• Title/Summary/Keyword: singular perturbation method

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Discrete controller order reduction with the closed-loop performance guaranteed (폐루프시스템의 성능을 보장하는 이산제어기 차수축소)

  • 오도창;정은태;박홍배
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.34S no.3
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    • pp.24-32
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    • 1997
  • This paper is on a discrete controller order reduction with the closed-loop stability and performance guaranteed. to achieve this, after finding the solutionsof two lyapunov inequalities and balancing the full order controller system, we find the reudced order controlers using the balanced truncation (BT) and the balanced singular perturbation approximation (BSPA). When the solutions of the two lyapunov inequalities exist, it is shown that the resulting controllers guarantee the closed-loop stability, and .inf.-norm error bounds are derived for the closed-loop performance region for the BT and in low frequency region for the BSPA. Finally, a numerical example is given to illustrate the validity of the proposed method.

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Higher Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Reaction-Diffusion Problems

  • Anilay, Worku Tilahun;Duressa, Gemechis File;Woldaregay, Mesfin Mekuria
    • Kyungpook Mathematical Journal
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    • v.61 no.3
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    • pp.591-612
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    • 2021
  • In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-diffusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for different values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

A Study on a New Approach to Robust Control and Torque Control Response Analysis of Manufacturing robot Based on Monitoring Simulator for Smart Factory

  • Kim, Hee-Jin;Kim, Dong-Ho;Jang, Gi-Won;Gu, Byeong-Hwa;Han, Sung-Hyun
    • Journal of the Korean Society of Industry Convergence
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    • v.24 no.4_1
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    • pp.397-409
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    • 2021
  • This study proposes a new approach to implimentation of robust control and torque control response analysis based on monitoring simulator for smart factory. According to the physical properties of a flexible manipulator, a two time-scale approach, namely, singular perturbation ap proach, is further utilized for thorough analysis and general controller design. It is shown that asymptotic motional tracking can be effectively achieved, whereas the force regulation errors can be made arbitrarily small. For demonstration of the proposed technology performance, experiments of a eight joint flexible manipulator are performed for the proposed control method, and the reliability of proposed control results are illustrated based on monitoring simulator.

Large-Signal Modulation Characteristics of a Diode Laser (다이오드 레이저의 대신호 변조특성)

  • Lee, Chang-Hee;Yoon, Tae-Hoon;Shin, Sang-Yung
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.23 no.1
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    • pp.91-100
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    • 1986
  • The nonlinear rate equations are solved analytically by using the singular perturbation method to study effects of the spontaneous emission factor and the photon lifetime on the primary resonance and the first subharmonic generation(i.e., the onset of the periocd-doubling route to chaos). By large signal modulation of Hitachi CSP laser HLP 1400, the resonance frequency shift than 100 ps with 1 GHz repetition rate are generated. The experimental observations are in reasonable agreement with the theoretical results obtained using measured parameters of the rate equations.

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An H Output Feedback Control for Singularly Perturbed Fuzzy Systems (특이섭동 퍼지시스템의 H 출력 궤환제어)

  • Yoo, Seog-Hwan;Choi, Byung-Jae
    • Journal of the Korean Institute of Intelligent Systems
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    • v.14 no.3
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    • pp.316-323
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    • 2004
  • This paper deals with an $H_{\infty}$ output feedback controller design for singularly perturbed T-S fuzzy systems. It is shown that the $H_{\infty}$ norm of the singularly perturbed T-S fuzzy system is less than ${\gamma}$ for a sufficiently small ${\varepsilon}$>0 if the $H_{\infty}$ norms of both the slow and fast subsystem are less than ${\gamma}$. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter ${\varepsilon}$. A numerical example is provided to demonstrate the efficacy of the proposed design method.

Design of Approximate Feedback Controller for Two-Time-Scale Aircraft Dynamics (양시등급 항공기 동력학의 근사 궤환 제어기 설계)

  • Shim, Kyu-Hong;Sawan, M.E.;Hong, Sung-Kyung
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.32 no.5
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    • pp.58-64
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    • 2004
  • A new method to obtain approximate solutions by placing the only poles of the slow subsystem for the two-time-scale aircraft dynamic systems. The two kinds of approximate solutions are obtained by a matrix block diagonalization. One is called the uncorrected solution, and the other is called the corrected solution. The former has an error of $O({\varepsilon})$, and the latter has an error of $O({\varepsilon}^2)$. Of course, both solutions are robust enough even though they are reduced solutions. The excellence of the proposed method is illustrated by an numerical example of an aircraft longitudinal dynamics.

