• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.3
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• pp.399-406
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• 1996

This paper presents a method of hierarchical state estimation of the time-varying linear systems via Block-pulse function(BPF). When we estimate the state of the systems where noise is considered, it is very difficult to obtain the solutions because minimum error variance matrix having a form of matrix nonlinear differential equations is included in the filter gain calculation. Therefore, hierarchical approach is adapted to transpose matrix nonlinear differential equations to a sum of low order state space equation from and Block-pulse functions are used for solving each low order state space equation in the form of simple and recursive algebraic equation. We believe that presented methods are very attractive nd proper for state estimation of time-varying linear systems on account of its simplicity and computational convenience. (author). 13 refs., 10 figs.

• Journal of Korea Society of Industrial Information Systems
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• v.16 no.4
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• pp.45-52
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• 2011

In the real-field of control cases for robot manipulators, there always exists a modeling error, which results the model has the uncertainties in its parameters and/or structure. In many modem applications, digital computers are extensively used to implement control algorithms to control such systems. The discretization of the nonlinear dynamic equations of such systems results in a complicated discrete dynamic equations. Therefore, it will be difficult to design a discrete-time controller to give good tracking performances in the presence of certain uncertainties. In this paper, a discrete-time sliding mode control algorithm for nonlinear and time varying robot manipulators with uncertainties is presented. Sufficient conditions for guaranteeing the convergence of the discrete-time SMC system are derived. As example simulations, the proposed SMC algorithm is applied to a two-link robotic manipulator with unknown dynamics. The results of the simulation indicate that the developed control scheme is effective in manipulators and electro-mechanical system control.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.201-207
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• 1998

In this study, a geometric nonlinear analysis formulation for spatial frames is developed using the 3D stability functions. For the formulation, the relationships of local and global coordinate systems in force, deformation, and the initial and current configurations of a frame are derived. The force-deformation relationship in global coordinate system is derived as well. The developed formulation is verified in each derivation by reducing the derived equations into 2D equations. The gradual plastification of connections and critical sections can be implemented effectively to this formulation for the complete second order inelastic advanced analysis of spatial frames.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.480-485
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• 1993

A method for obtaining optimal orbital maneuvers of a space vehicle has been developed by combining feedback linearization method with the elegance of the Lambert's theorem. To obtain solutions to nonlinear orbital maneuver problems. The full nonlinear equations of motion for space vehicle in polar coordinate system are transformed exactly into a controllable linear set in Brunovsky canonical form by using feedback linearization by choosing position vector as fully observable output vector. These equations are used to pose a linear optimal tracking problem with a solutions to Lambert's problem and a linear analytical solution of continuous low thrust problem as reference trajectories.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.160-170
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• 2008

Temperature control of an enclosed thermal system which has many applications including Rapid Thermal Processing (RTP) of semiconductor wafers showed an input-constraint violation for nonlinear controllers due to inherent strong coupling between the elements [1]. In this paper, a constrained nonlinear optimal control design is developed, which accommodates input constraints using the linear algebraic equivalence of the nonlinear controllers, for the temperature control of an enclosed thermal process. First, it will be shown that design of nonlinear controllers is equivalent to solving a set of linear algebraic equations-the linear algebraic equivalence of nonlinear controllers (LAENC). Then an input-constrained nonlinear optimal controller is designed based on that LAENC using the constrained linear least squares method. Through numerical simulations, it is demonstrated that the proposed controller achieves the equivalent performances to the classical nonlinear controllers with less total energy consumption. Moreover, it generates the practical control solution, in other words, control solutions do not violate the input-constraints.

• Smart Structures and Systems
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• v.25 no.6
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• pp.643-655
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• 2020

Active control of nonlinear vibration of stiffened functionally graded (SFG) cylindrical shell is studied in this paper. The system is subjected to axial and transverse periodic loads in the presence of thermal uncertainty. The material composition is considered to be continuously graded in the thickness direction, also these properties depend on temperature. The relations of strain-displacement are derived based on the classical shell theory and the von Kármán equations. For modeling the stiffeners on the cylindrical shell surface, the smeared stiffener technique is used. The Galerkin method is used to discretize the partial differential equations of motion. Some comparisons are made to validate the SFG model. For suppression of the nonlinear vibration, the linear and nonlinear control strategies are applied. For control objectives, the piezoelectric actuator is attached to the external surface of the shell and the thin ring piezoelectric sensor is attached to the middle internal surface of shell. The effect of PID, feedback linearization and sliding mode control on the suppression of vibration for SFG cylindrical shell is presented.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.615-632
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• 1998

Soliton solutions of a class of generalized nonlinear evo-lution equations are discussed analytically and numerically which is achieved using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical dolutions and the interactions between the solitons for the generalized nonlinear Schrodinger equations. The characteristic behavior of the nonlinear-ity admitted in the system has been investigated and the soliton state of the system in the limit of $\alpha\;\longrightarrow\;0$ and $\alpha\;\longrightarrow\;\infty$ has been studied. The results presented show that soliton phenomena are character-istics associated with the nonlinearities of the dynamical systems.

• Coupled systems mechanics
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• v.2 no.2
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• pp.159-174
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• 2013

The present work aims at investigating the nonlinear dynamics, bifurcations, and stability of an axially accelerating beam with an intermediate spring-support. The problem of a parametrically excited system is addressed for the gyroscopic system. A geometric nonlinearity due to mid-plane stretching is considered and Hamilton's principle is employed to derive the nonlinear equation of motion. The equation is then reduced into a set of nonlinear ordinary differential equations with coupled terms via Galerkin's method. For the system in the sub-critical speed regime, the pseudo-arclength continuation technique is employed to plot the frequency-response curves. The results are presented for the system with and without a three-to-one internal resonance between the first two transverse modes. Also, the global dynamics of the system is investigated using direct time integration of the discretized equations. The mean axial speed and the amplitude of speed variations are varied as the bifurcation parameters and the bifurcation diagrams of Poincare maps are constructed.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.2
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• pp.141-147
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• 2000

The nonlinear response statistics of an autoparameteric system under broad-band random excitation is investigated. The specific system examined is a vibration absorber system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The jump phenomenon was found by Gaussian closure method under random excitation.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.399-409
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• 2007

In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.