Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1979"
TL;DR: In this paper, a method of model reduction for reducing a high-order transfer function to its low-order models is introduced based upon the stability-equation method. But the transfer functions of reduced orders are obtained directly from the pole-zero patterns of the stability equations of the original transfer function.
Abstract: A method of model reduction for reducing a high-order transfer function to its low-order models is introduced based upon the stability-equation method. The transfer functions of reduced orders are obtained directly from the pole-zero patterns of the stability-equations of the original transfer function. Comparisons with methods in the current literature are made. Extension of the proposed method to discrete systems is given.
196 citations
TL;DR: In this article, the same bond graph used to model the system can be used to derive a complete or reduced order observer, which uses derivative causality in a new way and in some cases, the effects of completely unknown disturbances may be accounted for.
Abstract: Bond graph modeling techniques yield state equations intimately related to energy storage in physical systems. The easy physical interpretation of the state variables from a bond graph model aids in the realization of modern automatic control schemes involving state variable feedback. When it is inconvenient or impossible or measure certain state variables, the useful device of an observer may be used to estimate the missing state variables. It is shown that the same bond graph used to model the system can be used to derive a complete or reduced order observer. The partial observers use derivative causality in a new way and in some cases, the effects of completely unknown disturbances may be accounted for.
59 citations
TL;DR: In this article, a two-axis model-machine is described using a bond graph and a power-conserving transformation between the electrical quantities of the armature windings of the model machine and those of the real three phase armatures windings is developed.
Abstract: The theory of transient operations of synchronous machines—the so called two-reaction theory—was developed during the years 1926–1938. Doherty, Nickle and Park made the first efforts to find a complete theory. The problem then was solved by Kron for a general rotating electrical machine. In this paper the two-axis-model-machine is described using a bond graph. An example is given in which state-space-equations and output-equations are derived from the bond graph. A power-conserving transformation between the electrical quantities of the armature windings of the model machine and those of the real three phase armature windings is developed. This transformation is shown as a displacement modulated transformer structure which is central to the bond graph model.
43 citations
TL;DR: In this paper, the length of time required for all n people to know all of the information in a group of n people is shown to be log(n, k) = ⌜logk+1n⌝.
Abstract: Suppose we have a group of n people, each possessing an item of information not known to any of the others and that during each unit of time each person can send all of the information he knows to at most other people. Further suppose that each of at most k other people can send all of the information they know to him. Determine the length of time required, f(n, k), so that all n people know all of the information. We show f(n, k) = ⌜logk+1n⌝.
We define g(n, k) analogously except that no person may both send and receive information during a unit time period. We show ⌜logk+1n⌝≤g(n, k)≤2⌜logk+1n⌝ in general and further show that the upper bound can be significantly improvea in the cases k = 1 or 2. We conjecture g(n, k) = bk logk+1n+0(1) for a function bk we determine.
42 citations
TL;DR: In this paper, the authors present a technique which produces explicit Lagrange or Hamilton equations for mechanism dynamics suitable for computer solution, which can be used to solve the Euler-Lagrange equation.
Abstract: The practical simplicity of obtaining equations of motion using the methods of Lagrange and Hamilton is lost in the algebra of the Euler-Lagrange equation when many nonlinear constraints exist among the physical coordinates in the energy state functions. Such is the case for mechanical systems containing kinematic mechanisms. This paper presents a technique which produces explicit Lagrange or Hamilton equations for mechanism dynamics suitable for computer solution. A general matrix description of mechanism kinematics and inertial properties permits the algebra of the reduction from physical to generalized coordinates to be performed symbolically or numerically by a digital computer. The physical inertia transformed into properties associated with the generalized coordinates of the mechanism displays both physical and artificial behavior to account for conservation of momentum, kinetic co-energy and energy. The method produces equations efficient for numerical calculation and provides insight into the complex inertial dynamics of mechanisms. Vector bond graphs provide a conceptual basis for the technique and describe the energetic structure of the equations. A numerical example illustrates the procedure and results.
37 citations
TL;DR: In this article, the problem of matching the transfer function matrix of a given two-dimensional (2D) system to that of a desired 2-D model using state feedback is considered.
Abstract: This paper considers the problem of matching the transfer function matrix of a given two-dimensional (2-D) system to that of a desired 2-D model using state feedback. The approach followed refers to systems having square transfer function matrices and reduces the problem to that of solving a linear system of equations. Furthermore, necessary and sufficient conditions are established for exact matching. An example is included to illustrate the proposed method.
