Stability Analysis of Teleoperation System by State Convergence with Variable Time Delay

We propose a novel control scheme for bilateral teleoperation of n degree-of-freedom (DOF) nonlinear robotic systems with time-varying communication delay. A major contribution from this work lies in the demonstration that the structure of a state convergence algorithm can be also applied to nth-order nonlinear teleoperation systems. By choosing a Lyapunov Krasovskii functional, we show that the local-remote teleoperation system is asymptotically stable. The time delay of communication channel is assumed to be unknown and randomly time varying, but the upper bounds of the delay interval and the derivative of the delay are assumed to be known.

Analysis of a long-time delay circuit for digital application.

Includes bibliographical references.

Variability in time delay between two models of pulse oximeters for deriving the photoplethysmographic signals

Pulse oximetry is commonly used as an arterial blood oxygen saturation (SaO(2)) measure. However, its other serial output, the photoplethysmography (PPG) signal, is not as well studied. Raw PPG signals can be used to estimate cardiovascular measures like pulse transit time (PTT) and possibly heart rate (HR). These timing-related measurements are heavily dependent on the minimal variability in phase delay of the PPG signals. Masimo SET (R) Rad-9 (TM) and Novametrix Oxypleth oximeters were investigated for their PPG phase characteristics on nine healthy adults. To facilitate comparison, PPG signals were acquired from fingers on the same hand in a random fashion. Results showed that mean PTT variations acquired from the Masimo oximeter (37.89 ms) were much greater than the Novametrix (5.66 ms). Documented evidence suggests that I ms variation in PTT is equivalent to I mmHg change in blood pressure. Moreover, the PTT trend derived from the Masimo oximeter can be mistaken as obstructive sleep apnoeas based on the known criteria. HR comparison was evaluated against estimates attained from an electrocardiogram (ECG). Novametrix differed from ECG by 0.71 +/- 0.58% (p < 0.05) while Masimo differed by 4.51 +/- 3.66% (p > 0.05). Modem oximeters can be attractive for their improved SaO(2) measurement. However, using raw PPG signals obtained directly from these oximeters for timing-related measurements warrants further investigations.

Time delay estimation with hidden Markov models

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models to identify the lag (or delay) between different variables for such data. Adopting an information-theoretic approach, we develop a procedure for training HMMs to maximise the mutual information (MMI) between delayed time series. The method is used to model the oil drilling process. We show that cross-correlation gives no information and that the MMI approach outperforms maximum likelihood.

Fibre grating time delay element for phased array antennas

The authors have demonstrated an optical fibre grating based delay line which produces time delays in increments as small as 31 ps. The device could provide a true time delay component for a phased array antenna

The application of fibre Bragg grating networks as strain sensors and as phased array antenna true time delay elements

The fabrication of in-fibre Bragg gratings, and the application of arrays of such gratings as strain sensors and as true time delay elements for the control of phased array antennas is reported. Chirped period Bragg gratings were produced using the fibre deformation fabrication technique, with chirps of between 2.9nm and 17.3nm achieved. Arrays of 5mm and 2mm long uniform period Bragg gratings were fabricated using the inscription method, for use as true time delay elements,dissimilar wavefronts and their spectral characteristics recorded. The uniform period grating arrays were used to create minimum time delays of 9.09ps, 19.02ps and 31ps; making them suitable for controlling phased array antennas operating at RF frequencies of up to 3GHz, with 10° phase resolution. Four 4mm long chirped gratings were produced using the dissimilar wavefronts fabrication method, having chirps of 7nm, 12nm, 20nm and 30nm, and were used to create time delays of between 0.3ps and 59ps. Hence they are suitable for controlling phased array antennas at RF frequencies of up to 48GHz. The application of in fibre Bragg gratings as strain sensors within smart structure materials was investigated, with their sensitivity to applied strain and compression measured for both embedded and surface mounted uniform period and fibre Fabry-Perot filter gratings. A fibre Bragg grating sensor demultiplexing scheme based on a liquid crystal filled Fabry-Perot etalon tuneable transmission filter was proposed, successfully constructed and fully characterised. Three characteristics of the LCFP etalon were found to pose operational limitations to its application in a Bragg grating sensor system; most significantly, the resonance peak wavelength was highly (-2,77nm/°C) temperature dependent. Several methods for minimising this temperature sensitivity were investigated, but enjoyed only limited success. It was therefore concluded that this type (E7 filled) of LCFP etalon is unsuitable for use as a Bragg grating sensor demultiplexing element.

Near-constant time delay response of fibre grating Sagnac loop filters

A theoretical and experimental investigation of the time delay characteristics of fiber Bragg grating-based Sagnac loops (FBGSLs) is presented. Analytic expressions for the phase and time delay of the FBGSL have been derived and excellent agreement is found between their predictions and experimental results for configurations incorporating uniform-period and chirped-period gratings. For symmetrical grating structures, it is found that the FBGSL time delay response is similar to that of the incorporated grating; with asymmetrical gratings, the FBGSL response is quite different. It is shown that wavelength-division-multiplexing filters exhibiting near-zero dispersion characteristics can be implemented using FBGSLs.

Band-pass filter with flat time delay response based on fiber grating Sagnac loop

We have developed the analytic expressions for the phase response and time delay of FBGSL of arbitrary grating structure and found that the results from the modelling are in excellent agreement with that of the experimentally measured real devices. The theoretical and experimental investigation clearly reveals that FBGSLs utilizing uniform and linearly chirped gratings exhibit a near-constant time delay in the passbands. Such multi-channel bandpass filters should be highly attractive to WDM applications as they are operating in transmission regime and offering near-zero dispersion.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

Stabilization of standing waves through time-delay feedback

Standing waves are studied as solutions of a complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms. The onset is described as an instability of the uniform oscillations with respect to spatially periodic perturbations. The solution of the standing wave pattern is given analytically and studied through simulations. © 2013 American Physical Society.

Comments on multiple oscillatory solutions in systems with time-delay feedback

A complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms is considered. In particular, multiple oscillatory solutions and their properties are studied. We present novel results regarding the disappearance of limit cycle solutions, derive analytical criteria for frequency degeneration, amplitude degeneration, frequency extrema. Furthermore, we discuss the influence of the phase shift parameter and show analytically that the stabilization of the steady state and the decay of all oscillations (amplitude death) cannot happen for global feedback only. Finally, we explain the onset of traveling wave patterns close to the regime of amplitude death.

Control of pattern formation by time-delay feedback with global and local contributions

We consider the suppression of spatiotemporal chaos in the complex GinzburgLandau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations. © 2010 Elsevier B.V. All rights reserved.

Inverted decoupling internal model control for square stable multivariable time delay systems

This paper presents a new tuning methodology of the main controller of an internal model control structure for n×n stable multivariable processes with multiple time delays based on the centralized inverted decoupling structure. Independently of the system size, very simple general expressions for the controller elements are obtained. The realizability conditions are provided and the specification of the closed-loop requirements is explained. A diagonal filter is added to the proposed control structure in order to improve the disturbance rejection without modifying the nominal set-point response. The effectiveness of the method is illustrated through different simulation examples in comparison with other works.

H-infinity control design for time-delay linear systems: a rational transfer function based approach

The aim of this paper is to present new results on H-infinity control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to H-infinity analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equations arisen from H-infinity theory. The proposed algorithm is simple, efficient and easy to implement. Some examples illustrating state and output feedback design are solved and discussed in order to put in evidence the most relevant characteristic of the theoretical results. Moreover, a practical application involving a 3-DOF networked control system is presented.