# Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1998"

••

TL;DR: An algorithm for inferring the correct new mode and state variable values in the hybrid modeling framework, and a verification scheme that ensures hybrid models conform to physical system principles based on the principles of divergence of time and temporal evolution in behavior transitions are developed.

Abstract: Physical systems are by nature continuous, but often display nonlinear behaviors that make them hard to analyze. Typically, these nonlinearities occur at a time scale that is much smaller than the time scale at which gross system behavior needs to be described. In other situations, nonlinear effects are small and of a parasitic nature. To achieve efficiency and clarity in building complex system models, and to reduce computational complexity in the analysis of system behavior, modelers often abstract away any parasitic component parameter effects, and analyze the system at more abstract time scales. However, these abstractions often introduce abrupt, instantaneous changes in system behavior. To accommodate mixed continuous and discrete behavior, this paper develops a hybrid modeling formalism that dynamically constructs bond graph model fragments that govern system behavior during continuous operation. When threshold values are crossed, a meta-level control model invokes discontinuous state and model configuration changes. Discontinuities violate physical principles of conservation of energy and continuity of power , but the principle of invariance of state governs model behavior when the control module is active. Conservation of energy and continuity of power again govern behavior generation as soon as a new model configuration is established. This allows for maximally constrained continuous model fragments. The two primary contributions of this paper are an algorithm for inferring the correct new mode and state variable values in the hybrid modeling framework, and a verification scheme that ensures hybrid models conform to physical system principles based on the principles of divergence of time and temporal evolution in behavior transitions . These principles are employed in energy phase space analysis to verify physical consistency of models.

156 citations

••

TL;DR: In this article, an interpretation of fractional operators in the time domain is given, based on the four concepts of fractal geometry, linear filters, construction of a Cantor set and physical realisation.

Abstract: In this paper an interpretation of fractional operators in the time domain is given. The interpretation is based on the four concepts of fractal geometry, linear filters, construction of a Cantor set and physical realisation of fractional operators. It is concluded here that fractional operators may be grouped as filters with partial memory that fall between two extreme types of filters with complete memory and those with no memory. Fractional operators are capable of modelling systems with partial loss or partial dissipation. The fractional order of a fractional integral is an indication of the remaining or preserved energy of a signal passing through such system. Similarly, the fractional order of a differentiator reflects the rate at which a portion of the energy has been lost.

125 citations

••

Tektronix

^{1}TL;DR: This paper focuses on motion estimation and compensation techniques as tools that are used in video compression applications.

Abstract: Digitized visual information is a rapidly growing component of emerging video and multimedia services. In its raw digitized form visual information places large demands on bandwidth and storage requirements of applications. Picture and video compression is a key enabling technology for overcoming this problem. This paper focuses on motion estimation and compensation techniques as tools that are used in video compression applications.

50 citations

••

TL;DR: The author reviews and presents the theory involved in the design of experiments for parameter estimation, a process of importance for pharmacokinetics, the study of intermediary metabolism and other sections of biological research.

Abstract: In this article the author reviews and presents the theory involved in the design of experiments for parameter estimation, a process of importance for pharmacokinetics, the study of intermediary metabolism and other sections of biological research. The design of experiments involves both formal and informal aspects. The formal theories of identifiability of parameters and model distinguishability, and the generation of optimal sampling schedules, play major roles. After presenting these theories, both the formal and informal aspects are studied in the examination of a simple but realistic example.

44 citations

••

TL;DR: In this article, the authors propose a procedure for building bond graph representations of multibody systems with kinematic loops, which is systematic in the sense that no analytical derivation is necessary to construct the bond graph, and gives a more graphically and analytically exploitable representation compared to the Tiernego and Bos procedure.

Abstract: In this paper we propose a procedure for building bond graph representations of multibody systems with kinematic loops. It is systematic in the sense that no analytical derivation is necessary to construct the bond graph. It also gives a more graphically and analytically exploitable representation compared to the Tiernego and Bos procedure. Our method first considers the kinematic loops globally before building the body bond graphs. Therefore we have to detect a privileged frame for each kinematic loop in which we can express the kinematic constraint. Then we construct the corresponding junction structures of bodies whose variables are projected onto those privileged frames. After having presented criteria and a method for selecting the latter, two examples are given: the forming machine and the flyball governor.

