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Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1992"


Journal ArticleDOI
TL;DR: In this paper, an intrinsic Hamiltonian formulation of the equations of motion of network models of non-resistive physical systems is provided. But the connection between the Hamiltonian formalism and network dynamics is investigated through the representation of the invariants of the system.
Abstract: The aim of this paper is to provide an intrinsic Hamiltonian formulation of the equations of motion of network models of non-resistive physical systems. A recently developed extension of the classical Hamiltonian equations of motion considers systems with state space given by Poisson manifolds endowed with degenerate Poisson structures, examples of which naturally appear in the reduction of systems with symmetry. The link with network representations of non-resistive physical systems is established using the generalized bond graph formalism which has the essential feature of symmetrizing all the energetic network elements into a single class and introducing a coupling unit gyrator. The relation between the Hamiltonian formalism and network dynamics is then investigated through the representation of the invariants of the system, either captured in the degeneracy of the Poisson structure or in the topological constraints at the ports of the gyrative type network structure. This provides a Hamiltonian formulation of dimension equal to the order of the physical system, in particular, for odd dimensional systems. A striking example is the direct Hamiltonian formulation of electrical LC networks.

171 citations


Journal ArticleDOI
TL;DR: A game theoretic perspective is presented and analysed as the appropriate framework for the study of the flow control problem and a network—Pareto optimal solution—with two user optimal solutions—Nash and Stackelberg equilibria are compared.
Abstract: Multiple classes of traffic with differing and often conflicting requirements arise in an integrated telecommunications environment as users share the limited existing resources. In this paper, a game theoretic perspective is presented and analysed as the appropriate framework for the study of the flow control problem. Using the notion of power as the performance criterion, we compare a network—Pareto optimal solution—with two user optimal solutions—Nash and Stackelberg equilibria. The appropriateness of each solution is discussed given the operating characteristics of the system. A proposed greedy algorithm is shown to converge to the Nash equilibrium.

70 citations


Journal ArticleDOI
TL;DR: In this article, the authors used the conjugate gradient method to determine the unknown timewise variation of the strength of a plane surface heat source, located at a specified position inside a flat plate, from the knowledge of transient temperature measurements taken at one of the outer surfaces while both boundary surfaces are kept insulated.
Abstract: The conjugate gradient method is used to determine the unknown timewise variation of the strength of a plane surface heat source, located at a specified position inside a flat plate, from the knowledge of transient temperature measurements taken at one of the outer surfaces while both boundary surfaces are kept insulated. The advantage of the conjugate gradient method is that no a priori information is needed on the variation of the unknown quantity. The inverse analysis is performed by using the combination of the regular and modified conjugate gradient methods. The combined method is found to be more accurate than either of these two methods for the reason discussed in this work.

61 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a library of six types of joints that are common in building space mechanisms, which can be modeled using bond graph processors, or coded using any simulation language macro facility.
Abstract: The Karnopp-Margolis method of modeling mechanisms is not only intuitively appealing, but it is also equivalent to the classical Lagrangian multiplier approach that produces the dynamic equations in state space form (Zeid, Trans. ASME J. Dyn. Syst. Meas. Control , Vol. 111 , pp. 15–23, 1989 ). This paper details modeling space mechanisms and multibody systems using the Karnopp-Margolis method. A bond graph library is given for six types of joints that are common in building space mechanisms. These joints can be modeled using bond graph processors, or coded using any simulation language macro facility, and then stored in a library of joints. Using a suitable macro capability, bond graph processors, such as ENPORT or CAMP, can easily model multibody systems by using this library of joints. Moreover, bond graph models of joints may be used to investigate nonlinear properties of joints and to develop new types of joints.

45 citations


Journal ArticleDOI
TL;DR: In this paper, a simple strategy for the specified motion of a pendulum is given, motivated by engine cam-follower design, and the maximum value of the force required and the times at which these forces take place are determined.
Abstract: In many circumstances, it is desired to move a mass from one position to another without initiating a vibration in the mass being moved. Two such problems are considered here: the motion of a mass initiated by another mass, and the motion of a pendulum initiated by the specified motion of its support. In each case, it is desired that the system start at rest and come to rest in the second position. A simple strategy for the specified motion is given here. The method is motivated by engine cam-follower design. The force required to move the system in question is determined as well as the maximum value of the force required (and the times at which these forces take place) is determined.

