Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2000"

Stability analysis for neutral delay-differential systems

Abstract: In this paper, the problem of the stability analysis for neutral delay-differential systems is investigated. Using Lyapunov method, we present new sufficient conditions for the stability of the systems in terms of linear matrix inequality (LMI) which can be easily solved by various convex optimization algorithms. Numerical examples are given to illustrate the application of the proposed method.

Sliding mode controller for linear systems with mismatched time-varying uncertainties

Abstract: A new design approach of a sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. The coefficient matrix of the sliding function can be designed to satisfy a new matching condition provided time-varying uncertainties are bounded. It is shown that the system is invariant on the sliding surface. It is also shown that the stability of the closed-loop system is guaranteed. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed sliding mode controller.

Discrete evolutionary transform for time–frequency signal analysis

Abstract: In this paper, we introduce the discrete evolutionary transform (DET) capable of representing deterministic non-stationary signals. Besides the signal representation, the DET permits the computation of a kernel from which the evolutionary spectrum of the signal is obtained. The signal representation is modeled after the Wold–Cramer representation used for random non-stationary signals in Priestley's evolutionary spectral theory. The proposed transform generalizes the short-time Fourier transform and the spectrogram. To illustrate how to define the windows used in the DET we consider the Gabor and the Malvar cases. The Gabor-based window is time dependent and uses the bi-orthogonal analysis and synthesis windows of the expansion. The Malvar-based window is a function of time and of frequency, and depends on the orthogonal functions used in the expansion. Two types of transforms are shown: sinusoidal and chirp DETs. The sinusoidal DET represents well signals with narrow-band components, while the chirp transformation is capable of representing well signals with wide-band components provided that the instantaneous frequency information of the signal components is estimated. Examples are used to illustrate the implementation of the DET. The examples show the capability of the transform in providing excellent representation for a signal and a spectrum with very good time–frequency resolution.

Time–frequency maximum likelihood methods for direction finding

Abstract: This paper proposes a novel time–frequency maximum likelihood (t–f ML) method for direction-of-arrival (DOA) estimation for nonstationary signals impinging on a multi-sensor array receiver, and compares this method with conventional maximum likelihood DOA estimation techniques. Time–frequency distributions localize the signal power in the time–frequency domain, and as such enhance the effective SNR, leading to improved DOA estimation. The localization of signals with different time–frequency signatures permits the division of the time–frequency domain into smaller regions, each containing fewer signals than those incident on the array. The reduction of the number of signals within different time–frequency regions not only reduces the required number of sensors, but also decreases the computational load in multidimensional optimizations. Compared to the recently proposed time–frequency MUSIC (t–f MUSIC), the proposed t–f ML method can be applied to coherent environments, without the need to perform any type of preprocessing that is subject to both array geometry and array aperture.

Sensitivity bond graphs

Abstract: A sensitivity bond graph, of the same structure as the system bond graph, is shown to provide a simple and effective method of generating sensitivity functions of use in optimisation. The approach is illustrated in the context of partially known system parameter and state estimation.

Robust rationality and decisions under severe uncertainty

Abstract: This paper develops a prescriptive approach to decision-making with severely uncertain information, and explores risk-taking behavior, based on non-probabilistic set-models of information-gap uncertainty. Info-gap models are well suited for representing uncertainty arising from severe lack of information, and lead naturally to a decision strategy which maximizes the decision-maker's immunity to uncertainty, while also achieving no less than a specified minimum reward. We prove a “gambler's theorem” which quantifies the trade-off between reward and immunity to uncertainty. This trade-off forces the decision-maker to gamble, but without employing a probabilistic framework. We present a complementary theorem expressing the trade-off between immunity and windfall reward, and a further result characterizing the antagonism between robustness to failure and opportunity for success. Next, we develop a measure of risk-sensitivity based on the idea of immunity to uncertainty, without any probabilistic underpinning and without the assumptions of von Neumann–Morgenstern utility theory. We prove a theorem which establishes the relation between a decision-maker's aversion to uncertainty and the information which is available to him. Our final theorem establishes conditions in which the magnitude of the decision-maker's commitment of resources will increase with his fondness for risk.

