Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1981"
TL;DR: In this paper, the authors show how the bond graph methods used for conductive and convective heat transfer can be generalized to account for diffusion, convection, and accumulation of a variety of physical quantities and how pseudo bond graphs can aid in constructing and representing such models.
Abstract: True bond graphs, which use effort and flow variables whose product is power, can in principle be used to describe all types of physical systems. However, many system models do not use power variables and yet can be represented usefully as pseudo bond graphs. Pseudo bond graphs have been used particularly for open systems in which it is convenient to consider control volumes or compartments with boundaries across which mass can flow. In this paper, we show how the bond graph methods used for conductive and convective heat transfer can be generalized to account for diffusion, convection, and accumulation of a variety of physical quantities and how pseudo bond graphs can aid in constructing and representing such models. These models are known in mathematical biology as “compartmental models” and it is a main contribution of this paper to show that the same pseudo bond graphs apply to thermofluid and physiological dynamic models. The bond graphs build in some conservation principles automatically and yet have the flexibility to incorporate general multiport laws when necessary. Thus the pseudo bond graphs can exhibit system structure as do other network graphs and are very general in nature.
29 citations
TL;DR: Macagno as mentioned in this paper traced the origin of the concept of physical dimensions back to ideas previously used in analytic geometry and showed that the principle of homogeneity was used in the derivation of physical equations sixty years prior to the publication of Fourier's work and that the latter was aware of this paper, that may be considered the earliest publication on dimensional analysis.
Abstract: A paper by Macagno (3) in this Journal is discussed. The origin of the concept of physical dimensions is traced back to ideas previously used in analytic geometry. Descartes' use of the word “dimension” in the study of physical magnitudes is shown to have properties completely different from Fourier's dimensions, being therefore unimportant to the evolution of dimensional analysis. It is also shown that the principle of homogeneity was used in the derivation of physical equations sixty years prior to the publication of Fourier's work, and that the latter was aware of this paper, that may be considered the earliest publication on dimensional analysis.
29 citations
TL;DR: In this paper, a new combined time and frequency domain method for the model reduction of discrete systems in z-transfer function is presented, which preserves both frequency domain and time domain characteristics of the original systems.
Abstract: A new combined time and frequency domain method for the model reduction of discrete systems in z-transfer function is presented. First, the z-transfer functions are transformed into the w-domain by the bilinear transformation, z = (1+w)/(1−w). Then, four model reduction methods—Routh approximation, Hurwitz polynomial approxima- tion, stability equation, and retaining dominant poles—are used respectively to reduce the order of the denominator polynomials in the w-domain. Least squares estimate is then used to find the optimal coefficients in the numerator polynomials of the reduced models so that the unit step response errors are reduced to a minimum. The advantages of the proposed method are that both frequency domain and time domain characteristics of the original systems can be preserved in the reduced models, and the reduced models are always stable provided the original models are stable.
18 citations
TL;DR: In this article, the scattering of plane electromagnetic waves from eccentrically coated metallic spheres is considered, and the solution is obtained in terms of spherical vector wave functions in conjunction with related addition theorems.
Abstract: In this paper the scattering of plane electromagnetic waves from eccentrically coated metallic spheres is considered. Inhomogeneous, surface, singular integral equations are used to formulate the problem. Their solution is obtained in terms of spherical vector wave functions in conjunction with related addition theorems. Analytical, closed-form results are obtained in the case of small eccentricities kd , where d is the distance between the two centers and k the wave number of the dielectric coating. Thus the scattered field and the various scattering cross-sections of the problem are given by expressions of the form: S(d) = S(0)[1+g’(kd)+g”(kd) 2 +0(kd) 3 ] . Numerical and graphical results for various values of the parameters are also discussed.
18 citations
TL;DR: In this paper, a new method is employed to identify the unknown parameters of a bilinear system, which expands the system input and output by block pulse functions and reduces the original identification problem to an algebraic form.
