Phase Zeros Research Articles

Periodic defect modes of one-dimensional crystals containing single-negative materials

The transmission properties of a one-dimensional (1D) photonic crystal containing two kinds of single-negative (permittivity or permeability negative) material with an inserted array of defects (RHM and LHM) were presented by the transfer matrix method (TMM). The dependence of the defect modes on the structure parameters was discussed by using the TMM. In contrast to the Bragg gaps, the properties (the central frequency and width of the gap) of zero effective phase ( zero− φ eff ) and zero - n ¯ gap are invariant with a change in scale length and insensitive to the incident angles. The property of the periodic defect modes in the SNG host periodic structure was studied. It illustrates that the defect modes properties changed more by insert periodic defect than by single-media defect. The defect modes are sensitive to the parameters of the defect layers and the incident angle.

Signal-to-Noise Ratio Fundamental Limitations in Continuous-Time Linear Output Feedback Control

In the present technical note we study the fundamental limitation on stability that arise when an additive coloured Gaussian noise (ACGN) channel is explicitly considered over either the control or measurement paths of a linear time invariant (LTI) feedback loop. By considering a linear setting we can naturally express the fundamental limitation as a lower bound on the channel signal-to-noise ratio (SNR) required for stabilisability. We start by first obtaining a closed-form expression for the squared <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm of a partial fraction expansion with repeated poles in the Laplace domain. We then use the squared <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm result to obtain the closed-form expression for the infimal SNR required for stabilisability. The proposed closed-form includes the case of repeated unstable plant poles and non minimum phase (NMP) zeros.

Performance Bounds in ${\cal H}_{\infty}$ Optimal Control for Stable SISO Plants With Arbitrary Relative Degree

This note deals with performance bounds for the H infin-optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Nehari's Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem is obtained. Also, we derive an analytic expression for the optimal H infin cost as a function of the plant relative degree.

Phase-based block matching applied to motion estimation with unconventional beamforming strategies

A phase-based block matching method adapted to motion estimation with unconventional beamforming strategies is presented. The unconventional beamforming technique used allows us to obtain 2-D RF images with axial and lateral modulations. Based on these images, we propose a method that uses phase images instead of amplitude images. This way of proceeding allows us to provide an analytical solution to the local displacement estimation so that no minimization of a classical cost function is used for the local estimation. For this reason, the local estimator is directly applied to signals, without the need to process a complex cross-correlation function, as is done with most of the phase shift estimators. In this paper, the method is applied to elastography. Results with simulated data show that a downsampling of axial and lateral modulated signals leads to very little change in the accuracy and in the spatial resolution of the proposed method. For example, for decimation factors of 2 in the axial direction and of 4 in the lateral direction, the mean axial absolute error is 3 mum. The same estimation with original images provides a mean axial error of 0.7 microm. The accuracy of the lateral motion is unchanged in this case. The accuracy of our method with downsampled signals is an important issue in the purpose of a real-time implementation. With experimental data, for the same level of estimation error, classical block matching using the maximum of cross correlation as a local estimator requires images that are 36 times larger (in number of pixels) and consequently a computational time roughly 10 times longer. Our phase block matching is also shown to provide 10 percent less error than a motion estimation method based on seeking the zero of the complex correlation function phase. Finally, it is shown that given the separability of the local estimator that we propose, our method can be applied on both n-D signals and classical RF ultrasound images. The phase block matching method presented was implemented in real time on an ultrasound research scanner.

Direct confirmation of biaxiality in a bent-core mesogen through the measurement of electro-optic characteristics

We propose a method to confirm the biaxial phase in thermotropic nematic liquid crystals from measurement of the electro-optic characteristics. The electro-optic transmittance curve shows monotonic decrease to zero in the uniaxial phase but the curve shows a U-shaped behavior (or a monotonic decrease to nonzero transmittance) in the biaxial phase. In a bent-core mesogen 4,4′(1,3,4oxadiazole2,5diyl)dipheptylbenzoate (ODBP-Ph-C7), known to be in the nematic phase at temperatures between 173 and 222 °C, it has been found that its electro-optic curve at 190 °C shows a U-shaped behavior, while the curve at 210 °C shows a monotonic decrease to zero transmittance. We believe that these experimental results confirm the biaxial nature of ODBP-Ph-C7.

