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

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Starting with the baseline controller design, this paper proposes an integrated approach of active fault tolerant control based on proportional derivative extended state observer (PDESO) for linear parameter varying descriptor systems. The PDESO can simultaneously provide the estimates of the system states, sensor faults, and actuator faults. The L₂ robust performance of the closed-loop system to bounded exogenous disturbance and bounded uncertainty is achieved by a two-step design procedure adapted from the traditional observer-based controller design. Furthermore, an LMI pole-placement region and the L₂ robustness performance are combined into a multiobjective formulation by suitably combing the appropriate LMI descriptions. A parameter-varying system example is given to illustrate the design procedure and the validity of the proposed integrated design approach

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

Sensor fault diagnosis of singular delayed LPV systems with inexact parameters: an uncertain system approach

In this paper, sensor fault diagnosis of a singular delayed linear parameter varying (LPV) system is considered. In the considered system, the model matrices are dependent on some parameters which are real-time measurable. The case of inexact parameter measurements is considered which is close to real situations. Fault diagnosis in this system is achieved via fault estimation. For this purpose, an augmented system is created by including sensor faults as additional system states. Then, an unknown input observer (UIO) is designed which estimates both the system states and the faults in the presence of measurement noise, disturbances and uncertainty induced by inexact measured parameters. Error dynamics and the original system constitute an uncertain system due to inconsistencies between real and measured values of the parameters. Then, the robust estimation of the system states and the faults are achieved with H8 performance and formulated with a set of linear matrix inequalities (LMIs). The designed UIO is also applicable for fault diagnosis of singular delayed LPV systems with unmeasurable scheduling variables. The efficiency of the proposed approach is illustrated with an example.Peer ReviewedPostprint (author's final draft

Actuator fault diagnosis of singular delayed LPV systems with inexact measured parameters via PI unknown input observer

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this study, actuator fault diagnosis of singular delayed linear parameter varying (SDLPV) systems is considered. The considered system has a time-varying state delay and its matrices are dependent on some parameters that are measurable online. It is assumed that the measured parameters are inexact due to the existence of noise in real situations. The system with inexact measured parameters is converted to an uncertain system. Actuator fault diagnosis is carried out based on fault size estimation. For this purpose, the system is transformed to a polytopic representation and then a polytopic proportional integral unknown input observer (PI-UIO) is designed. The proposed observer provides simultaneous state and actuator fault estimation while attenuating, in the H8H8 sense, the effects of input disturbance, output noise and the uncertainty caused by inexact measured parameters. The design procedure of PI-UIO is formulated as a convex optimisation problem with a set of Linear Matrix Inequality (LMI) constraints in the vertices of the parameter domain, guaranteeing robust exponential convergence of the PI-UIO. The efficiency of the proposed method is illustrated with an electrical circuit example modelled as an SDLPV system.Peer ReviewedPostprint (author's final draft

An LPV Fault Tolerant control for semi-active suspension -scheduled by fault estimation

International audienceIn this paper, a novel fault tolerant control is proposed to accommodate damper faults (oil leakages) in a semi-active suspension system based on a quarter-car vehicle model. The fault accommodation is based on the Linear Parameter Varying (LPV) control strategy and involved in 2 steps. At first, a fast time-varying fault is estimated by using the fast adaptive fault estimation (FAFE) algorithm and based on an unknown input adaptive observer. Thanks to information about the estimated fault, the dissipativity domain of the semi-active suspension is adapted according to the fault. Then a single LPV fault tolerant controller is developed to manage the system performances. The controller solution, derived in the LPV/H ∞ framework, is based on the LMI solution for polytopic systems. Some simulation results are presented that show the effectiveness of this approach

Simultaneous actuator and sensor fault reconstruction of singular delayed linear parameter varying systems in the presence of unknown time varying delays and inexact parameters