Abstract: A new method is employed to identify the unknown parameters of a bilinear system. This method expands the system input and output by block pulse functions and reduces the original identification problem to an algebraic form. Furthermore, the dyad formed by block pulse functions and its integral are in diagonal forms, whereas the integration of the “triple-product” matrix can be reduced to the upper triangular form. Consequently, only very few calculations are required to find the solution for the algebraic equation. Two examples are given to show that the use of this method is considerably more economical in computation time than the use of Walsh function expansion.
15 citations
TL;DR: Under the criterion of asymptotic relative efficiency, it is shown that this design of detectors for strong mixing signals in strong mixing noise reduces to determining the solution of an integral equation, where only knowledge of the second order statistics of the randon processes involved is required.
Abstract: Design of detectors for strong mixing signals in strong mixing noise is considered, where a large degree of dependency may occur between the signal and noise. Under the criterion of asymptotic relative efficiency, it is shown that this design reduces to determining the solution of an integral equation, where only knowledge of the second order statistics of the randon processes involved is required. In particular, if the signal is independent of the noise and has nonzero mean, the optimal detector is the same as in the known constant signal case. It is also shown that it is possible to delete several regularity conditions which may be difficult to check in practice in the slightly more restrictive case where the maximal correlation coefficients of the signal and noise tend to zero.
14 citations
TL;DR: In this paper, a single mass flexible rotor on rigid supports with proportional and derivative feedback control was considered and the rotor-control system was considered as well as unbalance response and the results indicated that proportional control alone increases the rotor critical speed, but does not affect the system damping.
Abstract: This paper considers a single mass flexible rotor on rigid supports with proportional and derivative feedback control Undamped and damped free vibrations of the rotor-control system are considered as well as unbalance response Results indicate that proportional control alone increases the rotor critical speed, but does not affect the system damping Proportional control alone also decreases the system logarithmic decrement which tends to make the system more susceptible to external vibration excitations Derivative feedback control acts to increase the system damping, to reduce the response sensitivity, and is highly desirable
13 citations
TL;DR: Current research involving error and sensitivity analysis approaches useful for the design of aids for planning and decision support is surveyed, with one of the major uses for sensitivity analysis type results being in bounded prioritization of alternatives using ordinal information.
Abstract: This paper surveys contemporary research involving error and sensitivity analysis approaches useful for the design of aids for planning and decision support. Discussed are structural sensitivity considerations as well as the effects of errors, for both single and multi-attribute cases, in estimation or elicitation of probabilities and utilities. One of the major uses for sensitivity analysis type results is in bounded prioritization of alternatives using ordinal information. This use of sensitivity analysis is discussed and illustrated with examples.
13 citations
TL;DR: The degree of suboptimality is established as an index of both the system performance regarding the optimality criterion and the robustness to uncertainties in the interconnections among the subsystems as well as distortions of the individual control laws, raising further the confidence in suboptimal designs of large-scale systems.
Abstract: The purpose of this paper is to consider sensitivity of suboptimal decentralized control schemes for large-scale systems composed of interconnected subsystems It is shown that sensitivity of suboptimal systems with respect to distortions in the local control laws can be expressed in terms of the classical notions of the gain and phase margin measured directly by the degree of suboptimality of the decentralized control This establishes the degree of suboptimality as an index of both the system performance regarding the optimality criterion and the robustness to uncertainties in the interconnections among the subsystems as well as distortions of the individual control laws, thus raising further the confidence in suboptimal designs of large-scale systems
13 citations
TL;DR: The superiority of direct analog-to-digital transformation to the Constantinides approach is proven.
Abstract: The theoretical basis for the design of analog and digital filters by prototype and transformation is studied. Necessary and sufficient conditions are developed for a transformation to preserve realizibility as well as the frequency response. The attendant structural properties of such transformations are developed and compared with the reactance transformations of classical analog filter theory. The superiority of direct analog-to-digital transformation to the Constantinides approach is proven.