Recent observations of AB Dor and interpretation

AbstractWe use minimal empirical modelling techniques to interpret recent (2006–2007) photometry and spectroscopy of AB Dor. We compare, in particular, broadband (B and V) maculation effects with emission features in high‐resolution Ca II K‐line spectroscopy. We also compare emission effects in the Ca II Kand Hα lines observed at different rotational phases. We refer to a broader multiwavelength campaign, of which these optical data were a part, involving X‐ray and microwave observations to be published later. The broadband light curves are characterized by one outstanding macula, whereas the emission lines suggest 4 possible main chromospheric activity sites (‘faculae’). These appear at a similar latitude and with comparable size to the main umbra, but there are significant displacements in longitude. However, one strong facular concentration near phase zero may have a physical relationship to the main macula. The derived longitudes of these features would have been affected by differential rotation operating over the several months between the spectroscopic and photometric observations, but the difference of at least ∼30° between facula and umbra appears too great to allow their coincidence. The possibility of a large bipolar surface structure is considered, keeping in mind the bipolar character of solar activity centres: the activity of rapidly rotating cool stars being generally compared with that of the Sun, scaled up by a few orders of magnitude. Observed microwave activity may link to this same main photospheric and chromospheric centre picked up by the optical analysis. Characterization of macular and facular contributions in stellar activity sites would be improved with a closer timing of observations and higher signal to noise ratios in emission line data (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Analytic Estimation of Subsample Spatial Shift Using the Phases of Multidimensional Analytic Signals

In this correspondence, a method of analytic subsample spatial shift estimation based on an a priori n-D signal model is proposed. The estimation uses the linear phases of n analytic signals defined with the multidimensional Hilbert transform. This estimation proposes: i) an analytic solution to the n-D shift estimation and ii) an estimation without processing complex cross-correlation function or cross-spectra between signals contrary to most phase shift estimators. The method provides better performance in estimating subsample shifts than two classical estimators, one using the maximum of cross-correlation function and the other seeking the zero of the complex correlation function phase. Two delay estimators using the in-phase and quadrature-phase components of signals are also compared to our estimator. Like most estimators using the complex signal phases, the estimator proposed herein presents the advantage of unaltered accuracy when low sampled signals are used. Moreover, we show that this method can be applied to motion tracking with ultrasound images. Thus, included in a block-based motion estimation method and tested with ultrasound data, this estimator provides an analytical solution to the translation estimation problem.

A note on the proper frequency resolution for the room transfer function in the phased beam tracing method

In the simulation of acoustic response of a room, one cannot satisfactorily estimate the transfer function or the impulse response with a sparse frequency resolution. We have studied about the frequency resolution for a satisfactory estimation of room transfer function or the reverberation time using the phased beam tracing method. In order to investigate what happens with the frequency resolution, a number of frequency resolution (0.01–1Hz), which are usually employed in the numerical analysis, was tested for a room model. It was found that the total accumulated phase in a transfer function and the late part of an impulse response of a room are influenced by the frequency resolution. Main reason for the difference is the correct detection of non-minimum phase zeros, depending on the frequency resolution. A criterion for a proper frequency resolution was suggested by considering the modal density of three-dimensional space. When a sparse dataset was initially given, we showed that cubic spline interpolation can be used to enhance the precision of detection for non-minimum phase zeros.

