State Convergence Theory Applied to a Delayed Teleoperation System

State convergence is a control strategy that was proposed in the early 2000s to ensure stability and transparency in a teleoperation system under specific control gains values. This control strategy has been implemented for a linear system with or without time delay. This paper represents the first attempt at demonstrating, theoretically and experimentantally, that this control strategy can also be applied to a nonlinear teleoperation system with n degrees of freedom and delay in the communication channel. It is assumed that the human operator applies a constant force on the local manipulator during the teleoperation. In addition, the interaction between the remote manipulator and the environment is considered passive. Communication between the local and remote sites is made by means of a communication channel with variable time delay. In this article the theory of Lyapunov-Krasovskii was used to demonstrate that the local-remote teleoperation system is asymptotically stable.

Non uniform embedding based on relevance analysis with reduced computational complexity: application to the detection of pathologies from biosignal recordings

Nonlinear analysis tools for studying and characterizing the dynamics of physiological signals have gained popularity, mainly because tracking sudden alterations of the inherent complexity of biological processes might be an indicator of altered physiological states. Typically, in order to perform an analysis with such tools, the physiological variables that describe the biological process under study are used to reconstruct the underlying dynamics of the biological processes. For that goal, a procedure called time-delay or uniform embedding is usually employed. Nonetheless, there is evidence of its inability for dealing with non-stationary signals, as those recorded from many physiological processes. To handle with such a drawback, this paper evaluates the utility of non-conventional time series reconstruction procedures based on non uniform embedding, applying them to automatic pattern recognition tasks. The paper compares a state of the art non uniform approach with a novel scheme which fuses embedding and feature selection at once, searching for better reconstructions of the dynamics of the system. Moreover, results are also compared with two classic uniform embedding techniques. Thus, the goal is comparing uniform and non uniform reconstruction techniques, including the one proposed in this work, for pattern recognition in biomedical signal processing tasks. Once the state space is reconstructed, the scheme followed characterizes with three classic nonlinear dynamic features (Largest Lyapunov Exponent, Correlation Dimension and Recurrence Period Density Entropy), while classification is carried out by means of a simple k-nn classifier. In order to test its generalization capabilities, the approach was tested with three different physiological databases (Speech Pathologies, Epilepsy and Heart Murmurs). In terms of the accuracy obtained to automatically detect the presence of pathologies, and for the three types of biosignals analyzed, the non uniform techniques used in this work lightly outperformed the results obtained using the uniform methods, suggesting their usefulness to characterize non-stationary biomedical signals in pattern recognition applications. On the other hand, in view of the results obtained and its low computational load, the proposed technique suggests its applicability for the applications under study.

The elliptic rendezvous problem in DROMO formulation

The extension of DROMO formulation to relative motion is evaluated. The orbit of the follower spacecraft can be constructed through differences on the elements defining the orbit of the leader spacecraft. Assuming that the differences are small, the problemis linearized. Typical linearized solutions to relativemotion determine the relative state of the follower spacecraft at a certain time step. Because of the form of DROMO formulation, the performance of a frozen-anomaly transformation is explored. In this case, the relative state is computed for a certain value of the anomaly, equal for leader and follower. Since the time for leader and follower do not coincide, the implicit time delay needs to be corrected to recover the physical sense of the solution. When determining the relative orbit, numerical testing shows significant error reductions compared to previous linearized solutions.

Metodología de Diseño y Análisis de Sistemas Teleoperados Considerando Dinámica No Lineal

