A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Gain-Scheduled Fault Detection Filter For Discrete-time LPV Systems

The present work investigates a fault detection problem using a gain-scheduled filter for discrete-time Linear Parameter Varying systems. We assume that we cannot directly measure the scheduling parameter but, instead, it is estimated. On the one hand, this assumption imposes the challenge that the fault detection filter should perform properly even when using an inexact parameter. On the other, it avoids the burden associated with designing a complex estimation process for this parameter. We propose three design approaches: the ${\mathcal {H}_{2}}$ , ${\mathcal {H}_{\infty }}$ , and mixed ${\mathcal {H}_{2}} / {\mathcal {H}_{\infty }}$ gain-scheduled Fault Detection Filters designed via Linear Matrix Inequalities. We also provide numerical simulations to illustrate the applicability and performance of the proposed novel methods

Advances in state estimation, diagnosis and control of complex systems

This dissertation intends to provide theoretical and practical contributions on estimation, diagnosis and control of complex systems, especially in the mathematical form of descriptor systems. The research is motivated by real applications, such as water networks and power systems, which require a control system to provide a proper management able to take into account their specific features and operating limits in presence of uncertainties related to their operation and failures from component malfunctions. Such a control system is expected to provide an optimal operation to obtain efficient and reliable performance. State estimation is an essential tool, which can be used not only for fault diagnosis but also for the controller design. To achieve a satisfactory robust performance, set theory is chosen to build a general framework for descriptor systems subject to uncertainties. Under certain assumptions, these uncertainties are propagated and bounded by deterministic sets that can be explicitly characterized at each iteration step. Moreover, set-invariance characterizations for descriptor systems are also of interest to describe the steady performance, which can also be used for active mode detection. For the controller design for complex systems, new developments of economic model predictive control (EMPC) are studied taking into account the case of underlying periodic behaviors. The EMPC controller is designed to be recursively feasible even with sudden changes in the economic cost function and the closed-loop convergence is guaranteed. Besides, a robust technique is plugged into the EMPC controller design to maintain these closed-loop properties in presence of uncertainties. Engineering applications modeled as descriptor systems are presented to illustrate these control strategies. From the real applications, some additional difficulties are solved, such as using a two-layer control strategy to avoid binary variables in real-time optimizations and using nonlinear constraint relaxation to deal with nonlinear algebraic equations in the descriptor model. Furthermore, the fault-tolerant capability is also included in the controller design for descriptor systems by means of the designed virtual actuator and virtual sensor together with an observer-based delayed controller.Esta tesis propone contribuciones de carácter teórico y aplicado para la estimación del estado, el diagnóstico y el control óptimo de sistemas dinámicos complejos en particular, para los sistemas descriptores, incluyendo la capacidad de tolerancia a fallos. La motivación de la tesis proviene de aplicaciones reales, como redes de agua y sistemas de energía, cuya naturaleza crítica requiere necesariamente un sistema de control para una gestión capaz de tener en cuenta sus características específicas y límites operativos en presencia de incertidumbres relacionadas con su funcionamiento, así como fallos de funcionamiento de los componentes. El objetivo es conseguir controladores que mejoren tanto la eficiencia como la fiabilidad de dichos sistemas. La estimación del estado es una herramienta esencial que puede usarse no solo para el diagnóstico de fallos sino también para el diseño del control. Con este fin, se ha decidido utilizar metodologías intervalares, o basadas en conjuntos, para construir un marco general para los sistemas de descriptores sujetos a incertidumbres desconocidas pero acotadas. Estas incertidumbres se propagan y delimitan mediante conjuntos que se pueden caracterizar explícitamente en cada instante. Por otra parte, también se proponen caracterizaciones basadas en conjuntos invariantes para sistemas de descriptores que permiten describir comportamientos estacionarios y resultan útiles para la detección de modos activos. Se estudian también nuevos desarrollos del control predictivo económico basado en modelos (EMPC) para tener en cuenta posibles comportamientos periódicos en la variación de parámetros o en las perturbaciones que afectan a estos sistemas. Además, se demuestra que el control EMPC propuesto garantiza la factibilidad recursiva, incluso frente a cambios repentinos en la función de coste económico y se garantiza la convergencia en lazo cerrado. Por otra parte, se utilizan técnicas de control robusto pata garantizar que las estrategias de control predictivo económico mantengan las prestaciones en lazo cerrado, incluso en presencia de incertidumbre. Los desarrollos de la tesis se ilustran con casos de estudio realistas. Para algunas de aplicaciones reales, se resuelven dificultades adicionales, como el uso de una estrategia de control de dos niveles para evitar incluir variables binarias en la optimización y el uso de la relajación de restricciones no lineales para tratar las ecuaciones algebraicas no lineales en el modelo descriptor en las redes de agua. Finalmente, se incluye también una contribución al diseño de estrategias de control con tolerancia a fallos para sistemas descriptores