29 citations
27 citations
TL;DR: The Graph-Theoretical Field Model (GTM) as mentioned in this paper provides a unifying approach for developing numerical models of field and continuum problems by deriving discrete statements of the physical laws which govern the field behaviour.
Abstract: The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure. This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.
23 citations
TL;DR: In this paper, a bond graph model is derived for the geometric constraints of a three-axis flight table, and a method is introduced to make the local dependent inertias computable.
Abstract: A bond graph model is derived for the geometric constraints of a three-axis flight table. Gimbal dynamics are easily added even in asymmetrical and unbalanced cases. A method is introduced to make the local dependent inertias computable. The bond graph compares favourably to the Lagrangian approach as to modelling effort and accessibility of intermediate variables as well as having computational advantages.
23 citations
TL;DR: In this paper, a procedure is presented whereby the control volume equations for one-dimensional, compressible gas dynamics are cast into first-order, state variable form using causal bond graphs.
Abstract: A procedure is presented whereby the control volume equations for one-dimensional, compressible gas dynamics are cast into first-order, state variable form. These equations are interpreted using causal bond graphs. The resulting bond graph is shown to reduce to the classic I-C chain under acoustic constraints and to a more recently developed model of low speed thermal energy transport subject to associated constraints. Through example it is demonstrated that the control volume bond graph is easily coupled to an overall system model and thus can be digitally simulated as part of the overall nonlinear state space representation. The result is that a very accurate gas dynamic model can be coupled with an overall dynamic system model without requiring a prohibitively large number of equations.
21 citations
TL;DR: A network thermodynamic method is presented which utilizes SPICE2, a computer program for simulating nonlinear electrical circuits, to model and simulate a number of nonlinear, dynamic physiological systems.
Abstract: A network thermodynamic method is presented which utilizes SPICE2, a computer program for simulating nonlinear electrical circuits, to model and simulate a number of nonlinear, dynamic physiological systems. Ordinary circuit diagrams are presented along with bond graph representations to facilitate translation into the simulation language. Examples discussed are a compartmental model of sodium flow in frog skin, coupled salt and volume flow in kidney proximal tubule and a cancer chemotherapeutic agent's permeation and metabolism in a cancer cell.
TL;DR: In this article, a composite stabilizing controller is synthesized from the separate stabilizing controllers of the two subsystems, the mutually independent gains of which do not require knowledge of the small singular perturbation parameter.
Abstract: The stabilization of a class of singularly perturbed linear time-varying systems is considered through the separate stabilization of two lower dimensional subsystems in two different time-scales. A composite stabilizing controller is synthesized from the separate stabilizing controllers of the two subsystems, the mutually independent gains of which do not require knowledge of the small singular perturbation parameter.
TL;DR: In this article, an extended definition of reciprocity for a multiport junction structure based on the concept of essential gyrator coupling is proposed, and two theorems are given for junction structures containing gyrators.
Abstract: This paper proposes an extended definition of reciprocity for a multiport junction structure based on the concept of essential gyrator coupling. Two theorems are given for junction structures containing gyrators and an algorithm is presented for identifying essential gyrators. The results are useful both theoretically and for designing efficient computation procedures for junction structures.
TL;DR: A method is given for estimating a probability density when the measurements are corrupted by additive noise, and this method is shown to be consistent, and several bounds on the error are given.
Abstract: The problem of the estimation of a discrete probability density from independent observations is considered. For a wide class of noises, a method is given for estimating a probability density when the measurements are corrupted by additive noise. This method is shown to be consistent, and several bounds on the error are given. An application to the detection of a (nonparametric) random signal is discussed. Finally, the estimation of a probability density is considered where the measurements are noisy and some of the measurements are incorrect. This situation may arise when a machine collecting the data fails part of the time.
TL;DR: In this paper, explicit expressions of transfer functions for digital tan filters with lowpass, high-pass, band-pass and band-stop characteristics approximating given design specifications are presented, which can be easily applied for the cascade or time-sharing realization.
Abstract: Explicit expressions of transfer functions for digital tan filters with low-pass, high-pass, band-pass, and band-stop characteristics approximating given design specifications are advanced. The higher order transfer function satisfying the design specification is expressed as the product of first-order and second-order filter sections of identical forms but with different coefficient values. All coefficients of these low-order filter sections are expressed in explicit forms related simply to the specification values. Thus, the result developed can be easily applied for the cascade or time-sharing realization. The low-order filter section developed here can be implemented with the fewest multipliers. The design formulae for Butterworth, Chebyshev, inverse Chebyshev and elliptic approximations are included. The transfer functions for all these filters are expressed in the same form of low-order filter section with different coefficient values.