Cuando la separación física entre el sistema local y remoto es relativamente corta, el retardo no es perceptible; sin embargo, cuando el manipulador local y el manipulador remoto se encuentran a una distancia lejana uno del otro, el retardo de tiempo ya no es insignificante e influye negativamente en la realización de la tarea. El retardo de tiempo en un sistema de control introduce un atraso de fase que a su vez degrada el rendimiento del sistema y puede causar inestabilidad. Los sistemas de teleoperación pueden sacar provecho de la posibilidad de estar presente en dos lugares simultáneamente, sin embargo, el uso de Internet y otras redes de conmutación de paquetes, tales como Internet2, impone retardos de tiempo variables, haciendo que los esquemas de control ya establecidos elaboren soluciones para hacer frente a inestabilidades causadas por estos retardos de tiempo variables. En este trabajo de tesis se presenta el modelado y análisis de un sistema de teloperación bilateral no lineal de n grados de libertad controlado por convergencia de estado. La comunicación entre el sitio local y remoto se realiza mediante un canal de comunicación con retardo de tiempo. El análisis presentado en este trabajo considera que el retardo puede ser constante o variable. Los principales objetivos de este trabajo son; 1) Desarrollar una arquitectura de control no lineal garantizando la estabilidad del sistema teleoperado, 2) Evaluar la estabilidad del sistema considerando el retardo en la comunicación, y 3) Implementación de los algoritmos desarrollados para probar el desempeño de los mismos en un sistema experimental de 3 grados de libertad. A través de la teoría de Estabilidad de Lyapunov y el funcional Lyapunov-Krasovskii, se demuestra que el sistema de lazo cerrado es asintóticamente estable. Estas conclusiones de estabilidad se han obtenido mediante la integración de la función de Lyapunov y aplicando el Lema de Barbalat. Se demuestra también que se logra sincronizar las posiciones del manipulador local y remoto cuando el operador humano no mueve el manipulador local y el manipulador remoto se mueve libremente. El esquema de control propuesto se ha validado mediante simulación y en forma experimental empleando un sistema de teleoperación real desarrollado en esta tesis doctoral y que consta de un un manipulador serie planar de tres grados de libertad, un manipulador local, PHANTOM Omni, el cual es un dispositivo haptico fabricado que consta de 3 grados de libertad (en fuerza) y que proporciona realimentación de fuerza en los ejes x,y,z. El control en tiempo real se ha diseñado usando el Sistema Operativo en Tiempo Real QuaRC de QUARC en el lado local y el Simulink Real-Time Windows TargetTM en el lado remoto. Para finalizar el resumen se destaca el impacto de esta tesis en el mundo científico a través de los resultados publicados: 2 artículos en revistas con índice de impacto , 1 artículo en una revista indexada en Sistemas, Cibernética e Informática, 7 artículos en congresos y ha obtenido un premio en la 9a. Conferencia Iberoamericana en Sistemas, Cibernética e Informática, 2010. ABSTRACT When the physical separation between the local and remote system is relatively short, the delay is not noticeable; however, when the local manipulator and the remote manipulator are at a far distance from each other, the time delay is no longer negligible and negatively influences the performance of the task. The time delay in a control system introduces a phase delay which in turn degrades the system performance and cause instability. Teleoperation systems can benefit from the ability to be in two places simultaneously, however, the use of Internet and other packet switched networks, such as Internet2, imposes varying time delays, making established control schemes to develop solutions to address these instabilities caused by different time delays. In this thesis work we present a modeling and analysis of a nonlinear bilateral teloperation system of n degrees of freedom controlled by state convergence strategy. Communication between the local and remote site is via a communication channel with time delay. The analysis presented in this work considers that the time-delay can be constant or variable. The main objectives of this work are; 1) Develop a nonlinear control schemes to ensure the stability of the teleoperated system, 2) Evaluate the system stability considering the delay in communication, and 3) Implementation of algorithms developed to test the performance of the teleoperation system in an experimental system of 3 degrees of freedom. Through the Theory of Stability of Lyapunov and the functional Lyapunov-Krasovskii, one demonstrates that the closed loop system is asymptotically stable.. The conclusions about stability were obtained by integration of the Lyapunov function and applying Barbalat Lemma. It further shows that the positions of the local and remote manipulator are synchronize when the human operator stops applying a constant force and the remote manipulator does not interact with the environment. The proposed control scheme has been validated by means of simulation and in experimental form using a developed system of real teleoperation in this doctoral thesis, which consists of a series planar manipulator of three degrees of freedom, a local manipulator, PHANTOM Omni, which is an haptic device that consists of 3 degrees of freedom (in force) and that provide feeback force in x-axis, and, z. The control in real time has been designed using the Operating system in Real time QuaRC of Quanser in the local side and the Simulink Real-Time Windows Target in the remote side. In order to finalize the summary, the highlights impact of this thesis in the scientific world are shows through the published results: 2 articles in Journals with impact factor, one article in a indexed Journal on Systemics, Cybernetics and Informatics, 7 articles in Conferences and has won an award in 9a. Conferencia Iberoamericana en Sistemas, Cibernética e Informática, 2010.

