A UNIFIED APPROACH FOR DIGITAL REALIZATION OF FRACTIONAL ORDER OPERATOR IN DELTA DOMAIN

The fractional order operator ( , ) plays the pivotal role for the realization of fractional orders systems (FOS). For the realization of the FOS, fractional order operator (FOO) needs to be realized either in discrete or continuous time domain. Discrete time rational approximation of FOO in the -domain fails to provide meaningful information at fast sampling interval. Moreover, domain rational transfer function becomes highly sensitive with respect to its coefficients variation resulting to the poor finite word length effects for digital realization. In the other hand delta operator parameterized system allows to develop unification of continuous and discrete time formulations leading to the development of a unified framework for digital realization at fast sampling interval. The discrete time approximation of the FOO in delta domain is found to be robust to its coefficient variation in comparison to the shift operator based discretization of FOO. In this paper, discrete -operator parameterization is proposed for the digital realization using direct discretization of FOO. As a result, superior finite word length effect is observed for the realization of the FOO in discrete delta domain. Fractional order operator with different orders ( ) are considered for the realization purpose using the proposed method and the results obtained using MATLAB are presented for validation

DESIGN AND IMPLEMENTATION OF FRACTIONAL-ORDER CONTROLLER IN DELTA DOMAIN

In this work, a fractional-order controller (FOC) is designed in a discrete domain using delta operator parameterization. FOC gets rationally approximated using continued fraction expansion (CFE) in the delta domain. Whenever discretization of any continuous-time system takes place, the choice of sampling time becomes the most critical parameter to get most accurate results. Obtaining a higher sampling rate using conventional shift operator parameterization is not possible and delta operator parameterized discretize time system takes the advantages to circumvent the problem associated with the shift operator parameterization at a high sampling limit. In this work, a first-order plant with delay is considered to be controlled with FOC, and is implemented in discrete delta domain. The plant model is designed using MATLAB as well as in hardware. The fractional-order controller is tuned in the continuous domain and discretized in delta domain to make the discrete delta FOC. Continuous time fractional order operator (s±α) is directly discretized in delta domain to get the overall FOC in discrete domain. The designed controller in implemented using MATLABSimulink and dSPACE board such that dSPACEboard acts as the hardware implemented FOC. The step response characteristics of the closed-loop system using delta domain FOC resembles to that of the results obtained by continuous time controller. It proves that at a high sampling rate, the continuous-time result and discrete-time result are obtained hand to hand rather than the two individual cases. Therefore, the analysis and design of FOC parameterized with delta operator opens up a new area in the design and implementation of discrete FOC, which unifies both continuous and discrete-time results. The discrete model performance characteristics are evaluated in software simulation using MATLAB, and results are validated through the hardware implementation using dSPACE

Roundoff noise minimization in a modified direct-form delta operator IIR structure

Among various direct-form delta operator realized filter structures, the delta transposed direct-form II (δDFIIt) has been shown to produce the lowest roundoff noise gain in finite wordlength implementations. Recent analyses focus on the optimization of the free parameter Δ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified δDFIIt second-order section in which the Δs and filter coefficients at different branches are separately scaled to achieve improved roundoff noise gain minimization. Expressions for the filter coefficients are derived, and reduction of roundoff noise gain is verified by numerical examples.published_or_final_versio

Heat flow dynamics in thermal systems described by diffusive representation

The objective of this paper is to analyze the dynamics of heat flow in thermal structures working under constant temperature operation. This analysis is made using the tools of sliding mode controllers. The theory is developed considering that the thermal system can be described using diffusive representation. The experimental corroboration has been made with a prototype of a wind sensor for Mars atmosphere being controlled by a thermal sigma-delta modulator. This sensor structure allows to analyze experimentally the time-varying case since changes in wind conditions imply changes in the corresponding thermal models. The diffusive symbols of the experimental structures have been obtained from openloop measurements in which pseudo-random binary sequences of heat are injected in the sensor. With the proposed approach it is possible to predict heat flux transient waveforms in systems described by any arbitrary number of poles. This allows for the first time the analysis of lumped and distributed systems without any limitation on the number of poles describing it.Peer ReviewedPostprint (author's final draft