TL;DR: In this article, the equations of motion of a flywheel were generated by using the Bolt-Graphs to generate the critical frequencies at which non-zero equilibrium configurations exist for displacements (as opposed to the more familiar momenta) and the system dynamics matrix of the complete whirl motion has two zero eigenvalues.
Abstract: Bond graphs are used to generate the equations of motion of a whirling flywheel. The formulation is shown to be a natural one when control forces and moments are included for active control of the whirling modes. Critical frequencies are interpreted as rotational speeds at which non-zero equilibrium configurations exist for displacements (as opposed to the more familiar momenta) and arise when the system dynamics matrix of the complete whirl motion has two zero eigenvalues. In addition, oscillatory modes corresponding to non-zero eigenvalues are examined. Time simulations and other numerical results are given for an example flywheel system which has been proposed for electric utility energy storage.
TL;DR: In this article, the authors describe the preparation of a dynamic model required for simulation of a 30 kW electro-hydraulic system used to induce controlled vibration of a wide range of components, machines or structures.
Abstract: The paper describes the preparation of a dynamic model required for simulation of a 30 kW electro-hydraulic system used to induce controlled vibration of a wide range of components, machines or structures. The vibrator system is associated with a 28 tonne seismic block. The model is highly detailed to allow study of the system to its dynamic performance limits of around 300 Hz. The model consists of nearly eighty equations some of them nonlinear and discontinuous. The paper describes the orderly development of the model emanating from the bond graph approach. Some simulation results, with limited experimental correlation, are included.
TL;DR: In this paper, a linear closed-loop Stackelberg strategy for singularly perturbed systems is proposed, and a procedure to obtain a well-posed formulation of the problem, where both fast and slow modes are available for measurements, is given.
Abstract: This paper is concerned with a linear closed-loop Stackelberg strategy for singularly perturbed systems. A procedure to obtain a well-posed formulation of the problem, where both fast and slow modes are available for measurements, is given.
TL;DR: In this paper, an algorithm for solving nonlinear two-point boundary value problems is described. But the algorithm is based on a computational method for finding the general solution of systems of ordinary differential equations used in conjunction with the multi-point quasilinearization method of Miele.
Abstract: Nonlinear two-point boundary value problems have always been difficult to solve. The difficulty is compounded if the problem tends to be inherently unstable. This paper describes an algorithm for solving such sensitive boundary value problems. The procedure is based on a computational method for finding the general solution of systems of ordinary differential equations used in conjunction with the multi-point quasilinearization method of Miele. The method is demonstrated by solving Troesch's problem and a singular perturbation problem.
TL;DR: In this paper, an equation for the roulette in complex polar form was derived for a closed plane curve with points whose x and y coordinates may separately be expanded in Fourier series as functions of the polar angle, assuming these expansions are valid.
Abstract: A large group of closed plane curves may be classified as roulettes, including epicycloids, hypocycloids, and related epitrochoids and hypotrochoids. The equation for the roulette in complex polar form shows that any roulette may be described by the vector sum of two vectors of specified constant magnitudes rotating with constant angular velocities. Methods for plotting, and for electronic display of roulettes are described. An equation is derived for a roulette approximation for an N-sided regular polygon. In particular, an application to two-dimensional potential theory is described and illustrated by consideration of the roulette approximation for a square as an equipotential curve, with derivation of equations for equipotential curves in the field surrounding the square. General equations are derived for given closed plane curves with points whose x and y coordinates may separately be expanded in Fourier series as functions of the polar angle, assuming these expansions are valid. It is shown that, in general, a closed plane curve may be considered as being described by an infinite sum of vectors, each rotating in a circle. Simplifying effects of symmetry about a polar axis and/or about the origin are discussed, and methods for harmonic analysis of a given closed plane curve with aid of an electronic calculator are described.
TL;DR: In this article, the anti-Lagrangian equations for RM (M-memristor) networks are introduced, and the form of transformation of variables leaving the form for equations invariant is studied.
Abstract: The explicit topological formulation of dynamic equations in terms of scalar functions for RM (M-memristor) networks, called the anti-Lagrangian equations, is introduced. In general, two scalar functions are needed to set the anti-Lagrangian equations. The differential operators acting on these functions bear a certain anti-symmetry relationship with respect to the operators occuring in the standard Lagrangian equations for LC networks. The well-known stationary principles for pure R networks, as well as new quasi-stationary principles for pure M networks are shown to emerge naturally from anti-Lagrangian equations. The form of transformation of variables leaving the form of equations invariant is also studied.