Sonic anemometry of planetary atmospheres

The application of a recently developed model of sonic anemometers measuring process has revealed that these sensors cannot be considered as absolute ones when measuring spectral characteristics of turbulent wind speed since it is demonstrated that the ratios of measured to real spectral density functions depend on the composition and temperature of the considered planetary atmosphere. The new model of the measuring process of sonic anemometers is applied to describe the measuring characteristics of these sensors as fluid/flow dependent (against the traditional hypothesis of fluid/flow independence) and hence dependent on the considered planetary atmosphere. The influence of fluid and flow characteristics (quantified via the Mach number of the flow) and the influence of the design parameters of sonic anemometers (mainly represented by time delay between pulses shots and geometry) on turbulence measurement are quantified for the atmospheres of Mars, Jupiter, and Earth. Important differences between the behavior of these sensors for the same averaged wind speed in the three considered atmospheres are detected in terms of characteristics of turbulence measurement as well as in terms of optimum values of anemometer design parameters for application on the different considered planetary atmospheres. These differences cannot be detected by traditional models of sonic anemometer measuring process based on line averaging along the sonic acoustic paths.

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k W1=1/l (where k W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k W1=C l /l, where C l is usually lesser than unity and depends on all the new parameters taken into account by the present model.

On sonic anemometer measurement theory

In this paper a model for the measuring process of sonic anemometers (ultrasound pulse based) is presented. The differential equations that describe the travel of ultrasound pulses are solved in the general case of non-steady, non-uniform atmospheric flow field. The concepts of instantaneous line-average and travelling pulse-referenced average are established and employed to explain and calculate the differences between the measured turbulent speed (travelling pulse-referenced average) and the line-averaged one. The limit k1l=1 established by Kaimal in 1968, as the maximum value which permits the neglect of the influence of the sonic measuring process on the measurement of turbulent components is reviewed here. Three particular measurement cases are analysed: A non-steady, uniform flow speed field, a steady, non-uniform flow speed field and finally an atmospheric flow speed field. In the first case, for a harmonic time-dependent flow field, Mach number, M (flow speed to sound speed ratio) and time delay between pulses have revealed themselves to be important parameters in the behaviour of sonic anemometers, within the range of operation. The second case demonstrates how the spatial non-uniformity of the flow speed field leads to an influence of the finite transit time of the pulses (M≠0) even in the absence of non-steady behaviour of the wind speed. In the last case, a model of the influence of the sonic anemometer processes on the measurement of wind speed spectral characteristics is presented. The new solution is compared to the line-averaging models existing in the literature. Mach number and time delay significantly distort the measurement in the normal operational range. Classical line averaging solutions are recovered when Mach number and time delay between pulses go to zero in the new proposed model. The results obtained from the mathematical model have been applied to the calculation of errors in different configurations of practical interest, such as an anemometer located on a meteorological mast and the transfer function of a sensor in an atmospheric wind. The expressions obtained can be also applied to determine the quality requirements of the flow in a wind tunnel used for ultrasonic anemometer calibrations.

Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

Influence of delay time on regularity estimation for voice pathology detection

The employment of nonlinear analysis techniques for automatic voice pathology detection systems has gained popularity due to the ability of such techniques for dealing with the underlying nonlinear phenomena. On this respect, characterization using nonlinear analysis typically employs the classical Correlation Dimension and the largest Lyapunov Exponent, as well as some regularity quantifiers computing the system predictability. Mostly, regularity features highly depend on a correct choosing of some parameters. One of those, the delay time �, is usually fixed to be 1. Nonetheless, it has been stated that a unity � can not avoid linear correlation of the time series and hence, may not correctly capture system nonlinearities. Therefore, present work studies the influence of the � parameter on the estimation of regularity features. Three � estimations are considered: the baseline value 1; a � based on the Average Automutual Information criterion; and � chosen from the embedding window. Testing results obtained for pathological voice suggest that an improved accuracy might be obtained by using a � value different from 1, as it accounts for the underlying nonlinearities of the voice signal.