37 citations

••

TL;DR: It is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Bellman equation for the controlled system and thus guarantees both optimality and stability.

Abstract: In this paper we develop an optimality-based framework for designing controllers for discrete-time non-linear cascade systems. Specifically, using a non-linear—non-quadratic optimal control framework we develop a family of globally stabilizing backstepping-type controllers parameterized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Bellman equation for the controlled system and thus guarantees both optimality and stability.

35 citations

••

Cairo University

^{1}TL;DR: In this article, two novel oscillator circuits with both voltage and current outputs are proposed, which are related to each other by the adjoint network theorem, and each oscillator employs a current follower and a voltage follower, and has the advantage of independent control on the frequency of oscillation and the condition of the oscillation.

Abstract: Two novel oscillator circuits with both voltage and current outputs are proposed. The two oscillators are related to each other by the adjoint network theorem. Each oscillator employs a current follower and a voltage follower, and has the advantage of independent control on the frequency of oscillation and the condition of oscillation. A new minimum R,C oscillator with voltage and current outputs is also given. Two new two-resistor two-capacitor, current-mode and voltagemode oscillators are also included. PSpice simulation results illustrating the performance of the oscillator circuits are included.

31 citations

••

TL;DR: In this paper, the authors view the current status of multi-dimensional filters bank and wavelet design from the perspective of signal and system theory, and provide a flavor of techniques germane to this development by considering a few specific problems.

Abstract: Wereview the current status of multi-dimensional filters bank and wavelet design from the perspective of signal and system theory. The study of wavelets and perfect reconstruction filter banks are known to have roots in traditional filter design techniques. On the other hand, the field of multi-dimensional systems and signal processing has developed a set of tools intrinsic to itself, and has attained a certain level of maturity over the last two decades. We have recently noted a degree of synergy between the two fields of wavelets and multi-dimensional systems. This arises from the fact that many ideas crucial to wavelet design are inherently system theoretic in nature. While there are many examples of this synergy manifested in recent publications, we provide a flavor of techniques germane to this development by considering a few specific problems in detail. The construction of orthogonal wavelets can be essentially viewed as a circuit and system theoretic problem of design of energy dissipative (passive) filters, the multi-dimensional version of which has very close ties with a classic problem of lumped distributed passive network synthesis. Groebner basis techniques, matrix completion problems over rings of polynomials or rings of stable rational functions, i.e., Quillen Suslin (31) type problems are still other examples, which feature in our discussion in an important manner. A number of open problems are also cited. ©1998 The Franklin Institute. Published by Elsevier Science Ltd.

30 citations

••

TL;DR: In this paper, a review of recent studies on the modelling of epidemic processes using individual-based lattice epidemic models is presented, showing how, by analysing individual epidemic outbreaks, it is possible to gain insight into the spread of measles in certain small, largely susceptible, island population before the era of mass-vaccination.

Abstract: We review recent studies on the modelling of epidemic processes using individual-based lattice epidemic models. Originally introduced to investigate the emergence of spatio-temporal organisation in non-linear dynamical systems they are usually termed “forest-fire” models. However, their interpretation as a representation of communicable disease spread is readily apparent and we show how, by analysing individual epidemic outbreaks, it is possible to gain insight into the spread of measles in certain small, largely susceptible, island population before the era of mass-vaccination.

28 citations

••

TL;DR: The dynamic sliding mode controller joins features of a conventional sliding mode Controller (insensitivity to matched nonlinearities and disturbances) and a conventional dynamic compensator (accommodation to unmatched disturbances) to address nonlinear nonminimum phase output tracking.

Abstract: The output tracking in nonlinear nonminimum phase systems with matched and unmatched disturbances and matched nonlinearities is considered. The asymptotic linear output tracking with the desired (given) eigenvalues' placement is provided in a dynamic sliding manifold. The design algorithm of the sliding mode controller with the dynamic sliding manifold is developed. Addressing nonlinear nonminimum phase output tracking, the dynamic sliding mode controller joins features of a conventional sliding mode controller (insensitivity to matched nonlinearities and disturbances) and a conventional dynamic compensator (accommodation to unmatched disturbances).