Optimal Model Matching Design for High Bandwidth, High Resolution Positioning in AFM

This paper introduces a two degree of freedom control design for achieving robust high resolution, high bandwidth positioning systems. Feedback designs have demonstrated a significant improvement in the performance of the flexure-stage based positioning systems in atomic force microscopes (AFM) that provide large travels with high resolution. In this paper, an optimal model matching framework, where both the feedback and feedforward controllers form the decision variables, is presented which facilitates achieving better performance in terms of the resolution bandwidth and robustness to modeling uncertainties in the closed-loop device. Feedback-only designs, which significantly diminish nonlinear effects of piezoactuation and other modeling uncertainties, are restricted by practical and fundamental limitations such as the control saturation and the Bode integral law. These limitations, which become even more prominent due to non-minimum phase zeros in the context of flexure stages with non-collocated actuators and sensors, typically lead to trade-off between resolution, bandwidth and the robustness of the positioning system. A two degree of freedom controller, achieves a better trade-off by exploiting feedforward designs that are not subject to some limitations that constrain the feedback-only designs. We show that our 2DOF design achieves performance objectives that are impossible for feedback-only designs. Experiments on positioning stages on a AFM show bandwidth improvements as large as 300% over existing feedback base designs.

Indocyanine Green Plasma Disappearance Rate During the Anhepatic Phase of Orthotopic Liver Transplantation

Non-invasive pulse spectrophotometry to measure indocyanine green (ICG) elimination correlates well with the conventional invasive ICG clearance test. Nevertheless, the precision of this method remains unclear for any application, including small-for-size liver remnants. We therefore measured ICG plasma disappearance rate (PDR) during the anhepatic phase of orthotopic liver transplantation using pulse spectrophotometry. Measurements were done in 24 patients. The median PDR after exclusion of two outliers and two patients with inconstant signal was 1.55%/min (95% confidence interval [CI] = 0.8–2.2). No correlation with patient age, gender, body mass, blood loss, administration of fresh frozen plasma, norepinephrine dose, postoperative albumin (serum), or difference in pre and post transplant body weight was detected. In conclusion, we found an ICG-PDR different from zero in the anhepatic phase, an overestimation that may arise in particular from a redistribution into the interstitial space. If ICG pulse spectrophotometry is used to measure functional hepatic reserve, the verified average difference from zero (1.55%/min) determined in our study needs to be taken into account.

Adaptive Output Feedback Control of a Flexible Base Manipulator

This paper considers augmentation of an existing inertial damping mechanism by neural network-based adaptive control, for controlling a micromanipulator that is serially attached to a macromanipulator. The approach is demonstrated using an experimental test bed in which the micromanipulator is mounted at the tip of a cantilevered beam that resembles a macromanipulator with its joint locked. The inertial damping control combines acceleration feedback with position control for the micromanipulator so as to simultaneously suppress vibrations caused by the flexible beam while achieving precise tip positioning. Neural network-based adaptive elements are employed to augment the inertial damping controller when the existing control system becomes deficient due to modeling errors and uncertain operating conditions. There were several design challenges that had to be faced from an adaptive control perspective. One challenge was the presence of a nonminimum phase zero in an output feedback adaptive control design setting in which the regulated output variable has zero relative degree. Other challenges included flexibility in the actuation devices, lack of control degrees of freedom, and high dimensionality of the system dynamics. In this paper we describe how we overcame these difficulties by modifying a previous augmenting adaptive approach to make it suitable for this application. Experimental results are provided to illustrate the effectiveness of the augmenting approach to adaptive output feedback control design.

Dynamical Constraints on the Component Masses of the Cataclysmic Variable WZ Sagittae

