Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1996"
TL;DR: In this article, a theoretical model of an added mass representation for a flexible cylinder vibrating in a fluid medium is presented, where the fluid-structure interaction problem under the influence of harmonic ground and inertia dominated hydrodynamic loading is first studied by solving the coupled differential equations exactly.
Abstract: A theoretical model of an added mass representation for a flexible cylinder vibrating in a fluid medium is presented. To accomplish this, the fluid-structure interaction problem under the influence of harmonic ground and inertia dominated hydrodynamic loading, is first studied by solving the coupled differential equations exactly. Explicit expressions for computing the hydrodynamic interaction pressure and eigenquantities like natural frequencies and mode shapes are given here. However, this analytical model, as in many other mathematical models, suffers from a severe handicap; its expressions are too complicated and require the use of a computer program to generate the results. One solution which is of particular interest, is the computation of natural frequencies. Using the added mass representation, a simple formula for evaluating the natural frequency is proposed. The formula is very simple to use, requiring only a minimal computational effort on a standard calculator. Comparison with the analytical solutions shows that the formula is extremely accurate, with errors under 0.5% or less, in nearly all the cases tested. Also, more importantly, this accuracy does not appear to deteriorate in the computation of higher natural frequencies, and thus should be very useful for designers working in the dynamics of submerged structures, taking into account their hydrodynamic interactions.
85 citations
TL;DR: In this paper, two different algorithms for deriving the inverse system state equations from a bond graph model are presented, one based on causal path analysis and the other based on the concept of bicausality.
Abstract: Two different algorithms for deriving the inverse system state equations from a bond graph model are presented. The first method is based on the causal path analysis and it leads to the full-order inverse system. The second method which is procedural relies on the concept of bicausality and the state equations obtained from the resulting algorithm are those of a reduced inverse system. In both cases, some illustrative examples are given. The advantages of these methods are that they can easily be implemented in software using an algorithm of causality assignment and a procedure of causal paths analysis in a bond graph. Formal calculations of matrices are then avoided in the first case and also formal state transformations are not necessary to obtain the reduced inverse system in the second case.
66 citations
TL;DR: In this paper, the problem of input-output decoupling for linear systems with nonlinear uncertain structure, via an independent of the uncertainties static state feedback law, is studied and solved for the first time.
Abstract: In this paper the problem of input-output decoupling for linear systems with nonlinear uncertain structure, via an independent of the uncertainties static state feedback law, is studied and solved for the first time. The necessary and sufficient conditions for the problem to have a solution are established. The general analytical expressions of the feedback matrices and the decoupled closed loop system are derived. The decoupled closed loop system structural properties of pole assignment, stabilizability are also studied. All above results are successfully applied to control the longitudinal motion of an aircraft.
48 citations
TL;DR: An efficient and fast algorithm for the direct computation of Zernike moments is presented, based on using some properties of ZERNike polynomials.
Abstract: Zernike moments have been used as shape descriptors in several object recognition applications. The classical method of computing Zernike moments is dependent on the regular moments which makes them computationally expensive and inefficient. In this paper, we present an efficient and fast algorithm for the direct computation of Zernike moments. This algorithm is based on using some properties of Zernike polynomials.
43 citations
TL;DR: In this paper, the evolutionary spectral approach is used to analyse stationary nonGaussian signals, and the authors define wavelet transforms for discrete parameter time series, and show that higher order moments of these transforms are necessary to study nonlinear signals.
Abstract: Higher order spectral methods are widely used to analyse stationary nonGaussian signals. Using the evolutionary spectral approach, we develop methods for evaluating evolutionary bispectrum (time dependent bispectrum) and illustrate the approach with examples. We also define wavelet transforms for discrete parameter time series, and show that higher order moments of these transforms are necessary to study nonlinear signals. The methods are illustrated with examples.
22 citations
TL;DR: In this article, a specific modeling and a mode decoupling approach well adapted for non-linear discrete-time dynamic systems are presented. But the application of two-time scale discrete singular perturbation methods have been limited to the linear systems.