27 citations

••

TL;DR: In this paper, a set of piecewise constant orthogonal functions, termed sample-and-hold functions (SHF), is introduced for the analysis of control systems with SISO.

Abstract: The present work searches for a suitable set of orthogonal functions for the analysis of control systems with sample-and-hold ( S/H ). The search starts with the applicability of the well known block pulse function (BPF) set and uses an operational technique by defining a block pulse operational transfer function ( BPOTF ) to analyse a few control systems. The results obtained are found to be fairly accurate. But this method failed to distinguish between an input sampled system and an error sampled system. To remove these limitations, another improved approach was followed using a sample-and-hold operational matrix, but it also failed to come up with accurate results. Further, the method needed a large number of component block pulse functions leading to a much larger amount of storage as well as computational time. To search for a more efficient technique, a new set of piecewise constant orthogonal functions, termed sample-and-hold functions (SHF), is introduced. The analysis, based upon a similar operational technique, in the SHF domain results in the same accuracy as the conventional z -transform analysis. Here, the input signal is expressed as a linear combination of sample-and-hold functions; the plant having a Laplace transfer function G(s) is represented by an equivalent sample-and-hold operational transfer function ( SHOTF ), and the output in the SHF domain is obtained by means of simple matrix multiplication. This technique is able to do away with the laborious algebraic manipulations associated with the z -transform technique without sacrificing accuracy. Also, the accuracy does not depend upon m and the presented method does not need any kind of inverse transformation. A few linear sample-and-hold SISO control systems, open loop as well as closed loop, are analysed as illustrative examples. The results are found to match exactly with the z -transform solutions. Finally, an error analysis has been carried out to estimate the upper bound of the mean integral squared error (m.i.s.e.) of the SHF approximation of a function f(t) of Lebesgue measure.

••

TL;DR: In this article, a simple and new representation of mechanical joints by using vector bond graph elements is provided, where the power is conserved and the law of energy conservation is reserved through all elements.

Abstract: Even though the bond graph method was a useful tool in the modeling of physical systems, it has not been adopted for dealing with large mechanical systems in three-dimensional space. Due to the lack of vector concept, there were difficulties when the topology of the system was becoming more sophisticated. In order to deal with constrained mechanical systems by some types of joint using the bond graph terminology, a more effective method has to be devised. Considering the background, this paper provides a simple and new representation of mechanical joints by using vector bond graph elements. Also, force elements are modeled by the bond graph terminology. In the bond graph of this paper, the power is conserved and the law of energy conservation is reserved through all elements. As a result, the paper provides an effective and graphical tool for carrying out three-dimensional constrained mechanical dynamic problems with the vector bond graph.

••

TL;DR: In this article, the design of a minimal order observer which can estimate the state feedback control signal with arbitrarily given observer poles and K, has been worked on for many years, with the prevailing conclusion that it is an unsolved problem.

Abstract: The design of a minimal order observer which can estimate the state feedback control signal K x( t ) with arbitrarily given observer poles and K , has been worked on for many years, with the prevailing conclusion that it is an unsolved problem. This paper asserts for the first time that this design problem has been simplified to a set of linear equations K = K z diag{c 1 ,…,c r } D , where D is fully determined and other parameters are completely free, and where r is the observer order. This paper also asserts that only this set of linear equations can provide the unified upper bound of r , min { n , v 1 + … + v p } and min { n − m ,( v 1 − 1) + … + ( v p − 1)}, for strictly proper and proper observers, respectively, where n , m , p and v i ( i = 1,…, p ) are the plant order, number of outputs, number of inputs, and the descending order observability indexes, respectively. This general upper bound is lower than all other existing ones and is the lowest possible general upper bound.

••

Cairo University

^{1}TL;DR: In this article, two complementary sinusoidal oscillator circuits based on the Twin-T network are modified for chaos using a single discrete nonlinear device with antisymmetrical current-voltage characteristics, namely a junction field effect transistor (JFET) operating in its triode region.