Output feedback sliding mode control of base isolated structures

Abstract: The paper addresses the problem of designing stabilizing output feedback controllers for a class of nonlinear seismically excited base isolated structures with unknown parametrical uncertainties. Two types (non-adaptive and adaptive) of sliding mode controllers are presented. In both schemes, only the information on the displacements and velocities of the base and the first floor is used in the controller design. A numerical example is given to illustrate the effectiveness of the proposed strategy to a 10-storey frictional base isolated structure being subject to the El Centro earthquake.

Chua's circuit decomposition: a systematic design approach for chaotic oscillators

Abstract: The fact that Chua’s circuit can be physically decomposed into a sinusoidal oscillator coupled to an active voltage-controlled nonlinear resistor is demonstrated. The sinusoidal oscillator is the beating heart of Chua’s circuit and many novel implementations can be obtained by using di!erent sinusoidal oscillator engines. In particular, inductorless realizations can be derived not by replacing the passive inductor in the classical Chua’s circuit con"guration with an active RC emulation, but rather by replacing the passive LC tank resonator by a sinusoidal oscillator. We provide several circuit-design examples and verify our results experimentally. Finally, we state a conjecture which we believe forms a basis for the design of autonomous analog chaotic oscillators. ( 2000 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.

Stabilizing unstable periodic orbits of chaotic systems via an optimal principle

Abstract: A novel time-delayed control method is proposed for stabilizing inherent unstable periodic orbits (UPOs) in chaotic systems. Differing from the commonly used linear time-delayed feedback control form, we adopt an optimal control principle for the design of the time delayed feedback control. We explore the inherent properties of chaotic systems and use the system states and time-delayed system states in forming a performance index so that when the index is minimized, the resulting controller enables stabilization of the desired UPOs. The effectiveness of the method is confirmed by computer simulations.

Pseudo-bond graph model and simulation of a continuous stirred tank reactor

Abstract: A dynamic model is developed that allows us to represent the behavior of a continuous stirred tank reactor (CSTR) for the saponification of ethyl acetate with sodium hydroxide. The model is based on the bond graph technique, which lets us represent the molar and energy balances of the system. Various simulations were done using the ENPORT 5.2 program, enabling us to validate the model with data taken directly from the real system. A satisfactory behavior was obtained for the thermal variables involved, but for the concentration, the model tends to deviate even for values at steady state. This is due to the difficulty in estimating the experimental values of the reaction rate constants.

Physical interpretation of inverse dynamics using bicausal bond graphs

Abstract: A physical interpretation of the inverse dynamics of linear and non-linear systems is given in terms of the bond graph of the inverse system. It is argued that this interpretation yields physical insight to guide the control engineer. Examples are drawn from both robotic and process systems.

Robust filter design with pole constraints for discrete-time systems ☆

Abstract: The problem of full-order guaranteed cost H ∞ filtering design for discrete-time systems with polytope type uncertainty is investigated in this paper. The main purpose is to obtain a stable and proper linear filter such that the filtering error system remains robustly stable within a prespecified H ∞ attenuation level. Sufficient conditions for the existence of such robust filter are provided in terms of linear matrix inequalities, which can be efficiently solved by means of high-performance convex optimization procedures with global convergence assured. Moreover, as an improvement, the filter dynamics can be constrained to some specific regions inside the unit open disk.

Instantaneous spectral moments

Abstract: Density functions find application in many fields of science, math and engineering. In many cases, the density can be sufficiently characterized by some of its moments, particularly the mean, variance, skew and kurtosis. In signal analysis, densities of interest are the instantaneous power of the signal, the spectral density, and for signals with time-varying spectral content, the joint time–frequency density. As with densities in general, these signal densities may also be characterized by their low-order moments. For the case of the joint density, the moments are conditional moments, e.g., the mean frequency at a particular time. The first- and second-conditional moments of a time–frequency density have been well-studied in the past two decades; the third, fourth and higher conditional moments have not. In this paper, we propose candidates, utilizing an operator-theoretic approach, for the instantaneous spectral moments of a signal, in terms of its amplitude and phase. From these instantaneous spectral moments, we obtain expressions for the instantaneous spectral mean, variance, skew and kurtosis. We also address the question of designing kernels in the Cohen class of time–frequency distributions to obtain distributions with these moments.

