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It is well known that typical welding processes such as laser welding are nonlinear although mostly they are treated as linear system. For the purpose of automatic control, Identification of nonlinear system, especially welding processes is a necessary and fundamental problem. The purpose of this research is to develop a simple and practical identification and control for welding processes. Many investigations have shown the possibility to represent physical processes by nonlinear models, such as Hammerstein structure, consisting of a nonlinearity and linear dynamics in series with each other. Motivated by the fact that typical welding processes do not have non-zeroes, a novel two-step nonlinear Hammerstein identification method is proposed for laser welding processes. The method can be realized both in continuous and discrete case. To study the relation among parameters influencing laser processing, a standard diode laser processing system is built as system prototype. Based on experimental study, a SISO and 2ISO nonlinear Hammerstein model structure are developed to approximate the diode laser welding process. Specific persistent excitation signals such as PRTS (Pseudo-random-ternary-series) to Step signal are used for identification. The model takes welding speed as input and the top surface molten weld pool width as output. A vision based sensor implemented with a Pulse-controlled-CCD camera is proposed and applied to acquire the images and the geometric data of the weld pool. The estimated model is then verified by comparing the simulation and experimental measurement. The verification shows that the model is reasonably correct and can be use to model the nonlinear process for further study. The two-step nonlinear identification method is proved valid and applicable to traditional welding processes and similar manufacturing processes. Based on the identified model, nonlinear control algorithms are also studied. Algorithms include simple linearization and backstepping based robust adaptive control algorithm are proposed and simulated.

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The understanding of how structural components endure loads, in particular variable loads, is that these components gradually, over some period of time depending on the nature of the loading and the material, develop a microcrack. After some additional time and loading, the microcrack grows to a size that might be detected. Beyond that point, the microcrack propagates in a manner that can be reliably predicted by computer analysis codes. Consequently, one can define different stages for the life of a structural component. These are: 1) the period prior to the formation of a microcrack, 2) the period of microcrack growth, and finally 3) the period of crack growth. To date, structural health monitoring approaches that seek to detect cracks offer no insight into the extent of deterioration occurring in the initial stage that is a precursor to the formation of the microcrack or its growth. However, an approach that would facilitate monitoring the extent of the deterioration that takes place during this stage promises to improve life prediction capabilities of structural components. The challenge, thus, is to develop quantitative assessment of damage accumulation from the earliest stages of the fatigue process and to provide a structure's signature that is dependent of the damage stage. One such signature is the structure's response to forced excitation. The realization of such a goal would help in advancing structural health monitoring procedures using interrogative system identification techniques and determine sensitivities of physical parameters to damage. Additionally, vibration-based spectral quantities are related to physical properties of the structure under test. In this thesis, nonlinear response to parametric excitation is exploited for nonlinear system identification of metallic and composite beam-mass systems before damage initiation through intermediate states of damage progression to failure. Parametric identification procedure combines linear and higher order spectral analysis of vibration measurements and perturbation techniques for the derivation of the approximate solution of the system nonlinear governing differential equation. The possibility of using optical Fiber Bragg Grating sensors technology for damage localization is also assessed. Spectral moments and quantities obtained from fiber optic strain measurements are evaluated near and away from cracks to assess the relation between these moments and cracks. Variations in parameters representing natural frequency, damping and effective nonlinearities for different levels of progressive damage in a beam-mass system have been determined. Their percentage variations have been quantified to establish their sensitivities to damage initiation. The results show that damping and effective nonlinearity parameters are more sensitive to damage conditions than the natural frequency of the first mode. Crack localization is assessed by means of optical fiber technology for a composite beam-mass system. The results show that noise levels in fiber optic signals are high in comparison to strain gage signals. Of particular interest, however, is the observation that the nonlinear response is more pronounced near the cracks than away from them. / Ph. D.

An optimal solution of vortex-induced vibrations of structures would be a time-domain numerical simulation that simultaneously solves the fluid flow and structural response. Yet, the requirements in terms of computing power remains a major obstacle for implementing such a simulation. On the other hand, lower- or reduced-order models provide an alternative for determining structural response to forcing by fluid flow. The objective of this thesis is to provide a consistent approach for the development of reduced-order models for the lift and drag on oscillating cylinders and the identification of their parameters. Amplitudes and phases of higher-order spectral moments of the lift and drag coefficients data are combined with approximate solutions of the representative models to determine their parameters. The results show that the amplitude and phase of the trispectrum could be used to model the lift on the oscillating cylinder under different excitation conditions. Moreover, the amplitude and phase of the cross-bispectrum could be used to establish the lift-drag relation for oscillating cylinders. A forced van der Pol equation is used to represent the lift on a transversely oscillating cylinder, and a parametrically excited van der Pol equation is used to model the lift coefficient on an inline oscillating cylinder. All cases of excitations lead to close values for the damping and nonlinear parameters in the van der Pol equation. Consequently, and as shown in this thesis, different excitation cases could be used to identify the parameters in the governing equations. Moreover, the results show that the drag coefficient could be derived from the lift coefficient through a square relation that takes into account the effects of the forced motions. / Ph. D.