Contribution to the improvement of communication services in nanosatellite constellations using delay and disruption tolerant networking based architectures

Esta tesis se desarrolla dentro del marco de las comunicaciones satelitales en el innovador campo de los pequeños satélites también llamados nanosatélites o cubesats, llamados así por su forma cubica. Estos nanosatélites se caracterizan por su bajo costo debido a que usan componentes comerciales llamados COTS (commercial off-the-shelf) y su pequeño tamaño como los Cubesats 1U (10cm*10 cm*10 cm) con masa aproximada a 1 kg. Este trabajo de tesis tiene como base una iniciativa propuesta por el autor de la tesis para poner en órbita el primer satélite peruano en mi país llamado chasqui I, actualmente puesto en órbita desde la Estación Espacial Internacional. La experiencia de este trabajo de investigación me llevo a proponer una constelación de pequeños satélites llamada Waposat para dar servicio de monitoreo de sensores de calidad de agua a nivel global, escenario que es usado en esta tesis. Es ente entorno y dadas las características limitadas de los pequeños satélites, tanto en potencia como en velocidad de datos, es que propongo investigar una nueva arquitectura de comunicaciones que permita resolver en forma óptima la problemática planteada por los nanosatélites en órbita LEO debido a su carácter disruptivo en sus comunicaciones poniendo énfasis en las capas de enlace y aplicación. Esta tesis presenta y evalúa una nueva arquitectura de comunicaciones para proveer servicio a una red de sensores terrestres usando una solución basada en DTN (Delay/Disruption Tolerant Networking) para comunicaciones espaciales. Adicionalmente, propongo un nuevo protocolo de acceso múltiple que usa una extensión del protocolo ALOHA no ranurado, el cual toma en cuenta la prioridad del trafico del Gateway (ALOHAGP) con un mecanismo de contienda adaptativo. Utiliza la realimentación del satélite para implementar el control de la congestión y adapta dinámicamente el rendimiento efectivo del canal de una manera óptima. Asumimos un modelo de población de sensores finito y una condición de tráfico saturado en el que cada sensor tiene siempre tramas que transmitir. El desempeño de la red se evaluó en términos de rendimiento efectivo, retardo y la equidad del sistema. Además, se ha definido una capa de convergencia DTN (ALOHAGP-CL) como un subconjunto del estándar TCP-CL (Transmission Control Protocol-Convergency Layer). Esta tesis muestra que ALOHAGP/CL soporta adecuadamente el escenario DTN propuesto, sobre todo cuando se utiliza la fragmentación reactiva. Finalmente, esta tesis investiga una transferencia óptima de mensajes DTN (Bundles) utilizando estrategias de fragmentación proactivas para dar servicio a una red de sensores terrestres utilizando un enlace de comunicaciones satelitales que utiliza el mecanismo de acceso múltiple con prioridad en el tráfico de enlace descendente (ALOHAGP). El rendimiento efectivo ha sido optimizado mediante la adaptación de los parámetros del protocolo como una función del número actual de los sensores activos recibidos desde el satélite. También, actualmente no existe un método para advertir o negociar el tamaño máximo de un “bundle” que puede ser aceptado por un agente DTN “bundle” en las comunicaciones por satélite tanto para el almacenamiento y la entrega, por lo que los “bundles” que son demasiado grandes son eliminados o demasiado pequeños son ineficientes. He caracterizado este tipo de escenario obteniendo una distribución de probabilidad de la llegada de tramas al nanosatélite así como una distribución de probabilidad del tiempo de visibilidad del nanosatélite, los cuales proveen una fragmentación proactiva óptima de los DTN “bundles”. He encontrado que el rendimiento efectivo (goodput) de la fragmentación proactiva alcanza un valor ligeramente inferior al de la fragmentación reactiva. Esta contribución permite utilizar la fragmentación activa de forma óptima con todas sus ventajas tales como permitir implantar el modelo de seguridad de DTN y la simplicidad al implementarlo en