32 research outputs found

    A study on fault diagnosis in nonlinear dynamic systems with uncertainties

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    In this draft, fault diagnosis in nonlinear dynamic systems is addressed. The objective of this work is to establish a framework, in which not only model-based but also data-driven and machine learning based fault diagnosis strategies can be uniformly handled. Instead of the well-established input-output and the associated state space models, stable image and kernel representations are adopted in our work as the basic process model forms. Based on it, the nominal system dynamics can then be modelled as a lower-dimensional manifold embedded in the process data space. To achieve a reliable fault detection as a classification problem, projection technique is a capable tool. For nonlinear dynamic systems, we propose to construct projection systems in the well-established framework of Hamiltonian systems and by means of the normalised image and kernel representations. For nonlinear dynamic systems, process data form a non-Euclidean space. Consequently, the norm-based distance defined in Hilbert space is not suitable to measure the distance from a data vector to the manifold of the nominal dynamics. To deal with this issue, we propose to use a Bregman divergence, a measure of difference between two points in a space, as a solution. Moreover, for our purpose of achieving a performance-oriented fault detection, the Bregman divergences adopted in our work are defined by Hamiltonian functions. This scheme not only enables to realise the performance-oriented fault detection, but also uncovers the information geometric aspect of our work. The last part of our work is devoted to the kernel representation based fault detection and uncertainty estimation that can be equivalently used for fault estimation. It is demonstrated that the projection onto the manifold of uncertainty data, together with the correspondingly defined Bregman divergence, is also capable for fault detection

    On the exponential convergence of input-output signals of nonlinear feedback systems

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    We show that the integral-constraint-based robust feedback stability theorem for certain Lurye systems exhibits the property that the endogenous input-output signals enjoy an exponential convergence rate for all initial conditions of the linear time-invariant subsystem. More generally, we provide conditions under which a feedback interconnection of possibly open-loop unbounded subsystems to admit such an exponential convergence property, using perturbation analysis and a combination of tools including integral quadratic constraints, directed gap measure, and exponential weightings. As an application, we apply the result to first-order convex optimisation methods. In particular, by making use of the Zames-Falb multipliers, we state conditions for these methods to converge exponentially when applied to strongly convex functions with Lipschitz gradients.Comment: This paper has been submitted to Automatic

    Robust feedback control of flow separation using plasma actuators

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    This thesis addresses the problem of controlling the unsteady flow separation over an aerofoil using plasma actuators, with the aim of improving the performance of fluid systems through the use of robust feedback controllers. Despite the complexity of the dynamics of interest, it is shown how the problem of controlling flow separation can be successfully formulated and solved as a simple output regulation problem. First, a novel control-oriented reduced-order model for nonlinear systems evolving on attractors is obtained. Its application to the incompressible Navier-Stokes equations is proposed, in order to obtain a linear reduced-order model (whose state variables have a clear and consistent physical meaning) of the complex flow/actuator dynamics. On the basis of the proposed model, a new robust multivariable feedback control algorithm for flow separation suppression is designed, using real-time velocity measurements, which are available in realistic applications. The presented control scheme is tested in both Single-Input-Single-Output (SISO) and Multi-Input-Multi-Output (MIMO) configurations, thus allowing for optimising the closed-loop system, with the aim of selecting suitable numbers and positions of the actuator/sensor pairs along the aerofoil, as well as desired references for the real-time measurements, according to the specific application (e.g., flow separation suppression, mixing enhancement etc.). Accurate numerical simulations of incompressible flows around both 2D aerofoils and 3D wings are performed in order to optimise the closed-loop system and illustrate the effectiveness of the proposed approach in the presence of complex dynamics that are neglected at the design stage. Robust performances, with respect to both parameter variations (e.g. geometry of the domain and Reynolds number) and model uncertainties, are demonstrated. The designed controller is able to effectively suppress the flow separation along the aerofoil, as well as the shedding vortices, thus yielding both a reduction of the drag and an increase of the lift. This allows for stall avoidance and increased efficiency

    Optimised configuration of sensing elements for control and fault tolerance applied to an electro-magnetic suspension system

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    New technological advances and the requirements to increasingly abide by new safety laws in engineering design projects highly affects industrial products in areas such as automotive, aerospace and railway industries. The necessity arises to design reduced-cost hi-tech products with minimal complexity, optimal performance, effective parameter robustness properties, and high reliability with fault tolerance. In this context the control system design plays an important role and the impact is crucial relative to the level of cost efficiency of a product. Measurement of required information for the operation of the design control system in any product is a vital issue, and in such cases a number of sensors can be available to select from in order to achieve the desired system properties. However, for a complex engineering system a manual procedure to select the best sensor set subject to the desired system properties can be very complicated, time consuming or even impossible to achieve. This is more evident in the case of large number of sensors and the requirement to comply with optimum performance. The thesis describes a comprehensive study of sensor selection for control and fault tolerance with the particular application of an ElectroMagnetic Levitation system (being an unstable, nonlinear, safety-critical system with non-trivial control performance requirements). The particular aim of the presented work is to identify effective sensor selection frameworks subject to given system properties for controlling (with a level of fault tolerance) the MagLev suspension system. A particular objective of the work is to identify the minimum possible sensors that can be used to cover multiple sensor faults, while maintaining optimum performance with the remaining sensors. The tools employed combine modern control strategies and multiobjective constraint optimisation (for tuning purposes) methods. An important part of the work is the design and construction of a 25kg MagLev suspension to be used for experimental verification of the proposed sensor selection frameworks
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