• 제목/요약/키워드: singular perturbation method

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Sampled-Data Controller Design for Nonlinear Systems Including Singular Perturbation in Takagi-Sugeno Form (특이섭동을 포함한 타카기 - 수게노 형태의 비선형 시스템을 위한 새로운 샘플치 제어기의 설계기법 제안)

  • Moon, Ji Hyun;Lee, Jaejun;Lee, Ho Jae
    • Journal of the Korean Institute of Intelligent Systems
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    • 제26권1호
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    • pp.50-55
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    • 2016
  • This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.

[ $H_{\infty}$ ] Control for a Class of Singularly Perturbed Nonlinear Systems via Successive Galerkin Approximation

  • Kim, Young-Joong;Lim, Myo-Taeg
    • International Journal of Control, Automation, and Systems
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    • 제5권5호
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    • pp.501-507
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    • 2007
  • This paper presents a new algorithm for the closed-loop $H_{\infty}$ control of a class of singularly perturbed nonlinear systems with an 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 in the spirit of the general theory of singular perturbation. 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.

Coprime Factor Reduction of Parameter Varying Controller

  • Saragih, Roberd;Widowati, Widowati
    • International Journal of Control, Automation, and Systems
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    • 제6권6호
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    • pp.836-844
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    • 2008
  • This paper presents an approach to order reduction of linear parameter varying controller for polytopic model. Feasible solutions which satisfy relevant linear matrix inequalities for constructing full-order parameter varying controller evaluated at each polytopic vertices are first found. Next, sufficient conditions are derived for the existence of a right coprime factorization of parameter varying controller. Furthermore, a singular perturbation approximation for time invariant systems is generalized to reduce full-order parameter varying controller via parameter varying right coprime factorization. This generalization is based on solutions of the parameter varying Lyapunov inequalities. The closed loop performance caused by using the reduced order controller is developed. To examine the performance of the reduced-order parameter varying controller, the proposed method is applied to reduce vibration of flexible structures having the transverse-torsional coupled vibration modes.

AN INITIAL VALUE TECHNIQUE FOR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS WITH A SMALL NEGATIVE SHIFT

  • Rao, R. Nageshwar;Chakravarthy, P. Pramod
    • Journal of applied mathematics & informatics
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    • 제31권1_2호
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    • pp.131-145
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    • 2013
  • In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

A UNIFORMLY CONVERGENT NUMERICAL METHOD FOR A WEAKLY COUPLED SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY AND WEAK INTERIOR LAYERS

  • CHAWLA, SHEETAL;RAO, S. CHANDRA SEKHARA
    • Journal of applied mathematics & informatics
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    • 제33권5_6호
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    • pp.635-648
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    • 2015
  • We consider a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous source term. The diffusion term of each equation is associated with a small positive parameter of different magnitude. Presence of discontinuity and different parameters creates boundary and weak interior layers that overlap and interact. A numerical method is constructed for this problem which involves an appropriate piecewise uniform Shishkin mesh. The numerical approximations are proved to converge to the continuous solutions uniformly with respect to the singular perturbation parameters. Numerical results are presented which illustrates the theoretical results.

Mode Coupling at Oblique Incidence in a Corrugated Dielectric Waveguide: Analysis by the Singular Perturbation Method (굴곡형 격자도파로에서 비스듬히 입사하는 파동에 대한 모드 결합현상:특이접동 방법에 의한 해석)

  • Kim Hong-Koo;Shin Sang-Yung
    • Journal of the Korean Institute of Telematics and Electronics
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    • 제23권1호
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    • pp.27-35
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    • 1986
  • The optical wave interactions in a sinusoidally corrugated dielectric waveguide are analyzed for the oblique incidence case. The coupled mode equations which govern the interactions are derived by the singular perturbation method for the TE-TE mode coupling. The results are compared with those of normal mode analysis by Wagatsuma et al. and total field analysis by Stegeman et al. Phase mismatching effects on the diffraction efficiency are also investigated.