POSITIVE RADIAL SOLUTIONS FOR A CLASS OF ELLIPTIC SYSTEMS CONCENTRATING ON SPHERES WITH POTENTIAL DECAY

  • Carriao, Paulo Cesar;Lisboa, Narciso Horta;Miyagaki, Olimpio Hiroshi
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.839-865
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    • 2013
  • We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.

Exponential Stabilization of a Class of Underactuated Mechanical Systems using Dynamic Surface Control

  • Qaiser, Nadeem;Iqbal, Naeem;Hussain, Amir;Qaiser, Naeem
    • International Journal of Control, Automation, and Systems
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    • v.5 no.5
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    • pp.547-558
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    • 2007
  • This paper proposes a simpler solution to the stabilization problem of a special class of nonlinear underactuated mechanical systems which includes widely studied benchmark systems like Inertia Wheel Pendulum, TORA and Acrobot. Complex internal dynamics and lack of exact feedback linearizibility of these systems makes design of control law a challenging task. Stabilization of these systems has been achieved using Energy Shaping and damping injection and Backstepping technique. Former results in hybrid or switching architectures that make stability analysis complicated whereas use of backstepping some times requires closed form explicit solutions of highly nonlinear equations resulting from partial feedback linearization. It also exhibits the phenomenon of explosions of terms resulting in a highly complicated control law. Exploiting recently introduced Dynamic Surface Control technique and using control Lyapunov function method, a novel nonlinear controller design is presented as a solution to these problems. The stability of the closed loop system is analyzed by exploiting its two-time scale nature and applying concepts from Singular Perturbation Theory. The design procedure is shown to be simpler and more intuitive than existing designs. Design has been applied to important benchmark systems belonging to the class demonstrating controller design simplicity. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and performance is verified using numerical simulations.

Infulence of doppler effects on the tracking performance of a dely locked loop (도플러 효과에 의한 지연 동기 루프의 추적 성능분석)

  • 임성준;유흥균
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.23 no.4
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    • pp.857-864
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    • 1998
  • The infuluence of Doppler effects on the tracking performance of a noncoherent second-order delay locked loop (DLL) operating on a data modulated signal is investigated. For the perfoermance analysis we consider the tracking accuracy (steady state error and jitter) of the linear DLL and the reliability of the nonlinear loop. The nonlinear analysis concerning the loop reliability makes use of an asympototic expansion for the MTLL(mean time to lose lock) which has been derived by applying the singular perturbation method. In particular, we give optimal loop parameters and the optimal bandwidth of the bandpass filter in the loop arms to achieve a maximum MTLL. Since Doppler effects can be producesd comparatively in LEO system, we can espect the more reliable DLL loop design. by using the results of the circuit simulation, the delay lock loop is synthesized in FPGA, and verified to get the GPS data from the STR-2770 GPS simulator system. So, the synthesized logic circuit is shown be accurately performed.

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Observation of the Mesoscale Phenomena by Ocean Acoustic Tomography in the East Sea (동해에서 해양음향토모그래피에 의한 중규모 현상 관측)

  • Na, Jung-Yul;Han, Sang-Kyu;Lee, Jae-Hak;Shim, Tae-Bo;Kim, Kuh
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.4 no.3
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    • pp.170-179
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    • 1999
  • The SUS (Signal, Underwater Sound)-OAT experiment was carried out in the Ulleung Basin of the East Sea on 3 June 1997. The SUS-OAT system consisted of aircraft deployed shots as sources and a vertical line array (VLA) tethered by a receiver ship was used to survey a large area where a mesoscale warm eddy appears frequently. The experiment was carried out such that explosive charges set to detonate at 800 ft depth were dropped in a rectangular ($120{\times}120$ km). Sources were a rapidly deployable SUS charge (MK 61 MOD 0), and receiver is a fixed VLA, 90 m in length (150-240 m in receiver depth), composed of 10 elements equally spaced. The reference ray paths are computed by range-dependent acoustic model in canonical ocean based on the historical data. The singular value decomposition (SVD) method is used to obtain the horizontal perturbation of the temperature fields. Horizontal distributions of temperature fields at 150 m and 200 m depth show a weak warm eddy observed by AXBT and the inversely estimated temperature shows similar patterns in terms of the location of the warm eddy. In conclusion, the SUS-OAT experiment has been successful to estimate the position of warm eddy and its temperature field in the East Sea of Korea.

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