541 research outputs found

    Sliding Mode Dirichlet Boundary Stabilization of Uncertain Parabolic PDE Systems With Spatially Varying Coefficients

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    Abstract-We consider the robust boundary stabilization problem of an unstable parabolic partial differential equation (PDE) system with uncertainties entering from both the spatially-dependent parameters and from the boundary conditions. The parabolic PDE is transformed through the Volterra integral into a damped heat equation with uncertainties, which contains the matched part (the boundary disturbance) and the mismatched part (the parameter variations). In this new coordinates, an infinite-dimensional sliding manifold that ensures system stability is constructed. For the sliding mode boundary control law to satisfy the reaching condition, an adaptive switching gain is used to cope with the above uncertainties, whose bound is unknown

    Systems control theory applied to natural and synthetic musical sounds

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    Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

    Sliding mode control method having terminal convergence in finite time

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    An object of this invention is to provide robust nonlinear controllers for robotic operations in unstructured environments based upon a new class of closed loop sliding control methods, sometimes denoted terminal sliders, where the new class will enforce closed-loop control convergence to equilibrium in finite time. Improved performance results from the elimination of high frequency control switching previously employed for robustness to parametric uncertainties. Improved performance also results from the dependence of terminal slider stability upon the rate of change of uncertainties over the sliding surface rather than the magnitude of the uncertainty itself for robust control. Terminal sliding mode control also yields improved convergence where convergence time is finite and is to be controlled. A further object is to apply terminal sliders to robot manipulator control and benchmark performance with the traditional computed torque control method and provide for design of control parameters

    Control of systems modeled by hyperbolic partial diferential equations

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    Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2017.Sistemas com parâmetros distribuídos representam uma vasta gama de processos da engenharia. Neste caso, as variáveis do sistema irão conter termos dependentes do tempo assim como gradientes espaciais e, portanto, é natural representa-los por equações diferenciais parciais. Exemplos podem ser encontrados em diversas áreas: desde processos químicos e térmicos, sistemas de produção e distribuição de energia, e problemas relacionados ao transporte de fluidos e ciência médica. Esta tese trata dois tipos de problemas: estabilização de equações diferenciais parciais lineares hiperbólicas com variável de controle na condição de contorno e controle regulatório de sistemas descritos por equações diferenciais parciais quasi-lineares hiperbólicas com variável de controle no domínio. Com relação ao primeiro, estudaram-se duas metodologias de controle: (i) uma lei de controle estática que garante convergência do sistema para o ponto de equilíbrio desejado. A metodologia de controle utiliza uma função de Lyapunov para encontrar os valores dos parâmetros do controlador que garantem estabilidade exponencial em malha fechada. Resultados de simulação para o problema de supressão de golfadas em sistemas de produção de petróleo são apresentados para ilustrar a eficiência do método; (ii) uma lei de controle baseada nas ferramentas clássicas do domínio da frequência. Neste caso, aplicamos a transformada de Laplace na equação diferencial parcial para obter uma função de transferência irracional e então, ferramentas clássicas do domínio da frequência são usadas para projetar o controlador, de maneira similar aos sistemas de dimensão finita com função de transferência racional. Estes resultados foram aplicados experimentalmente no problema de controle de oscilações termoacústicas do tubo de Rijke, mostrando a efetividade do método. Para o segundo problema, utiliza-se o método das características combinado com a técnica de controle por modos deslizantes. O método das características é usado para transformar o sistema de equações diferenciais parciais em um conjunto de equações diferenciais ordinárias que descrevem o sistema original. O projeto de controle é então realizado a partir deste conjunto de equações diferenciais ordinárias através de resultados bem conhecidos da teoria de equações diferenciais ordinárias. Os resultados obtidos foram testados experimentalmente em dois sistemas de escala industrial: uma planta solar e um fotobiorreator tubular.Abstract : Distributed parameter systems represent a wide range of engineeringprocesses. In this case, the system variables will contain temporally dependentterms as well spatial gradients and, therefore, it is natural to representthem by partial dierential equations. Examples can be found in manyelds: chemical and thermal processes, production and distribution energysystems, and problems related to uid transport and medical science.This thesis deals with two dierent problems: stabilization of linear hyperbolicpartial dierential equations with boundary control and regulatorycontrol of systems described by quasilinear hyperbolic partial dierentialequations with in domain control. Concerning the boundary control problem,we studied two control methodologies: (i) a static control law thatguarantees convergence of the system to the desired equilibrium point. Thiscontrol methodology uses a Lyapunov function to nd the values of thecontrol parameters that guarantee closed-loop exponential stability. Simulationresults for the slugging control problem in oil production facilities arepresented to illustrate the eciency of the methodology; (ii) a control lawbased on the frequency domain tools. In this case, we applied the Laplacetransform on the partial dierential equation to obtain an irrational transferfunction and then classical frequency domain tools are used to designthe control law. These results were applied experimentally to the controlproblem of thermoacoustic oscillations in the Rijke tube, showing the effectivenessof the method. Regarding the regulatory control problem, weuse the method of characteristics together with the sliding mode controlmethodology. The method of characteristics is used to transform the partialdierential equations into a system of ordinary dierential equations thatdescribes the original system without any kind of approximation. Then,the control design is performed on the ordinary dierential equations withwell-known results of the theory of lumped parameter systems. The resultswere validated experimentally in two industrial scale systems: a solar powerplant and a tubular photobioreactor