12 citations
TL;DR: Two different bond-graph schemes for the modeling of circulating fluids are discussed and compared in this article, where the flow path is broken into segments and each segment has separate hydraulic and thermal submodels which are linked with active bonds.
Abstract: Two different bond-graph schemes for the modeling of circulating fluids are discussed and compared. The first uses a heuristic approach wherein the flow path is broken into segments. Each segment has separate hydraulic and thermal submodels which are linked with active bonds. The model is general enough to handle natural convective flows, heat storage, conduction, forced convective heat transfer and heat energy sources. The second method, applicable to pumped flows, uses a modal analysis approach to derive state equations for the modal temperatures, the time varying coefficients of the spatially varying mode shapes in a separation of variables solution for the temperature partial differential equation. Two examples are worked to illustrate the models. Numerical simulation results are presented using the first method and a simple analytic solution given to illustrate the second.
TL;DR: In this paper, the probability of wheel climb commencing is calculated using Nadal's formula as a basis, which is maintained with normal probability density functions used to describe the two arguments in the formula, namely contact plane angle and coefficient of friction at the contact point.
Abstract: The probability of wheel climb commencing is calculated using Nadal's formula as a basis. In particular, the functional form of Nadal's formula is maintained with normal probability density functions used to describe the two arguments in Nadal's formula, namely contact plane angle and coefficient of friction at the contact point. The theoretical value of the probability of wheel climb commencing for a given lateral/vertical force ratio value at the wheel flange–railhead interface is then compared with experimental results for positive angles of attack. Theoretical results for negative angles of attack are generated for several cases.
TL;DR: In this paper, the properties of special pairs of tree counting polynomials that relate to a class of incomplete graphs and their complements are presented, which are related by the previously defined binary complementing operation.
Abstract: The properties of special pairs of tree counting polynomials that relate to a class of incomplete graphs and their complements are presented. These polynomial pairs are related by the previously defined binary complementing operation.In contrast with alternative graph representations, they offer the possibility of serving as a convenient signature for the specific configurations. In Part II, a new constructive procedure is presented for deriving these polynomials. It is shown that the new algorithmic approach facilities obtaining the polynomials for cases not readily obtained by use of generic factors of the basic subgraphs.
TL;DR: In this article, a computer-aided method for simplification and identification of linear discrete systems via step-response matching is presented, where Golub's algorithm for solving least squares problem is used to find the optimum coefficients of the reduced model.
Abstract: A computer-aided method for simplification and identification of linear discrete systems via step-response matching is presented. Golub's algorithm for solving least-squares problem is used to find the optimum coefficients of the reduced model. The advantages of this method are (1) for model reduction, both the time response and frequency response within the bandwidth region of the reduced model are very close to those of the original system; and (2) for system identification, the identified model is very close to the original system. In the illustrative examples considered in this paper the results of the proposed method appear to be better than those of other methods in the current literature.
TL;DR: A floating-point arithmetic unit (FPAU), based on the residue number system, is reported which can perform addition, subtraction and multiplication and it will be shown that by using parallel small word-length architectures, a high speed FPAU can be realized.
Abstract: A floating-point arithmetic unit (FPAU), based on the residue number system, is reported which can perform addition, subtraction and multiplication. As a result, several classic problems associated with RNS based digital filters such as: overflow detection, sign detection and non-integer filter coefficients are overcome by virtue of thefloating-point representation of rational numbers over a large dynamic range. The FPAU has potential applications in computing, digital filtering, and implementing high speed, high precision Fast Fourier Transform (FFT) and Winograd Fourier Transform (WFTA). It will be shown that by using parallel small word-length architectures (viz. microprocessors), a high speed FPAU can be realized.
TL;DR: A simple numerical method for computing the time domain response of linear time invariant systems described by their transfer functions is presented, equivalent to very high order, absolutely stable numerical integration.