A NEW APPROACH FOR DIRECT DISCRETIZATION OF FRACTIONAL ORDER OPERATOR IN DELTA DOMAIN

The fractional order system (FOS) comprises fractional order operator. In order to obtain the discretized version of the fractional order system, the first step is to discretize the fractional order operator, commonly expressed as s±m, 0 < m < 1. The fractional order operator can be used as fractional order differentiator or integrator, depending upon the values of . In general, there are two approaches for discretization of fractional order operator, one is indirect method of discretization and another is direct method of discretization. The direct discretization method capitalizes the method of formation of generating function where fractional order operator s±mis expressed as a function of Z in the shift operator parameterization and continued fraction expansion (CFE) method is then utilized to get the corresponding discrete domain rational transfer function. There is an inherent problem with this discretization method using shift operator parameterization (discrete Z-domain). At fast sampling time, the discretized version of the continuous time operator or system should resemble that of the continuous time counterpart if the sampling theorem is satisfied. At very high sampling rate, the shift operator parameterized system fails to provide meaningful information due to its numerical ill conditioning. To overcome this problem, Delta operator parameterization for discretization is considered in this paper, where at fast sampling rate, the continuous time results can be obtained from the discrete time experiments and therefore a unified framework can be developed to get the discrete time results and continuous time results hand to hand. In this paper a new generating function is proposed to discretize the fractional order operator using the Gauss-Legendre 2-point quadrature rule. Additionally, the function has been expanded using the CFE in order to obtain rational approximation of the fractional order operator. The detailed mathematical formulations along with the simulation results in MATLAB, with different fractional order systems are considered, in order to prove the newness of this formulation for discretization of the FOS in complex Delta domain

Identification and control of diffusive systems applied to charge trapping and thermal space sensors

The work underlying this Thesis, has contributed to the main study and characterization of diffusive systems. The research work has been focused on the analysis of two kind of systems. On the one hand, the dynamics of thermal anemometers has been deeply studied. These sensors detect the wind velocity by measuring the power dissipated of a heated element due to forced convection. The thermal dynamics of different sensor structures have been analyzed and modeled during the Thesis work. On the other hand, we have dealed with microelectromechanical systems (MEMS). The dynamics of charge trapped in the dielectric layer of these systems has also been studied. It is know, that this undesired effect has been associated to diffusion phenomena. In this Thesis a characterization method based on the technique of Diffusive Representation (DR), for linear and nonlinear time-varying diffusive systems, is presented. This technique allows to describe a system with an arbitrary order state-space model in the frequency domain. The changes in the dynamics of a system over time may come as a result of the own actuation over the device or as a result of an external disturbance. In the wind sensor case, the time variation of the model comes from the wind, which is an external disturbance, whereas in the MEMS case, changes in the actuation voltage generate time-variation in the model. The state-space models obtained from DR characterization have proven to be able to reproduce and predict the behaviour of the devices under arbitrary excitations. Specifically, in the case of wind sensors, the thermal dynamics of these sensors, under constant temperature operation, has been predicted for different wind velocities using Sliding Mode Controllers. As it has been observed, these controllers also help to understand how the time response of a