527,741 research outputs found

    Super-Resolution Radar

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    In this paper we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the input signal is given by a weighted superposition of delayed and Doppler shifted versions of the input. This problem arises in a multitude of applications such as wireless communications and radar imaging. Due to practical constraints, the input signal has finite bandwidth B, and the received signal is observed over a finite time interval of length T only. This gives rise to a delay and Doppler resolution of 1/B and 1/T. We show that this resolution limit can be overcome, i.e., we can exactly recover the continuous delay-Doppler pairs and the corresponding attenuation factors, by solving a convex optimization problem. This result holds provided that the distance between the delay-Doppler pairs is at least 2.37/B in time or 2.37/T in frequency. Furthermore, this result allows the total number of delay-Doppler pairs to be linear up to a log-factor in BT, the dimensionality of the response of the system, and thereby the limit for identifiability. Stated differently, we show that we can estimate the time-frequency components of a signal that is S-sparse in the continuous dictionary of time-frequency shifts of a random window function, from a number of measurements, that is linear up to a log-factor in S.Comment: Revised versio

    Specification and Data Presentation in Linear Control Systems-Part Two

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    This is the second part of a 2 volume report on the specification and data presentation in linear control systems. This volume deals with Sample Data Systems, Linear Time Variable Parameter Systems, and Performance Indices, which are respectively Chapter II, III, and IV of the volume. Since these subjects are somewhat unrelated, a separate abstract is given at the beginning of each chapter, with the exception of the introductory Chapter I. The separate chapter abstracts are repeated here for the convenience of the reader. Abstract - Linear Sampled Data Control Systems The specifications recommended, for use with sampled data control systems are those recommended for linear, continuous systems [1]. These specifications must be supplemented, as is dictated by the requirements of a particular system, by compatibility considerations that are detailed in the following sections. Abstract - The Specification of Linear Time Variable Parameter Systems Linear time variable parameter (LTVP) systems are defined and subdivided into those systems with fast or slow variations and/or large or small variations. The methods of analysis of such systems are reviewed, and the following recommendations are made. Specifications 1) Time Domain Specifications (a) LTVP systems with fast variation of parameters. Simulated unfrozen system step function responses should all lie within a prescribed envelope. Whenever possible, the actual system response should be obtained. (b) LTVP systems with slow variation of parameters. Simulated or actual frozen or unfrozen system step function responses should all lie within a prescribed envelope. 2) Frequency Domain Specifications (a) LTVP system with fast variation of parameters. Frequency domain specifications are not recommended. (b) LTFP system with slow variation of parameters. The family of frequency response curves of the system frozen at different instants should all lie within a predetermined envelope. Data Presentation It is recommended that the region of variation of closed loop poles of the frozen system be exhibited on the complex plane. Thus, for example, if the only varying parameter is an open loop gain, then the region of variation of the closed loop poles will correspond to the root loci over the total range of variation of gain. It is also recommended that a family of Nyquist diagrams corresponding to the system frozen at different instants be displayed in the case of system with slow variations of parameters. Abstract - Performance Index This study was undertaken to determine whether or not Performance Indices should be used to evaluate and specify control systems* It is recommended that they not be used at this time by the Air Force for the stated purpose. A performance index is defined and detailed discussions are presented for the various performance indices. Analytical methods for evaluating performance indices are presented

    Maximum dynamic response of linear elastic SDOF systems based on an evolutionary spectral model for thunderstorm outflows

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    The study aims to estimate the maximum dynamic response of linear elastic SDOF systems subjected to thunderstorm outflows. Starting from a recently developed Evolutionary Power Spectral Density (EPSD) model for the wind velocity, the dynamic response is decomposed into a time-varying mean and a non-stationary random fluctuation. The EPSD and the Non-Geometrical Spectral Moments (NGSMs) of the random fluctuation are derived both accounting and neglecting the transient dynamics due to the modulating function of the load. The mean value of the maximum nonstationary fluctuating component of the response is estimated based on the definition of an equivalent stationary process following an approach proposed in the literature. In order to mitigate the overestimations of the maximum dynamic response due to the Poisson approximation, analogously to the formulation developed by Der Kiureghian for withe noise excitation, an equivalent expected frequency is introduced for thunderstorm excitation. Finally, the maximum dynamic response to thunderstorms is estimated as the sum of the maximum mean and fluctuating parts and a numerical validation of the results against real recorded thunderstorms is provided, highlighting the reliability of adding up the mean and fluctuating contributions and the advantages and limits of neglecting the transient dynamics

    Digital repetitive control under varying frequency conditions

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    Premi extraordinari doctorat curs 2011-2012, àmbit d’Enginyeria IndustrialThe tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.Award-winningPostprint (published version

    Application of point-process system identification techniques to complex physiological systems

