Hypertracking and Hyperrejection: Control of Signals beyond the Nyquist Frequency

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here

Waveform reconstruction with a Cs based free-induction-decay magnetometer

We demonstrate an optically pumped magnetometer (OPM) operated in a free-induction-decay (FID) configuration that is capable of tracking oscillating magnetic signals in the presence of a 50 uT static field. Excellent waveform reconstruction is demonstrated for low frequency modulations with respect to the Nyquist limited bandwidth. A 100 pT oscillation was successfully reconstructed using signal averaging, and an optimum sensitivity of 3.9 pT/sqrt{Hz} was measured from the spectrum of the residuals relative to the sinusoidal fit. The impact of the pump-probe repetition rate and spin depolarization on the frequency response of the sensor is investigated in detail using miniaturized vapor cell technology, with the (-3 dB) bandwidths residing beyond the Nyquist limit in each case. We also discuss technical limitations associated with the magnetometer when exposed to oscillating fields of sufficiently high amplitude or frequency. This is discussed in the context of potential distortions arising in the reproduced signals, induced by frequency-modulation (FM) and aliasing artefacts

Unsupervised Frequency Tracking beyond the Nyquist Limit using Markov Chains

This paper deals with the estimation of a sequence of frequencies from a corresponding sequence of signals. This problem arises in fields such as Doppler imaging where its specificity is twofold. First, only short noisy data records are available (typically four sample long) and experimental constraints may cause spectral aliasing so that measurements provide unreliable, ambiguous information. Second, the frequency sequence is smooth. Here, this information is accounted for by a Markov model and application of the Bayes rule yields the a posteriori density. The maximum a postariori is computed by a combination of Viterbi and descent procedures. One of the major features of the method is that it is entirely unsupervised. Adjusting the hyperparameters that balance data-based and prior-based information is done automatically by ML using an EM-based gradient algorithm. We compared the proposed estimate to a reference one and found that it performed better: variance was greatly reduced and tracking was correct, even beyond the Nyquist frequency

Beyond the frame rate: Measuring high-frequency fluctuations with light intensity modulation

Power spectral density measurements of any sampled signal are typically restricted by both acquisition rate and frequency response limitations of instruments, which can be particularly prohibitive for video-based measurements. We have developed a new method called Intensity Modulation Spectral Analysis (IMSA) that circumvents these limitations, dramatically extending the effective detection bandwidth. We demonstrate this by video-tracking an optically-trapped microsphere while oscillating an LED illumination source. This approach allows us to quantify fluctuations of the microsphere at frequencies over 10 times higher than the Nyquist frequency, mimicking a significantly higher frame rate.Comment: 4 pages, 2 figure

Compressive Sampling for Remote Control Systems

In remote control, efficient compression or representation of control signals is essential to send them through rate-limited channels. For this purpose, we propose an approach of sparse control signal representation using the compressive sampling technique. The problem of obtaining sparse representation is formulated by cardinality-constrained L2 optimization of the control performance, which is reducible to L1-L2 optimization. The low rate random sampling employed in the proposed method based on the compressive sampling, in addition to the fact that the L1-L2 optimization can be effectively solved by a fast iteration method, enables us to generate the sparse control signal with reduced computational complexity, which is preferable in remote control systems where computation delays seriously degrade the performance. We give a theoretical result for control performance analysis based on the notion of restricted isometry property (RIP). An example is shown to illustrate the effectiveness of the proposed approach via numerical experiments

Reset control for DC-DC converters: an experimental application

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Power converters in grid connected systems are required to have fast response to ensure the stability of the system. The standard PI controllers used in most power converters are capable of fast response but with significant overshoot. In this paper a hybrid control technique for power converter using a reset PI + CI controller is proposed. The PI + CI controller can overcome the limitation of its linear counterpart (PI) and ensure a fast flat response for power converter. The design, stability and cost of feedback analysis for a DC-DC boost converter employing a PI + CI controller is explored in this work. The simulation and experimental results which confirm the fast, flat response will be presented and discussed.Peer ReviewedPostprint (published version

Retrieving shallow shear-wave velocity profiles from 2D seismic-reflection data with severely aliased surface waves