Abstract: Application of two-time scale discrete singular perturbation methods have been limited to the linear systems. The area of discrete-time non-linear systems has received little attention. This paper deals with the singular perturbation model of non-linear discrete-time dynamic systems. We present a specific modelling and a mode decoupling approach well adapted for such systems. A comparison principle is used for grouping slow and fast states of a class of non-linear discrete systems. Finally, an example is given to show the feasibility of the theoretical results.
22 citations
TL;DR: A method for determining matchable impedance regions of passive LC ladder networks with any component value ranges is proposed and general mathematical results of addition and inversion impedance transformations involved in the approach are formulated.
Abstract: Impedance matching domain problems of tunable matching networks are described in this paper. A method for determining matchable impedance regions of passive LC ladder networks with any component value ranges is proposed. Matching domains of the most popular II, T and L networks whose component value ranges are arbitrary are determined both analytically and graphically. Computer-aided domain plotting is discussed and various examples are presented. The applications of impedance matching domain problems are also analysed. In the Appendix general mathematical results of addition and inversion impedance transformations involved in the approach are formulated.
20 citations
TL;DR: This paper starts with deriving α-stable models for impulsive noise and serves as an illustration of the Generalized Central Limit Theorem, which states that the first-order distributions in all observed time series follow, to a higher or lesser degree, a stable law.
Abstract: Symmetric, α-stable random variables and processes have, recently, been receiving increasing attention from the signal processing and communication communities as statistical models for signals and noises that contain impulsive components. This paper is intended as a comprehensive review of the fundamental concepts and results of signal processing with α-stable processes with emphasis placed on acquainting engineers with this emerging discipline in signal processing and revealing its potential applications. In particular, we start with deriving α-stable models for impulsive noise. This derivation serves as an illustration of the Generalized Central Limit Theorem, which states that the first-order distributions in all observed time series follow, to a higher or lesser degree, a stable law. We proceed to present new, fast algorithms for estimation of the parameters of α-stable interference and address two signal detection problems. These problems also build intuition on the differences between Gaussian and non-Gaussian, α-stable signal processing, as well as indicate the performance gains that are to be expected if the signal processing algorithms are designed on the basis of a non-Gaussian, α-stable assumption rather than on a Gaussianity assumption. In the paper, we follow a presentation style that emphasizes only the highlights of the field and omit the fine mathematical details. However, we have included a large number of references to the literature for the interested reader to study further.
18 citations
TL;DR: In this paper, a two-step iterative procedure is proposed for the optimal reduced-order modeling of linear time-invariant single-input single-output (SISO) systems.
Abstract: A new two-step iterative procedure is proposed for the optimal reduced-order modeling of linear time-invariant single-input single-output (SISO) systems. The performance index of optimal reduction is taken to be a quadratic function of the error between the time responses of the original and reduced models. At each iteration cycle, the numerator dynamics is first determined by solving a set of linear equations, and the denominator polynomial is then determined by a gradient-based search technique. The main features of the proposed procedure are that it searches the Routh stability parameters rather than the denominator polynomial coefficients of the reduced model, and computes the performance index and its gradients by a computationally efficient parametric algorithm. As a consequence, the need of stability monitoring in the step of searching optimal denominator polynomial for the reduced model is avoided, and the gradient vector evaluated exactly and efficiently for a gradient-based parameter search. Moreover, the constraint of zero steady-state response error can be easily handled.
18 citations
TL;DR: In this paper, a model matching controller design technique is presented to facilitate direct specification of the disturbance response of a closed-loop system, where the desired disturbance response characteristics are implicated through an appropriately chosen reference model.
Abstract: A new model matching controller design technique is presented to facilitate direct specification of the disturbance response of a closed-loop system. The desired disturbance response characteristics are implicated through an appropriately chosen reference model. This approach substantially reduces the trial-and-error iterations necessary to meet the design requirements. A simple reference model specification procedure allows arbitrary choice for the reference Transfer Function poles (to control response time) while guaranteeing the physical realizability of the controller and asymptotic rejection of various types of disturbances such as step, ramp, etc. The Frequency Domain Controller Synthesis Techniques produce low-order, practically implementable controllers. The power of the design approach is demonstrated by several illustrative examples. It is shown that ensuring good disturbance rejection characteristics is sufficient to guarantee satisfactory set-point response, and not vice versa.