Abstract: Two complementary sinusoidal oscillator circuits based on the Twin-T network are modified for chaos using a single discrete nonlinear device with antisymmetrical current-voltage characteristics, namely a junction field effect transistor (JFET) operating in its triode region. The two oscillators' design equations are used as a starting point for chaos modification. Mathematical models that describe the observed behaviour in both circuits are derived. Experimental results, PSpice circuit simulations and numerical simulations of the mathematical models agree well and are included.

••

TL;DR: In this article, the important transfer function design problems of input-output decoupling, exact model matching and disturbance rejection, via static measurement output feedback, are studied for the case of generalized state space systems.

Abstract: The important transfer function design problems of input-output decoupling, exact model matching and disturbance rejection, via static measurement output feedback, are studied for the case of generalized state space systems. Necessary and sufficient conditions for the solvability of these problems are established. The general analytical expressions of the respective controller matrices are derived. The above results are also extended to cover the combined problem of disturbance rejection with simultaneous decoupling and the problem of disturbance rejection with simultaneous exact model matching.

••

TL;DR: In this article, a combined experimental and analytical investigation of the problem of buckling of unilaterally constrained, finite, rectangular, elastic plates is reported, where the plates are modeled along the lines of classical plate theory employing the Kirchhoff-love hypothesis.

Abstract: The results from a combined experimental and analytical investigation of the problem of buckling of unilaterally constrained, finite, rectangular, elastic plates is reported. The plates are modeled along the lines of classical plate theory employing the Kirchhoff-Love hypothesis. The presence of a unilateral constraint is accounted for through the use of a nonlinear elastic foundation model that exhibits a deformation sign dependent force-displacement relation. Using Galerkin's method, the resulting system of governing nonlinear equations are solved iteratively. Different boundary conditions are considered and the results for some boundary conditions are compared and shown to be in good agreement with ‘exact’ results reported earlier for infinite plates. The results from an experimental investigation has further revealed that the buckling mode of the plate may involve regions or points of contact with the substrate beneath the buckling plate. The shadow Moire technique is used to show clearly that the mode shape is periodic and contains points and/or regions of contact. The results obtained from the theoretical investigation are found to bound the experimental values. It is clear that the stiffness of a post-buckled plate with unilateral constraints is highly influenced by whether the buckled portion involves points (or regions) of contact or not. Thus, in analytical model development, associated with addressing the problem of delamination buckling in layered plates, the possibility of the delaminated portion contacting the substrate beneath cannot be excluded. The present study has demonstrated the validity of using nonlinear foundation models in the buckling analysis of unilaterally constrained rectangular plates.

••

TL;DR: A model is described for the complex patterns formed by bacterial colonies, specifically Escherichia coli, and derive and analyse a model firmly based on experimental data, and the results from the model compare well with experiment.

Abstract: Although the development of spatial pattern and form is a central issue in biology the mechanisms which generate them are generally unknown. The interdisciplinary modelling challenge is to construct realistic mechanisms which capture the key biological processes and show how they are orchestrated to create the observed pattern. We discuss two specific patterning problems of current widespread interest in biomedicine. In the first, possible mechanisms of dermal wound healing are reviewed with a discussion of what is needed of realistic models for studying wound healing. We then list a series of open problems. In the second problem we describe a model for the complex patterns formed by bacterial colonies, specifically Escherichia coli, and derive and analyse a model firmly based on experimental data. The results from the model compare well with experiment. Mathematically, the class of models discussed gives rise to novel systems of partial differential equations which pose challenging problems, both analytical and numerical. The models have provided the experimentalist with insight as to how such patterns might be formed and have suggested possible experiments to elucidate the underlying biological processes.

••

TL;DR: It is shown, that a similar approach may be applied to the synthesis of a control system of hopping apparatus which would be supplied by a telescopic leg as well as by two segment legs.

Abstract: A problem of a control of the hopping apparatus model is considered. Relations determined by a program mode of movement are presented. The problem of synthesis of a stabilization system is reduced to a periodic linear quadratic problem. Flexibility of such a procedure of synthesis is noted. In particular, it is shown, that a similar approach may be applied to the synthesis of a control system of hopping apparatus which would be supplied by a telescopic leg as well as by two segment legs. Examples of synthesis of a control system of hopping apparatus are considered. The results of the simulation of the apparatus start process are presented.

••

TL;DR: In this paper, a sufficient condition is proposed for asymptotically stabilizing the large-scale perturbed systems with a prescribed stability degree by using decentralized state-feedback controllers.