45 citations


Journal ArticleDOI
TL;DR: In this paper, the authors propose to eliminate the derivative causality by defining an I-field or an IC-field using generalized momenta and (if necessary) generalized coordinates as is done when applying Lagrange's or Hamilton's equations.
Abstract: Dynamic system models involving rigidly coupled inertia elements often result in derivative causality problems when represented in bond graph form. This means that explicit state equations can only be obtained after algebraic manipulation. The problem is particularly severe when geometric nonlinearities are involved as represented by displacement modulated transformers. A practical solution is to eliminate the derivative causality by defining an I-field or an IC-field using generalized momenta and (if necessary) generalized coordinates as is done when applying Lagrange's or Hamilton's equations. The inversion of a mass matrix is required. In the worst case, the inversion may have to be done repeatedly during a computer simulation.

42 citations


Journal ArticleDOI
TL;DR: In this article, an algorithm for the causal augmentation of bond graphs with algebraic loops is given, which involves bond graph manipulation rather than equation-based manipulation, and a number of illustrative examples are given.
Abstract: An algorithm for the causal augmentation of bond graphs with algebraic loops is given. Unlike previous algorithms, this involves bond graph—rather than equation— manipulation. A number of illustrative examples are given.

36 citations


Journal ArticleDOI
TL;DR: In this article, a new approach to the input-output decoupling problem of linear time-invariant systems via proportional state and output feedback is presented, which reduces the solution of the decoupled problem to that of solving a linear algebraic system of equations.
Abstract: A new approach to the input-output decoupling problem of linear time-invariant systems via proportional state and output feedback is presented. A major feature of the proposed approach is that it reduces the solution of the decoupling problem to that of solving a linear algebraic system of equations. This system of equations greatly facilitates the solution of the following four major aspects of the decoupling problem: necessary and sufficient conditions, general analytical expressions for the controller matrices, general analytical expressions for the diagonal elements of the closed-loop system, and the structural properties of the closed-loop system.

30 citations


Journal ArticleDOI
TL;DR: In this paper, two techniques suitable for 2D separable-denominator digital filters are developed for synthesizing the filter structure with low sensitivity, one free from 12 scaling constraints on the state variables, and the other under the scaling constraints.
Abstract: This paper treats the coefficient sensitivity of two-dimensional (2-D) separable-denominator digital filters using the Roesser local state-space model. Two techniques suitable for 2-D separable-denominator digital filters are developed for synthesizing the filter structure with low sensitivity, one free from 12 scaling constraints on the state variables, and the other under the scaling constraints. In the paper, it is clarified that the filter structures with low sensitivity can be easily derived from the balanced realization. Finally, an example is given to illustrate the utility of the proposed techniques.

27 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe special magic labelings of vertices, edges and faces of a special class of plane graphs with 3-sided internal faces, in which the labels of nodes and edges incident with a face sum to a value prescribed for that face.
Abstract: The paper describes special magic labelings of vertices, edges and faces of a special class of plane graphs with 3-sided internal faces, in which the labels of vertices and edges incident with a face sum to a value prescribed for that face.

27 citations


Journal ArticleDOI
TL;DR: In this paper, a simple method based on the concept of contracted graphs is presented for the enumeration of basic kinematic chains with simple and multiple joints, and all possible acceptable contracted graphs are listed according to the numbers of links and degrees of freedom of basic Kinematic Chains.
Abstract: This paper presents a simple method, based on the concept of contracted graphs, for the enumeration of basic kinematic chains with simple and multiple joints. All possible acceptable contracted graphs are listed according to the numbers of links and degrees of freedom of basic kinematic chains. Next, vertices of degree two are added to each contracted graph to generate all possible kinematic chains. Then, degenerate and isomorphic kinematic chains are identified and deleted to obtain nonisomorphic, basic kinematic chains. The enumeration of one degree-of-freedom, eight-link basic kinematic chains is used as an example to illustrate the enumeration process. The result of this work is beneficial to the creative design of mechanisms.

Journal ArticleDOI
TL;DR: This method calculates a low order autoregressive moving average (ARMA) predictor equation from a high order ARMA equation that minimizes the sum of the squares of the prediction errors when the input is white noise.
Abstract: A model reduction method based on the least squares algorithm is derived. This method calculates a low order autoregressive moving average (ARMA) predictor equation from a high order ARMA equation. The low order ARMA equation minimizes the sum of the squares of the prediction errors when the input is white noise. This is almost equivalent to minimizing the sum of the squares of the error in the impulse response function. Transfer function models can also be used and a steady-state gain constraint can be incorporated into the procedure. The merits of this method of model order reduction are shown with three examples. In these examples, the proposed method produced results that compared favorably with highly regarded existing model reduction techniques which require many more computations.