Set-point weighted PID controllers for unstable systems

Abstract: The methods proposed by Astrom and Hagglund (IFAC Adaptive Control of Chemical Processes, Pergamon Press, New York, 1985, pp. 205–210), Mantz and Tacconi (Int. J. Control 49 (1989) 1465–1471; Ind. Eng. Chem. Res. 20 (1990) 1249–1253) for selection of set-point weighting parameters for stable systems are extended to unstable first-order plus time-delay (FOPTD) systems. Since these methods require the real part of the dominant pole, an analytical solution is derived for calculation of dominant poles of the closed-loop system given the PID controllers settings. For PID controller settings given by DePaor and O'Malley (Int. J. Control 49 (1989) 1273–1284) and Clement and Chidambaram (Chem. Eng. Commun. 62 (1997) 63–74), the set-point weighting parameters are calculated and simple equations are given for the parameters in terms of e (ratio of time delay to dominant time constant). Simulation results on an unstable FOPTD transfer function model and higher-order transfer function model show that the overshoot is significantly reduced by employing the set-point weighting parameters in the PID controller. The performances of the closed-loop servo responses for all the extended methods are compared.

Delay-dependent robust and reliable H∞ control for uncertain time-delay systems with actuator failures

Abstract: This paper focuses on the synthesis problem of delay-dependent robust and reliable H∞ control for linear time-delay systems with norm-bounded time-varying parameter uncertainty in the state and delayed-state matrices and also with actuator failures among a prespecified subset of actuators. Actuator failures are considered as disturbance signals of arbitrary values to the system. An LMI (Linear Matrix Inequality) method is given for the delay-dependent memoryless state feedback synthesis problem to quadratically stabilize the given systems with an H∞-norm bound constraints on attenuation of augmented disturbances, including failure signals in cases of actuator failures for any admissible uncertainty.

Deriving simulation models from bond graphs with algebraic loops.: The extension to multibond graph systems

Abstract: The first part of this paper makes an introduction to the causal problems raised in some bond graph models when implementing causality As a consequence, zero-order causal paths (ZCPs) provided of algebraic loops appear Variables involved in these loops are related themselves by means of algebraic assignments An algorithm to detect and open all the zero-order causal paths existing in any bond graph model is described Opening of topological loops will be the employed method Break variables will be the key to open the loops The algorithm selects in an optimized way the number of variables necessary to open all the topological loops corresponding to the ZCPs existing in the model The result is a set of differential-algebraic equations solved using a backward-differential formulae numerical method How to solve multibond graph systems including zero-order causal paths is the subject of the second part of this paper The constitutive relationships of multibond resistors, transformers and gyrators give way to a new class of zero-order causal paths whose most important characteristic is that their associated topological loops involve more than one direction In medium–large models these relationships produce a combinatory explosion of causal paths only treatable via software The same presented algorithms will be able to analyze and optimally choose the appropriate break variables to open all the zero-order causal paths

Robustness analysis of digital feedback control systems with time-varying sampling periods

Abstract: In the present paper, we study robustness properties of a class of digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of first-order ordinary differential equations), a nonlinear digital controller (described by systems of first-order ordinary difference equations), and appropriate interface elements between the plant and controller (A/D and D/A converters). For such systems, we establish results for exponential stability of an equilibrium (in the Lyapunov sense) in the presence of vanishing perturbations and for the boundedness of solutions (i.e., Lagrange stability) under the influence of nonvanishing perturbations. We apply these results in the study of quantization effects.

Definitions of Instantaneous Frequency under physical constraints

Abstract: Ville's definition of Instantaneous Frequency (IF), even though widely used and accepted, fails in most cases of practical interest. This failure has been often reported, namely in the multicomponent case. In this paper, we will analyze the advantages and shortcomings of that definition, and determine when and why it fails, integrating all previously reported cases of failure in a simple unified theory. We will also be able to extrapolate and predict the behavior of the traditional definition for any type of multicomponent signal. Alternative definitions of IF are discussed.