Fault detection filter and fault accommodation controller design for uncertain systems

Model-based Fault Detection (FD) and Fault Accommodation (FA) approaches have been applied in a variety of cases. We propose several techniques to include uncertainties in the design process. First, we focus on the design of the Fault Detection Filter (FDF) and Fault Accommodation Controller (FAC) for Markovian Jump Linear Systems (MJLS). The MJLS framework allows us to include the network behavior (packet loss) during the design of the FDF and FAC.Second, we propose an FDF and FAC design for the MJLS, under the assumption that the Markov chain mode is not directly accessible. Since we are using the MJLS framework to model the network behavior, the assumption that the network state is not instantly accessible is useful because from a practical standpoint this is a truthful assumption. Third, from the results presented for the MJLS framework, we provided follow-up results using Lur'e Markov Jump System. This is compelling since on some occasions the non-linear behavior cannot be ignored. Therefore, applying the Lur'e MJS framework allows us to consider the same assumptions from MJLS, but now adds the non-linearities. Fourth, we propose the design Gain-Scheduled FDF and FAC for Linear Parameter Varying (LPV) systems, under the assumption that the schedule parameter is not directly acquired. We assume that the schedule parameter is subject to additive noise. This imprecision is included during the design, using change of variables and multi-simplex techniques. Finally, throughout the thesis, we provide some numerical examples to illustrate the viability of the proposed approaches

Fault Detection for Cyber-Physical Systems: Smart Grid case

The problem of fault detection and isolation in cyber-physical systems is growing in importance following the trend to have an ubiquitous presence of sensors and actuators with network capabilities in power networks and other areas. In this context, attacks to power systems or other vital components providing basic needs might either present a serious threat or at least cost a lot of resources. In this paper, we tackle the problem of having an intruder corrupting a smart grid in two different scenarios: a centralized detector for a portion of the network and a fully distributed solution that only has limited neighbor information. For both cases, differences in strategies using Set-Valued Observers are discussed and theoretical results regarding a bound on the maximum magnitude of the attacker’s signal are provided. Performance is assessed through simulation, illustrating, in particular, the detection time for various types of faults in IEEE testbed scenarios

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

Fault-Tolerant Flight Control Using One Aerodynamic Control Surface

University of Minnesota Ph.D. dissertation. June 2018. Major: Aerospace Engineering and Mechanics. Advisor: Peter Seiler. 1 computer file (PDF); xiii, 291 pages.Small unmanned aircraft systems (UAS) have recently found increasing civilian and commercial applications. On-board fault management is one of several technical challenges facing their widespread use. The aerodynamic control surfaces of a fixed-wing UAS perform the safety-critical functions of stabilizing and controlling the aircraft. Failures in one or more of these surfaces, or the actuators controlling them, may be managed by repurposing the other control surfaces and/or propulsive devices. A natural question arises in this context: What is the minimum number of control surfaces required to adequately control a handicapped aircraft? The answer, in general, depends on the control surface layout of the aircraft under consideration. For some aircraft, however, the answer is one. If the UAS is equipped with only two control surfaces, such as the one considered in this thesis, then this limiting case is reached with a single control surface failure. This thesis demonstrates, via multiple flight tests, the autonomous landing of a UAS using only one aerodynamic control surface and the throttle. In seeking to arrive at these demonstrations, this thesis makes advances in the areas of model-based fault diagnosis and fault-tolerant control. Specifically, a new convex method is developed for synthesizing robust output estimators for continuous-time, uncertain, gridded, linear parameter-varying systems. This method is subsequently used to design the fault diagnosis algorithm. The detection time requirement of this algorithm is established using concepts from loss-of-control. The fault-tolerant controller is designed to operate the single control surface for lateral control and the throttle for total energy control. The fault diagnosis algorithm and the fault-tolerant controller are both designed using a model of the aircraft. This model is first developed using physics-based first-principles and then updated using system identification experiments. Since this aircraft does not have a rudder, the identification of the lateral-directional dynamics requires some novelty

Feasible, Robust and Reliable Automation and Control for Autonomous Systems

The Special Issue book focuses on highlighting current research and developments in the automation and control field for autonomous systems as well as showcasing state-of-the-art control strategy approaches for autonomous platforms. The book is co-edited by distinguished international control system experts currently based in Sweden, the United States of America, and the United Kingdom, with contributions from reputable researchers from China, Austria, France, the United States of America, Poland, and Hungary, among many others. The editors believe the ten articles published within this Special Issue will be highly appealing to control-systems-related researchers in applications typified in the fields of ground, aerial, maritime vehicles, and robotics as well as industrial audiences