Journal ArticleDOI
TL;DR: In this paper, conditions on the gains of finite-dimensional controllers such as proportional plus derivative controllers are developed to ensure the stability of the controlled process against delay variations, and these results are applied to the stability analysis and stabilization of the metal rolling process.
Abstract: The metal rolling process is modelled as a delay differential system with noncommensurate delays. Stability conditions for delay differential systems have been recently developed using asymptotic stability tests and the Lyapunov approach. These results are applied to the stability analysis and stabilization of the metal rolling process. Conditions on the gains of finite dimensional controllers such as proportional plus derivative controllers are developed to ensure the stability of the controlled process against delay variations.

Journal ArticleDOI
TL;DR: The robustness of this approach is illustrated by using a fully connected network that resembles a Hopfield network in this paper, where the authors show that it is possible to solve the system using connectionist paradigms.
Abstract: Fredholm integral equations of the first kind are examples of ill-posed problems in the Hadamard sense. Conventional methods of discretization often result in an ill-conditioned system of equations. The traditional approach is to solve this system using a variety of regularization schemes. An alternative is to solve the system using connectionist paradigms. The robustness of this approach is illustrated by using a fully connected network that resembles a Hopfield network.

Journal ArticleDOI
TL;DR: In this paper, the behavior of the radiated electric field from a half-wave dipole in free space excited by a single-cycle sinusoidal voltage was studied, and the zero-order approximate solution for the current along the antenna in the frequency domain was used, so that the time-dependent current as well as the r-electric field can be calculated and interpreted easily.
Abstract: The behavior of the radiated electric field from a half-wave dipole in free space excited by a single-cycle sinusoidal voltage is studied. The zero-order approximate solution for the current along the antenna in the frequency domain is used, so that the time-dependent current as well as the radiated electric field can be calculated and interpreted easily. Under a suitable matched condition, the time dependent current along each half-section of the dipole is made up of a current pulse traveling from the feed-point and a reflected one from the end-point. However, the radiated electric field consists of five overlapping signals exhibiting that radiation takes place only from the discontinuities of the dipole antenna. Both current and the radiated electric field are extended in time due to the reflection of current from the end-points of the dipole antenna. It appears that the spectral bandwidth of the radiated electric field is narrower than that of the exciting voltage pulse. This phenomenon may be due to the filtering effect of the half-wave dipole.

Journal ArticleDOI
TL;DR: In this paper, a graph notation is presented to clarify the kinematic structure of simple and compound differential gear trains efficiently, which can be applied to any type of differential gear train with any number of links by only knowing the gear ratios of all mating gears.
Abstract: This paper presents a new graph notation to clarify the kinematic structure of simple and compound differential gear trains efficiently. This graph notation is then used to derive the kinematic equations of differential gear trains. The absolute rotational speeds for simple and compound differential spur, helical- and bevel-gear trains can easily be determined without the need to develop any intermediate equations. The equation can be applied to any type of differential gear train with any number of links by only knowing the gear ratios of all mating gears.

Journal ArticleDOI
TL;DR: In this paper, a new definition of a "strictly positive real" function is presented, and is used to provide necessary and sufficient conditions for the exponential stability of a coupled system comprising a 1-port robot with a strictly positive real admittance, and a one-port environment with a positive real (but otherwise arbitrary) impedance.
Abstract: This paper builds upon recent work that has addressed the stability of a feedback- controlled robot coupled to a passive, dynamic environment. A new definition of a “strictly positive real” function is presented, and is used to provide necessary and sufficient conditions for the exponential stability of a coupled system comprising a 1-port robot with a strictly positive real admittance, and a 1-port environment with a positive real (but otherwise arbitrary) impedance. The distinction between the new definition and conventional definitions of a strictly positive real function is founded in physical systems theory; the new definition relies upon distinct roles for efforts and flows, and upon the concept of an excess state. This definition will provide a useful design constraint for the development of robust robot controllers.