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Discrete model reduction over disc-type analytic domains (디스크형태의 해석적영역을 가지는 이산모델 차수축소)

  • 오도창;정은태;이갑래;박홍배
    • Journal of the Korean Institute of Telematics and Electronics S
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    • 제35S권5호
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    • pp.27-34
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    • 1998
  • This paper is on 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 the generalized singular perturbation approximation and the direct truncation are generalized to GSPA and DT over a disc. Furthermore, it is shown that the reduced order model over a smaller domaing has a smaller .inf.-norm error bound. And the poposed reduction method is used to obtain the regional pole placement property.

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Power Efficient Precoding by Reducing the Effect of the Largest Singular Value of channel Inverse Matrix (채널 역변환 매트릭스의 가장 큰 싱귤러 값 영향을 줄이는 다중 사용자 프리코딩)

  • Ro, Se Yong;Yang, Hyun Wook;Chong, Jong Wha
    • Journal of Korea Society of Digital Industry and Information Management
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    • 제8권4호
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    • pp.115-120
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    • 2012
  • In multi-user multi-input multi-output (MU-MIMO) system, zero forcing beamforming (ZFB) is regarded as a realistic solution for transmitting scheme due to its low complexity and simple structure. However, ZFB shows a significant performance degradation when channel matrix has large condition number. In this case, the largest singular value of the channel inversion matrix has a dominant effect on transmit power. In this paper, we propose a perturbation method for reducing an effect of the dominant singular value. In the proposed algorithm, channel inverse matrix is first decomposed by SVD for the transmit signal to be expressed as a combination of singular vectors. Then, the transmit signal is perturbed to reduce the coefficient of the singular vector corresponding to the largest singular value. When a number of transmit antennas is 4, the simulation results of this paper shows that the proposed method shows 8dB performance enhancement at 10-3 uncoded bit error rate (BER) compared with conventional ZFB. Also, the simulation results show that the proposed method provides a comparable performance to Tomlinson-Harashima Precoding (THP) with much lower complexity.

Robust control of a flexible manipulator with artificial pneumatic muscle actuators (유연한 공압인공근육로봇의 강건제어)

  • 박노철;박형욱;박영필;정승호
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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    • pp.1704-1707
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    • 1997
  • In this work, position and vibratiion control of a two-link manipulator with one flexible link, which an unkoun but bounded payload mass and two pair of artificial muscle-type penumatic actuators, are investgated. A flexible link robot has advantages over a figid link robot in the sense that it is much safer when it cones into contact with its environment, including humans. Furthermore, for the sake of safety, it would be more desirabel if an actuator could deliver required force while maintaining proper compliance. An artificial muscle-type penumatic actuator is adequate for such cases. In this study, a controller based on singular perturbation method, adaptive and sliding mode contro, and .mu.-synthesis is developed. The effectiveness of the proposed control scheme is confirmed through simulations and experiments.

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Generalized singular perturbation approximation preserving positive real property of discrete system (이산시스템의 positive real 특성을 유지하는 일반화된 특이 섭동 근사화)

  • 오도창;김재권;방경호;박홍배
    • Journal of the Korean Institute of Telematics and Electronics S
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    • 제34S권9호
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    • pp.50-59
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    • 1997
  • This paper is on the generalized singular perturbation approximation (GSPA) preserving the discrete positive real property. We transform the discrete positive real(PR) system into a stochastically banlanced system and get the reduced order discrete system from the GSPA of the full order stochastically balanced system. eSPECIALLY, WHEN THE FREE PARAMETER OF THE gspa IS .+-.1, we show that the reduced order discrete system retains stability, minimality, and positive real and stochstically balancing properties. And we derived the .inf.-norm error bound with the reduced order discrete strictly positive real(SPR) system by the proposed method. Finally, we give an example to ascertain the properties of the proposed reduced order discrete system and to compare with the conventional methods.

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