Abstract: The present paper is concerned with the decentralized stabilization problem for a class of large-scale systems with time-varying interconnected matrices and nonlinear uncertainties. A new sufficient condition is proposed for asymptotically stabilizing the large-scale perturbed systems with a prescribed stability degree by using decentralized state-feedback controllers. All the information needed here is only the possible bounds of the time-varying interconnected matrices and nonlinear uncertainties. This condition is shown to be less conservative than the ones reported recently. The results can be extended to a class of large-scale systems with delays. Two illustrative examples are included to demonstrate the superiority of the obtained results.

••

TL;DR: Some criteria are proposed to guarantee the α-stability for a class of nonlinear systems with multiple time delays and two numerical examples are provided to illustrate main results.

Abstract: In this paper, the α-stability of nonlinear systems with multiple time delays is considered. Some criteria are proposed to guarantee the α-stability for a class of nonlinear systems with multiple time delays. Two numerical examples are provided to illustrate our main results.

••

TL;DR: In this paper, a mode-decoupling approach was proposed to yield two separate subsystems containing the slow and fast parts of a two-time-scale nonlinear system, and an asymptotic stabilizing composite feedback control was proposed.

Abstract: A class of discrete-time nonlinear systems which are two-time-scale is treated. Using the singular perturbation theory in a systematic way, we present a mode-decoupling approach which yields two separate subsystems containing the slow and fast parts. Furthermore, a two-time-scale analysis and design procedure for stabilization and regulation is presented. The controllability and stabilizability invariance of the fast subsystem is shown and an asymptotic stabilizing composite feedback control is proposed. Finally, it is shown that the composite control produces a finite cost which tends to the optimal cost of a slow problem as the singular perturbation parameter tends to zero.

••

TL;DR: In this paper, the authors present new simultaneous pole and zero placement schemes based on the use of feedforward and feedback compensators, where the plant is allowed to possess unstable zeros which are not required to be included as zeros of the reference model.

Abstract: This paper presents new simultaneous pole and zero placement schemes based on the use of feedforward and feedback compensators. The main novelty is that the plant is allowed to possess unstable zeros which are not required to be included as zeros of the reference model. The control objective of model-following is achieved by including a feedforward compensator between either the reference or the control signals and the plant output which is incorporated to the usual schemes consisting in a precompensator and a feedback compensator. Basically, two control schemes are presented, but some extensions are given allowing signal feedforward injections at intermediate state variables of the plant instead of the standard injections at the output and the use of blocking filters for the significant frequencies of the output of the feedforward compensator. These schemes lead to two diophantine equations, one being used for standard pole placement while the other being basically used for the placement of zeros in prescribed positions. Several numerical simulations are given to illustrate the capability of the schemes for simultaneous pole and zero placement in the absence and in the presence of noise and their application for adaptive control.

••

Cairo University

^{1}TL;DR: It is shown that three recently reported current conveyor based lowpass filters are originated from a passive RLC filter and two new grounded-capacitor current mode low pass filters are also introduced.

Abstract: It is shown that three recently reported current conveyor based lowpass filters are originated from a passive RLC filter. Two new grounded-capacitor current mode lowpass filters are also introduced. Frequency limitation equations based on the non-ideal current conveyors are given. PSpice simulation results are included.

••

TL;DR: This manuscript examines the areas of communicating and interpreting published models and describes a facility, called a ‘model library’, that is being developed to make published models available on the Internet.

Abstract: Models are tools that are used to predict the structure and the behavior of a system. They are usually developed to fit a particular set of data, however, once developed, they can be applied to other studies; to predict the behavior of the system under different conditions, explore the structure of parts of the system that were not sampled, identify areas that are lacking in data, and optimize the design of new studies. For published models to be interpreted and applied widely to other studies, models need to be communicated clearly. Papers describing models should contain full descriptions of the physiological relevance and mathematical rigor of the model. A working version of the model then needs to be made available to other investigators. This manuscript examines the areas of communicating and interpreting published models and describes a facility, called a ‘model library’, that is being developed to make published models available on the Internet. With better communication, information in models can be extracted and used to bridge the gap between theory and experiment to extend our understanding of complex systems and optimize the use of experimental resources.