The inversion of surface-wave phase-velocity dispersion curves provides a reliable method to derive near-surface shear-wave velocity profiles. In this work, we invert phase-velocity dispersion curves estimated from 2D seismic-reflection data. These data cannot be used to image the first 50 m with seismic-reflection processing techniques due to the presence of indistinct first breaks and significant NMO-stretching of the shallow reflections. A surface-wave analysis was proposed to derive information about the near surface in order to complement the seismic-reflection stacked sections, which are satisfactory for depths between 50 and 700 m. In order to perform the analysis, we had to overcome some problems, such as the short acquisition time and the large receiver spacing, which resulted in severe spatial aliasing. The analysis consists of spatial partitioning of each line in segments, picking of the phase-velocity dispersion curves for each segment in the f-k domain, and inversion of the picked curves using the neighborhood algorithm. The spatial aliasing is successfully circumvented by continuously tracking the surface-wave modal curves in the f-k domain. This enables us to sample the curves up to a frequency of 40 Hz, even though most components beyond 10 Hz are spatially aliased. The inverted 2D VS sections feature smooth horizontal layers, and a sensitivity analysis yields a penetration depth of 20–25 m. The results suggest that long profiles may be more efficiently surveyed by using a large receiver separation and dealing with the spatial aliasing in the described way, rather than ensuring that no spatially aliased surface waves are acquired.Fil: Onnis, Luciano Emanuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Osella, Ana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali

Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation

In this article, a framework is presented for the joint optimization of the analog transmit and receive filter with respect to a parameter estimation problem. At the receiver, conventional signal processing systems restrict the two-sided bandwidth of the analog pre-filter $B$ to the rate of the analog-to-digital converter $f_s$ to comply with the well-known Nyquist-Shannon sampling theorem. In contrast, here we consider a transceiver that by design violates the common paradigm $B\leq f_s$. To this end, at the receiver, we allow for a higher pre-filter bandwidth $B>f_s$ and study the achievable parameter estimation accuracy under a fixed sampling rate when the transmit and receive filter are jointly optimized with respect to the Bayesian Cram\'{e}r-Rao lower bound. For the case of delay-Doppler estimation, we propose to approximate the required Fisher information matrix and solve the transceiver design problem by an alternating optimization algorithm. The presented approach allows us to explore the Pareto-optimal region spanned by transmit and receive filters which are favorable under a weighted mean squared error criterion. We also discuss the computational complexity of the obtained transceiver design by visualizing the resulting ambiguity function. Finally, we verify the performance of the optimized designs by Monte-Carlo simulations of a likelihood-based estimator.Comment: 15 pages, 16 figure

The S2 VLBI Correlator: A Correlator for Space VLBI and Geodetic Signal Processing

We describe the design of a correlator system for ground and space-based VLBI. The correlator contains unique signal processing functions: flexible LO frequency switching for bandwidth synthesis; 1 ms dump intervals, multi-rate digital signal-processing techniques to allow correlation of signals at different sample rates; and a digital filter for very high resolution cross-power spectra. It also includes autocorrelation, tone extraction, pulsar gating, signal-statistics accumulation.Comment: 44 pages, 13 figure

Universal fractional-order design of linear phase lead compensation multirate repetitive control for PWM inverters

Repetitive control (RC) with linear phase lead compensation provides a simple but very effective control solution for any periodic signal with a known period. Multirate repetitive control (MRC) with a downsampling rate can reduce the need of memory size and computational cost, and then leads to a more feasible design of the plug-in repetitive control systems in practical applications. However, with fixed sampling rate, both MRC and its linear phase lead compensator are sensitive to the ratio of the sampling frequency to the frequency of interested periodic signals: (1) MRC might fails to exactly compensate the periodic signal in the case of a fractional ratio; (2) linear phase lead compensation might fail to enable MRC to achieve satisfactory performance in the case of a low ratio. In this paper, a universal fractional-order design of linear phase lead compensation MRC is proposed to tackle periodic signals with high accuracy, fast dynamic response, good robustness, and cost-effective implementation regardless of the frequency ratio, which offers a unified framework for housing various RC schemes in extensive engineering application. An application example of programmable AC power supply is explored to comprehensively testify the effectiveness of the proposed control scheme