A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

Detection and Isolation of Simultaneous Additive and Parametric Faults in Nonlinear Stochastic Dynamical Systems

This paper presents a new fault detection and isolation scheme for dealing with simultaneous additive and parametric faults. The new design integrates a system for additive fault detection based on Castillo and Zufiria, 2009 and a new parametric fault detection and isolation scheme inspired in Munz and Zufiria, 2008 . It is shown that the so far existing schemes do not behave correctly when both additive and parametric faults occur simultaneously; to solve the problem a new integrated scheme is proposed. Computer simulation results are presented to confirm the theoretical studies.

Improving automatic detection of obstructive sleep apnea through nonlinear analysis of sustained speech

We present a novel approach for the detection of severe obstructive sleep apnea (OSA) based on patients' voices introducing nonlinear measures to describe sustained speech dynamics. Nonlinear features were combined with state-of-the-art speech recognition systems using statistical modeling techniques (Gaussian mixture models, GMMs) over cepstral parameterization (MFCC) for both continuous and sustained speech. Tests were performed on a database including speech records from both severe OSA and control speakers. A 10 % relative reduction in classification error was obtained for sustained speech when combining MFCC-GMM and nonlinear features, and 33 % when fusing nonlinear features with both sustained and continuous MFCC-GMM. Accuracy reached 88.5 % allowing the system to be used in OSA early detection. Tests showed that nonlinear features and MFCCs are lightly correlated on sustained speech, but uncorrelated on continuous speech. Results also suggest the existence of nonlinear effects in OSA patients' voices, which should be found in continuous speech.

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

Acoustic characterisation of cinema screens

As a consequence of cinema screens being placed in front of screen-speakers, a reduction in sound quality has been noticed. Cinema screens not only let the sound go through them, but also absorb a small amount of it and reflect the sound which impacts on the screen to the back, coming forward again in case it impacts on the loudspeaker. This backwards reflection in addition to the signal coming from the loudspeaker can lead to constructive or destructive interference at certain frequencies which usually results in comb filtering. In this project, this effect has been studied through researching amongst various data sheet provided by different manufacturers, acoustical measurements completed in the large anechoic chamber of the ISVR and some theoretical models developed with MatLab software. If results obtained with MatLab are accurate enough in comparison to the real measurements taken in the anechoic chamber this would lead to a good way to predict which would be the attenuation added to the system at each frequency, given that not all manufacturers provide an attenuation curve, but only an average attenuation. This average attenuation might be useless as sound waves have different wavelengths and its propagation through partitions varies. In fact, sound is composed by high and low frequencies, where high frequencies are characterised by a small wavelength which is usually easier to attenuate than low frequencies that characterised by bigger wavelengths. Furthermore, this information would be of great value to both screen manufacturers, who could offer a much more precise data in their data sheets; and customers, who would have a great amount of information to their disposal before purchasing and installing anything in their cinemas, being able to know by themselves which screen or loudspeaker should be best to meet their expectative. RESUMEN. La aparición de la digitalización de las bandas sonoras para las películas hace posible la mejora en la calidad de sonido de los cines. Sin embargo, un aspecto a tener en cuenta en esta calidad del sonido es la transmisión de éste a través de la pantalla, ya que normalmente tras ella se encuentran situados los altavoces. Las propiedades acústicas varían dependiendo del tipo de pantalla que se utilice, además de haber poca información a la que acceder para poder valorar su comportamiento. A lo largo de este proyecto, se analizan tres muestras de pantallas distintas donadas por distintos fabricantes para poder llegar a la conclusión de dependiendo del tipo de pantalla cuál es la distancia óptima a la que localizar la pantalla respecto al altavoz y con qué inclinación. Dicho análisis se realizó en la cámara anecoica del ISVR (University of Southampton) mediante la construcción de un marco de madera de 2x2 m en el que tensar las pantallas de cine, y un altavoz cuyo comportamiento sea el más similar al de los altavoces de pantalla reales. Los datos se captaron mediante cuatro micrófonos colocados en posiciones distintas y conectados al software Pulse de Brüel & Kjær, a través del cual se obtuvieron las respuestas en frecuencia del altavoz sin pantalla y con ella a diferentes distancias del altavoz. Posteriormente, los datos se analizaron con MatLab donde se calculó la atenuación, el factor de transmisión de la presión (PTF) y el análisis cepstrum. Finalmente, se realizó un modelo teórico del comportamiento de las pantallas perforadas basado en las placas perforadas utilizadas para atenuar el sonido entre distintas habitaciones. Como conclusión se llegó a que las pantallas curvadas son acústicamente más transparentes que las pantallas perforadas que a partir de 6 kHz son más acústicamente opacas. En las pantallas perforadas la atenuación depende del número de perforaciones por unidad de área y el diámetro de éstas. Dicha atenuación se reducirá si se reduce el diámetro de las perforaciones de la pantalla, o si se incrementa la cantidad de perforaciones. Acerca del efecto filtro peine, para obtener la mínima amplitud de éste la pantalla se deberá situar a una distancia entre 15 y 30 cm del altavoz, encontrando a la distancia de 30 cm que la última reflexión analizada a través de Cepstrum llega 5 ms más tarde que la señal directa, por lo cual no debería dañar el sonido ni la claridad del habla.