Abstract: A simple numerical method for computing the time domain response of linear time invariant systems described by their transfer functions is presented. The method does not require computation of transfer function poles or residues; it is not influenced by the multiplicity of poles or zeroes, nor does it require computation of the matrix exponential. Rather, it is based on a numerical method for inverting Laplace transforms. It is equivalent to very high order, absolutely stable numerical integration. Stiff systems present no problems.
TL;DR: In this paper, some generalizations of the classical ruin problem in probability theory are investigated and applied to analyze the sequential dead-zone limiter detector and the sequential four-level sign detector.
Abstract: Some generalizations of the classical ruin problem in probability theory are investigated and are applied to analyze the sequential dead-zone limiter detector and the sequential four-level sign detector. The performances of these detectors are then compared to that of the sequential sign detector in terms of the relative efficiency (RE) and the asymptotic relative efficiency (ARE).
TL;DR: In this article, the authors describe the optimal power flow problem and progress toward its solution since its inception in theory to its present form and present and future applications of Optimal Power Flow programs in system planning and system operations and control.
Abstract: This paper describes the Optimal Power Flow problem and progress toward its solution since its inception in theory to its present form. Present and future applications of Optimal Power Flow programs in system planning, and system operations and control will be presented. The sensitivity calculation and application to optimal power flow theory will be presented.
TL;DR: In this paper, the use of amplitude modulation (AM) techniques for frequency conversion in high power applications is subject to certain severe restrictions of performance, which can be largely overcome by using phase modulation (PM) methods which involve two channels of AM in each electrical supply line.
Abstract: Load voltage waveforms corresponding to symmetrical phase-angle triggering and integral-cycle triggering in single-phase thyristor circuits, and also the waveform due to half-wave rectification, are all discrete forms of amplitude modulation In each case the modulated output voltage is obtained from a sinusoidal (supply) carrier signal by use of a rectangular modulating function, dependent on thyristor switching The use of amplitude modulation (AM) techniques for frequency conversion in high power applications is subject to certain severe restrictions of performance These restrictions can be largely overcome by the use of phase modulation (PM) methods which involve two channels of AM in each electrical supply line Appropriate waveforms may be realised by the use of controlled switching of thyristors These are arranged in combinations of inverse-parallel connected pairs forming subtractor modulators Certain thyristor commutation problems arise in PM systems at high power levels These problems can be overcome by producing so-called AM/PM waveforms that combine the separate advantages of AM and PM systems
TL;DR: In this paper, it was shown that a homogeneous two-variable Reactance Function (HTRF) can be expressed as a product of linear factors in the two-variables.
Abstract: It is shown in this paper that Homogeneous Two-variable Reactance Polyno- mials (HTRP's) can be expressed as a product of linear factors in the two-variables. Further, a Homogeneous Two-variable Reactance Function (HTRF) can be characterized in terms of the alteration property involving the coefficients of the linear factors of the HTRP in the numerator and denominator. Synthesis procedures for HTRF's are discus- sed; these realizations follow from the single variable RL- or RC-functions associated with a HTRF. Additional properties of HTRF, which will enable us to generate Two- variable Positive Real Functions and Two-variable Reactance Functions are also discussed.
TL;DR: In this article, the Lanchester attrition-rate coefficients are used to predict the outcome of a combat between two homogeneous military forces modelled by variable-coefficient Lanchester-type equations for area fire.
Abstract: New important battle-outcome-prediction conditions are developed for combat between two homogeneous military forces modelled by variable-coefficient Lanchester-type equations for area fire. Such conditions are very significant in modern operations research for developing important insights into the dynamics of combat. However, similar differential-equation models do arise in other fields of science and technology such as mathematical ecology and epidemiology, and consequently our new mathematical results may also find application there. These new important “simple approximate” battle-outcome-prediction conditions depend on not only the combat-attrition model but also the battle-termination model, and they are developed for two different types of battle-termination conditions (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). They are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and a generalization of Lanchester’s famous linear law to variable-coefficient combat is involved in their development. Certain integrability properties of the Lanchester attrition-rate coefficients figure prominently in these results, and an important physical interpretation (relating to logistics considerations) is given for these properties.
