoid solving highly coupled nonlinear matrix equations that commonly arises in multiobjective synthesis problem. Using LMI formulation, this convex optimization problem can in turn be cast as generalized eigenvalue minimization problem, where an attractive algorithm based on the method of centers has been recently introduced to find its solution [30, 361. In the present paper we will restrict our discussion to state feedback case with Popov multipliers. A more general case of output feedback and other types of multipliers will be addressed in a future paper.

• 한국소음진동공학회논문집
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• 제15권4호
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• pp.437-444
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• 2005

이 논문은 비압축성 유동장에 노출된 2차원 플랩이 있는 날개의 단면에 대한 강인한 공탄성 제어기법을 소개하고 있다. 강인한 제어기는 다목적 상태궤환 합성법을 위해 선형행렬부등식을 이용하여 설계되었다. 제어기의 설계목적은 모델불확실성이 존재하는 상황에서 주파수영역에서의 성능과 시간영역에서의 성능을 함께 만족시키는 것으로 하였다. 수치예제들은 2차원-3자유도 플랩이 있는 날개 단면의 공탄성 응답을 감쇠시키는데 있어서 선형행렬부등식의 접근법의 유효성을 잘 제시하고 있다.