• Journal of Institute of Control, Robotics and Systems
• /
• v.12 no.5
• /
• pp.497-504
• /
• 2006

This paper presents a new technique that derives the dynamic acceleration bounds of multiple cooperating robot systems from given individual torque limits of robots. A set of linear algebraic homogeneous equation is derived from the dynamic equations of multiple robots with friction contacts. The mobility of the robot system is analyzed by the decomposition of the null space of the linear algebraic equation. The acceleration bounds of multiple robot systems are obtained from the joint torque constraints of robots by the medium of the decomposed null space. As the joint constraints of the robots are given in the infinite norm sense, the resultant acceleration bounds of the systems are described as polytopes. Several case studies are presented to validate the proposed method in this paper.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.3
• /
• pp.263-269
• /
• 1999

In this paper, an unifying design algorithm is presented for efficient digital implementation of continuous PID controller using general discrete orthogonal functions. The proposed algorithm is an algebraic method to determine controller parameters, which can unify controller design procedures divided into three ways. A set of linear equations for the controller design are derived from simple algebraic transformation based on general discrete orthogonal functions. By solving these equations, all of the controller parameters can be determined directly and simultaneously, which thus makes the design procedure systematic and straightforward. It does not involve any trial and error procedure, hence the difficulty of conventional approach can be avoided. The simulation results and discussions are given to demonstrate the efficiency of the proposed method.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2001.09a
• /
• pp.117-124
• /
• 2001

A simplified method fur the eigenpair sensitivities of damped system with multiple eigenvalues is presented. This approach employs a reduced equation to determine the sensitivities of eigenpairs of the damped vibratory systems with multiple natural frequencies. In the proposed method, adjacent eigenvectors and orthonormal conditions are used to compute an algebraic equation whose order is (n+m)x(n+m), where n is the number of coordinates and m the number of multiplicity of multiple natural frequencies. The proposed method is an improved Lee and Jung's method which was developed previously. Two equations are used to find eigenvalue derivatives and eigenvector derivatives in Lee and Jung's method. A significant advantage of this approach over Lee and Jung's method is that one algebraic equation newly developed is enough to compute such eigenvalue derivatives and eigenvector derivatives. This method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters. To demonstrate the theory of the proposed method and its possibilities in the case of multiple eigenvalues, the finite element model of the cantilever beam and 5-DOF mechanical system in the case of a non-proportionally damped system are considered as numerical examples. The design parameter of the cantilever beam is its height. and that of the 5-DOF mechanical system is a spring.

• Journal of the Korean Society for Precision Engineering
• /
• v.12 no.5
• /
• pp.57-68
• /
• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.579-587
• /
• 2012

A fourth-order family of triparametric extensions of Jarratt's method are proposed in this paper to find a simple root of nonlinear algebraic equations. Convergence analysis including numerical experiments for various test functions apparently verifies the fourth-order convergence and asymptotic error constants.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.26 no.1
• /
• pp.122-128
• /
• 1989

In this paper we propose a new method for solving a set of nonlinear algebraic equations encountered in the DC and transient analyses of electronic circuits. This method will be called Quadratic Newton-Raphson Method (QNRM), since it is based on the Newton-Raphson Method (NRM) but effectively takes into accoujnt the second order derivative terms in the Taylor series expansion of the nonlinear algebraic equations. The second order terms are approximated by linear terms using a carefully estimated solution at each iteration. Preliminary simulation results show that the QNRM saves the overall computational time significantly in the DC and transient analysis, compared with the conventional NRM.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2009.04a
• /
• pp.135-138
• /
• 2009

Most of the studies use model order reduction for low frequency (LF) response analysis due to their high computational efficiency. In LF response analysis, one of model order reduction, algebraic substructuring (AS) retains all LF modes when using the modal superposition. However, in mid-frequency (MF) response analysis, the LF modes make very little contribution and also increase the number of retained modes, which leads to loss of computational efficiency. Therefore, MF response analysis should consider low truncated modes to improve the computational efficiency. The current work is focused on improving the computational efficiency using a AS and a frequency sweep algorithm. Finite element simulation for a MEMS resonator array showed that the performance of the presented method is superior to a conventional method.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.6
• /
• pp.1000-1006
• /
• 2007

This paper presents a methodology to calculate an optimal solution of equilibrium to differential algebraic equations for power systems. It employs a nonlinear interior point method to solve the optimization formulation which includes dynamic equations representing the two-axis synchronous generator model with AVR and speed governing controls, algebraic equations, and steady-state nonlinear loads. This paper also adopts two algorithms for the improvement of solution convergence. In power system analysis and control, equilibrium optimization (EOPT) is applicable for diverse purposes that need the consideration of dynamic model characteristics at a steady-state condition.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.2
• /
• pp.161-171
• /
• 1999

Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.1113-1118
• /
• 2004

This paper presents the dynamic analysis method for an electromechanical system. The engineer has at his disposal a variety of software simulation tools. However, difficulties arise when the study of the behavior of complex electromechanical systems in combination with coupling element is required. Typical examples of such systems are machines for factory automation, home automation, and office automation. Dynamic systems analysis packages or electronic systems analysis packages offer the restrictive to simulate these mixed systems such electromechanical product. Electronic circuit analysis algorithm is easily incorporated into a multi-body dynamics analysis algorithm. The governing equation of electronic circuit is formulated as a differential algebraic equation form including both electrical and mechanical variables and is simultaneously solved in every time step. This analysis method clearly demonstrates the application potential for mixed electromechanical simulation.