Decomposition of biomedical signals for enhancement of their time–frequency distributions

Abstract: Bilinear time–frequency distributions have been widely utilized in the analysis of nonstationary biomedical signals. A problem often arises where the time–frequency components with small-amplitude values cannot be displayed clearly. This problem results from a masking effect on these components caused by the presence of high-energy slow waves and sharp patterns in the input which produce large values in the time–frequency distribution. These large values often appear in the time–frequency plane as irregular patterns in the low-frequency range (due to slow waves), and as wide-band, impulsive components at certain points in time (due to sharp patterns). In this work we present an effective signal pre-processing method using a nonlinear operation on wavelet coefficients. This method equalizes the energy of different time–frequency components in the data so that the masking effect is greatly reduced, while the original time–frequency features of the input signal are preserved. Comparative experiments on electroencephalographic data with and without using this method have shown a clear improvement in the readability and sensitivity in bilinear time–frequency distributions.

Time–frequency analysis and classification of temporomandibular joint sounds☆

Abstract: In this paper, we present a method for time–frequency analysis and classification of temporomandibular joint (TMJ) sounds based on evolutionary spectrum. Many researchers have worked on sounds recorded from patients with pain and/or mechanical disfunction at TMJ. It is generally accepted that a detailed analysis of TMJ sounds might offer valuable information for diagnosis and initiation of a treatment. In this work, TMJ sounds from patients with different symptoms were recorded by means of accelerometers during jaw opening and closing cycles. Then, four main categories of TMJ signals were defined based on patient's medical examination and evolutionary spectra. A method is presented to classify TMJ sounds using their joint time–frequency moments and neural networks.

A new adaptive center weighted median filter using counter propagation networks

Abstract: A new type of adaptive center weighted median filters is developed for impulsive noise reduction of an image without the degradation of an original signal. The weight in the proposed filter is decided by the weight controller based on counter propagation networks. This controller classifies an input vector into some cluster according to its feature and gives the weight corresponding to the cluster. The parameters in the weight controller are adjustable by using the learning algorithm. The degradation of the original signal can be reduced by the proposed technique. An example is also given to illustrate the utility of the proposed technique.

Principle and applications of asymmetric crosstalk-resistant adaptive noise canceler

Abstract: This paper analyzes the performance of the crosstalk-resistant adaptive noise canceler (CTRANC). The CTRANC system's symmetric structure causes inconsistent performance when treating noise coming from different angles. To solve this problem, an asymmetric CTRANC (ACTRANC) structure using a delay unit on the primary channel to guarantee causality of the system is proposed. This system is analyzed in steady state assuming that the primary and reference signals are uncorrelated. The ACTRANC allows flexible alignment of the noise source with the sensor array in advanced communication applications such as adaptive noise cancellation, acoustic echo cancellation, and adaptive beamforming. Experiments are presented to demonstrate ACTRANC's performance improvement for various noise orientations.

Minimax robust nonstationary signal estimation based on a p-point uncertainty model

Abstract: We propose a time-varying Wiener filter for nonstationary signal estimation that is robust in a minimax sense. This robust Wiener filter optimizes worst-case performance within novel “p-point” uncertainty classes of nonstationary random processes. Furthermore, it features constant performance within these uncertainty classes and requires less detailed prior knowledge than the ordinary time-varying Wiener filter. We also propose a time–frequency formulation that is intuitively appealing since signal subspaces are replaced by time–frequency regions, and an efficient on-line implementation using local cosine bases. Our theory is illustrated by numerical simulations and a real-data example.

Instantaneous frequency and group delay of a filtered signal

Abstract: We present a method for obtaining the time–frequency structure of a signal that has been filtered. A simple procedure is given for obtaining the instantaneous frequency when the signal and filter are asymptotic signals.

