Auxiliary Delay Research Articles

Self-Vernier Effect-Assisted Optical Fiber Sensor Based on Microwave Photonics and Its Machine Learning Analysis

Optical Vernier effect has been recently demonstrated as a tool to enhance the sensitivity of optical fiber interferometric sensors and has become a hot topic in the last few years. The generation of the Vernier effect relies on the superposition of interferograms of two interferometers (a sensing one and a reference one) with marginally different optical path differences (OPDs), where an amplitude modulation-like signal is sustained in the output spectrum. The Vernier modulation envelope exhibits significantly magnified sensitivity in response to external perturbations, compared to the individual sensing interferometer, providing a new route to new generations of ultra-sensitive optical fiber sensors. However, the construction of a Vernier effect-based sensor needs careful integration of two interferometers with a precise OPD deviation, which is challenging if not impossible sometimes. Additionally, the interrogation of a Vernier effect-based sensor requires the acquisition of its spectrum in a broad wavelength (frequency) window with a large number of sampling points, followed by cumbersome processing for the extraction of the Vernier envelope signal. In this article, we propose a new concept of the self-Vernier effect for the sensitivity improvement of optical fiber sensors. A proof-of-concept demonstration is performed using a single low-coherent microwave-photonic Fabry-Perot interferometer (FPI) with an addition of an auxiliary delay path. The self-Vernier effect is obtained by the overlap between the microwave interferogram of the FPI and its slightly time-delayed one. Detailed analyses regarding the principle, mathematical modeling, and experimental investigation are given. Moreover, we propose and demonstrate a new demodulation approach to the Vernier effect-based sensor through machine learning analysis by directly and statistically learning the embedded relation between the measurand of interest and the output spectrum. It is appreciated that the necessity of the frequency observation window and the number of sampling points can be remarkably reduced through machine learning analysis. The present interrogation strategy is highly generalizable and can be readily applied to optical-domain Vernier effect-based optical fiber sensors.

Laser Feedback FMCW Ranging System Based on Multiple-Equal-Phase-Subdivision Resampling

In this article, we propose a laser feedback frequency-modulated continuous-wave (FMCW) ranging system based on multiple-equal-phase-subdivision (MEPS) resampling. An auxiliary interferometer is employed to generate clock signal for resampling to suppress the spectral broadening caused by the nonlinearity of frequency modulation. Different from the conventional FMCW system, interference occurs between the light returning from the target and the intra-cavity light, which enables the reference arm of the measuring interferometer to be removed. The length of the auxiliary fiber required by the Nyquist sampling theorem is compressed through MEPS resampling, which reduces the size of the auxiliary path and expands the detection range. The MEPS-resampling-based distance ranging by an auxiliary delay fiber (shorter than the target distance) is demonstrated through simulation and tests. And a series of experiments are conducted to evaluate the effectiveness of the proposed system. Experimental results show that the system has a resolution of 1.98 mm and linearity of 4.99×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> . The repeatability, characterized by the standard deviation, is tested to be less than 35.2 μm. The combination of the laser feedback interferometry (which has the advantages of compactness and auto-alignment), MEPS resampling, and the FMCW optical ranging enables the proposed system to maintain high resolution and precision with a simpler structure.

Delay-Dependent Functional Observer Design for Linear Systems With Unknown Time-Varying State Delays.

Partial state estimation has numerous applications in practice. Nevertheless, designing delay-dependent functional observers (FOs) for systems with unknown time delays is rigorous and still an open dilemma. This paper addresses the problem for linear time-invariant systems with state time-varying delays. The delay is assumed to be bounded in an interval with a bounded derivative. A sliding mode FO structure that is robust against the delay uncertainties is established to this aim. The structure employs an auxiliary delay function that can be defined based on the existing knowledge on the actual delay values. Delay-dependent sufficient conditions for the stability of the observer are obtained using the Lyapunov Krasovskii approach, and are expressed in terms of a linear matrix inequality and two rank conditions. The delay-free observer structure is additionally studied and the necessary and sufficient conditions for its stability are obtained. Two descriptive numerical examples and simulation results demonstrate the design procedure and emphasize the effectiveness of the proposed observer design algorithm.

The buffer phenomenon in ring-like chains of unidirectionally connected generators

We introduce a new object, namely, a system of ordinary differential equations which is a mathematical model of a ring-like chain of unidirectionally connected RCL-generators. To study periodic solutions of travelling wave type of this system, some special tricks are used which reduce the existence and stability problems for cycles to the investigation of auxiliary delay equations. Using this approach, we establish that the number of stable travelling waves simultaneously existing in the chain increases unboundedly as the number of links of the chain increases, that is, the well-known buffer phenomenon occurs.

New methods for the investigation of periodic solutions in ring systems of unidirectionally coupled oscillators

We consider special systems of ordinary differential equations, namely, the so-called ring chains of unidirectionally coupled oscillators. A new method is developed for the investigation of the problems of existence and stability of periodic solutions for this class of systems. As a specific feature of this approach, we can mention the use of certain auxiliary delay systems for the determination of cycles and the analysis of their properties. The proposed method is illustrated by a specific example.