The stringent regulations of emission levels from heavy duty vehicles create a demand for new methods for reducing harmful emissions from diesel engines. This thesis deals with the modelling of the nitrogen oxide (NOx) emissions from heavy duty vehicles using a selective catalyst as an aftertreatment system, utilising ammonia (NH3) for its reduction. The process of the selective catalytic reduction (SCR) is nonlinear, since the result of the chemical reactions involved depends on the load operating point and the temperature. The purpose of this thesis is to investigate different methods for nonlinear system identification of SCR systems with control applications in mind. The main focus of the thesis is on finding suitable techniques for effective NOx reduction without the need of over dosage of ammonia. By using data collected from a simulator together with real measured data, new black-box identification techniques are developed. Scaling and convergence properties of the proposed algorithms are analysed theoretically. Some of the resulting models are used for controller development using e.g. feedback linearisation techniques, followed by validation in a simulator environment. The benefits of nonlinear modelling and control of the SCR system are highlighted in a comparison with control based on linear models of the system. Further, a multiple model approach is investigated for simultaneous control of NOx and tailpipe ammonia. The results indicate an improvement in terms of ammonia slip reduction in comparison with models that do not take the ammonia slip into account. Another approach to NOx reduction is achieved by controlling the SCR temperature using techniques developed for LPV systems. The results indicate a reduction of the accumulated NOx.

Cracks often exist in structural members that are exposed to repeated loading, which will certainly lower the structural integrity. A crack on a structural member introduces a local flexibility which is a function of the crack depth and location. This may cause nonlinear dynamic response of the structure. In this thesis, a new method is suggested to detect and locate a crack in a structural component. The method is based on the fact that nonlinear response of a structure with a crack will be a function of the crack location and crack magnitude. The method suggested is the extension of a recently developed technique for identification of non-linearity in vibrating multi degree of freedom system. In this method, experimentally measured receptances at different forcing levels are used as input, and the existence and location of a nonlinearity are sought. In order to validate the method, simulated experimental data is used. Characteristics of a cracked beam are simulated by using experimentally obtained analytical expressions, given in the literature. The structure itself is modelled by using finite element method. Several case studies are performed to test and demonstrate the applicability, efficiency and sensitivity of the method suggested. The effect of crack depth on nonlinear system response is also studied in numerical examples.

Dans le monde industriel comme dans le monde scientifique, le développement de capteurs a toujours répondu à la volonté d’observer l’inobservable. La caméra rapide fait partie de ceux-là puisqu’elle permet de dévoiler des dynamiques invisibles, de la formation de fissure au vol du moustique. Dans un environnement extrêmement concurrentiel, ces caméras sont principalement limitées par le nombre d’images acquises par seconde. Le but de cette thèse est d’augmenter la capacité de dévoiler la dynamique invisible en enrichissant l’acquisition initiale par des modèles dynamiques. La problématique consiste alors à élaborer des méthodes permettant de relier en temps réel un modèle et la perception d’un système réel. Les bénéfices de cette utilisation offrent ainsi la possibilité de faire de l’interpolation, de la prédiction et de l’identification. Cette thèse est composée de trois parties. La première est axée sur la philosophie du traitement vidéo et propose d’utiliser des modèles élémentaires et génériques. Un algorithme d’estimation de grands mouvements est proposé mais l’approche actuellement proposée n’est pas assez générique pour être exploitée dans un contexte industriel. La deuxième partie propose d’utiliser des méthodes d’assimilation de données séquentielle basées sur la famille des filtres de Kalman afin d’associer un modèle avec des observations par caméras rapides pour des systèmes mécaniques. La troisième partie est une application à l’analyse modale expérimentale non linéaire. Deux schémas d’assimilation temps réel multicapteurs sont présentés et leur mise en œuvre est illustrée pour de la reconstruction 3D et de la magnification. / The development of sensors has always followed the ambition of industrial and scientific people to observe the unobservable. High speed cameras are part of this adventure, revealing invisible dynamics such as cracks formation or subtle mosquito flight. Industrial high speed vision is a very competitive domain in which cameras stand out through their acquisition speed. This thesis aims to broaden their capacity by augmenting the initial acquisition with dynamic models. This work proposes to develop methods linking in real time a model with a real system. Aimed benefits are interpolation, prediction and identification. Three parts are developed. The first one is based on video processing and submits to use kinematic elementary and generic models. An algorithm of motion estimation for large movements is proposed but the generic nature does not allow a sufficient knowledge to be conclusive. The second part proposes using sequential data assimilation methods known as Kalman filters. A scheme to assimilate video data with a mechanical model is successfully implemented. An application of data assimilation in modal analysis is developed. Two multi sensors real time assimilation schemes for nonlinear modal identification are proposed. These schemes are integrated in two applications on 3D reconstruction and motion magnification.