equipos con muchas limitaciones de CPU y memoria. La implementación de estas contribuciones se han contemplado inicialmente como parte de la carga útil del nanosatélite QBito, que forma parte de la constelación de 50 nanosatélites que se está llevando a cabo dentro del proyecto QB50. ABSTRACT This thesis is developed within the framework of satellite communications in the innovative field of small satellites also known as nanosatellites (<10 kg) or CubeSats, so called from their cubic form. These nanosatellites are characterized by their low cost because they use commercial components called COTS (commercial off-the-shelf), and their small size and mass, such as 1U Cubesats (10cm * 10cm * 10cm) with approximately 1 kg mass. This thesis is based on a proposal made by the author of the thesis to put into orbit the first Peruvian satellite in his country called Chasqui I, which was successfully launched into orbit from the International Space Station in 2014. The experience of this research work led me to propose a constellation of small satellites named Waposat to provide water quality monitoring sensors worldwide, scenario that is used in this thesis. In this scenario and given the limited features of nanosatellites, both power and data rate, I propose to investigate a new communications architecture that allows solving in an optimal manner the problems of nanosatellites in orbit LEO due to the disruptive nature of their communications by putting emphasis on the link and application layers. This thesis presents and evaluates a new communications architecture to provide services to terrestrial sensor networks using a space Delay/Disruption Tolerant Networking (DTN) based solution. In addition, I propose a new multiple access mechanism protocol based on extended unslotted ALOHA that takes into account the priority of gateway traffic, which we call ALOHA multiple access with gateway priority (ALOHAGP) with an adaptive contention mechanism. It uses satellite feedback to implement the congestion control, and to dynamically adapt the channel effective throughput in an optimal way. We assume a finite sensor population model and a saturated traffic condition where every sensor always has frames to transmit. The performance was evaluated in terms of effective throughput, delay and system fairness. In addition, a DTN convergence layer (ALOHAGP-CL) has been defined as a subset of the standard TCP-CL (Transmission Control Protocol-Convergence Layer). This thesis reveals that ALOHAGP/CL adequately supports the proposed DTN scenario, mainly when reactive fragmentation is used. Finally, this thesis investigates an optimal DTN message (bundles) transfer using proactive fragmentation strategies to give service to a ground sensor network using a nanosatellite communications link which uses a multi-access mechanism with priority in downlink traffic (ALOHAGP). The effective throughput has been optimized by adapting the protocol parameters as a function of the current number of active sensors received from satellite. Also, there is currently no method for advertising or negotiating the maximum size of a bundle which can be accepted by a bundle agent in satellite communications for storage and delivery, so that bundles which are too large can be dropped or which are too small are inefficient. We have characterized this kind of scenario obtaining a probability distribution for frame arrivals to nanosatellite and visibility time distribution that provide an optimal proactive fragmentation of DTN bundles. We have found that the proactive effective throughput (goodput) reaches a value slightly lower than reactive fragmentation approach. This contribution allows to use the proactive fragmentation optimally with all its advantages such as the incorporation of the security model of DTN and simplicity in protocol implementation for computers with many CPU and memory limitations. The implementation of these contributions was initially contemplated as part of the payload of the nanosatellite QBito, which is part of the constellation of 50 nanosatellites envisaged under the QB50 project.