17 citations
TL;DR: The practicality and feasibility of these approaches are demonstrated by utilizing them to model actual physical nonlinear systems given experimental input-output data from such systems.
Abstract: The purpose of this paper is twofold. The first objective is to develop a discrete frequency-domain orthogonal third-order Volterra model valid for both nonGaussian and Gaussian stationary random inputs in order to eliminate the presence of ‘interference’ terms. The second objective is to develop a sparse third-order frequency-domain Volterra model by identifying the most significant frequency-domain Volterra kernel coefficients using a given amount of raw experimental times series data. The concept of coherence function is extended to the orthogonal higher-order model in order to quantify the goodness of both the model and its constituent linear, quadratic, and cubic components and, then, is utilized as a criterion to select the most significant frequency-domain Volterra kernel coefficients to be included in the sparse Volterra model. Identification of the most significant frequency-domain Volterra coefficients is based upon a frequency-domain extension of the well-known orthogonal-search method. Finally, the practicality and feasibility of these approaches are demonstrated by utilizing them to model actual physical nonlinear systems given experimental input-output data from such systems.
TL;DR: For simple r-regular graphs, an edge reduction and three transformations (S -, X -, and H - transformations) are defined in this paper to preserve the regularity.
Abstract: For simple r-regular graph, an edge-reduction and three transformations ( S - , X - , and H - transformations ) are defined which preserve the regularity. In the case r = 3, relations between them are discussed and it is proved that for any two connected cubic graphs with the same order one is obtained from the other by a finite sequence of S - transformations . Then it defines a metric on the set of connected cubic graphs.
TL;DR: A variant wave-scattering approach for physical system modeling and analysis that adopts duplexed wave signals to quantify the propagation, storage and dissipation of energy localized between and within system elements is presented.
Abstract: This paper presents a variant wave-scattering approach for physical system modeling and analysis that adopts duplexed wave signals to quantify the propagation, storage and dissipation of energy localized between and within system elements. This energetic perspective of wave-scattering techniques can exploit the relationship to bond graph methods to complement techniques in multiport modeling and analysis. Examples are presented that illustrate the use of wave-scattering methods for treating distributed-parameter effects, nonlinear effects, and switching effects in system models. Furthermore, the methods presented lay the groundwork for extending network analysis and synthesis methods to multi-energy domain and mixed lumped/distributed-parameter systems.
TL;DR: In this control architecture, it will be shown that the robotic manipulator can track precisely both the trained and untrained trajectories.
Abstract: A simple and effective method for trajectory tracking of robotic manipulator is proposed. The first step is to employ a neural network to learn the characteristics of the inverse dynamics of the robotic manipulator in an off-line manner. Then the neural network is placed in series with the robotic manipulator for on-line operation and the desired trajectory is fed into the neural network to obtain the corresponding torques. If all the characteristics of the inverse dynamics are learned by the neural network, then the corresponding torques will generate the desired trajectory. However, considering that the input patterns of the neural network may not be rich enough to excite all modes of the system, a classical PID controller is added for compensation. This controller is placed at the input node of the robotic manipulator to compensate the characteristics that have not been learned by the neural network. In this control architecture, it will be shown that the robotic manipulator can track precisely both the trained and untrained trajectories. Simulation examples are included to illustrate the validity of the proposed method.
TL;DR: In this article, a modified robust maximum likelihood higher-order statistics estimator is derived based on the assumption that the obtained estimates (moments or cumulants) follow a generalized Gaussian distribution (GGD) of parameter α.
Abstract: The purpose of this paper is twofold. First, a modified robust maximum likelihood higher-order statistics estimator is derived based on the assumption that the obtained estimates (moments or cumulants) follow a generalized Gaussian distribution (GGD) of parameter α. By determining the parameter α which corresponds to the lowest bias and variance of estimation the most appropriate GGD is determined as a function of data length. Then the efficiency of various higher-order statistics (HOS) estimators is assessed in terms of VLSI implementation merits such as data throughout delay, cost, and round-off noise performance. The obtained results provide guidelines in choosing the appropriate estimator in HOS applications.
