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

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

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

Wind Turbine Reliability Improvement by Fault Tolerant Control

This thesis investigates wind turbine reliability improvement, utilizing model-based fault tolerant control, so that the wind turbine continues to operate satisfactorily with the same performance index in the presence of faults as in fault-free situations. Numerical simulations are conducted on the wind turbine bench mark model associated with the considered faults and comparison is made between the performance of the proposed controllers and industrial controllers illustrating the superiority of the proposed ones

A Control Systems Perspective to Condition Monitoring and Fault Diagnosis

Modern industrial processors, engineering systems and structures, have grown significantly in complexity and in scale during the recent years. Therefore, there is an increase in the demand for automatic processors, to avoid faults and severe break downs, through predictive maintenance. In this context, the research into nonlinear systems analysis has attained much interest in recent years as linear models cannot be used to represent some of these systems. In the field of control systems, the analysis of such systems is conducted in the frequency domain using methods of Frequency Response Analysis. Generalised Frequency Response Functions (GFRFs) and the Nonlinear Output Frequency Response Functions (NOFRFs) are Frequency Response Analysis techniques used for the analysis of nonlinear dynamical behaviour in the frequency domain. The problem of Condition Monitoring and Fault Diagnosis has been investigated in the perspective of modelling, signal processing and multivariate statistical analysis, data-driven methods such as neural networks have gained significant popularity. This is because possible faulty conditions related to complex systems are often difficult to interpret. In such a background, recently, a new data-driven approach based on a systems perspective has been proposed. This approach uses a controls systems analysis method of System Identification and Frequency Response Analysis and has been shown before as a potential technique. However, this approach has certain practical concerns regarding real-world applications. Motivated by these concerns in this thesis, the following contributions are put forward: 1. The method of evaluating NOFRFs, using input-output data of a nonlinear system may experience numerical errors. This is a major concern, hence the development of a method to overcome these numerical issues effectively. 2. Frequency Response Analysis cannot be used in its current state for nonlinear systems that exhibit severe nonlinear behaviour. Although theoretically, it has been argued that this is possible, even though, it has been impossible in a practical point of view. Therefore, the possibility and the manner in which Frequency Response Analysis can be conducted for these types of systems is presented. 3. Development of a System Identification methodology to overcome the issues of inadequately exciting inputs and appropriately capturing system dynamics under general circumstances of Condition Monitoring and Fault Diagnosis. In addition to the above, the novel implementation of a control systems analysis approach is implemented in characterising corrosion, crack depth and crack length on metal samples. The approach is applied to the data collected, using a newly proposed non-invasive Structural Health Monitoring method called RFID (Radio Frequency IDentification) wireless eddy current probing. The control systems analysis approach along with the RFID wireless eddy current probing method shows the clear potential of being a new technology in non-invasive Structural Health Monitoring systems

Fault tolerant control for nonlinear aircraft based on feedback linearization

The thesis concerns the fault tolerant flight control (FTFC) problem for nonlinear aircraft by making use of analytical redundancy. Considering initially fault-free flight, the feedback linearization theory plays an important role to provide a baseline control approach for de-coupling and stabilizing a non-linear statically unstable aircraft system. Then several reconfigurable control strategies are studied to provide further robust control performance:- A neural network (NN)-based adaption mechanism is used to develop reconfigurable FTFC performance through the combination of a concurrent updated learninglaw. - The combined feedback linearization and NN adaptor FTFC system is further improved through the use of a sliding mode control (SMC) strategy to enhance the convergence of the NN learning adaptor. - An approach to simultaneous estimation of both state and fault signals is incorporated within an active FTFC system.The faults acting independently on the three primary actuators of the nonlinear aircraft are compensated in the control system.The theoretical ideas developed in the thesis have been applied to the nonlinear Machan Unmanned Aerial Vehicle (UAV) system. The simulation results obtained from a tracking control system demonstrate the improved fault tolerant performance for all the presented control schemes, validated under various faults and disturbance scenarios.A Boeing 747 nonlinear benchmark model, developed within the framework of the GARTEUR FM-AG 16 project “fault tolerant flight control systems”,is used for the purpose of further simulation study and testing of the FTFC scheme developed by making the combined use of concurrent learning NN and SMC theory. The simulation results under the given fault scenario show a promising reconfiguration performance

Data-driven fault diagnosis of awind farm benchmark model

The fault diagnosis of wind farms has been proven to be a challenging task, and motivates the research activities carried out through this work. Therefore, this paper deals with the fault diagnosis of a wind park benchmark model, and it considers viable solutions to the problem of earlier fault detection and isolation. The design of the fault indicator involves data-driven approaches, as they can represent effective tools for coping with poor analytical knowledge of the system dynamics, noise, uncertainty, and disturbances. In particular, the proposed data-driven solutions rely on fuzzy models and neural networks that are used to describe the strongly nonlinear relationships between measurement and faults. The chosen architectures rely on nonlinear autoregressive with exogenous input models, as they can represent the dynamic evolution of the system over time. The developed fault diagnosis schemes are tested by means of a high-fidelity benchmark model that simulates the normal and the faulty behaviour of a wind farm installation. The achieved performances are also compared with those of a model-based approach relying on nonlinear differential geometry tools. Finally, a Monte-Carlo analysis validates the robustness and reliability of the proposed solutions against typical parameter uncertainties and disturbances.The fault diagnosis of wind farms has been proven to be a challenging task, and motivates the research activities carried out through this work. Therefore, this paper deals with the fault diagnosis of a wind park benchmark model, and it considers viable solutions to the problem of earlier fault detection and isolation. The design of the fault indicator involves data-driven approaches, as they can represent effective tools for coping with poor analytical knowledge of the system dynamics, noise, uncertainty, and disturbances. In particular, the proposed data-driven solutions rely on fuzzy models and neural networks that are used to describe the strongly nonlinear relationships between measurement and faults. The chosen architectures rely on nonlinear autoregressive with exogenous input models, as they can represent the dynamic evolution of the system over time. The developed fault diagnosis schemes are tested by means of a high-fidelity benchmark model that simulates the normal and the faulty behaviour of a wind farm installation. The achieved performances are also compared with those of a model-based approach relying on nonlinear differential geometry tools. Finally, a Monte-Carlo analysis validates the robustness and reliability of the proposed solutions against typical parameter uncertainties and disturbances

FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation

Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approachPostprint (author's final draft