Linear Physical Systems Research Articles

A time domain method for determining the relaxation time spectra

Many electromagnetic field problems can be expressed as a Fredholm integral equation of the first kind or the second kind. The step response of many linear physical systems may be analysed as sums of decaying exponentials. The paper describes a procedure (which improves the performance of gradient techniques) for the calculation of the amplitudes and the relaxation times which fit the sum of exponential functions to the experimental data. This method is applied to simulated and experimental data in order to validate the algorithm.

Analysis of signals from superposed relaxation processes

System functions of many linear physical systems or autocorrelation functions of their output signals are often a sum of relaxator terms with different relaxation times and amplitudes. In the time domain a superposition of exponential decays e−γt is observed, while in the frequency domain a sum of relaxator terms of structure 1/(γ+iω) is measured. Thus, the response is either the Laplace transform of the system function or its Stieltjes transform, respectively. In both cases it is the task of an analyst to gain the relaxation times and weights from the measured signal. An exact reconstruction of the system function is limited by the noise, measuring time, and number of points measured. In this paper procedures for the approximate reconstruction of the system function are introduced. The equivalence of most of them is shown and their properties are discussed. An expression for the limit of resolution is derived for a given signal-to-noise ratio. The results are applicable to experimental data from various physical systems. For illustration the autocorrelation function of the light scattered from polymer solutions and the response of photoconductors are used.

CACHE: An Interactive Control System Analysis and Design Package

CACHE is an interactive control engineering educational software package implemented on a personal computer workstation. The objective of this paper is to highlight the features of CACHE. CACHE provides undergraduate and graduate control engineering students with a comprehensive set of computational and graphics tools incorporating both classical and modern control engineering methodologies. The paper describes the menu-driven hierarchical command structure and the functions of the three CACHE subsystems: database manager, calculator, and plotter. The database manager maintains both state-space and frequency-domain transfer function models of linear time-invariant physical systems. CACHE includes analysis and design tools for both continuous-time and discrete-time systems. The application of CACHE is illustrated through the design of a position servomechanism.

Power and energy in linearized physical systems

Although no truly linear physical systems exist, linearized system models are very often used in practice to study the dynamics of real systems and components. Here, the relations between the power and energy in a non-linear physical system and the analogous quantities associated with variables representing small deviations from steady-state values are studied. Sometimes a linearized system is energetically similar to the non-linear system from which it was derived, and in other cases, new types of energy elements appear which were not present in the original system. In order to show the structure of the systems, the results are presented in both equation form and in the form of bond graphs which are unique in exhibiting the power and energy structure of system models.

Aspects of the Clausius-Shannon identity: emphasis on the components of transitive information in linear, branched and composite physical systems.

In this paper I consider how information is required to specify various systems. It is shown that the transitive information of any physical system, is distributed among three distinct components. One of these, the selective component, is required to specify the elemental parts of the system. Another, the connective component, is required to specify the macrostructure of the system; that is the way the parts are put together. And a third, the conformative component, is required to specify the intrinsic complexion or microstructure of the system. An interesting method for analyzing branched systems which takes account of connective ambiguity is described in some detail. The relationship between information and entropy, known as the Clausius-Shannon Identity, is then discussed with reference to selected thermodynamic models: and that aspect of information which is often overlooked, namely the distinction, between transitive and intransitive information is highlighted. The applications (or perhaps more correctly, the limitations of applying this treatment) to problems of biological interest are also indicated.

Aspects of the Clausius-Shannon Identity: Emphasis on the components of transitive information in linear, branched and composite physical systems

Aspects of the Clausius-Shannon Identity: Emphasis on the components of transitive information in linear, branched and composite physical systems

New Lagrangian and Hamiltonian functions for linear dissipative physical systems with ideal drivers

A new potential function is derived for dissipative physical systems with ideal drivers. The Lagrangian thus formulated satisfies the Euler-Lagrange equation, and the Hamiltonian thus derived satisfies the canonical-form Euler-Lagrange equation. State models can be obtained from a given system graph and vice versa if the state model is realizable.