Non-destructive optical characterisation of fruits with time-resolved reflectance spectroscopy.

Increasing attention is being paid to the possible development of non-invasive tests for the assessment of the quality of fruits We propose a novel non-destructive method for the measurement of the internal optical properties of fruits and vegetables by means of time resolved reflectance spectroscopy in the visible and NIR range. A fully automated instrumentation for time-resolved reflectance measurements was developed It is based on mode-locked laser sources and electronics for time-correlated single photon counting, and provides a time-resolution of 120-160 ps The system was used to probe the optical properties of several species and varieties of fruits and vegetables in the red and NIR range (650-1000 nm). In most fruits, the absorption line shape is dominated by the absorption peak of water, centred around 970 nm Generally, the absorption spectra also show the spectral features typical of chlorophyll, with maximum at 675 nm In particular, for what concerns apples, variations in peak intensity are observed depending on the variety, the degree of ripeness as well as the position on the apple. For all the species and varieties considered, the transport scattering coefficient decreases progressively upon increasing the wavelength.

On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity

We study a parabolic–elliptic chemotactic system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.

Nonlinear models for lateral dynamics of railway vehicles on bridges subject to wind action

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require threedimensional coupled vehicle-bridge models, wheree consideration of wheel to rail contact is a key aspect. Furthermore, an adequate evaluation of safety of rail traffic requires nonlinear models. A nonlinear coupled model is proposed here for vehicle-structure vertical and lateral dynamics. Vehicles are considered as fully three-dimensional multibody systems including gyroscopic terms and large rotation effects. The bridge structure is modeled by means of finite elements which may be of beam, shell or continuum type and may include geometric or material nonlinearities. The track geometry includes distributed track alignment irregularities. Both subsystems (bridge and vehicles) are described with coordinates in absolute reference frames, as opposed to alternative approaches which describe the multibody system with coordinates relative to the base bridge motion. The wheelrail contact employed is a semi-Hertzian model based on realistic wheel-rail profiles. It allows a detailed geometrical description of the contact patch under each wheel including multiple-point contact, flange contact and uplift. Normal and tangential stresses in each contact are integrated at each time-step to obtain the resultant contact forces. The models have been implemented within an existing finite element analysis software with multibody capabilities, Abaqus (Simulia Ltd., 2010). Further details of the model are presented in Antolín et al. (2012). Representative applications are presented for railway vehicles under lateral wind action on laterally compliant viaducts, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

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.

Advances in Control of Teleoperation System by State Convergence

In this work, we proposes a control strategy by state convergence applied to bilateral control of a nonlinear teleoperator system with constant delay. The bilateral control of the teleoperator system considers the case when the human operator applies a constant force on the local manipulator and when the interaction of the remote manipulator with the environment is considered passive. The stability analysis is performed using Lyapunov-Krasovskii functional, it showed that using an control algorithm by state convergence for the case with constant delay, the nonlinear local and remote teleoperation system is asymptotically stable, also speeds converge to zero and position tracking is achieved. This work also presents the implementation of an experimental platform. The mechanical structure of the arm that is located in the remote side has been built and the electric servomechanism has been mounted to control their movement.

Control of a Teleoperation System by State Convergence with Variable Time Delay

In this paper, we propose a novel control scheme for bilateral teleoperation of n degree-of-freedom (DOF) nonlinear robotic systems with time-varying communication delay. We consider that the human operator contains a constant force on the local manipulator. The local and remote manipulators are coupled using state convergence control scheme. By choosing a Lyapunov-Krasovskii functional, we show that the local-remote teleoperation system is asymptotically stable. It is also shown that, in the case of reliable communication protocols, the proposed scheme guarantees that the remote manipulator tracks the delayed trajectory of the local manipulator. 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.

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.