In this article, robust fault diagnosis of a class of singular delayed linear parameter varying systems is considered. The considered system has delayed dynamics with unknown time varying delays and also it is affected by noise, disturbance and faults in both actuators and sensors. Moreover, in addition to the aforementioned unknown inputs and uncertainty, another source of uncertainty related to inexact measures of the scheduling parameters is present in the system. Making use of the descriptor system approach, sensor faults in the system are added as additional states into the original state vector to obtain an augmented system. Then, by designing a suitable proportional double integral unknown input observer (PDIUIO), the states, actuator, and sensor faults are estimated. The uncertainty due to the mismatch between the inexact parameters that schedule the observer and the real parameters that schedule the original system is formulated with an uncertain system approach. In the PDIUIO, the uncertainty induced by unknown inputs (disturbance, noise and actuator, and sensor faults), unknown delays, and inexact parameter measures are attenuated in H8 sense with different weights. The constraints regarding the existence and the robust stability of the designed PDIUIO are formulated using linear matrix inequalities. The efficiency of the proposed method is verified using an application example based on an electrical circuit.Peer ReviewedPostprint (author's final draft

Comparison of observer approaches for actuator fault estimation in semi-active suspension systems

International audienceIn this paper, the actuator fault estimation problem of semi-active suspension systems is considered. For instance, an oil leakage in the damper could cause a reduction of the damping force. The fault estimation requires a modeling of the damper fault (both multiplicative and additive fault models can be used). Three observer-based approaches are compared for fault estimation: an observer using fast adaptive fault estimation (FAFE) approach (used for estimation of additive faults), a parametric adaptive observer (AO) and a switched LPV observer (LPVO) (both intended to estimate mulplicative faults); Since the damper fault estimation is strongly affected by the unknown road disturbances, an H ∞ performance objective is used to reduce the effect of disturbances on the estimation error for performance assessment. Some simulations are performed on a quarter car model to validate these methodologies and a comparison is then given to shows the interest of each method. Keywords: Fault estimation, semi-active damper fault, adaptive observer, fast fault adaptive estimation, LPV observer

Unknown input observer approaches to robust fault diagnosis

This thesis focuses on the development of the model-based fault detection and isolation /fault detection and diagnosis (FDI/FDD) techniques using the unknown input observer (UIO) methodology. Using the UI de-coupling philosophy to tackle the robustness issue, a set of novel fault estimation (FE)-oriented UIO approaches are developed based on the classical residual generation-oriented UIO approach considering the time derivative characteristics of various faults. The main developments proposed are:- Implement the residual-based UIO design on a high fidelity commercial aircraft benchmark model to detect and isolate the elevator sensor runaway fault. The FDI design performance is validated using a functional engineering simulation (FES) system environment provided through the activity of an EU FP7 project Advanced Fault Diagnosis for Safer Flight Guidance and Control (ADDSAFE).- Propose a linear time-invariant (LTI) model-based robust fast adaptive fault estimator (RFAFE) with UI de-coupling to estimate the aircraft elevator oscillatory faults considered as actuator faults.- Propose a UI-proportional integral observer (UI-PIO) to estimate actuator multiplicative faults based on an LTI model with UI de-coupling and with added H∞ optimisation to reduce the effects of the sensor noise. This is applied to an example on a hydraulic leakage fault (multiplicative fault) in a wind turbine pitch actuator system, assuming that thefirst derivative of the fault is zero. - Develop an UI–proportional multiple integral observer (UI-PMIO) to estimate the system states and faults simultaneously with the UI acting on the system states. The UI-PMIO leads to a relaxed condition of requiring that the first time derivative of the fault is zero instead of requiring that the finite time fault derivative is zero or bounded. - Propose a novel actuator fault and state estimation methodology, the UI–proportional multiple integral and derivative observer (UI-PMIDO), inspired by both of the RFAFE and UI-PMIO designs. This leads to an observer with the comprehensive feature of estimating faults with bounded finite time derivatives and ensuring fast FE tracking response.- Extend the UI-PMIDO theory based on LTI modelling to a linear parameter varying (LPV) model approach for FE design. A nonlinear two-link manipulator example is used to illustrate the power of this method

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