TL;DR: In this paper, a general bond graph model for a variable-ratio power transmission mechanism is proposed, where the characteristics of the energy storage element in conjunction with a single velocity (or torque) input and the external load fully determine the dynamic behavior of the device.
Abstract: Kinematically constrained motion is generally accepted as a fundamental requirement for a mechanism to function as a power transmitting device. There exists, however, a class of mechanism which although kinematically unconstrained, can, by incorporation of energy storage elements, function as a power transmitter. An example of such a mechanism is the automatic, variable ratio power transmission invented in the early twenties by G. Constantinesco, which generated a lot of interest among the engineering fraternity at the time. A typical device consists of a crank-driven nine-bar mechanism which possesses two degrees of mobility. The single velocity (or torque) source supplies the input power, which is transmitted to the output shaft by means of unidirectional drives. The characteristics of the energy storage element in conjunction with a single velocity (or torque) input and the external load fully determine the dynamic behavior of the device. During operation, the input energy is distributed between the load and the energy storage depending on the requirements of the load. For a given input power and external load, the device will adjust the velocity of the output shaft to absorb that power; i.e., it will operate as an automatic, variable ratio power transmission. This paper concentrates on the formulation of a general bond graph model for the mechanism. The model possesses mixed causality and non-linear structure. Some results of digital simulation of the bond graph model of a particular mechanism are provided.
TL;DR: In this article, a method for obtaining restrictions of the derivative of Positive Real Functions (Dissipative Operators) is proposed, where the coefficients of the Taylor expansion of PRF (driving point impedance or admittance) must satisfy certain derived inequalities.
Abstract: Dissipative operators appear in abundance in the study of dynamical systems. In the classical circuit theory they are presented as Positive Real Functions. The coefficients of the Taylor expansion of PRF (driving-point impedance or admittance) must satisfy certain derived inequalities. A method is suggested for obtaining restrictions of the derivative of Positive Real Functions (Dissipative Operators).
TL;DR: In this paper, a general class of the linear time-invariant multivariable two-dimensional (2-D) digital systems using state feedback is analyzed and studied, where the initial conditions of the system are assumed to be random processes with known mean and covariance.
Abstract: The problem analyzed and studied in this paper refers to a general class of the linear time-invariant multivariable two dimensional (2-D) digital systems using state feedback A growing interest has developed over the past few years into problems involving signals and systems that depend on more than one variable In order to be able to give a quantitative formulation of the problem, the mathematical model is either assumed or derived In either case there is always a discrepancy between the actual system and its mathematical model However, once a realistic model is chosen, sensitivity plays an important role in assessing the behavior of the system or its components under varying conditions It is shown here that using matrix minimization techniques we can derive a set of non-linear matrix equations which constitute the necessary conditions that must be satisfied for an optimal low sensitivity solution for a general class of multivariable systems The initial conditions of the system are assumed to be random processes with known mean and covariance and the low sensitivity input vector is implemented via state feedback
TL;DR: In this article, a general procedure is outlined for obtaining single or coupled transmission line models to represent the propagation of surface wave modes in conductively unshielded dielectric waveguides.