TL;DR: In this article, the dynamic modelling of dense nets, cloths, and gridworks is approached through Hamilton's principle and Fourier series, and the technique is examined in consequence of natural frequencies, travelling waves and wave propagation.
Abstract: The dynamic modelling of dense nets, cloths and gridworks is approached through Hamilton's principle and Fourier series. The technique is examined in consequence of natural frequencies, travelling waves and wave propagation. The model is checked with previously deducible results and it is shown that only a few terms of the Fourier series are necessary. The approach is readily extendible to laminates and to reinforcements.
TL;DR: In this paper, it is shown that a two-pole or 12 dB roll off model more accurately reflects the behaviour of the OA's for the above active-R realizations.
Abstract: Active-R filters are designed using internally compensated operational amplifiers (OA) and resistors only. A one-pole or 6 dB roll off model for the PA's is assumed in these designs. This model is adequate for active-RC filters. However, for active-R filters such an assumption leads to serious accuracy as well as stability problems, thereby limiting the highest operating frequency of these filters to well below their potential maximum. It is shown in this article that a two-pole or 12 dB roll off model more accurately reflects the behaviour of the OA's for the above active-R realizations. A quantitative measure of the limitation imposed by this model on such realizations is also presented. Extensive computer simulation and experimental tests have been carried out that verify closely the theoretical predictions.
TL;DR: In this paper, necessary and sufficient conditions for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade were obtained.
Abstract: Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of its transmission zeros either at the origin or at finity. Conditions are also obtained when each of the two-ports is a Fujisawa-type lowpass ladder.
TL;DR: In this paper, a closed-form analytical expression for evaluation of the output noise voltage of active-R filters has been developed, which is applicable to any low-pass, band-pass or high-pass two-amplitude active-r realization.
Abstract: A closed-form analytical expression for evaluation of the output noise voltage of active-R filters has been developed. The expression is applicable to any low-pass, band-pass or high-pass two amplifier second order active-R realization. The expression for the noise voltage has been derived in terms of the filter specifications and parameters of noise sources contained within the filter. Thus, it is very convenient for practical calculations. The expression is also useful for obtaining a design that minimizes the magnitude of the output noise. Experimental measurements indicate close agreement with the theroetical analysis.
TL;DR: In this article, the problem of least squares state estimation of stochastic continuous-time linear systems is reconsidered and a concise derivation of the least-squares minimal order estimator is presented using an innovations approach.
Abstract: The problem of least-squares state estimation of stochastic continuous-time linear systems is reconsidered. A concise derivation of the least-squares minimal-order estimator is presented using an innovations approach. An important result is the reinstatement of the problem in a least-squares estimation framework independent of deterministic observer theory. A second result is thus the clarification of previous approaches to the problem, particularly in relation to observer theory.
TL;DR: Transitional XY filters (TXY) are considered with characteristics that vary smoothly from those of filter X to those offilter Y as a parameter is varied continuously.
Abstract: Transitional XY filters (TXY) are considered with characteristics that vary smoothly from those of filter X to those of filter Y as a parameter is varied continuously. Emphasis is placed on transitional ultraspherical—Thomson (TUT) filters and transitional ultraspherical “ a ”-ultraspherical “ b ” (TABU) filters.
TL;DR: Experimental data relative to membrane mediated inhibition of protein synthesis by potassium carriers, dicyclohexyl-18-crown-6 and valinomycin are fitted to dynamical equations suggested from the bond graphs.
Abstract: Bond graphs are used in order to understand the mechanism of interaction of three important and inter-related processes of reticulocyte metabolism: potassium efflux through the cell membrane, ATP metabolism and protein synthesis. Experimental data relative to membrane mediated inhibition of this synthesis by potassium carriers, dicyclohexyl-18-crown-6 and valinomycin, are then fitted to dynamical equations suggested from the bond graphs.
TL;DR: In this paper, the graph theoretic aspects of controllability and observability are examined and related to the tensorial formulation of Part I of the paper Particular emphasis is given to the significance of the system digraph decomposition and the relevance of this to certain system algebraic properties of interest in control theory.
Abstract: The graph theoretic aspects of controllability and observability are examined and related to the tensorial formulation of Part I of the paper Particular emphasis is given to the significance of the system digraph decomposition and the relevance of this to certain system algebraic properties of interest in control theory