• Title, Summary, Keyword: Nonlinear Systems of Equations

Search Result 422, Processing Time 0.035 seconds

Analysis of Stability for Overhead Crane Systems (천정 크레인시스템의 안정성 해석)

  • Ban Gab Su;Lee Kwang Ho;Mo Chang Ki;Lee Jong Gyu
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.22 no.4
    • /
    • pp.128-135
    • /
    • 2005
  • Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

BOUNDARY VALUE PROBLEM FOR A CLASS OF THE SYSTEMS OF THE NONLINEAR ELLIPTIC EQUATIONS

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
    • /
    • v.17 no.1
    • /
    • pp.67-76
    • /
    • 2009
  • We show the existence of at least two nontrivial solutions for a class of the systems of the nonlinear elliptic equations with Dirichlet boundary condition under some conditions for the nonlinear term. We obtain this result by using the variational linking theory in the critical point theory.

  • PDF

Application of Volterra Functional Series to the Analysis of Nonlinear Systems Represented by Nonlinear Differential Equations (비선형 미분방정식으로 표현되는 비선형 시스템의 해석을 위한 볼테리 시리즈의 응용)

  • Sung, Dan-Keun
    • Journal of the Korean Institute of Telematics and Electronics
    • /
    • v.25 no.3
    • /
    • pp.315-321
    • /
    • 1988
  • The input-output relation for nonlinear systems can e explicitly represented by the volterra functional series and it is characterized by the Volterra kernels. A block diagram reduction method is proposed to determine the Volterra kernels for nonlinear differential equations and is compared with the direct substitution techniques. The former method can significantly reduce the computational complexity. A degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

  • PDF

HIGH-ORDER NEWTON-KRYLOV METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS

  • Darvishi, M.T.;Shin, Byeong-Chun
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.15 no.1
    • /
    • pp.19-30
    • /
    • 2011
  • In [21], we compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, we propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. We provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

Application of Volterra functional series to the analysis of nonlinear systems (비선형 시스템 해석을 위한 볼테라 시리지의 응용)

  • 성단근
    • 제어로봇시스템학회:학술대회논문집
    • /
    • /
    • pp.145-149
    • /
    • 1987
  • The input-output relation for nonlinear systems can be explicitly represented by the Voltera functional series and it is characterized by the Volterra Kernels. A block diagram reduction method is introduced to determine the Volterra Kernels for the nonlinear systems represented by nonlinear differential equations. Degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

  • PDF

A New Approach for Motion Control of Constrained Mechanical Systems: Using Udwadia-Kalaba′s Equations of Motion

  • Joongseon Joh
    • International Journal of Precision Engineering and Manufacturing
    • /
    • v.2 no.4
    • /
    • pp.61-68
    • /
    • 2001
  • A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

  • PDF

High conservative nonlinear vibration equations by means of energy balance method

  • Bayat, Mahmoud;Pakar, Iman;Bayat, Mahdi
    • Earthquakes and Structures
    • /
    • v.11 no.1
    • /
    • pp.129-140
    • /
    • 2016
  • This paper presents He's Energy Balance Method (EBM) for solving nonlinear oscillatory differential equations. Three strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with numerical solutions using Runge-Kutta's algorithm. The effects of different important parameters on the nonlinear response of the systems are studied. The results show the presented method is potentially to solve high nonlinear vibration equations.

A Study of Nonlinear Behaviors in Power Systems with SMES (SMES를 포함하는 전력계통의 비선형현상 해석에 관한 연구)

  • Ahn, Byong-Hak;Lee, Byong-Jun
    • The Transactions of the Korean Institute of Electrical Engineers A
    • /
    • v.48 no.4
    • /
    • pp.379-387
    • /
    • 1999
  • In general, solving or analyzing nonilinear dynamical equations is very difficult and requires special techniques. To avoid these difficulties, systems are generally linearized in an attempt to predict their begavior. These linearized equations, however, may not predict true system behavior. Therefore, the nonlinear dynamical analysis using bifurcation theory may become a fundamental framework in understanding nonlinear situation in power systems. In this paper, we propose a systematic procedure based on a bifurcation theory to analyze nonlinear behaviors in power systems. We show usefulness of our procedure by applying 3-bus model system. In addition, we consider nonlinear model of SMES and verify the effect of SMES in power system's nonlinear behaviors.

  • PDF

GENERALIZED DISCRETE HALANAY INEQUALITIES AND THE ASYMPTOTIC BEHAVIOR OF NONLINEAR DISCRETE SYSTEMS

  • Xu, Liguang
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.5
    • /
    • pp.1555-1565
    • /
    • 2013
  • In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

Energy based approach for solving conservative nonlinear systems

  • Bayat, M.;Pakar, I.;Cao, M.S.
    • Earthquakes and Structures
    • /
    • v.13 no.2
    • /
    • pp.131-136
    • /
    • 2017
  • This paper concerns two new analytical approaches for solving high nonlinear vibration equations. Energy Balance method and Hamiltonian Approach are presented and successfully applied for nonlinear vibration equations. In these approaches, there is no need to use small parameters to solve and only with one iteration, high accurate results are reached. Numerical procedures are also presented to compare the results of analytical and numerical ones. It has been established that, the proposed approaches are in good agreement with numerical solutions.