Magnetic Attitude Control System for a Small Satellite. Impact on the Thermal Performance

El principal objetivo de la tesis es estudiar el acoplamiento entre los subsistemas de control de actitud y de control térmico de un pequeño satélite, con el fin de buscar la solución a los problemas relacionados con la determinación de los parámetros de diseño. Se considera la evolución de la actitud y de las temperaturas del satélite bajo la influencia de dos estrategias de orientación diferentes: 1) estabilización magnética pasiva de la orientación (PMAS, passive magnetic attitude stabilization), y 2) control de actitud magnético activo (AMAC, active magnetic attitude control). En primer lugar se presenta el modelo matemático del problema, que incluye la dinámica rotacional y el modelo térmico. En el problema térmico se considera un satélite cúbico modelizado por medio de siete nodos (seis externos y uno interno) aplicando la ecuación del balance térmico. Una vez establecido el modelo matemático del problema, se estudia la evolución que corresponde a las dos estrategias mencionadas. La estrategia PMAS se ha seleccionado por su simplicidad, fiabilidad, bajo coste, ahorrando consumo de potencia, masa coste y complejidad, comparado con otras estrategias. Se ha considerado otra estrategia de control que consigue que el satélite gire a una velocidad requerida alrededor de un eje deseado de giro, pudiendo controlar su dirección en un sistema inercial de referencia, ya que frecuentemente el subsistema térmico establece requisitos de giro alrededor de un eje del satélite orientado en una dirección perpendicular a la radiación solar incidente. En relación con el problema térmico, para estudiar la influencia de la velocidad de giro en la evolución de las temperaturas en diversos puntos del satélite, se ha empleado un modelo térmico linealizado, obtenido a partir de la formulación no lineal aplicando un método de perturbaciones. El resultado del estudio muestra que el tiempo de estabilización de la temperatura y la influencia de las cargas periódicas externas disminuye cuando aumenta la velocidad de giro. Los cambios de temperatura se reducen hasta ser muy pequeños para velocidades de rotación altas. En relación con la estrategia PMAC se ha observado que a pesar de su uso extendido entre los micro y nano satélites todavía presenta problemas que resolver. Estos problemas están relacionados con el dimensionamiento de los parámetros del sistema y la predicción del funcionamiento en órbita. Los problemas aparecen debido a la dificultad en la determinación de las características magnéticas de los cuerpos ferromagnéticos (varillas de histéresis) que se utilizan como amortiguadores de oscilaciones en los satélites. Para estudiar este problema se presenta un modelo analítico que permite estimar la eficiencia del amortiguamiento, y que se ha aplicado al estudio del comportamiento en vuelo de varios satélites, y que se ha empleado para comparar los resultados del modelo con los obtenidos en vuelo, observándose que el modelo permite explicar satisfactoriamente el comportamiento registrado. ABSTRACT The main objective of this thesis is to study the coupling between the attitude control and thermal control subsystems of a small satellite, and address the solution to some existing issues concerning the determination of their parameters. Through the thesis the attitude and temperature evolution of the satellite is studied under the influence of two independent attitude stabilization and control strategies: (1) passive magnetic attitude stabilization (PMAS), and (2) active magnetic attitude control (AMAC). In this regard the mathematical model of the problem is explained and presented. The mathematical model includes both the rotational dynamics and the thermal model. The thermal model is derived for a cubic satellite by solving the heat balance equation for 6 external and 1 internal nodes. Once established the mathematical model of the problem, the above mentioned attitude strategies were applied to the system and the temperature evolution of the 7 nodes of the satellite was studied. The PMAS technique has been selected to be studied due to its prevalent use, simplicity, reliability, and cost, as this strategy significantly saves the overall power, weight, cost, and reduces the complexity of the system compared to other attitude control strategies. In addition to that, another control law that provides the satellite with a desired spin rate along a desired axis of the satellite, whose direction can be controlled with respect to the inertial reference frame is considered, as the thermal subsystem of a satellite usually demands a spin requirement around an axis of the satellite which is positioned perpendicular to the direction of the coming solar radiation. Concerning the thermal problem, to study the influence of spin rate on temperature evolution of the satellite a linear approach of the thermal model is used, which is based on perturbation theory applied to the nonlinear differential equations of the thermal model of a spacecraft moving in a closed orbit. The results of this study showed that the temperature stabilization time and the periodic influence of the external thermal loads decreases by increasing the spin rate. However, the changes become insignificant for higher values of spin rate. Concerning the PMAS strategy, it was observed that in spite of its extended application to micro and nano satellites, still there are some issues to be solved regarding this strategy. These issues are related to the sizing of its system parameters and predicting the in-orbit performance. The problems were found to be rooted in the difficulties that exist in determining the magnetic characteristics of the ferromagnetic bodies (hysteresis rods) that are applied as damping devices on-board satellites. To address these issues an analytic model for estimating their damping efficiency is proposed and applied to several existing satellites in order to compare the results with their respective in-flight data. This model can explain the behavior showed by these satellites.