The study of nonlinear dynamical systems via the spectrum of the Koopman operator has emerged as a paradigm shift, from the Poincaré's geometric picture that centers the attention on the evolution of states, to the Koopman operator's picture that focuses on the evolution of observables. The Koopman operator-theoretic framework rests on the idea of lifting the states of a nonlinear dynamical system to a higher dimensional space; these lifted states are referred to as the Koopman eigenfunctions. To determine the Koopman eigenfunctions, one performs a nonlinear transformation of the states by relying on the so-called observables, that is, scalar-valued functions of the states. In other words, one executes a change of coordinates from the state space to another set of coordinates, which are denominated Koopman canonical coordinates. The variables defined on these intrinsic coordinates will evolve linearly in time, despite the underlying system being nonlinear. Since the Koopman operator is linear, it is natural to exploit its spectral properties. In fact, the theory surrounding the spectral properties of linear operators has well-known implications in electric power systems. Examples include small-signal stability analysis and direct methods for transient stability analysis based on the Lyapunov function. From the applications' standpoint, this framework based on the Koopman operator is attractive because it is capable of revealing linear and nonlinear modes by only applying well-established tools that have been developed for linear systems. With the challenges associated with the high-dimensionality and increasing uncertainties in the power systems models, researchers and practitioners are seeking alternative modeling approaches capable of incorporating information from measurements. This is fueled by an increasing amount of data made available by the wide-scale deployment of measuring devices such as phasor measurement units and smart meters. Along these lines, the Koopman operator theory is a promising framework for the integration of data analysis into our mathematical knowledge and is bringing an exciting perspective to the community. The present dissertation reports on the application of the Koopman operator for identification, estimation, and control of electric power systems. A dynamic state estimator based on the Koopman operator has been developed and compares favorably against model-based approaches, in particular for centralized dynamic state estimation. Also, a data-driven method to compute participation factors for nonlinear systems based on Koopman mode decomposition has been developed; it generalizes the original definition of participation factors under certain conditions. / PHD / Electric power systems are complex, large-scale, and given the bidirectional causality between economic growth and electricity consumption, they are constantly being expanded. In the U.S., some of the electric power grid facilities date back to the 1880s, and this aging system is operating at its capacity limits. In addition, the international pressure for sustainability is driving an unprecedented deployment of renewable energy sources into the grid. Unlike the case of other primary sources of electric energy such as coal and nuclear, the electricity generated from renewable energy sources is strongly influenced by the weather conditions, which are very challenging to forecast even for short periods of time. Within this context, the mathematical models that have aided engineers to design and operate electric power grids over the past decades are falling short when uncertainties are incorporated to the models of such high-dimensional systems. Consequently, researchers are investigating alternative data-driven approaches. This is not only motivated by the need to overcome the above challenges, but it is also fueled by the increasing amount of data produced by today’s powerful computational resources and experimental apparatus. In power systems, a massive amount of data will be available thanks to the deployment of measuring devices called phasor measurement units. Along these lines, the Koopman operator theory is a promising framework for the integration of data analysis into our mathematical knowledge, and is bringing an exciting perspective on the treatment of high-dimensional systems that lie in the forefront of science and technology. In the research work reported in this dissertation, the Koopman operator theory has been exploited to seek for solutions to some of the challenges that are threatening the safe, reliable, and efficient operation of electric power systems.

The aim of the thesis is to improve the control quality of the adaptive systems (Self Tuning Controllers). The thesis mainly deals with problematical identification part of the adaptive system. This part demonstrates a weak point for existing adaptive systems. Paradoxically, the quality of the adaptive system depends mainly on the identification part because on the basis of the process model obtained by identification are worked out parameters of a control part, afterwards the control action plan is established. Knowledge of the modern control methods is used and a new identification algorithm for closed loop identification is proposed. This simple, fast and efficient algorithm overcomes all disadvantages of current classical identification methods based on least mean-square algorithms. The possibility of the choice of a short sample time, one tuning parameter ability to adjust the control process, the ability to identify processes in real use belong to its main goals. This algorithm was built in the adaptive system and then it was tested on a set of simulation and real models with surprisingly excellent results. The successful implementation of the algorithm into the programmable logic controller was also realized. One part of the thesis introduces a new universal graphics environment for testing and verifying control algorithms.