FMCW 레이저 거리 측정기의 비선형성 보정 방법

본 논문에서는 연속파 주파수 변조(FMCW) 레이저 거리 측정기에서 주파수 변화의 비선형성을 보정하는 기술을 제안하였다. FMCW 기반의 레이저 거리측정기는 높은 거리 분해능을 위해 주파수 변화의 선형성이 요구되며, 비선형성이 존재할 경우 비트 신호의 주파수가 일정하지 않아 거리 측정 성능에 심각한 영향을 미치게 된다. 하지만 일반적으로 주파수 변조를 위해 사용하는 VCO(Voltage Controlled Oscillator)의 출력은 비선형적인 특성을 가지게 된다. 이와 같은 주파수 변화의 비선형성을 보정하기 위하여 본 논문에서는 보조 딜레이 구조를 사용하였다. 보조 딜레이 구조에서 생성되는 신호는 거리 정보를 가진 비트 신호와 동일한 변화율을 가지며, ADC(Analog to Digital Converter)의 Trigger 신호로 사용된다. 즉, 비트 신호의 주파수와 동일한 변화율을 가지는 신호를 Trigger로 사용하여 비트 신호를 샘플링 함으로 비선형성이 보정되어 일정한 비트 주파수를 얻을 수 있고, 따라서 정확한 거리 측정을 할 수 있게 된다. 이에 대한 성능을 검증하기 위해 실험을 수행하여 그 결과를 제시하였다. 제안한 방식에 의해 비성형성으로 인한 FMCW 레이저 거리 측정기의 측정 오차를 개선하여 시스템의 성능이 향상되는 것을 확인할 수 있었다. We propose a correction method of nonlinear frequency sweep in an FMCW(Frequency Modulated Continuous Wave) laser range finder. FMCW laser range finder requires linear frequency sweep for high resolution, and nonlinear frequency sweep makes the system performance degrade. In general, VCO(Voltage Controlled Oscillator) which is a component used for frequency modulation in FMCW method has nonlinear property. To correct the nonlinear frequency sweep, we utilize an auxiliary delay structure for generating trigger signal of ADC(Analog to Digital Converter). Because the trigger signal has same rate of change with the beat signal, the nonlinearity of the beat signal can be corrected. the experimental results show that the proposed method effectively eliminates the nonlinear frequency sweep problem and enhances the system performance.

Critical parameters of integral systems with a class of analytic kernels

The critical frequencies of integral delay systems with a class of analytic kernels are determined via an auxiliary delay free system, and an upper bound on the number of critical frequencies is obtained. The critical delays are obtained by substituting these frequencies into the characteristic equation of the system. The procedure is validated with a number of nontrivial examples.

Stochastic stability of genetic regulatory networks with a finite set delay characterization

In this paper, the delay-distribution-dependent stability is derived for the stochastic genetic regulatory networks (GRNs) with a finite set delay characterization and interval parameter uncertainties. One important feature of the obtained results here is that the time-varying delays are assumed to be random and the sum of the occurrence probabilities of the delays is assumed to be 1. By employing a new Lyapunov-Krasovskii functional dependent on auxiliary delay parameters which allow the time-varying delays to be not differentiable, less conservative mean-square stochastic stability criteria are obtained. Finally, two examples are given to illustrate the effectiveness and superiority of the derived results.

Exponential stability of genetic regulatory networks with random delays

This paper on global exponential stability in the mean square sense of genetic regulatory networks (GRNs) is motivated by a practical consideration that different genes have different time delays for transcription and translation, and in some cases, each multimer is assigned to a randomly chosen gene promoter site as an activator or inhibitor. One important feature of the obtained results reported here is that the time-varying delays are assumed to be random and their probability distributions are known a priori. By employing the information of the probability distributions of the time delays, we present some stability criteria for the uncertain delayed genetic networks with SUM regulatory logic where each transcription factor acts additively to regulate a gene. The effects of both variation range and distribution probability of the time delays are taken into account in the proposed approach. Another feature of the results is that a novel Lyapunov functional dependence on auxiliary delay parameters is exploited, which renders the results to be potentially less conservative and allows the time-varying delays to be not differentiable. The theoretical findings are illustrated and verified with two examples.

Lyapunov matrices for a class of neutral type time delay systems

A class of neutral type time delay systems is presented for which computation of Lyapunov matrices is reduced to a solution of an auxiliary delay free system of linear differential matrix equations with a special set of two point boundary conditions.

Delayed State-Feedback H∞ Control

The design of H∞ controllers v.thich are based on delayed measurements of the full state vector of linear-time invariant systems is considered.Sufficient conditions are given for a prescribed bound on the H∞-norm of the closedloop, in terms of a positive semi-definite solution to an algebraic Riccati equation and by performing a singular values test on an auxiliary delay system.In the case these conditions are satisfied, the resulting controller has the structure of a linear time invariant delay system. The simplicity of the application of the proposed method is illustrated by two examples. The results are extended to the case where the measurement ofeach entry of the state vector is subject to a different delay.

Adaptive sidelobe cancellation of wide-band multipath interference

The steady-state performance of a narrow-band sidelobe canceller using a single auxiliary element with tapped delay line is analyzed for a simple two-path interference model, and an impulse response model is developed to provide insight as to the cancellation performance that might be expected. Computer solutions are then presented for various combinations of signal and multipath parameters. It is shown that auxiliary delay taps are required for effective cancellation of wide-band multipath interference, even for fractional bandwidth-delay products. Good cancellation is generally achieved provided that 1) the delay line taps are spaced much closer than the Nyquist sampling rate, and 2) the total length of the delay line considerably exceeds the longest multipath delay, depending on multipath component strengths.

Fair termination revisited—with delay

A proof method for establishing the fair termination and total correctness of both nondeterministic and concurrent programs is presented. The method calls for the extension of state by auxiliary delay variables which count down to the instant in which certain action will be scheduled. It then uses well-founded ranking to prove fair termination allowing nested fair selection and loops.