Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional-derivative control strategy is presented, where the derivative gain is to make the closed-loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Stabilization for a class of rectangular descriptor systems via time delayed dynamic compensator

Abstract: This paper focuses on the stabilization problem for a class of rectangular descriptor systems through dynamic compensation. Such class of systems may not be stabilized by delayfree dynamic compensators, while delayed dynamic compensator could achieve such purpose. We provide a design scheme of time-delayed dynamic compensator which makes the closed-loop system admissible. The design involves solving a quadratic matrix inequality, and consequently, we build a linear matrix inequality (LMI) based algorithm to compute compensator gains. We verify that, under certain circumstances for which delay-free dynamic compensators fail to stabilize, the proposed method works well. An illustrative example demonstrates the usefulness of the present scheme

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Robustness Improvement by Dynamic State Feedback Stabilization

A general perception is that dynamic state feedback controllers may have superior capabilities compared to the static feedback ones. Although, for nominal systems, such superiority does not exist, it may hold true for systems other than the nominal one. This thesis investigates such capabilities of dynamic state feedback controllers. First, the case of systems with time-invariant uncertainties is considered. It appears that only a limited number of example systems exist for which dynamic feedback controller has superior ability to improve tolerable uncertainty bounds. This thesis shows that not only the available ones but there exist a class of systems for which such improvement may occur. This claim has been verified by presenting more numerical examples in the category. Second, this thesis considers the class of systems with feedback delays, more specifically, systems having both input and output delays. The superiority of dynamic feedback controllers for such systems appears to be not investigated so far in literature. However, it is observed, for the first time, that if one considers a dynamic state feedback controller but with an artificial delay in its state then the tolerable delay margin improves considerably. The performance of such a controller is investigated thoroughly for scalar systems using a continuous pole placement technique for delay systems

New results in relay feedback analysis and multivariable stability margins

Ph.DDOCTOR OF PHILOSOPH

Robust stability assessment for future power systems

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.Cataloged from PDF version of thesis. "Due to the condition of the original material, there are unavoidable flaws in this reproduction. Some pages in the original document contain text that is illegible"--Disclaimer Notice page.Includes bibliographical references (pages 119-128).Loss of stability in electrical power systems may eventually lead to blackouts which, despite being rare, are extremely costly. However, ensuring system stability is a non-trivial task for several reasons. First, power grids, by nature, are complex nonlinear dynamical systems, so assessing and maintaining system stability is challenging mainly due to the co-existence of multiple equilibria and the lack of global stability. Second, the systems are subject to various sources of uncertainties. For example, the renewable energy injections may vary depending on the weather conditions. Unfortunately, existing security assessment may not be sufficient to verify system stability in the presence of such uncertainties. This thesis focuses on new scalable approaches for robust stability assessment applicable to three main types of stability, i.e., long-term voltage, transient, and small-signal stability. In the first part of this thesis, I develop a novel computationally tractable technique for constructing Optimal Power Flow (OPF) feasibility (convex) subsets. For any inner point of the subset, the power flow problem is guaranteed to have a feasible solution which satisfies all the operational constraints considered in the corresponding OPF. This inner approximation technique is developed based on Brouwer's fixed point theorem as the existence of a solution can be verified through a self-mapping condition. The self-mapping condition along with other operational constraints are incorporated in an optimization problem to find the largest feasible subsets. Such an optimization problem is nonlinear, but any feasible solution will correspond to a valid OPF feasibility estimation. Simulation results tested on several IEEE test cases up to 300 buses show that the estimation covers a substantial fraction of the true feasible set. Next, I introduce another inner approximation technique for estimating an attraction domain of a post-fault equilibrium based on contraction analysis. In particular, I construct a contraction region where the initial conditions are "forgotten", i.e., all trajectories starting from inside this region will exponentially converge to each other. An attraction basin is constructed by inscribing the largest ball in the contraction region. To verify contraction of a Differential-Algebraic Equation (DAE) system, I also show that one can rely on the analysis of extended virtual systems which are reducible to the original one. Moreover, the Jacobians of the synthetic systems can always be expressed in a linear form of state variables because any polynomial system has a quadratic representation. This makes the synthetic system analysis more appropriate for contraction region estimation in a large scale. In the final part of the thesis, I focus on small-signal stability assessment under load dynamic uncertainties. After introducing a generic impedance-based load model which can capture the uncertainty, I propose a new robust small signal (RSS) stability criterion. Semidefinite programming is used to find a structured Lyapunov matrix, and if it exists, the system is provably RSS stable. An important application of the criterion is to characterize operating regions which are safe from Hopf bifurcations. The robust stability assessment techniques developed in this thesis primarily address the needs of a system operator in electrical power systems. The results, however, can be naturally extended to other nonlinear dynamical systems that arise in different fields such as biology, biomedicine, economics, neuron networks, and optimization. As the robust assessment is based on sufficient conditions for stability, there is still room for development on reducing the inevitable conservatism. For example, for OPF feasibility region estimation, an important open question considers what tighter bounds on the nonlinear residual terms one can use instead of box type bounds. Also, for attraction basin problem, finding the optimal norms and metrics which result in the largest contraction domain is an interesting potential research question.by Hung Dinh Nguyen.Ph. D