system, under closed loop, can be accelerated beyond the natural limit imposed by its own thermal circuit if the thermal filter associated to the sensor structure has only one significative time constant. The experimental corroboration of the thermal analysis is presented with various prototypes of wind sensors for Mars atmosphere. On one side, the time-varying thermal dynamics models of two different prototypes of a spherical 3-dimensional wind sensor, developed by the Micro and Nano Technologies group of the UPC, have been obtained. On the other side, the engineering model prototype of the wind sensor of the REMS (Rover Environmental Monitoring Station) instrument that it is currently on board the Curiosity rover in Mars has been characterized. For the characterization of the dynamics of the parasitic charge trapped in the dielectric layer of a MEMS device, the experimental validation is obtained through quasi-differential capacitance measurements of a two-parallel plate structure contactless capacitive MEMS.El trabajo que subyace a esta Tesis, ha contribuido principalmente al estudio y la caracterización de los sistemas difusivos. El trabajo de investigación se ha centrado en el análisis de dos tipos de sistemas. Por un lado, la dinámica de los anemómetros térmicos ha sido estudiada en profundidad. Estos sensores detectan la velocidad del viento a través de la medida de la potencia disipada en un elemento caliente debido a la convección forzada. Durante el trabajo de esta Tesis, se ha analizado y modelado la dinámica térmica de diferentes sensores . Por otro lado, se han tratado también los sistemas microelectromecánicos (MEMS). Se ha estudiado la dinámica de la carga atrapada en la capa dieléctrica de estos sistemas. Este fenómeno lento e indeseado está asociado a fenómenos de difusión. En esta Tesis se presenta un método de caracterización basado en la técnica de Representación Difusa (DR), para sistemas difusivos lineales y no lineales que varían en el tiempo. Esta técnica permite describir un sistema con un modelo de variables de estado de orden arbitrario en el dominio frecuencial. Los cambios en la dinámica de un sistema a lo largo del tiempo pueden ser debidos a la propia actuación sobre el dispositivo o como resultado de una perturbación externa. En el caso del sensor de viento, la variación de tiempo del modelo proviene de la propia variación del viento, la cual es una perturbación externa, mientras que en el caso de los dispositivos MEMS, los cambios en la tensión de actuación generan variaciones en el tiempo en el modelo. Los modelos de variables de estado obtenidos a partir de la caracterización con Representación Difusiva tienen la capacidad de reproducir y predecir el comportamiento de dichos dispositivos ante excitaciones arbitrarias. En concreto, en el caso de los sensores de viento, la dinámica térmica de estos sensores, operando a temperatura constante, se ha predicho para diferentes velocidades de viento, usando la teoría de los Sliding Mode Controllers (Controladores de Modo Deslizante). Tal y como se ha observado, estos controladores ayudan también a comprender cómo la respuesta temporal de un sistema, en lazo cerrado, puede acelerarse más allá del límite natural impuesto por su propio circuito térmico si el filtro térmico asociado a la estructura del sensor tiene solo una constante de tiempo significativa. La corroboración experimental del análisis térmico se presenta con varios prototipos de sensores de viento para la atmósfera de Marte. Por un lado, se han obtenido los modelos de la dinámica térmica variable en el tiempo de dos prototipos diferentes de un sensor de viento 3D esférico, desarrollado por el grupo de Micro y Nano Tecnologías de la UPC. Por otro lado, se ha caracterizado el prototipo de modelo de ingeniería del sensor de viento del instrumento REMS (Rover Environmental Monitoring Station) que está actualmente abordo del rover Curiosity en Marte. Para la caracterización de la dinámica de la carga atrapada en la capa dieléctrica de un dispositivo MEMS, la validación experimental se ha obtenido a través de medidas cuasi-diferenciales de la capacidad de un dispositivo MEMS con estructura de dos placas paralelas

