• Title/Summary/Keyword: singular perturbation method

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Multi-Input Multi-Output Nonlinear Autopilot Design for Ship-to-Ship Missiles

  • Im Ki-Hong;Chwa Dong-Kyoung;Choi Jin-Young
    • International Journal of Control, Automation, and Systems
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    • v.4 no.2
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    • pp.255-270
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    • 2006
  • In this paper, a design method of nonlinear autopilot for ship-to-ship missiles is proposed. Ship-to-ship missiles have strongly coupled dynamics through roll, yaw, and pitch channel in comparison with general STT type missiles. Thus it becomes difficult to employ previous control design method directly since we should find three different solutions for each control fin deflection and should verify the stability for more complicated dynamics. In this study, we first propose a control loop structure for roll, yaw, and pitch autopilot which can determine the required angles of all three control fins. For yaw and pitch autopilot design, missile model is reduced to a minimum phase model by applying a singular perturbation like technique to the yaw and pitch dynamics. Based on this model, a multi-input multi-output (MIMO) nonlinear autopilot is designed. And the stability is analyzed considering roll influences on dynamic couplings of yaw and pitch channel as well as the aerodynamic couplings. Some additional issues on the autopilot implementation for these coupled missile dynamics are discussed. Lastly, 6-DOF (degree of freedom) numerical simulation results are presented to verify the proposed method.

$H_{\infty}$ Composite Control for Singularly Perturbed Nonlinear Systems via Successive Galerkin Approximation

  • Kim, Young-Joong;Kim, Beom-Soo;Shin, Eun-Chul;Yoo, Ji-Yoon;Lim, Myo-Taeg
    • 제어로봇시스템학회:학술대회논문집
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    • 2004.08a
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    • pp.407-412
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    • 2004
  • This paper presents a new algorithm for the closed-loop $H_{\infty}$ composite control of singularly perturbed nonlinear systems with a exogenous disturbance, using the successive Galerkin approximation(SGA). The singularly perturbed nonlinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale via singular perturbation theory, and two $H_{\infty}$ control laws are obtained to each subsystem by using the SGA method. The composite control law that consists of two $H_{\infty}$ control laws of each subsystem is designed. One of the purposes of this paper is to design the closed-loop $H_{\infty}$ composite control law for the singularly perturbed nonlinear systems via the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

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Design of Singularly Perturbed Delta Operator Systems with Low Sensitivity (낮은 민감도를 지니는 특이섭동 델타연산자 시스템의 설계)

  • Shim, Kyu-Hong;Sawan, M.E.;Lee, Kyung-Tae
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.32 no.7
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    • pp.76-82
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    • 2004
  • A method of designing a state feedback gam achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system The present paper extends the previous study to the discrete system and the ${\delta}-operating$ system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

Approximation of the State Variables of the Original System from the Balanced Reduced Model (발란싱축소화로 구한 축소모델로부터 원 시스템 상태변수를 구하는 방법)

  • 정광영
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.333-333
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    • 2000
  • When the generalized singular perturbation method is used for model reduction, the state variables of the original system is reconstructed from the reduced order model. The state reduction error is defined, which shows how well the reconstructed state variables approximate the state variables of the original system equation.

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Uniformly Convergent Numerical Method for Singularly Perturbed Convection-Diffusion Problems

  • Turuna, Derartu Ayansa;Woldaregay, Mesfin Mekuria;Duressa, Gemechis File
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.629-645
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    • 2020
  • A uniformly convergent numerical method is developed for solving singularly perturbed 1-D parabolic convection-diffusion problems. The developed method applies a non-standard finite difference method for the spatial derivative discretization and uses the implicit Runge-Kutta method for the semi-discrete scheme. The convergence of the method is analyzed, and it is shown to be first order convergent. To validate the applicability of the proposed method two model examples are considered and solved for different perturbation parameters and mesh sizes. The numerical and experimental results agree well with the theoretical findings.

Uncertainty Modeling and Robust Control for LCL Resonant Inductive Power Transfer System

  • Dai, Xin;Zou, Yang;Sun, Yue
    • Journal of Power Electronics
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    • v.13 no.5
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    • pp.814-828
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    • 2013
  • The LCL resonant inductive power transfer (IPT) system is increasingly used because of its harmonic filtering capabilities, high efficiency at light load, and unity power factor feature. However, the modeling and controller design of this system become extremely difficult because of parameter uncertainty, high-order property, and switching nonlinear property. This paper proposes a frequency and load uncertainty modeling method for the LCL resonant IPT system. By using the linear fractional transformation method, we detach the uncertain part from the system model. A robust control structure with weighting functions is introduced, and a control method using structured singular values is used to enhance the system performance of perturbation rejection and reference tracking. Analysis of the controller performance is provided. The simulation and experimental results verify the robust control method and analysis results. The control method not only guarantees system stability but also improves performance under perturbation.

DISCRETE MODEL REDUCTION OVER DISC-TYPE ANALYTIC DOMAINS AND $\infty$-NORM ERROR BOUND

  • Oh, Do-Chang;Lee, Kap-Rai;Um, Tae-Ho;Park, Hong-Bae
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10a
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    • pp.64-68
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    • 1996
  • In this note, we propose the discrete model reduction method over disc-type analytic domains. We define Hankel singular value over the disc that is mapped by standard bilinear mapping. And GSPA(generalized singular perturbation approximation) and DT(direct truncation) are generalized to GSPA and DT over a disc. Furthermore we show that the reduced order model over a smaller domain has a smaller L$_{\infty}$ norm error bound..

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NUMERICAL INTEGRATION METHOD FOR SINGULAR PERTURBATION PROBLEMS WITH MIXED BOUNDARY CONDITIONS

  • Andargie, Awoke;Reddy, Y.N.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.1273-1287
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    • 2008
  • In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

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PERFORMANCE OF RICHARDSON EXTRAPOLATION ON SOME NUMERICAL METHODS FOR A SINGULARLY PERTURBED TURNING POINT PROBLEM WHOSE SOLUTION HAS BOUNDARY LAYERS

  • Munyakazi, Justin B.;Patidar, Kailash C.
    • Journal of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.679-702
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    • 2014
  • Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

$\mu$-Controller Design using Genetic Algorithm (유전알고리즘을 이용한 $\mu$제어기 설계)

  • 기용상;안병하
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1996.11a
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    • pp.301-305
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    • 1996
  • $\mu$ theory can handle the parametric uncertainty and produces more non-conservative controller than H$_{\infty}$ control theory. However an existing solution of the theory, D-K iteration, creates a controller of huge order and cannot handle the real or mixed real-complex perturbation sets. In this paper, we use genetic algorithms to solve these problems of the D-K iteration method. The Youla parameterization is used to obtain all stabilizing controllers and the genetic algorithms determines the values of the state feedback gain, the observer gain, and Q parameter to minimize $\mu$, the structured singular value, of given system. From an example, we show that this method produces lower order controller which controls a real parameter-perturbed plant than D-K iteration method.

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