We present phase-resolved spectroscopy of the short-period cataclysmic variable WZ Sge obtained with the Hubble Space Telescope. We were able to resolve the orbital motion of a number of absorption lines that likely probe the environment near the accreting white dwarf. The radial velocities derived from simultaneous fits to 13 absorption lines indicate an orbital velocity semi-amplitude of K-UV (47 +/- 3) km s(-1). However, we find that the phase zero is offset from the white dwarf ephemeris by +0.1. Our offset and velocity amplitude are very similar to constraints derived from optical emission lines from the quiescent accretion disk, despite the fact that we are probing material much closer to the primary. If we associate the UV amplitude with K-1, our dynamical constraints together with the published K-2 estimates and the known binary inclination of i = 77 +/- 2 imply 0.88 M-circle dot < M-1 < 1.53 M-circle dot, 0: 078 M-circle dot < M-2 < 0.13 M-circle dot, and 0.075 < q = M-2/M-1 < 0.101. If we interpret the mean velocity of the UV lines [-(16 +/- 4) km s(-1)] as being due to the gravitational redshift caused in the high-g environment near the white dwarf, we find v(grav) (56 +/- 5) km s(-1), which provides an independent estimate on the mass of the primary of M-1 (0.85 +/- 0.04) M-circle dot when coupled with a mass-radius relation. Our primary mass estimates are in excellent agreement and are also self-consistent with spectrophotometric fits to the UV fluxes despite the observed phase offset. It is at this point unclear what causes the observed phase offset in the UV spectra and by how much it distorts the radial velocity signature from the underlying white dwarf.

Basal expression rate of comK sets a ‘switching‐window’ into the K‐state of Bacillus subtilis

Bacillus subtilis cell population divides into a competent fraction and a non-competent fraction in the stationary phase. The transition from the non-competent state (with basal ComK concentration) to the K-state (with high ComK concentration) behaves like a bistable switch. To better understand the mechanism that sets the fraction of cells that switch into the K-state (K-fraction), we characterized the basal comK expression in individual non-competent cells and found a large cell-to-cell variation. Basal expression rate increased exponentially, reached a maximum and decreased towards zero in the stationary phase. Concomitantly, the intrinsic switching rate increased and decreased with a time lag. When switching was induced prematurely by reduction of ComK proteolysis, the K-fraction increased strongly. Our data support a model in which the average basal level of ComK raises during late exponential phase and due to noise in basal comK expression only those cells that are on the high end of comK expression trigger the autocatalytic feedback for ComK transcription. We show that a subsequent shut-down of basal expression rate sets a 'time-window' for switching and is thus involved in determining the K-fraction in the bimodal population.

Fundamental limit of discrete-time systems in tracking multi-tone sinusoidal signals

This paper studies the tracking performance of linear time-invariant multi-variable discrete-time systems. The specific problem under consideration is to track a multi-tone sinusoidal reference signal consisting of linear combinations of a step and several sinusoidal signals, whereas the tracking performance is measured by the energy of the error response between the output of the plant and the reference signal. Our purpose is to find the fundamental limit for the best attainable performance, under any control structures and parameters, and we seek to determine this limit analytically in terms of the given plant and reference characteristics. Both the full-information and partial-information tracking schemes are formulated and investigated to address these goals, which are concerned with whether or not the reference information is fully available for tracking. Analytical expressions are developed in full generality under full-information tracking, and for a more specialized case under partial-information scheme. In addition, an optimal cheap control design is constructed to show that the performance limit can be attained asymptotically in the full-information case. The results show that in general plant nonminimum phase zeros and reference modes can interact to fundamentally constrain a system's tracking ability. They also show that absence of full reference information can degrade the tracking performance, thus demonstrating an intrinsic trade-off between the tracking objective and the availability of the reference information.

DISCRETE-TIME ADAPTIVE CONTROL FOR CONTINUOUS-TIME SYSTEMS USING N-DELAY LIMITING-ZERO MODEL AND ITS APPLICATION TO A DD SERVO SYSTEM

A new method for designing a discrete-time adaptive control system for continuous-time system is presented. Using a new discrete-time model called the n-delay limiting-zero model, this method avoids the problem that the non-minimum phase zeros which arise in the case of rapid sampling of the continuous-time systems having the relative degree greater than one. In this paper, first, the motivation and principle of the n-delay limiting-zero model of the continuous-time system is discussed. Next, the procedure of constructing the adaptive control system based on the n-delay limiting-zero model is presented. Moreover, in order to illustrate the effectiveness of the proposed method, computer simulations and on-line experiments for DD servo system are carried out.

