• Title/Summary/Keyword: Linear Stability Theory

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Smart modified repetitive-control design for nonlinear structure with tuned mass damper

  • ZY Chen;Ruei-Yuan Wang;Yahui Meng;Timothy Chen
    • Steel and Composite Structures
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    • v.46 no.1
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    • pp.107-114
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    • 2023
  • A new intelligent adaptive control scheme was proposed that combines observer disturbance-based adaptive control and fuzzy adaptive control for a composite structure with a mass-adjustable damper. The most important advantage is that the control structures do not need to know the uncertainty limits and the interference effect is eliminated. Three adjustable parameters in LMI are used to control the gain of the 2D fuzzy control. Binary performance indices with weighted matrices are constructed to separately evaluate validation and training performance using the revalidation learning function. Determining the appropriate weight matrix balances control and learning efficiency and prevents large gains in control. It is proved that the stability of the control system can be ensured by a linear matrix theory of equality based on Lyapunov's theory. Simulation results show that the multilevel simulation approach combines accuracy with high computational efficiency. The M-TMD system, by slightly reducing critical joint load amplitudes, can significantly improve the overall response of an uncontrolled structure.

Estimation of the vibration fatigue of a linear elastic system based on a desiign sensitivity analysis (설계 만감도 해석을 활용한 선형 시스템 진동내구 평가)

  • Kim, Chan-Jung;Kim, Ku-Sik;Kang, Ho-Young;Jin, Yeo-Hwa;Lee, Bong-Hyun
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2010.10a
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    • pp.491-496
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    • 2010
  • The direct design modification of problematic component is disallowed in order to sacrifice other major factors such as a stability or a major performance. So, the best design policy is to risvise the immature structural medchanism under the minimal design change as soon as possible. For this paper presents a new design sensitivity analysis based on transmissibility rtio (TR) of response acceleration to find a proper candidate for the minimal design modification. The new sensitivity analysis is based on the fact that the sensitivity of TR over a small design change is inversly proportinal to the magnitude of TR. The theory of proposed design sensitivity analysis is simulated with the variance of TR over a dynamic change. Then, new methodology is appplied for a linear elastic specimen to detect the most sensitive node over a design change using measured accleration data during uni-axial vibration test, The physical verification of the sensitivity method is conducted on the CAE model of a linear elastic specimen by adding concentration mass and the vibration fatigue of the simple specimen is analyzed to estimate the relationship between fatigue behaviors and sensitivity consequences.

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Nonlinear stability of non-axisymmetric functionally graded reinforced nano composite microplates

  • Loghman, Abbas;Arani, Ali Ghorbanpour;Barzoki, Ali Akbar Mosallaie
    • Computers and Concrete
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    • v.19 no.6
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    • pp.677-687
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    • 2017
  • The nonlinear buckling response of nano composite anti-symmetric functionally graded polymeric microplate reinforced by single-walled carbon nanotubes (SWCNTs) rested on orthotropic elastomeric foundation with temperature dependent properties is investigated. For the carbon-nanotube reinforced composite (CNTRC) microplate, a uniform distribution (UD) and four types of functionally graded (FG) distribution are considered. Based on orthotropic Mindlin plate theory, von Karman geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is employed to calculate the non-linear buckling response of the plate. Effects of FG distribution type, elastomeric foundation, aspect ratio (thickness to width ratio), boundary condition, orientation of foundation orthotropy and temperature are considered. The results are validated. It is found that the critical buckling load without elastic medium is significantly lower than considering Winkler and Pasternak medium.

Adaptive Sliding Mode Control for Compensation of Uncertainty in Feedback Linearized Skid-to-Turn (STT) Missiles (궤환선형화된 STT 미사일의 불확실성 보상을 위한 적응 슬라이딩 모드 제어)

  • 김민수;좌동경;최진영
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.3
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    • pp.267-274
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    • 1999
  • This paper proposes an adaptive sliding mode control scheme for an autopilot design of Skid-to-Turn (STT) missiles. The feedback linearization controller eliminates nonlinear terms in STT dynamics and makes the entire system linear. But the modeling errors in dynamics and the external disturbances exert bad influence on the performance of the feedback linearization controller. To handle these uncertainties, an adaptive control scheme is developed, where a bound of the uncertainties is estimated by an adaptive law based on a sliding surface. The asymptotic output tracking is proved by using the Lyapunov stability theory. Simulations for STT missiles illustrate the validity of the proposed scheme.