TL;DR: In this paper, a new class of parameter-dependent Lyapunov functions for discrete-time systems is proposed to guarantee robust stability in the presence of time-varying rate-restricted plant uncertainty.
Abstract: In this paper we construct a new class of parameter-dependent Lyapunov functions for discrete-time systems to guarantee robust stability in the presence of time-varying rate-restricted plant uncertainty. Extensions to a class of time-varying nonlinear uncertainty that generalizes the discrete-time multivariable Popov criterion are also considered. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of slowly time-varying real parameters.
TL;DR: A multiple channel subband adaptive noise canceler is developed to deal with the multipath, multisource nature of the noise present in the car and its effectiveness was verified through computer simulations, which were carried out using real transfer functions estimated by an HP3563A Control Systems Analyzer.
Abstract: This paper presents the development of adaptive noise cancelation systems for improving the intelligibility of speech transmitted in hands-free cellular phones. Both periodic and random noise cancelation techniques are developed. A narrow band noise cancelation technique, which generates the reference signal internally, thereby achieving selective cancelation of harmonics for reducing the speech distortion is proposed. The theory and design issues of subbands are explored and their application to noise cancelation is verified. A multiple channel subband adaptive noise canceler is developed to deal with the multipath, multisource nature of the noise present in the car and its effectiveness was verified through computer simulations, which were carried out using real transfer functions estimated by an HP3563A Control Systems Analyzer.
TL;DR: In this paper, a unified framework for discrete-time optimal nonlinear analysis and feedback control is developed to guarantee the stability and optimality of closed-loop nonlinear systems by means of a Lyapunov function, which can clearly be seen as the solution to the steady-state form of the discrete time Bellman equation.
Abstract: In this paper we develop a unified framework to address the problem of discrete-time optimal nonlinear analysis and feedback control Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution to the steady-state form of the discrete-time Bellman equation thus guaranteeing both stability and optimality The overall framework provides the foundation for extending discrete-time linearquadratic controller synthesis to nonlinear-nonquadratic problems
TL;DR: In this paper, the authors considered discrete-time positive linear systems having the nonnegative orthant reachable from the origin in a finite time interval with nonnegative inputs, and the solution of the positive realization problem for this class of systems is given.
Abstract: The positive realization problem for linear systems is to find, for a given transfer function, all possible realizations with a state space of minimal dimension such that the resulting system is a positive system. In this paper, discrete-time positive linear systems having the nonnegative orthant reachable from the origin in a finite time interval with nonnegative inputs, are considered and the solution of the positive realization problem for this class of systems is given.
TL;DR: In this article, the pull-in range Ω p of a second-order, Type I phase-locked loop (PLL) is defined as the maximum value of loop detuning ωos for which pullin occurs from anywhere on the PLL's phase plane.
Abstract: The pull-in range Ω p of a second-order, Type I phase-locked loop (PLL) is defined as the maximum value of loop detuning ωos for which pull-in occurs from anywhere on the PLL's phase plane. That is, pull-in is guaranteed from anywhere on the phase plane if |ω os | p . Simple approximations are available for computing Ω p . The concept is expanded here, and a definition is given for the PLL's half-plane pull-in range Ω 2 . Simply stated, pull-in is guaranteed from anywhere on the phase plane's lower-half if 0 os 2 . Unlike the parameter Ω p , a simple approximation for Ω 2 is not available. However, a Galerkin based algorithm is presented for computing the PLL's half-plane pull-in range Ω 2 , and it is applied to a simple example.
TL;DR: In this paper, a new controller design method that not only effectively suppresses vibration in flexible systems, but also has the ability to save control energy is presented. And the feasibility of applying this method to a simple and flexible structure confirms the direct relationship between their optimization criterion and effectiveness in vibration suppression.