PERFORMANCE LIMITATION OF SYSTEMS UNDER SIGNAL-TO-NOISE CONSTRAINED CHANNEL

This paper re-discusses [1] and [11], where the prob- lems of feedback stabilization over a signal-to-noise ratio (SNR) constrained channel are studied. The first paper considers both continuous and discrete-time minimum phase systems, while the second extends the results to non-minimum phase ones and pro- poses a linear time-varying feedback strategies to eliminate the effect of non-minimum phase zeros in SNR limited stabilization. In general, the limitations on the ability to stabilize a plant over an SNR constrained channel are imposed mainly by unstable poles and non-minimum phase zeros of the plant.

Iterative learning control with advanced output data for nonlinear non-minimum phase systems

This paper investigates iterative learning control of nonlinear discrete time non-minimum phase systems in tracking problems. The main objective of this paper is to find an input-to-output mapping in order to stabilize the non-minimum phase systems and to obtain an input update law for handling uncertain systems. In conventional approaches on the tracking of non-minimum phase systems, zero dynamics is stabilized from the system equations and the input is calculated from the state information. For the learning of uncertain systems, conventional approaches depend on the output-to-state and state-to-input mappings. In the proposed method, the inverse system is stabilized using the input-to-output mapping for nonlinear non-minimum phase systems. A new input update law is proposed based on the relative degree and the number of non-minimum phase zeros. This makes the overall proposed learning system have a simple structure as in the classical ILC.

On Overshoot and Nonminimum Phase Zeros

It is widely known that real nonminimum phase zeros lead to step response undershoot, and that the size of the undershoot necessarily tends to infinity as the settling time tends to zero. In this note, we show that the presence of two or more real nonminimum phase zeros can lead to step response overshoot in addition to undershoot. A lower bound on the overshoot is derived, and it is shown that the overshoot, like the undershoot, necessarily tends to infinity as the settling time tends to zero. The results are derived for single-input-single-output linear time-invariant continuous-time systems, and apply to both open-loop control and general two degree-of-freedom closed-loop control

On Performance Limitation in Tracking a Sinusoid

This note studies the performance limitation of a feedback system with a given linear time-invariant (LTI) plant in tracking a sinusoidal signal. It continues and goes beyond some recent studies in the same topic in which it is assumed that the controller can access all the past and future values of the reference signal. In this note, we consider the more realistic (and more difficult) situation where the controller only accesses the current and past values of the reference. An explicit formula of the best attainable performance is obtained for a single-input-single-output (SISO) system which depends on the nonminimum phase zeros of the plant and the frequency of the reference sinusoid. Compared to the previously studied case when the future of the reference is available, this formula clearly shows the extra effort one has to pay due to the lack of the reference information. A partial result for a multiple-input-multiple-output (MIMO) system is also given.

MIMO Linear Equalization With an$H^infty$Criterion

In this paper, we study the problem of linearly equalizing the multiple-input multiple-output (MIMO) communications channels from an $H^infty$ point of view. $H^infty$ estimation theory has been recently introduced as a method for designing filters that have acceptable performance in the face of model uncertainty and lack of statistical information on the exogenous signals. In this paper, we obtain a closed-form solution to the square MIMO linear $H^infty$ equalization problem and parameterize all possible $H^infty$ -optimal equalizers. In particular, we show that, for minimum phase channels, a scaled version of the zero-forcing equalizer is $H^infty$ -optimal. The results also indicate an interesting dichotomy between minimum phase and nonminimum phase channels: for minimum phase channels the best causal equalizer performs as well as the best noncausal equalizer, whereas for nonminimum phase channels, causal equalizers cannot reduce the estimation error bounds from their a priori values. Our analysis also suggests certain remedies in the nonminimum phase case, namely, allowing for finite delay, oversampling, or using multiple sensors. For example, we show that $H^infty$ equalization of nonminimum phase channels requires a time delay of at least $l$ units, where $l$ is the number of nonminimum phase zeros of the channel.