Abstract: A general procedure is outlined for obtaining single or coupled transmission line models to represent the propagation of surface wave modes in conductively unshielded dielectric waveguides. The procedure uses a homogeneous electrically or magnetically walled waveguide having the same dimensions as the dielectric of the surface waveguide, to produce a set of orthogonal eigenfunctions. These eigenfunctions are projected upon Maxwell's equations resulting in a system of transmission lines coupled together through a wave immittance, which represents the ratio of a longitudinal and a transverse field component at the dielectric-air interface. Examples are given for various modes of the dielectric slab and the dielectric rod, in particular the HE1n modes for the latter. The transmission line models derived for these examples consist of a single trasmission line found directly by projection or reduced from a coupled transmission line model by port elimination, or of two transmission lines coupled together. All circuit models derived preserve the basic properties of surface waves (e.g. no solution below cut-off), and any of the single line models can be solved to give explicit approximate algebraic formulae for the propagation constant as a function of frequency. Numerical results show that the dispersion curves calculated from the models versus exact values are generally excellent over the entire frequency spectrum.
TL;DR: In this article, a generalised equation of modulation is introduced to represent the various forms of power frequency modulation, and mixed modulation systems of both PM and FM nature are introduced to solve the disadvantages and undesirable features associated with pure FM modulation.
Abstract: Amplitude Modulation (AM) and Phase Modulation (PM) processes of discrete form have been discussed in a previous associated paper. This present paper discusses discrete Frequency Modulation (FM) in power frequency circuits, highlighting their advantages compared with amplitude and phase modulations. Mixed modulation systems of both PM and FM nature are introduced to solve the disadvantages and undesirable features associated with pure FM modulation. A generalised equation of modulation is introduced to represent the various forms of power frequency modulation.
TL;DR: In this paper, a set of non-linear differential equations are derived for dynamic systems which may exhibit simultaneous changes in their electrical, fluid, mechanical and thermal states, based on considerations of the physics of components and their eventual topology when forming an assembly.
Abstract: Equations of motion in the form of sets of non-linear differential equations are derived for dynamic systems which may exhibit simultaneous changes in their electrical, fluid, mechanical and thermal states. These equations are based on considerations of the physics of components and their eventual topology when forming an assembly. The effect of thermal environment is shown when its capacity is finite and when it is not.
TL;DR: In this article, an analytical solution of the magnetic field diffusion through two concentric cylinders of different conductivities is derived using a generalized Ohm's law which considers both solid and fluid conductors.
Abstract: The diffusion of the magnetic field due to a step current in an infinitely long ideal conductor, through infinite media is discussed. An analytical solution of the field diffusion through two concentric cylinders of different conductivity is derived using a generalized Ohm's law which considers both solid and fluid conductors. A rigorous mathematical treatment which can be generalized to any number of conducting cylinders is presented. The limiting case of an external superconducting medium is discussed and it is shown that with all the other parameters fixed it represents a lower limit in diffusion time.
TL;DR: In this paper, a class of functions on a bounded irregular region Ω⊂R 2 which are of compact support, smooth and locally polynomials are constructed using ordinary B-splines associated with the square containing Ω.
Abstract: In this article we construct a class of functions on a bounded irregular region Ω⊂R 2 which are of compact support, smooth and locally polynomials. The basic tool is the use of ordinary B-splines associated with the square containing Ω. This construction is then used for approximating the solution of Poisson's boundary value problem. The approximation is carried out through a least squares finite element method applied to the above class. Aside from some computational experiments, the objective is to emphasize the ease of generating the basis elements and the role of Kernel function in a convergence proof.
TL;DR: In this article, an important variable-coefficient nonlinear differential-equation model for combat between two homogeneous military forces is studied and conditions under which the nonlinear Helmbold-type differential equation model may be transformed into a linear combat model.
Abstract: An important variable-coefficient nonlinear differential-equation model for combat between two homogeneous military forces is studied. Results for the representation of force-level trajectories are given as well as new important “simple-approximate” battle- outcome-prediction conditions. Such conditions are very significant in modern operations research for developing important insights into the dynamics of combat. Conditions are also investigated under which the nonlinear Helmbold-type differential-equation model may be transformed into a linear combat model. These results allow one to study inefficiences of scale in combat and provide important insights into the tradeoffs between quantity and quality of weapon systems.