Coherent spectrometry with noise signals

Coherent spectrometry with noise signals is described as Fourier transform spectrometry with deterministic signals which are samples from a stochastic process. Input-output relations needed for the processing of measured signal records are derived from the theories of linear physical systems and of sampled functions. The apparatus for obtaining noise-stimulated nuclear-magnetic-resonance spectra is described and results are presented for the spectrum of o-dichlorobenzene. A qualitative comparison is made with Fourier transform spectrometry based on pulsed signals, and the use of pseudorandom binary signals is briefly considered.

The inversion of a class of linear operators

o ^ b, satisfying the conditions of Definition 1.2. This paper is concerned primarily with those linear operators, the P-operators, which are abstractions from that class of linear physical systems whose output signals at a given time do not depend on their input signals at a later time; and with a sub-family of the P-operators, the Pi-operators which include all stationary linear_ operators. The Poperators are the Volterra operators on QL. Necessary conditions and sufficient conditions for a P-operator to have an inverse which is a P-operator are found; and a necessary and sufficient condition for a Pi-operator to have an inverse which is a P-operator is given in Theorem 3.1. In addition it is shown that if Sf is a Pi-operator and JS^1 is a P-operator then JS^1 may be written as the product of two operators whose generating functions may be found by successive approximation techniques. An analogue of Lane's inversion theorem for stationary operators on QCOL is found as a special case of these results. In [1] subspaces of the space of functions which are quasicontinuous on an interval [α, b] for which every linear operator £f may be written as a σ-mean Stieltjes integral of the form J*ff(s) = f(t)dL(t, s) are investigated. In this paper we will be concerned with one such subspace, Q£, and with a class of linear operators on QLi the P-operators, which are essentially the abstractions from that class of linear physical systems whose output signals at a given time do not depend on their input signals at a later time. In particular we shall be concerned with determining conditions which will guarantee that a P-operator has an inverse which is a P-operator. In §2 some of the basic properties of P-operators are developed and in § 3 a subfamily of these operators, the Px-operators, are introduced. The Pj-operators have the property that if a PΓoperator, 3ίΓ, has an inverse which is a P-operator then the generating function for may be determined by successive approximation techniques. In

Theory of linear physical systems

Theory of linear physical systems

Review of 'Theory of Linear Physical Systems'

Review of 'Theory of Linear Physical Systems'

Theory of Linear Physical Systems

Theory of Linear Physical Systems

Discrete compensation of sampled-data and continuous control systems

This paper presents a method of compensation to be applied to continuous as well as to sampled-data systems which reduces to zero any overshoot or error after a prescribed finite time. This prescribed response is applicable to step or ramp inputs and could be extended to acceleration or higher order inputs. It is shown that this response can be accomplished using the modified z-transform1 which yields the system response for all instants of time. The procedure, illustrated in examples, is applicable to general linear physical systems with no inherent delays. The compensated system may be designed so that shifts in gain or other dynamical disturbances have a small effect on the prescribed response. In conclusion, the method presented is powerful in synthesizing control systems to tally with a prescribed response and furthermore is straightforward in its application.

On the Zeros of Polynomials and the Degree of Stability of Linear Systems

A method is presented for finding the zeros of any nth degree real or complex polynomial as its coefficients (or their parameters) are varied. Several new theorems are presented. The method is based on new theorems, some concerning determinants, and on known theorems. It is applied to characteristic equations of linear physical systems with or without feedback. Root trajectories in the complex plane can be visualized without plotting them from ``root trajectory diagrams'' which show curve families for real or complex roots of a polynomial equation in a plane having two coefficients of the polynomial equation as coordinates. The diagrams can be used in the converse manner to determine the coefficient values corresponding to a desired dominant complex pair or real root.