Journal ArticleDOI
TL;DR: In this paper, the effect of matrix cracks on the eigenfrequencies of unsymmetrical, cross-ply laminates is investigated and the cracks are modelled as aligned slit cracks across the ply thickness and transverse to the laminate plane.
Abstract: The effect of matrix cracks on the eigenfrequencies of unsymmetrical, cross-ply laminates is investigated. The cracks are modelled as aligned slit cracks across the ply thickness and transverse to the laminate plane. The distribution of cracks is assumed statistically homogenous for a given average crack density. The results are given for antisymmetrically and unsymmetrically laminated plates. The effect of reduction in the laminate stiffness is studied by plotting the ratio of the fundamental and higher order frequencies of cracked and uncracked laminates against the aspect ratio, crack density and relative layer thicknesses. It is observed that the amount of reduction in the vibration frequencies is substantially less than the reduction in the affected elastic moduli of the material.

Journal ArticleDOI
Abstract: Vibration control of a horizontal rotor with an asymmetrical moment of inertia is investigated. A linear optimal control system is developed to stabilize and control the rotor system by using the mathematical model of a rotor system expressed in the rotating coordinates. An approximated dynamical equation of a long rotor system is derived and used to obtain the compensator in analytical form (which saves much computational effort in control design), and is particularly useful in hardware implementation. Simulation results show the efficiency of the proposed strategy. The influences of weighting matrices and the effects of the asymmetrical moment of inertia on system performance for different controllers are also assessed.

Journal ArticleDOI
TL;DR: In this paper, the optimal heating rate for a plate with temperature dependent thermal conductivity and two internally located continuous plane heat sources of different strength was determined that at the final specified time tf, the final tempererature distribution in the slab approximated as closely as possible a specified uniform temperature Td with a minimum amount of energy used for the heating.
Abstract: The optimal heating rate for a plate with temperature dependent thermal conductivity and two internally located continuous plane heat sources of different strength is so determined that at the final specified time tf, the final tempererature distribution Tf in the slab approximated as closely as possible a specified uniform temperature Td with a minimum amount of energy used for the heating. The locations and the timewise variation of the strengths of the plane heat sources satisfying such requirements are determined.

Journal ArticleDOI
TL;DR: In this paper, a combination of Eulerian and Lagrangian frames of reference is used to determine the convected entropy flows and to further the complete interaction of the variables, as demonstrated by a simple example.
Abstract: Compressible fluid in pipes transports several energy domains, well represented by multi-bondgraphs, where the standard marks, causality, power direction and activation display the structure of the underlying equations. Basic components are resistors from which heat exchangers and thermofluid machines (turbines) follow by extension. They are interconnected by thermofluid multiport accumulators that provide computable causalities. Causalities and equations follow from consideration of the number of degrees of freedom related to the number of state variables; they lead to a combination of Eulerian and Lagrangian frames of reference. Power conservation allows one to determine the convected entropy flows and to further the complete interaction of the variables, as demonstrated by a simple example.

Journal ArticleDOI
TL;DR: In this paper, a unified procedure to solve any remainder problem for the unknown number using the spirit of the Theorem is presented, given any divisors and their corresponding remainders.
Abstract: The Chinese Remainder Theorem dates back to the first century. In this paper we provide a unified procedure to solve any remainder problem for the unknown number using the spirit of the Theorem. Given any divisors and their corresponding remainders, this unified procedure leads to the unknown number. Examples are given to cover different cases.

Journal ArticleDOI
TL;DR: In this article, the authors derived analytical expressions for the acoustic eigenfrequencies and modes in a soft-walled spherical cavity with an eccentric inner acoustically small sphere.
Abstract: Analytical expressions are derived for the acoustic eigenfrequencies and modes in a soft-walled spherical cavity with an eccentric inner acoustically small sphere. A straightforward and very simple approach is employed to obtain a first-order perturbation of the cavity eigenfunctions and the corresponding eigenfrequency shifts. The results are useful in a variety of problems connected with acoustic levitation and with excitation or probing of resonant cavities. Some suggestions are made about the best positioning of the probe, for more exact measurement of the eigenfrequency of any mode in the unperturbed cavity. Graphical results for some of the lower-order modes are given for various values of the parameters.