    Decentralized sliding mode control and estimation for large-scale systems

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    This thesis concerns the development of an approach of decentralised robust control and estimation for large scale systems (LSSs) using robust sliding mode control (SMC) and sliding mode observers (SMO) theory based on a linear matrix inequality (LMI) approach. A complete theory of decentralized first order sliding mode theory is developed. The main developments proposed in this thesis are: The novel development of an LMI approach to decentralized state feedback SMC. The proposed strategy has good ability in combination with other robust methods to fulfill specific performance and robustness requirements. The development of output based SMC for large scale systems (LSSs). Three types of novel decentralized output feedback SMC methods have been developed using LMI design tools. In contrast to more conventional approaches to SMC design the use of some complicated transformations have been obviated. A decentralized approach to SMO theory has been developed focused on the Walcott-Żak SMO combined with LMI tools. A derivation for bounds applicable to the estimation error for decentralized systems has been given that involves unknown subsystem interactions and modeling uncertainty. Strategies for both actuator and sensor fault estimation using decentralized SMO are discussed.The thesis also provides a case study of the SMC and SMO concepts applied to a non-linear annealing furnace system modelderived from a distributed parameter (partial differential equation) thermal system. The study commences with a lumped system decentralised representation of the furnace derived from the partial differential equations. The SMO and SMC methods derived in the thesis are applied to this lumped parameter furnace model. Results are given demonstrating the validity of the methods proposed and showing a good potential for a valuable practical implementation of fault tolerant control based on furnace temperature sensor faults

    Machine Learning and Deep Learning applications for the protection of nuclear fusion devices

