• Title/Summary/Keyword: linear differential systems

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A continuous solution of the heat equation based on a fuzzy system

  • Moon, Byung-Soo;Hwang, In-Koo;Kwon, Kee-Choon
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.3 no.1
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    • pp.13-17
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    • 2003
  • A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

Closed-Form Solutions to Free Vibration Response of Single Degree of Freedom Systems with Coulomb Friction (쿨롱마찰을 갖는 단자유도계의 자유진동응답에 관한 닫힌 해)

  • Lee, Sung-Kyung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.33 no.1
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    • pp.9-16
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    • 2020
  • The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness.

Development of Legibility Distance Model for VMS Messages using In-Vehicle DGPS Data (DGPS를 이용한 VMS 메시지 판독거리 모형개발)

  • O, Cheol;Kim, Won-Gi;Lee, Su-Beom;Lee, Cheong-Won;Kim, Jeong-Wan
    • Journal of Korean Society of Transportation
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    • v.25 no.5
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    • pp.23-32
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    • 2007
  • Variable message sign (VMS), which is used for providing real-time information on traffic conditions and incidents, is one of the important components of intelligent transportation systems. VMS messages need to meet the requirements with the consideration of human factors that messages should be readable and understandable while driving. This study developed a legibility distance model for VMS messages using in-vehicle differential global positioning data (DGPS). Traffic conditions, highway geometric conditions, and VMS message characteristics were investigated for establishing the legibility model based on multiple linear regression analysis. The height of VMS characters, speed, and the number of lanes were identified as dominant factors affecting the variation of legibility distances. It is expected that the proposed model would play a significant role in designing VMS messages for providing more effective real-time traffic information.

Design of robust servo systems and application to control of training simulator for radio-controlled helicopter (강인한 서보계설계와 R/C헬리콥터 트레이닝 시뮬레이터 제어에의 응용)

  • 김상봉;박순실
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.15 no.2
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    • pp.497-506
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    • 1991
  • In this paper, a new construction for training simulator of R/C helicopter based on two types of servo controller is proposed. Two modified algorithms (algorithm I and II) for servo controller design are presented. Algorithm I is developed by adopting Davison's method in the case that the expressions for the homogeneous differential equations of reference input and disturbance are different types, and algorithm II is done by considering error weighting function for the servo controller of algorithm I . The linear fractional transformation method is incorporated in both design methods in order to assign the closed loop poles of the servo system in a specified region. The helicopter simulator is composed by the gimbals with two freedom of rolling and pitching. The reliability and validity for the design methods of the proposed servo controller are investigated through the practical experiment for the simulator by using 16bits micro-computer with A/D and D/A converters. It can be observered from the experimental results that the proposed servo controller is applicable to practical plants since the simulator is robust for the arbitrary disturbance and it follows to the given reference input without significant steady state error.

Design of Low Voltage Linear Tunable Transconductors using the Series Composite Transistor (직렬 복합 트랜지스터를 이용한 저전압 가변 트랜스컨덕터의 설계)

  • Yun, Chang-Hun;Yu, Young-Gyu;Choi, Seok-Woo
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.38 no.5
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    • pp.52-58
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    • 2001
  • In this paper, the low voltage linear tunable transconductors using the series composite transistor are presented. Due to the series composite transistor operating in the saturation region and the triode region, the proposed circuits have wide input range at low supply voltage. The designed transconductors have been simulated by HSPICE using $0.25{\mu}m$ n-welll CMOS process. Simulation results show that the cutoff frequency is 309M Hz and the THD of less than 1.1% can be obtained for the differential input signal of up to l.5VP-P with the input signal frequency of l0MHz.

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Inverse problem for semilinear control systems

  • Park, Jong-Yeoul;Jeong, Jin-Mun;Kwun, Young-Chel
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.603-611
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    • 1996
  • Let consider the following problem: find an element u(t) in a Banach space U from the equation $$ x'(t) = Ax(t) + f(t,x(t)) + \Phi_0 u(t), 0 \leq t \leq T $$ with initial and terminal conditions $$ x(0) = 0, x(T) = \phi $$ in a Banach space X where $\phi \in D(A)$. This problem is a kind of control engineering inverse problem and contains nonlinear term, so that it is difficult and interesting. Thee proof main result in this paper is based on the Fredholm property of [1] in section 3. Similar considerations of linear system have been dealt with in many references. Among these literatures, Suzuki[5] introduced this problem for heat equation with unknown spatially-varing conductivity. Nakagiri and Yamamoto[2] considered the identifiability problem, which A is a unknown operator to be identified, where the system is described by a linear retarded functional differential equation. We can also apply to determining the magnitude of the control set for approximate controllability if X is a reflexive space, i.e., we can consider whether a dense subset of X is covered by reachable set in section 4.