••

[...]

TL;DR: The main difficulty in understanding solvation phenomena arises from the effects of electrostatics in complex biomolecular systems as discussed by the authors, and the fundamental concepts and methodologies in evaluating electrostatic contributions to solvation.

Abstract: Water serves as a critical solvent for a remarkable array of molecules; in particular it profoundly influences the structure and activity of proteins, and their molecular interactions. Our ability to understand biological processes and to develop innovative applications for biotechnology depend in large part on understanding the biophysics of proteins in their solvated environment. The main difficulty in understanding solvation phenomena arises from the effects of electrostatics in complex biomolecular systems. In this paper we survey and critique the fundamental concepts and methodologies in evaluating electrostatic contributions to solvation.

••

TL;DR: In this paper, a realization of two-dimensional (2D) adaptive finite impulse response (FIR) filters using affine projection method is proposed, which is superior to that of the 2-D least mean square (LMS) and normalized LMS (NLMS) algorithms.

Abstract: This paper proposes a realization of two-dimensional (2-D) adaptive finite impulse response (FIR) filters using affine projection method. The convergence property of the proposed algorithm is superior to that of the 2-D least mean square (LMS) and normalized LMS (NLMS) algorithms. This algorithm has properties that lie between those of NLMS and recursive least squares (RLS) algorithms. The convergence of this filter can be proved. The generalization of the proposed algorithm is also discussed. To illustrate the utility of the proposed technique, this filter is applied to the 2-D system identification.

••

TL;DR: In this paper, the minimum-time and the control which minimizes the cost function and leads the system from a given initial state to a fixed final one are compared. But the minimum time and the optimal control are not compared.

Abstract: E. I. Verriest and F. L. Lewis have presented in (1) a new method to approximate the minimum-time control of linear continuous-time systems avoiding the Bang-Bang control. Their method relied on the optimization of a cost including time energy and precision terms. Our purpose in this article is to extend their work to discrete-time linear systems. Indeed, we consider a linear discrete-time system and a quadratic cost including time and energy term, and we look for the minimum-time and the control which minimizes the cost function and leads the system from a given initial state to a fixed final one. By selecting the magnitude of the energy term, one may balance off the requirement for minimum-time versus the one for keeping the state and inputs small over the considered interval of time. Finally we give a method to compute the minimum-time and the optimal control.

••

TL;DR: In this paper, it was shown that Pars's argument was based on a major assumption which is unnecessary and that acceleration dependent forces do not appear to violate the fundamental postulate of Newtonian mechanics.

Abstract: Pars argued that for particle mechanics, the idea of allowing forces to be functions of accelerations is foreign to Newtonian mechanics. It is inconsistent with one of the fundamental postulates of Newtonian mechanics. This was attested by a set of (thought) experiments. We show that Pars's argument was in fact based on a major assumption which is unnecessary. As this assumption is removed, acceleration dependent forces do not appear to violate the fundamental postulate.

••

TL;DR: In this article, the authors present an exact relationship between the buckling load of circular plates based on the Reddy (third-order shear deformation) plate theory and that of the classical Kirchhoff plate theory.

Abstract: This paper presents an exact relationship between the buckling load of circular plates based on the Reddy (third-order shear deformation) plate theory and that of the classical Kirchhoff plate theory. The relationship allows one to obtain the exact buckling solutions of Reddy plates from the well-known Kirchhoff solutions for circular plates with (i) simply supported edges, (ii) clamped edges, (iii) simply supported edges with elastic rotational restraints, and (iv) free edges with the centre clamped. Unlike the Mindlin plate theory, there is no need for a shear correction factor in the Reddy plate theory. A comparison of buckling results between the Mindlin, Reddy and three-dimensional elasticity plates is also given.

••

TL;DR: In this paper, it was shown that the steady state property of the unobservable part of a given nonlinear dynamics is equivalent to the existence of a state detector (detectability).

Abstract: It is shown that the steady state property of the unobservable part of a given nonlinear dynamics is equivalent, under some boundedness assumptions, to the existence of a state detector (detectability). This property is illustrated, discussed and related to the existence of partial observers; local and global aspects are considered.