Content Delivery System for Optimal VoD Streaming

The demand of video contents has rapidly increased in the past years as a result of the wide deployment of IPTV and the variety of services offered by the network operators. One of the services that has especially become attractive to the customers is real-time video on demand (VoD) because it offers an immediate streaming of a large variety of video contents. The price that the operators have to pay for this convenience is the increased traffic in the networks, which are becoming more congested due to the higher demand for VoD contents and the increased quality of the videos. As a solution, in this paper we propose a hierarchical network system for VoD content delivery in managed networks, which implements redistribution algorithm and a redirection strategy for optimal content distribution within the network core and optimal streaming to the clients. The system monitors the state of the network and the behavior of the users to estimate the demand for the content items and to take the right decision on the appropriate number of replicas and their best positions in the network. The system's objectives are to distribute replicas of the content items in the network in a way that the most demanded contents will have replicas closer to the clients so that it will optimize the network utilization and will improve the users' experience. It also balances the load between the servers concentrating the traffic to the edges of the network.

Broadband Channel Long Delay Cluster Measurements and Analysis at 2.4GHz in Subway Tunnels

The delay caused by the reflected ray in broadband communication has a great influence on the communications in subway tunnel. This paper presents measurements taken in subway tunnels at 2.4 GHz, with 5 MHz bandwidth. According to propagation characteristics of tunnel, the measurements were carried out with a frequency domain channel sounding technique, in three typical scenarios: line of sight (LOS), Non-line-of-sight (NLOS) and far line of sight (FLOS), which lead to different delay distributions. Firstly IFFT was chosen to get channel impulse response (CIR) h(t) from measured three-dimensional transfer functions. Power delay profile (PDP) was investigated to give an overview of broadband channel model. Thereafter, a long delay caused by the obturation of tunnel is observed and investigated in all the scenarios. The measurements show that the reflection can be greatly remained by the tunnel, which leads to long delay cluster where the reflection, but direct ray, makes the main contribution for radio wave propagation. Four important parameters: distribution of whole PDP power, first peak arriving time, reflection cluster duration and PDP power distribution of reflection cluster were studied to give a detailed description of long delay characteristic in tunnel. This can be used to ensure high capacity communication in tunnels

Analysis of the geometric altimetry to support aircraft optimal profiles within future 4D trajectory management

The use of barometric altimetry is to some extent a limiting factor on safety, predictability and efficiency of aircraft operations, and reduces the potential of the trajectory based operations capabilities. However, geometric altimetry could be used to improve all of these aspects. Nowadays aircraft altitude is estimated by applying the International Standard Atmosphere which differs from real altitude. At different temperatures for an assigned barometric altitude, aerodynamic forces are different and this has a direct relationship with time, fuel consumption and range of the flight. The study explores the feasibility of using sensors providing geometric reference altitude, in particular, to supply capabilities for the optimization of vertical profiles and also, their impact on the vertical Air Traffic Management separation assurance processes. One of the aims of the thesis is to assess if geometric altitude fulfils the aeronautical requirements through existing sensors. Also the thesis will elaborate on the advantages of geometric altitude over the barometric altitude in terms of efficiency for vertical navigation. The evidence that geometric altitude is the best choice to improve the efficiency in vertical profile and aircraft capacity by reducing vertical uncertainties will also be shown. In this paper, an atmospheric study is presented, as well as the impact of temperature deviation from International Standard Atmosphere model is analyzed in order to obtain relationship between geometric and barometric altitude. Furthermore, an aircraft model to study aircraft vertical profile is provided to analyse trajectories based on geometric altitudes.

Effect of a variable delay in delayed dynamical systems

We report numerical evidence of the effects of a periodic modulation in the delay time of a delayed dynamical system. By referring to a Mackey-Glass equation and by adding a modula- tion in the delay time, we describe how the solution of the system passes from being chaotic to shadow periodic states. We analyze this transition for both sinusoidal and sawtooth wave mod- ulations, and we give, in the latter case, the relationship between the period of the shadowed orbit and the amplitude of the modulation. Future goals and open questions are highlighted.

Optical Multistability and Oscillations in Hybrid Optical Bistable Systems with Short Delay Times

Optical instabilities in the output light from a bistable optical device (BOD) with a delayed feedback was predicted by Ikeda [1]. Gibbs et al. [2] gave the first experimental verification of this type of instabilities. From that time several groups have studied the instabilities of the BOD for different relations between the delay time tR and the time constant ح of the system. In a previous paper [3] an empirical and analytical study of instabilities in hybrid BOD was reported by us. The employed set up is shown in Fig. 1.