Abstract: In this study, we present a new controller design method that not only effectively suppresses vibration in flexible systems, but also has the ability to save control energy. The proposed method allows integrated determination of sensor/actuator location and feedback gain by minimizing the sum of the integral flexible system energy and the integral control energy. Also, the cost function is characterized by an effective representation of control systems, and is determined via an efficient solution of the Lyapunov equation. The optimization problem is solved by a recursive quadratic programming algorithm. The feasibility of applying this method to a simple and flexible structure confirms the direct relationship between our optimization criterion and effectiveness in vibration suppression.
TL;DR: An adaptive generalised trimmed mean estimator for unimodal distributions is developed here to provide a unified approach to trimmed mean estimation and is employed to estimate the autocorrelations and the third-order cumulants of simulated signals from various distributions as well as output signals from MA and ARMA systems.
Abstract: The trimmed mean estimator truncates both sides of the probability distribution by the same amount. For asymmetric distributions one needs to truncate the distribution on the left and right tails by different amounts which depend on the detailed properties—like the length of tails and asymmetry—of probability distributions. An adaptive generalised trimmed mean estimator for unimodal distributions is developed here to provide a unified approach to trimmed mean estimation. As realisations of different random processes vary very much in length of tails and asymmetry, an asymmetric generalised Gaussian distribution that covers a wide range of tails and asymmetry is employed to approximate the distributions of discrete data. Using this distribution, truncation points of the discrete distribution on both sides have been obtained. The adaptive generalised trimmed mean estimator is employed to estimate the autocorrelations and the third-order cumulants of simulated signals from various distributions as well as output signals from MA and ARMA systems. Finally the algorithm is applied to the bispectral analysis of event-related EEG-signals.
TL;DR: In this paper, the integral of powers of Gaussian white noise is used to derive a generalization of the Fokker-Planck-Kolmogorov equation, which can be used in a variational approach to neighbouring stochastic optimal control.
Abstract: In order to obtain an approximate solution to the optimal control of nonlinear stochastic systems, one used to suppose that the magnitude of the noise is small enough in such a manner that one can apply a linearization around the deterministic trajectory defined by the system in the absence of noise. When this assumption is not satisfied (i.e. when the magnitude of the noise is of some importance), it is necessary to improve this approximation by taking into account the nonlinear terms of the Taylor's expansion, so that, as a result, we are so dealing with stochastic systems subject to powers of Gaussian white noise. In an engineering mathematics framework, in order to cope with the mathematical difficulties so involved, we propose an approach via the central limit theorem. We first define the integral of powers of Gaussian white noise, whereby we can derive a generalization of the Fokker-Planck-Kolmogorov equation. Then we show how this result can be used in a variational approach to neighbouring stochastic optimal control, via the moment equations.
TL;DR: In this paper, the channel impulse response and the noise model are estimated from the higher-order (fourth, e.g.) cumulant function and the second-order correlation function of the received data via a least-squares Cumulant/correlation matching criterion.
Abstract: Existing approaches to blind channel estimation and deconvolution (equalization) focus exclusively on channel or inverse-channel impulse response estimation. It is well-known that the quality of the deconvolved output depends crucially upon the noise statistics also. Typically it is assumed that the noise is white and the signal-to-noise ratio is known. In this paper we remove these restrictions. Both the channel impulse response and the noise model are estimated from the higher-order (fourth, e.g.) cumulant function and the (second-order) correlation function of the received data via a least-squares cumulant/correlation matching criterion. It is assumed that the noise higher-order cumulant function vanishes (e.g. Gaussian noise, as is the case for digital communications). Consistency of the proposed approach is established under certain mild sufficient conditions. The approach is illustrated via simulation examples involving blind equalization of digital communications signals.
TL;DR: A new stabilizability criterion and the corresponding memoryless state feedback control laws that guarantee to stabilize the mentioned system are developed by making use of the Lyapunov stability approach associated with norm or matrix measure techniques.