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    This Thesis addresses the use of artificial intelligence methods for the protection of nuclear fusion devices with reference to the Joint European Torus (JET) Tokamak and the Wendenstein 7-X (W7-X) Stellarator. JET is currently the world's largest operational Tokamak and the only one operated with the Deuterium-Tritium fuel, while W7-X is the world's largest and most advanced Stellarator. For the work on JET, research focused on the prediction of “disruptions”, and sudden terminations of plasma confinement. For the development and testing of machine learning classifiers, a total of 198 disrupted discharges and 219 regularly terminated discharges from JET. Convolutional Neural Networks (CNNs) were proposed to extract the spatiotemporal characteristics from plasma temperature, density and radiation profiles. Since the CNN is a supervised algorithm, it is necessary to explicitly assign a label to the time windows of the dataset during training. All segments belonging to regularly terminated discharges were labelled as 'stable'. For each disrupted discharge, the labelling of 'unstable' was performed by automatically identifying the pre-disruption phase using an algorithm developed during the PhD. The CNN performance has been evaluated using disrupted and regularly terminated discharges from a decade of JET experimental campaigns, from 2011 to 2020, showing the robustness of the algorithm. Concerning W7-X, the research involved the real-time measurement of heat fluxes on plasma-facing components. THEODOR is a code currently used at W7-X for computing heat fluxes offline. However, for heat load control, fast heat flux estimation in real-time is required. Part of the PhD work was dedicated to refactoring and optimizing the THEODOR code, with the aim of speeding up calculation times and making it compatible with real-time use. In addition, a Physics Informed Neural Network (PINN) model was proposed to bring thermal flow computation to GPUs for real-time implementation

    Optimization based control design techniques for distributed parameter systems

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    The study presents optimization based control design techniques for the systems that are governed by partial differential equations. A control technique is developed for systems that are actuated at the boundary. The principles of dynamic inversion and constrained optimization theory are used to formulate a feedback controller. This control technique is demonstrated for heat equations and thermal convection loops. This technique is extended to address a practical issue of parameter uncertainty in a class of systems. An estimator is defined for unknown parameters in the system. The Lyapunov stability theory is used to derive an update law of these parameters. The estimator is used to design an adaptive controller for the system. A second control technique is presented for a class of second order systems that are actuated in-domain. The technique of proper orthogonal decomposition is used first to develop an approximate model. This model is then used to design optimal feedback controller. Approximate dynamic programming based neural network architecture is used to synthesize a sub-optimal controller. This control technique is demonstrated to stabilize the heave dynamics of a flexible aircraft wings. The third technique is focused on the optimal control of stationary thermally convected fluid flows from the numerical point of view. To overcome the computational requirement, optimization is carried out using reduced order model. The technique of proper orthogonal decomposition is used to develop reduced order model. An example of chemical vapor deposition reactor is considered to examine this control technique --Abstract, page iii

    Delayed effects and critical transitions in climate models

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    There is a continuous demand for new and improved methods of understanding our climate system. The work in this thesis focuses on the study of delayed feedback and critical transitions. There is much room to develop upon these concepts in their application to the climate system. We explore the two concepts independently, but also note that the two are not mutually exclusive. The thesis begins with a review of delay differential equation (DDE) theory and the use of delay models in climate, followed by a review of the literature on critical transitions and examples of critical transitions in climate. We introduce various methods of deriving delay models from more complex systems. Our main results center around the Saltzman and Maasch (1988) model for the Pleistocene climate (`Carbon cycle instability as a cause of the late Pleistocene ice age oscillations: modelling the asymmetric response.' Global biogeochemical cycles, 2(2):177-185, 1988). We observe that the model contains a chain of first-order reactions. Feedback chains of this type limits to a discrete delay for long chains. We can then approximate the chain by a delay, resulting in scalar DDE for ice mass. Through bifurcation analysis under varying the delay, we discover a previously unexplored bistable region and consider solutions in this parameter region when subjected to periodic and astronomical forcing. The astronomical forcing is highly quasiperiodic, containing many overlapping frequencies from variations in the Earth's orbit. We find that under the astronomical forcing, the model exhibits a transition in time that resembles what is seen in paleoclimate records, known as the Mid-Pleistocene Transition. This transition is a distinct feature of the quasiperiodic forcing, as confi rmed by the change in sign of the leading nite-time Lyapunov exponent. Additional results involve a box model of the Atlantic meridional overturning circulation under a future climate scenario and time-dependent freshwater forcing. We find that the model exhibits multiple types of critical transitions, as well as recovery from potential critical transitions. We conclude with an outlook on how the work presented in this thesis can be utilised for further studies of the climate system and beyond.European Commissio
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