Identification and control of diffusive systems applied to charge trapping and thermal space sensors

The work underlying this Thesis, has contributed to the main study and characterization of diffusive systems. The research work has been focused on the analysis of two kind of systems. On the one hand, the dynamics of thermal anemometers has been deeply studied. These sensors detect the wind velocity by measuring the power dissipated of a heated element due to forced convection. The thermal dynamics of different sensor structures have been analyzed and modeled during the Thesis work. On the other hand, we have dealed with microelectromechanical systems (MEMS). The dynamics of charge trapped in the dielectric layer of these systems has also been studied. It is know, that this undesired effect has been associated to diffusion phenomena. In this Thesis a characterization method based on the technique of Diffusive Representation (DR), for linear and nonlinear time-varying diffusive systems, is presented. This technique allows to describe a system with an arbitrary order state-space model in the frequency domain. The changes in the dynamics of a system over time may come as a result of the own actuation over the device or as a result of an external disturbance. In the wind sensor case, the time variation of the model comes from the wind, which is an external disturbance, whereas in the MEMS case, changes in the actuation voltage generate time-variation in the model. The state-space models obtained from DR characterization have proven to be able to reproduce and predict the behaviour of the devices under arbitrary excitations. Specifically, in the case of wind sensors, the thermal dynamics of these sensors, under constant temperature operation, has been predicted for different wind velocities using Sliding Mode Controllers. As it has been observed, these controllers also help to understand how the time response of a system, under closed loop, can be accelerated beyond the natural limit imposed by its own thermal circuit if the thermal filter associated to the sensor structure has only one significative time constant. The experimental corroboration of the thermal analysis is presented with various prototypes of wind sensors for Mars atmosphere. On one side, the time-varying thermal dynamics models of two different prototypes of a spherical 3-dimensional wind sensor, developed by the Micro and Nano Technologies group of the UPC, have been obtained. On the other side, the engineering model prototype of the wind sensor of the REMS (Rover Environmental Monitoring Station) instrument that it is currently on board the Curiosity rover in Mars has been characterized. For the characterization of the dynamics of the parasitic charge trapped in the dielectric layer of a MEMS device, the experimental validation is obtained through quasi-differential capacitance measurements of a two-parallel plate structure contactless capacitive MEMS.El trabajo que subyace a esta Tesis, ha contribuido principalmente al estudio y la caracterización de los sistemas difusivos. El trabajo de investigación se ha centrado en el análisis de dos tipos de sistemas. Por un lado, la dinámica de los anemómetros térmicos ha sido estudiada en profundidad. Estos sensores detectan la velocidad del viento a través de la medida de la potencia disipada en un elemento caliente debido a la convección forzada. Durante el trabajo de esta Tesis, se ha analizado y modelado la dinámica térmica de diferentes sensores . Por otro lado, se han tratado también los sistemas microelectromecánicos (MEMS). Se ha estudiado la dinámica de la carga atrapada en la capa dieléctrica de estos sistemas. Este fenómeno lento e indeseado está asociado a fenómenos de difusión. En esta Tesis se presenta un método de caracterización basado en la técnica de Representación Difusa (DR), para sistemas difusivos lineales y no lineales que varían en el tiempo. Esta técnica permite describir un sistema con un modelo de variables de estado de orden arbitrario en el dominio frecuencial. Los cambios en la dinámica de un sistema a lo largo del tiempo pueden ser debidos a la propia actuación sobre el dispositivo o como resultado de una perturbación externa. En el caso del sensor de viento, la variación de tiempo del modelo proviene de la propia variación del viento, la cual es una perturbación externa, mientras que en el caso de los dispositivos MEMS, los cambios en la tensión de actuación generan variaciones en el tiempo en el modelo. Los modelos de variables de estado obtenidos a partir de la caracterización con Representación Difusiva tienen la capacidad de reproducir y predecir el comportamiento de dichos dispositivos ante excitaciones arbitrarias. En concreto, en el caso de los sensores de viento, la dinámica térmica de estos sensores, operando a temperatura constante, se ha predicho para diferentes velocidades de viento, usando la teoría de los Sliding Mode Controllers (Controladores de Modo Deslizante). Tal y como se ha observado, estos controladores ayudan también a comprender cómo la respuesta temporal de un sistema, en lazo cerrado, puede acelerarse más allá del límite natural impuesto por su propio circuito térmico si el filtro térmico asociado a la estructura del sensor tiene solo una constante de tiempo significativa. La corroboración experimental del análisis térmico se presenta con varios prototipos de sensores de viento para la atmósfera de Marte. Por un lado, se han obtenido los modelos de la dinámica térmica variable en el tiempo de dos prototipos diferentes de un sensor de viento 3D esférico, desarrollado por el grupo de Micro y Nano Tecnologías de la UPC. Por otro lado, se ha caracterizado el prototipo de modelo de ingeniería del sensor de viento del instrumento REMS (Rover Environmental Monitoring Station) que está actualmente abordo del rover Curiosity en Marte. Para la caracterización de la dinámica de la carga atrapada en la capa dieléctrica de un dispositivo MEMS, la validación experimental se ha obtenido a través de medidas cuasi-diferenciales de la capacidad de un dispositivo MEMS con estructura de dos placas paralelas.Postprint (published version

Event-based fractional order control

The present study provides a generalization of event-based control to the field of fractional calculus, combining the benefits brought by the two approaches into an industrial-suitable control strategy. During recent years, control applications based on fractional order differintegral operators have gained more popularity due to their proven superior performance when compared to classical, integer order, control strategies. However, the current industrial setting is not yet prepared to fully adapt to complex fractional order control implementations that require hefty computational resources; needing highly-efficient methods with minimum control effort. The solution to this particular problem lies in combining benefits of event-based control such as resource optimization and bandwidth allocation with the superior performance of fractional order control. Theoretical and implementation aspects are developed in order to provide a generalization of event-based control into the fractional calculus field. Different numerical examples validate the proposed methodology, providing a useful tool, especially for industrial applications where the event-based control is most needed. Several event-based fractional order implementation possibilities are explored, the final result being an event-based fractional order control methodology. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Roadmap on optical security

Postprint (author's final draft