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Precision indices of neural networks for medicines: structure-activity correlation relationships

  • Zhu, Hanxi;Aoyama, Tomoo;Yoshihara, Ikuo;Lee, Seung-Woo;Kim, Wook-Hyun
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.481-481
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    • 2000
  • We investigated the structure-activity relationships on use of multi-layer neural networks. The relationships are techniques required in developments of medicines. Since many kinds of observations might be adopted on the techniques, we discussed some points between the observations and the properties of multi-layer neural networks. In the structure-activity relationships, an important property is not that standard deviations are nearly equal to zero for observed physiological activity, but prediction ability for unknown medicines. Since we adopted non-linear approximation, the function to represent the activity can be defined by observations; therefore, we believe that the standard deviations have not significance. The function was examined by "leave-one-out" method, which was originally introduced for the multi-regression analysis. In the linear approximation, the examination is significance, however, we believe that the method is inappropriate in case of nonlinear fitting as neural networks; therefore, we derived a new index fer the relationships from the differential of information propagation in the neural network. By using the index, we discussed physiological activity of an anti-cancer medicine, Mitomycine derivatives. The neuro-computing suggests that there is no direction to extend the anti-cancer activity of Mitomycine, which is close to the trend of anticancer developing.

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An Efficient Solution for Multibody Dynamics Composed of Flexible Beams (유연한 보로 구성된 다물체 동역학의 효율적인 해법)

  • 이기수;금영탁
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.12
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    • pp.2298-2305
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    • 1992
  • To obtain the convenient solution of the multibody dynamic systems composed of flexible beams, linear finite element technique is adopted and the nodal coordinates are interpolated in the global inertia frame. Mass matrix becomes an extremely simple constant matrix and the force vector also becomes extremely simple because Coriolis acceleration and centrifugal force are not required. And the elastic force is also simply computed from the moving frame attached to the material. To solve the global differential algebraic euation. an ODE technique is adopted after Lagrange multiplier is computed by the accelerated iterative technique, and the time demanding procedures such as Newton-Raphson iterations and decomposition of the big matrix are not required. The accuracy of the present solution is checked by a well-known example problem.

Studies on vibration control effects of a semi-active impact damper for seismically excited nonlinear building

  • Lu, Zheng;Zhang, Hengrui;Masri, Sami F.
    • Smart Structures and Systems
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    • v.24 no.1
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    • pp.95-110
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    • 2019
  • The semi-active impact damper (SAID) is proposed to improve the damping efficiency of traditional passive impact dampers. In order to investigate its damping mechanism and vibration control effects on realistic engineering structures, a 20-story nonlinear benchmark building is used as the main structure. The studies on system parameters, including the mass ratio, damping ratio, rigid coefficient, and the intensity of excitation are carried out, and their effects both on linear and nonlinear indexes are evaluated. The damping mechanism is herein further investigated and some suggestions for the design in high-rise buildings are also proposed. To validate the superiority of SAID, an optimal passive particle impact damper ($PID_{opt}$) is also investigated as a control group, in which the parameters of the SAID remain the same, and the optimal parameters of the $PID_{opt}$ are designed by differential evolution algorithm based on a reduced-order model. The numerical simulation shows that the SAID has better control effects than that of the optimized passive particle impact damper, not only for linear indexes (e.g., root mean square response), but also for nonlinear indexes (e.g., component energy consumption and hinge joint curvature).

Recovery-Key Attacks against TMN-family Framework for Mobile Wireless Networks

  • Phuc, Tran Song Dat;Shin, Yong-Hyeon;Lee, Changhoon
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.15 no.6
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    • pp.2148-2167
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    • 2021
  • The proliferation of the Internet of Things (IoT) technologies and applications, especially the rapid rise in the use of mobile devices, from individuals to organizations, has led to the fundamental role of secure wireless networks in all aspects of services that presented with many opportunities and challenges. To ensure the CIA (confidentiality, integrity and accessibility) security model of the networks security and high efficiency of performance results in various resource-constrained applications and environments of the IoT platform, DDO-(data-driven operation) based constructions have been introduced as a primitive design that meet the demand of high speed encryption systems. Among of them, the TMN-family ciphers which were proposed by Tuan P.M., Do Thi B., etc., in 2016, are entirely suitable approaches for various communication applications of wireless mobile networks (WMNs) and advanced wireless sensor networks (WSNs) with high flexibility, applicability and mobility shown in two different algorithm selections, TMN64 and TMN128. The two ciphers provide strong security against known cryptanalysis, such as linear attacks and differential attacks. In this study, we demonstrate new probability results on the security of the two TMN construction versions - TMN64 and TMN128, by proposing efficient related-key recovery attacks. The high probability characteristics (DCs) are constructed under the related-key differential properties on a full number of function rounds of TMN64 and TMN128, as 10-rounds and 12-rounds, respectively. Hence, the amplified boomerang attacks can be applied to break these two ciphers with appropriate complexity of data and time consumptions. The work is expected to be extended and improved with the latest BCT technique for better cryptanalytic results in further research.