Eduardo E. Paolini

Hopf bifurcation for maps: a frequency-domain approach

The application of the graphical Hopf theorem (GHT) as a tool for detecting invariant cycles in maps is presented. The invariant cycle emerging from the bifurcation is approximated using an analogous version of the GHT for continuous-time systems. This technique is formulated in the so-called frequency domain and it involves the use of the Nyquist stability criterion and the harmonic balance method. Some examples are included for illustration.

Charge coupled devices for detection of coherent neutrino-nucleus scattering

In this article the feasibility of using charge coupled devices (CCD) to detect low-energy neutrinos through their coherent scattering with nuclei is analyzed. The detection of neutrinos through this standard model process has been elusive because of the small energy deposited in such interaction. Typical particle detectors have thresholds of a few keV, and most of the energy deposition expected from coherent scattering is well below this level. The CCD detectors discussed in this paper can operate at a threshold of approximately 30 eV, making them ideal for observing this signal. On a CCD array of 500 g located next to a power nuclear reactor the number of coherent scattering events expected is about 3000 events/year. Our results shows that a detection with a confidence level of 99% can be reached within 16 days of continuous operation; with the current 52 g detector prototype this time lapse extends to five months.

Results of the engineering run of the Coherent Neutrino Nucleus Interaction Experiment (CONNIE)

The CONNIE detector prototype is operating at a distance of 30 m from the core of a 3.8 GWth nuclear reactor with the goal of establishing Charge-Coupled Devices (CCD) as a new technology for the detection of coherent elastic neutrino-nucleus scattering. We report on the results of the engineering run with an active mass of 4 g of silicon. The CCD array is described, and the performance observed during the first year is discussed. A compact passive shield was deployed around the detector, producing an order of magnitude reduction in the background rate. The remaining background observed during the run was stable, and dominated by internal contamination in the detector packaging materials. The in-situ calibration of the detector using X-ray lines from fluorescence demonstrates good stability of the readout system. The event rates with the reactor ON and OFF are compared, and no excess is observed coming from nuclear fission at the power plant. The upper limit for the neutrino event rate is set two orders of magnitude above the expectations for the standard model. The results demonstrate the cryogenic CCD-based detector can be remotely operated at the reactor site with stable noise below 2 e− RMS and stable background rates. The success of the engineering test provides a clear path for the upgraded 100 g detector to be deployed during 2016.

STUDY OF DEGENERATE BIFURCATIONS IN MAPS: A FEEDBACK SYSTEMS APPROACH

The dynamical behavior of nonlinear maps undergoing degenerate period doubling or degenerate Hopf bifurcations is studied via a frequency-domain approach. The technique is based on a discrete-time feedback representation of the system and the application of the well-known engineering tools of harmonic balance to approximate the emerging solutions. More specifically, the results are a higher-order extension of the previous developments obtained by the authors for nondegenerate bifurcations. Two examples are included for illustration.

On robust stability analysis of a control system using Laguerre series

Abstract A methodology to characterize the uncertainty description of nominal stable, time invariant linear control systems based on frequency response measurements is presented. The frequency response of the uncertain plant is modeled using series of Laguerre orthonormal functions. An algorithm to test robust stability is developed. A gain margin measure is also given.

Controlling an Inverted Pendulum with Bounded Controls

The dynamical behaviour of a simple underactuated mechanical system with a bounded continuous control law is analyzed. The system consists of a pendulum with an inertia disk mounted on its free extreme. It is driven applying torques to the inertia disk by means of a DC motor. The closed-loop system exhibits a rich and complex dynamic when a control parameter is varied. A numerical analysis reveals Hopf, fold and homoclinic bifurcations as the main phenomena. It is shown that the pendulum can be stabilized in its inverted position with zero velocity of the disk if the controller’s gains are appropriately chosen.

Frequency Analysis of PWM Inverters With Dead-Time for Arbitrary Modulating Signals

The effect of dead-time on the spectrum of pulse-width modulated signals is analyzed in this paper. The study is valid for arbitrary, band-limited modulating signals, extending previous results in the literature. A simple distortion index is developed that can be used at the design stage to select dead-time or switching frequency based on maximum allowed distortion. Experimental results with various band-limited signals reveal a very good agreement between the theoretical results and the experiments.

Simple Real-Time Digital PWM Implementation for Class-D Amplifiers With Distortion-Free Baseband

A real-time, digital algorithm for pulse width modulation (PWM) with distortion-free baseband is developed in this paper. The algorithm not only eliminates the intrinsic baseband distortion of digital PWM but also avoids the appearance of side-band components of the carrier in the baseband even for low switching frequencies. Previous attempts to implement digital PWM with these spectral properties required several processors due to their complexity; the proposed algorithm uses only several FIR filters and a few multiplications and additions and therefore is implemented in real time on a standard DSP. The performance of the algorithm is compared with that of uniform, double-edge PWM modulator via experimental measurements for several bandlimited modulating signals.

Low Distortion Switching Amplifier With Discrete-Time Click Modulation

An all-digital Class-D amplifier based on a discrete-time implementation of the click modulator is presented. The algorithm is able to generate binary signals with separated baseband, displacing the harmonic content produced by the modulation process above certain frequency chosen by the designer. Perfect demodulation can be achieved by a simple low-pass filter. Previous implementations of the discrete-time click modulator reported in the literature suffer from aliasing in the frequency domain. The approach proposed here avoids aliasing, without the necessity to increase (interpolate) the sampling frequency of the signals. Following a brief theoretical introduction, the performance of the proposed architecture is demonstrated by experimental measurements performed on an H-bridge amplifier. An 88 dB signal-to-noise ratio (SNR) and a total harmonic distortion (THD) + N less than 0.04% is attainable over the entire audio band, extending from 20 Hz up to 20 kHz; on the other hand, no traces of IMD appear above the predicted noise floor. These performance indices are obtained for switching rates as low as 40 kHz. The reduction of the switching frequency provides more flexibility for the design of the demodulation stage allowing to trade off between the complexity of the demodulation filter and the achievable efficiency of the switching stage.

Alias-Free Digital Click Modulator

An alias-free, discrete-time click modulator is developed in this paper. Previous approaches rely on translating the continuous-time click modulator to a discrete-time setting, although a key component in the click modulator - the analytic exponential modulator-cannot be exactly transformed to the discrete domain. Every discrete-time version of the click modulator reported in the literature is prone to aliasing effects that are ameliorated, but not eliminated, using interpolation techniques. The precision of the switching times of the output square wave is critical to click modulation because uncertainties in their determination adversely affect the performance and SNR of the modulator. A novel method that uses frequency domain information to compute these switching times without error is also presented. This two techniques are used to develop an off-line discrete-time click modulator that achieves a SNR larger than 180 dB for both multitonal and bandpass signals.