Journal ArticleDOI
TL;DR: In this article, the drift velocity, mean energy and ionization coefficients in nitrogen are re-evaluated using the Monte Carlo technique over the range of 50 ⩽ E/N/N⩽ 560 Td.
Abstract: The drift velocity, mean energy and ionization coefficients in nitrogen are re-evaluated using the Monte Carlo technique over the range of 50 ⩽ E/N ⩽ 560 Td Recently published data on cross-sections, including ten vibrational levels and eighteen excitation levels, are used in the simulation for the first time The theoretical swarm parameters agree very well with experimental and other theoretical results with only a slight modification of the cross-sections New data on collision frequencies for ionization, dissociation and various excitation states are reported

Journal ArticleDOI
T.N. Lucas1
TL;DR: In this article, a tabular method for reducing polynomial degrees by the stability equation criterion is given, which is the consequence of an interesting multipoint Taylor approximation property which is shown to hold for the method.
Abstract: A tabular method for reducing polynomial degrees by the stability equation criterion is given. It is the consequence of an interesting multipoint Taylor polynomial approximation property which is shown to hold for the method. The resulting iterative Routh- type algorithm is easily applied to the system transfer function numerator and denominator polynomials and does away with the need to employ time-constant form and root-finding methods. Numerical examples are given to illustrate the new approach.

Journal ArticleDOI
TL;DR: A speaker-dependent, isolated-word speech recognition system is presented which is based on the use of the fast Fourier transform for extracting features from the speech input and compares them against previously stored word templates using dynamic time warping to identify the uttered word.
Abstract: A speaker-dependent, isolated-word speech recognition system is presented which is based on the use of the fast Fourier transform for extracting features from the speech input. The algorithm then normalizes those features and compares them against previously stored word templates using dynamic time warping in order to identify the uttered word. The system has been successfully implemented and provided good results when tested using a small dictionary.

Journal ArticleDOI
TL;DR: In this article, the combined use of the time moment and Pade approximation methods (in time space and frequency domain description), coupled with three powerful dominant pole selection criteria, is introduced for the purpose of application to high-order MIMO linear time-invariant state-space original system models, in order to obtain corresponding adequate reduced order model(s).
Abstract: The combined use of the time moment and Pade approximation methods (in time space and frequency domain description), coupled with three powerful dominant pole selection criteria, is introduced for the purpose of application to high-order MIMO linear time-invariant state-space original system models, in order to obtain corresponding adequate reduced order model(s). The proposed approach has been applied successfully to a 10 th-order two-input two-output time-invariant linear model of a practical power system.

Journal ArticleDOI
TL;DR: In this paper, a graph-theoretical approach was used to derive general formulae for potential energies of gravity and elastic forces as well as for the generalized forces related to both potential and nonpotential forces acting on a system of particles.
Abstract: The process of determining the generalized forces (as a function of generalized coordinates and system parameters) of a system consisting of mass particles and springs is often extremely laborious. In this paper, a method is presented where the derived formulae have a form of evident functions not only of generalized coordinates and system parameters but also of the topological structure of a system. This paper contains the derivation of general formulae for potential energies of gravity and elastic forces as well as for the generalized forces related to both potential and nonpotential forces acting on a system of particles. It is assumed that the system of particles has a topological tree structure, and that linear springs are situated arbitrarily between the particles. The method is based on a graph-theoretical approach and is consistent with the kinetic energy calculation presented in Arczewski (J. Franklin Inst. , Vol. 329 , pp. 469–481, 1992) .

Journal ArticleDOI
TL;DR: In this paper, reduction formulas and integral representations for Kampe de Feriet functions Fp:2;1q:1;0 which are associated with certain classes of incomplete integrals of Bessel or cylindrical functions (including, for example, incomplete Lipschitz-Hankel integrals) are obtained.
Abstract: Reduction formulas and integral representations for Kampe de Feriet functions Fp:2;1q:1;0 which are associated with certain classes of incomplete integrals of Bessel or cylindrical functions (including, for example, incomplete Lipschitz—Hankel integrals) are obtained. In addition, more general series identities related to these Kampe de Feriet functions are derived and a new derivation of Lerch's theorem for the partial sums of the coefficients of a special case of Gauss's hypergeometric function is provided.

Journal ArticleDOI
TL;DR: In this article, a graph-theoretical approach for equation-of-motion derivation for open kinematic chains of particles is presented. But the method is not consistent with the kinetic energy and generalized forces calculation presented in Arczewski's paper.
Abstract: This paper presents a new algorithm of the equation-of-motion derivation for open kinematic chains of particles. It contains a derivation of equations of motion and two examples for their application. The method is based on the graph-theoretical approach and is consistent with the kinetic energy and generalized forces calculation presented in Arczewski (J. Franklin Inst. , Vol. 329 , pp. 469–481 and pp. 483–491, 1992) .