Nonminimum phase tracking in MIMO systems with square input–output dynamics via dynamic sliding manifolds

Abstract: The approximate causal output tracking problem in nonlinear multi-input/multi-output (MIMO) nonminimum phase systems is addressed via sliding mode control. A class of MIMO nonlinear systems with matched nonlinearities as well as matched and unmatched disturbances, where the number of inputs, outputs, and the total relative degree are equal, is considered. The output tracking problem is solved using dynamic sliding manifold technique. The linear bounded error dynamics with desired eigenvalue placement forced by unmatched disturbance and causal reference output profile are provided. Addressing nonminimum phase condition, the sliding mode controller (SMC) joins features of a conventional SMC (insensitivity to matched nonlinearities and disturbances) and a conventional dynamic compensator (accomodation to unmatched disturbances). Theoretical results are demonstrated on a numerical example.

Gabor's signal expansion and the Gabor transform on a non-separable time-frequency lattice

Abstract: Gabor's signal expansion and the Gabor transform are formulated on a general, non-separable time–frequency lattice instead of on the traditional rectangular lattice. The representation of the general lattice is based on the rectangular lattice via a shear operation, which corresponds to a description of the general lattice by means of a lattice generator matrix that has the Hermite normal form. The shear operation on the lattice is associated with simple operations on the signal, on the synthesis and the analysis window, and on Gabor's expansion coefficients; these operations consist of multiplications by quadratic phase terms. Following this procedure, the well-known bi-orthogonality condition for the window functions in the rectangular sampling geometry, can be directly translated to the general case. In the same way, a modified Zak transform can be defined for the non-separable case, with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the rectangular sampling geometry.

A model matching approach for designing decentralized MIMO controllers

Abstract: A frequency-domain methodology for the design of decentralized control systems for multiple-input–multiple-output (MIMO) plants is presented. The method allows the designer to directly specify the disturbance response of the individual loops. The desired responses are incorporated through appropriately chosen reference models. A streamlined reference specification procedure is developed, which allows the designer to visualize the tradeoff between robustness and response speed. This makes it easy to pick a meaningful reference model, and significantly reduces the trial and error iterations necessary to meet the design requirements. The method is applicable to stable, non-minimum phase, irrational, and to a certain class of unstable plant models. The frequency-domain controller synthesis technique produces low order, easily implementable controllers, making the method attractive to the industry. The design examples demonstrate that achieving good disturbance rejection in each individual loop in most cases guarantees satisfactory set-point response, and good decoupling.

The statistics of time–frequency analysis

Abstract: This paper discusses time–frequency analysis from a statistical signal processing perspective. Certain nonstationary stochastic processes, known as “locally stationary processes”, have covariance functions which yield nonnegative Wigner distributions. An extension to this class of processes to include signals with frequency modulation is presented. For such processes, time–frequency spectra may be defined without invoking “local-” or “quasi-” stationarity. The bilinear class of time–frequency distributions are estimators of these time–frequency spectra. An analysis of the statistical properties of these estimators, including moments and distributional properties, is presented. A derivation of an asymptotic Cramer–Rao Lower Bound on the variance, together with results on the bias and variance, demonstrates that a trade-off exists between time–frequency resolution and the variance of the estimated representation. While perfect time–frequency resolution is possible, it can only be achieved through a corresponding increase in variance.

Signal synthesis and positive time–frequency distributions

Abstract: A method for obtaining a generalized transfer function (GTF) of a linear time-varying system based on evolutionary spectral theory is proposed. This GTF can be used to synthesize the signal, and its magnitude squared function results in the signal's positive time–frequency distribution that satisfies the marginals (i.e., a Cohen–Posch TFD). The procedure allows any prior estimate of the GTF to be modified such that the resulting posterior GTF is closest in the least square sense to the prior and satisfies the above-mentioned properties. Examples are presented to illustrate the performance of the method.

A study of an inverse method for the estimation of impulsive heat flux

Abstract: The adaptive input estimation approach which is based on the Kalman filter technique combined with a variable forgetting factor as a weighting function in recursive least-squares algorithm is adopted to investigate the estimation of impulsive heat flux of inverse heat conduction problem from experimental data. Four specific charge designs for igniters with impulsive heat flux input are solved to illustrate the effectiveness and good accuracy of the presented method.