Fusion de données capteurs étendue pour applications vidéo embarquées

This thesis deals with sensor fusion between camera and inertial sensors measurements in order to provide a robust motion estimation algorithm for embedded video applications. The targeted platforms are mainly smartphones and tablets. We present a real-time, 2D online camera motion estimation algorithm combining inertial and visual measurements. The proposed algorithm extends the preemptive RANSAC motion estimation procedure with inertial sensors data, introducing a dynamic lagrangian hybrid scoring of the motion models, to make the approach adaptive to various image and motion contents. All these improvements are made with little computational cost, keeping the complexity of the algorithm low enough for embedded platforms. The approach is compared with pure inertial and pure visual procedures. A novel approach to real-time hybrid monocular visual-inertial odometry for embedded platforms is introduced. The interaction between vision and inertial sensors is maximized by performing fusion at multiple levels of the algorithm. Through tests conducted on sequences with ground-truth data specifically acquired, we show that our method outperforms classical hybrid techniques in ego-motion estimation.Le travail réalisé au cours de cette thèse se concentre sur la fusion des données d'une caméra et de capteurs inertiels afin d'effectuer une estimation robuste de mouvement pour des applications vidéos embarquées. Les appareils visés sont principalement les téléphones intelligents et les tablettes. On propose une nouvelle technique d'estimation de mouvement 2D temps réel, qui combine les mesures visuelles et inertielles. L'approche introduite se base sur le RANSAC préemptif, en l'étendant via l'ajout de capteurs inertiels. L'évaluation des modèles de mouvement se fait selon un score hybride, un lagrangien dynamique permettant une adaptation à différentes conditions et types de mouvements. Ces améliorations sont effectuées à faible coût, afin de permettre une implémentation sur plateforme embarquée. L'approche est comparée aux méthodes visuelles et inertielles. Une nouvelle méthode d'odométrie visuelle-inertielle temps réelle est présentée. L'interaction entre les données visuelles et inertielles est maximisée en effectuant la fusion dans de multiples étapes de l'algorithme. A travers des tests conduits sur des séquences acquises avec la vérité terrain, nous montrons que notre approche produit des résultats supérieurs aux techniques classiques de l'état de l'art

Advances in Control of Power Electronic Converters

This book proposes a list of contributions in the field of control of power electronics converters for different topologies: DC-DC, DC-AC and AC-DC. It particularly focuses on the use of different advanced control techniques with the aim of improving the performances, flexibility and efficiency in the context of several operation conditions. Sliding mode control, fuzzy logic based control, dead time compensation and optimal linear control are among the techniques developed in the special issue. Simulation and experimental results are provided by the authors to validate the proposed control strategies