Abstract: In this paper, we address the robust stabilization problem by a memoryless state feedback of linear continuous systems including state time delay and parametric perturbations. Both time delay and parametric perturbations are time-varying and two classes of highly structured and unstructured perturbations are discussed respectively. By making use of the Lyapunov stability approach associated with norm or matrix measure techniques, a new stabilizability criterion and the corresponding memoryless state feedback control laws that guarantee to stabilize the mentioned system are developed. The main feature of the present schemes is that the proposed stabilizability criterion does not involve any matching conditions. Besides defining a family of allowable memoryless state feedback control laws to stabilize the time-delay systems with any one of the two classes of perturbation, it can also determine feedback controllers to guarantee that the closed-loop system have a specified stability degree. Finally, we give a numerical example and computer simulations to confirm the validity and to demonstrate the applicability of the present schemes.
TL;DR: In this paper, the dimensional-directional, the dimensional, the directional and the reduced-dimensional-dimensional equations are defined and the principle of Dimensional Directional Homogeneity is established and the Buckingham π theorem is reformulated.
Abstract: The method of dimensional-directional analysis is established by a way which consists of the representation of the physical quantities as quaternions. Two dimensional-directional bases are obtained for the particular case of Newtonian mechanics. The dimensional-directional, the dimensional, the directional and the reduced-dimensional-directional equations are defined. Furthermore, the Principle of Dimensional-directional Homogeneity is established and the Buckingham π theorem is reformulated. Some examples show the powerfulness of the dimensional-directional analysis. Finally, the conversion matrices for a change of dimensional-directional basis are given.
TL;DR: In this article, an inverse analysis is applied to identify simultaneously the constant thermal conductivity k and heat capacity C of the fluid in liminar forced convection inside a circular duct from the knowledge of transient temperature measurements taken at a single location in the downstream region.
Abstract: An inverse analysis is applied to identify simultaneously the constant thermal conductivity k and heat capacity C of the fluid in liminar forced convection inside a circular duct from the knowledge of transient temperature measurements taken at a single location in the downstream region. Transient temperatures are generated by suddenly applying a constant wall heat flux over a finite length of the duct at the inlet region. The iterative algorithm of Levenberg-Marquardt method is used to solve the resulting system of algebraic equations in the minimization procedure. The effects of sensor location both in the axial and radial directions, heated length of the duct, magnitude of applied wall heat flux, the number of measurements, and errors involved in the measured data on the accuracy of estimations are studied.
TL;DR: In this article, a comprehensive comparative analysis of the presently less known systems and the relatively similar well known Rayleigh oscillator and other related oscillators is carried out by relying on numerical simulation work.
Abstract: Switching Mode Limit-Cycle Resonant Oscillators constitute a distinct and useful class of systems in the field of oscillators. Previous works have described the oscillatory processes of such systems as being closely similar to those of other limit-cycle oscillators. The present paper shows analytically, and demonstrates by way of simulation, that the dynamic behaviour of such systems at relaxation is unique. A comprehensive comparative analysis of the presently less known systems and the relatively similar well known Rayleigh oscillator and other related oscillators is carried out by relying on numerical simulation work.
TL;DR: In this paper, the concept of strictly positive real (SPR) transfer functions is examined and it is shown that commonly used frequency domain conditions for SPR do not satisfy some of the most basic elements of the definition and properties of this class of functions.
Abstract: The concept of strictly positive real (SPR) transfer functions is examined. It is shown that commonly used frequency domain conditions for SPR do not satisfy some of the most basic elements of the definition and properties of this class of functions. For a given Hurwitz polynomial a, a degree n, we find the set of all possible polynomials b that make the ratio b a SPR, and (i) proper, and (ii) improper. Further, we show that the set of all possible bs can be parametrized in terms of, respectively, n + 1 and n + 2 numbers that satisfy a simple constraint.
TL;DR: An original algorithm that jointly estimates the synchronism and the equalizer without any training period (blind estimation) is proposed and validated using both synthetic and real data.
Abstract: This article concerns the problem of blind equalization. In practical situations, one must synchronize the receiver with the transmitter. The classical use of two separate algorithms, one for synchronization and one for equalization, does not work correctly as the channel interference increases. In such cases, one must prefer a joint estimation of the two unknown parameters (synchronization and equalization). Here, an original algorithm that jointly estimates the synchronism and the equalizer without any training period (blind estimation) is proposed. This algorithm is validated using both synthetic and real data. This study is limited to constant modulation schemes such as PSK.