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    This thesis is concerned with the application of system identification techniques to the analysis of complex physiological systems. The techniques are applied to neuronal spike-train data obtained from elements of the neuromuscular system. A brief description of the neuromuscular system is given in chapter 1, along with a more detailed discussion of the muscle spindle, which is the component of the neuromuscular system which this study deals with. In addition, some possibilities for system identification studies of the muscle spindle are discussed. The identification procedure is based on statistical methods for the treatment of point-process data. The point-process representation of a spike-train is introduced in chapter 2 with definitions of time and frequency domain point-process parameters. Estimates for these parameters are given, along with expressions for their asymptotic distributions. The linear point-process system identification model is introduced and estimates are described for the model parameters in terms of the previously defined point-process parameters. These point-process and linear parameter estimates are applied to muscle spindle spike-train data. In the analysis of a single spike-train certain important features only show up in the frequency domain, and for input and output spike-trains a linear transfer function type description is constructed in the frequency domain. The mathematical model of this transfer function is used as the basis for an analogue computer simulation of a subsystem of the muscle spindle. This consists of a linear first order filter followed by an encoder which generates output spikes. Data logged from the simulation is processed in the same manner as experimental data, and the effect of varying the simulation parameters on the linear model estimates is looked at. It is shown that in general the linear model description reflects the properties of the linear filter in the simulation, and varying the simulation parameters can be used to accurately match results from simulated data with those obtained from real data. Chapter 3 compares the point-process approach with a more conventional filtering and sampled data approach to estimate power spectra. The filtering of spike-trains with broad band spectra is investigated, and this shows up a pitfall in the choice of filter cut-off frequency. It is concluded that the point-process approach is preferable due to shorter computational times, and the well documented statistical propeties of the point-process estimates. The application of the point-process techniques described in chapter 2 to the analysis of more general spike-train data is considered in chapter 4. Three techniques for measuring the degree of coupling between two spike-trains are compared, and the point-process frequency domain measure is found to be the most sensitive. This measure is also applied to a data set containing a strong single periodicity, and the ability to detect coupling at a single harmonic is demonstrated. The analysis of coupling between spike-trains in the frequency domain is extended to deal with multiple spike-trains, and the ability to distinguish genuine coupling from the effect of a common input is shown to be a powerful tool which can be used to investigate communications pathways in neural systems. Finally, one special feature of the muscle spindle response to a spike-train input is analysed using the simulation. It is demonstrated that the point-process approach can produce results about a particular phenomenon from a single experiment much more rapidly than using a repetitive trial and error approach. Chapter 5 considers the extension of the linear point-process identification model introduced in chapter 2. Higher order time and frequency domain point-process parameters are defined and estimates given. In the time domain, a new technique for rapidly generating higher order time domain parameters is developed. The quadratic point-process model is introduced and solutions for its parameters given. These estimates are applied to muscl

    Adaptive traffic signal control using approximate dynamic programming

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    This thesis presents a study on an adaptive traffic signal controller for real-time operation. An approximate dynamic programming (ADP) algorithm is developed for controlling traffic signals at isolated intersection and in distributed traffic networks. This approach is derived from the premise that classic dynamic programming is computationally difficult to solve, and approximation is the second-best option for establishing sequential decision-making for complex process. The proposed ADP algorithm substantially reduces computational burden by using a linear approximation function to replace the exact value function of dynamic programming solution. Machine-learning techniques are used to improve the approximation progressively. Not knowing the ideal response for the approximation to learn from, we use the paradigm of unsupervised learning, and reinforcement learning in particular. Temporal-difference learning and perturbation learning are investigated as appropriate candidates in the family of unsupervised learning. We find in computer simulation that the proposed method achieves substantial reduction in vehicle delays in comparison with optimised fixed-time plans, and is competitive against other adaptive methods in computational efficiency and effectiveness in managing varying traffic. Our results show that substantial benefits can be gained by increasing the frequency at which the signal plans are revised. The proposed ADP algorithm is in compliance with a range of discrete systems of resolution from 0.5 to 5 seconds per temporal step. This study demonstrates the readiness of the proposed approach for real-time operations at isolated intersections and the potentials for distributed network control

    Frequency-Domain Analysis of Linear Time-Periodic Systems

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    In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature

    A nyquist criterion for time-varying periodic systems, with application to a hydraulic test bench

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    In this paper, stability results dedicated to sampled periodic systems are applied to a mechanical system whose stiffness exhibits quick variations: a hydraulic test bench used to achieve mechanical test on complex structures. To carry out this application, time-varying w transformation representation of sampled periodic systems are first introduced. An extension of the Nyquist Criterion to sampled periodic systems is then given. Finally, this theorem is applied to evaluate the stability degree of the hydraulic test bench controlled using CRONE control methodology
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