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The Effect of Electron Diffusion on the Instability of a Townsend Discharge (전자 확산 효과가 Townsend 방전 불안정성에 미치는 영향)

  • Mikhailenko, Vladimir
    • Journal of the Korean Vacuum Society
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    • v.21 no.3
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    • pp.130-135
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    • 2012
  • The role of the electron diffusion on the stability of a Townsend discharge was investigated with the linear stability theory for the one-dimensional fluid equation with drift-diffusion approximation. It was proved that the discovered instability occurs as a result of the coupled action of electron diffusion and the perturbed electric field by space charge. The larger electron diffusion results in the faster growth rate at the regime of small perturbation of the electric field by space charges.

Synchronization of Chaos Systems via Sampled-Data Control (카오스 시스템의 동기화를 위한 샘플치 데이터 제어)

  • Lee, Tae-H.;Park, Ju-H.;Kwon, O.M.;Lee, S.M.
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.61 no.4
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    • pp.617-621
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    • 2012
  • This paper considers the synchronization problem of chaotic systems. For this problem, the sampled-data control approach is used to achieve asymptotic synchronization of two identical chaotic systems. Based on Lyapunov stability theory, a new stability condition is obtained via linear matrix inequality formulation to find the sampled-data feedback controller which achieves the synchronization between chaotic systems. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

Absolutely Stable Region for Missile Guidance Loop (유도탄 유도루프의 절대안정한 시간영역)

  • Kim, Jong-Ju;Lyou, Joon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.3
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    • pp.244-249
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    • 2008
  • In this paper, the stable region for missile guidance loop employing an integrated proportional navigation guidance law is derived. The missile guidance loop is formulated as a closed-loop control system consisting of a linear time-invariant feed-forward block and a time-varying feedback gain. By applying the circle criterion to the system, a bound for the time of flight up to which stability can be assured is established as functions of flight time. Less conservative results, as compared to the result by Popov criterion, are obtained.

Robust Stable Conditions Based on the Quadratic Form Lyapunov Function (2차 형식 Lyapunov 함수에 기초한 강인한 안정조건)

  • Lee, Dong-Cheol;Bae, Jong-Il;Jo, Bong-Kwan;Bae, Chul-Min
    • Proceedings of the KIEE Conference
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    • 2004.07d
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    • pp.2212-2214
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    • 2004
  • Robust stable analysis with the system bounded parameteric variation is very important among the various control theory. This study is to investigate the robust stable conditions using the quadratic form Lyapunov function in which the coefficient matrix is affined linear system. The quadratic stability using the quadratic form Lyapunov function is not investigated yet. The Lyapunov unction is robust stable not to be dependent by the variable parameters, which means that the Lyapunov function is conservative. We suggest the robust stable conditions in the Lyapunov function in which the variable parameters are dependent in order to reduce the conservativeness of quadratic stability.

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Robust $\textrm{H}_\infty$ Control Design for the Space Station with Structured Parameter Uncertainty

  • Byun, Kuk-Whan;Bong-Wie;Dabid-Gaiier;John-Sunkel
    • 제어로봇시스템학회:학술대회논문집
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    • 1991.10a
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    • pp.431-441
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    • 1991
  • A robust H$_{\infty}$ control design methodology and its application to a Space Station attitude and momentum control problem are presented. This new approach incorporates nonlinear multi-parameter variations in the state-space formulation of H$_{\infty}$ control theory. An application of this robust H$_{\infty}$ control synthesis technique to the Space Station control problem yields a remarkable result in stability robustness with respect to the moments-of-inertia variation of about 73% in one of the structured uncertainty directions. The performance and stability of this new robust H$_{\infty}$ controller for the Space Station are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.que.

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On Compositional Convection in Near-Eutectic Solidification System Cooled from a Bottom Boundary

  • Hwang, In Gook
    • Korean Chemical Engineering Research
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    • v.55 no.6
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    • pp.868-873
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    • 2017
  • Natural convection is driven by the compositional buoyancy in solidification of a binary melt. The stabilities of convection in a growing mushy layer were analyzed here in the time-dependent solidification system of a near-eutectic melt cooled impulsively from below. The linear stability equations were transformed to self-similar forms by using the depth of the mushy layer as a length scale. In the liquid layer the stability equations are based on the propagation theory and the thermal buoyancy is neglected. The critical Rayleigh number for the mushy layer increases with decreasing the Stefan number and the Prandtl number. The critical conditions for solidification of aqueous ammonium chloride solution are discussed and compared with the results of the previous model for the liquid layer.