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

Predictive control approaches to fault tolerant control of wind turbines

This thesis focuses on active fault tolerant control (AFTC) of wind turbine systems. Faults in wind turbine systems can be in the form of sensor faults, actuator faults, or component faults. These faults can occur in different locations, such as the wind speed sensor, the generator system, drive train system or pitch system. In this thesis, some AFTC schemes are proposed for wind turbine faults in the above locations. Model predictive control (MPC) is used in these schemes to design the wind turbine controller such that system constraints and dual control goals of the wind turbine are considered. In order to deal with the nonlinearity in the turbine model, MPC is combined with Takagi-Sugeno (T-S) fuzzy modelling. Different fault diagnosis methods are also proposed in different AFTC schemes to isolate or estimate wind turbine faults.The main contributions of the thesis are summarized as follows:A new effective wind speed (EWS) estimation method via least-squares support vector machines (LSSVM) is proposed. Measurements from the wind turbine rotor speed sensor and the generator speed sensor are utilized by LSSVM to estimate the EWS. Following the EWS estimation, a wind speed sensor fault isolation scheme via LSSVM is proposed.A robust predictive controller is designed to consider the EWS estimation error. This predictive controller serves as the baseline controller for the wind turbine system operating in the region below rated wind speed.T-S fuzzy MPC combining MPC and T-S fuzzy modelling is proposed to design the wind turbine controller. MPC can deal with wind turbine system constraints externally. On the other hand, T-S fuzzy modelling can approximate the nonlinear wind turbine system with a linear time varying (LTV) model such that controller design can be based on this LTV model. Therefore, the advantages of MPC and T-S fuzzy modelling are both preserved in the proposed T-S fuzzy MPC.A T-S fuzzy observer, based on online eigenvalue assignment, is proposed as the sensor fault isolation scheme for the wind turbine system. In this approach, the fuzzy observer is proposed to deal with the nonlinearity in the wind turbine system and estimate system states. Furthermore, the residual signal generated from this fuzzy observer is used to isolate the faulty sensor.A sensor fault diagnosis strategy utilizing both analytical and hardware redundancies is proposed for wind turbine systems. This approach is proposed due to the fact that in the real application scenario, both analytical and hardware redundancies of wind turbines are available for designing AFTC systems.An actuator fault estimation method based on moving horizon estimation (MHE) is proposed for wind turbine systems. The estimated fault by MHE is then compensated by a T-S fuzzy predictive controller. The fault estimation unit and the T-S fuzzy predictive controller are combined to form an AFTC scheme for wind turbine actuator faults

Mathematical control of complex systems 2013

Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)

Adaptive Optimal Control of Faulty Nonlinear DC Microgrids with Constant Power Loads: Dual-Extended Kalman Filter Approach

This article investigates the problem of estimating actuator fault and states and controlling the bus voltage in direct current microgrids (DC MGs) with linear and nonlinear constant power loads (CPLs). It is considered that the DC MG states are not fully measurable and the utilized sensors are not ideal and noisy. Additionally, the actuator fault occurs and it is modeled as an additive term in the power system dynamics. These issues, including nonlinearities, un-measurable states, noisy measures, and actuator fault indispensably degrade the operation of the DC MG. To solve this issue, initially, a dual-extended Kalman filter (dual-EKF) is suggested for the fault and state estimation. It decomposes the process of estimating the state and actuator fault to reduce the online computational burden. For the control purpose, a linear parameter varying (LPV) model predictive control (MPC) is suggested to regulate the current and voltage of the DC MG. It benefits the nonlinear system modeling of LPV representation and constrained-based design procedure of the MPC to result in an accurate and low online computational burden dealing with system constraints. By deploying the overall robust adaptive dual-EKF estimation-based LPV-MPC, there is no need to have any prior knowledge of all system states and actuator faults in prior. The theoretical analysis and controller design are validated by numerical simulations on a typical islanded DC MG and comparisons are done with state-of-the-art estimation and control strategies.©2022 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 works.fi=vertaisarvioitu|en=peerReviewed

Linear Parameter Varying Approaches as Advanced Control Techniques: Application to Vehicle Dynamics

TCC(graduação) - Universidade Federal de Santa Catarina. Centro Tecnológico. Engenharia de Controle e Automação.Ce travail de Fin-d’études présente plusieurs techniques de modélisation, identification et de la commande avancée appliqués a l’étude des systèmes de suspensions semi-actifs. Ce travail est divisé en trois domaines principaux: développement et l’application des techniques LPV pour l’identification des défauts sur les actionneurs dans les systèmes de suspension; développement et mise-en-œuvre d’un système de contrôle prédictif basé sur modèle appliqué en temps réel sur des suspensions semi-actifs; développement des techniques LPV de reconfiguration pour la commande tolerant aux défauts des systèmes de suspension. Les stratégies de commande développées sont analysées par simulation et validation et se montrent satisfaisantes.This End-of-Studies Work presents a range of techniques of Modeling, Identification and Advanced Control applied to the study of Semi-Active Suspensions in Vehicular Systems. This work is divided into three main branches: i) development and application of LPV fault identification techniques on actuators of suspension systems; ii) development and implementation of a real-time model predictive control scheme applied the control of semi- active suspensions; iii) development and application of LPV reconfiguration techniques for fault tolerant control of suspension system. The developed control strategies are analysed through simulation and validation on a mechatronic test-bench and prove themselves satisfactory.Este Trabalho de Conclusão de Curso apresenta diversas técnicas de Modelagem, Identifi- cação e Controle Avançado aplicadas ao estudo de Suspensões Semi-Ativas em Sistemas Veiculares. Este trabalho é divido em três eixos principais: i) Desenvolvimento e aplicação de técnicas LPV de Identificação de Falhas em amortecedores de sistemas de suspensão; ii) Desenvolvimento e implementação de um sistema de Controle Preditivo baseado em modelo aplicado em tempo-real para o controle de suspensões semi-ativas; iii) Desenvolvimento e aplicação de técnicas de reconfiguração LPV para o Controle Tolerante a Falhas de sistemas de suspensão. As técnicas e o desenvolvimento feito são analisados através de simulação e validação em uma plataforma mecatrônica experimental e demonstram-se satisfatórios

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

On-line estimation approaches to fault-tolerant control of uncertain systems

This thesis is concerned with fault estimation in Fault-Tolerant Control (FTC) and as such involves the joint problem of on-line estimation within an adaptive control system. The faults that are considered are significant uncertainties affecting the control variables of the process and their estimates are used in an adaptive control compensation mechanism. The approach taken involves the active FTC, as the faults can be considered as uncertainties affecting the control system. The engineering (application domain) challenges that are addressed are: (1) On-line model-based fault estimation and compensation as an FTC problem, for systems with large but bounded fault magnitudes and for which the faults can be considered as a special form of dynamic uncertainty. (2) Fault-tolerance in the distributed control of uncertain inter-connected systems The thesis also describes how challenge (1) can be used in the distributed control problem of challenge (2). The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control action and the second acting as an adaptive compensation for significant uncertainties and fault effects. The fault effects are a form of uncertainty which is considered too large for the application of passive FTC methods. The thesis considers several approaches to robust control and estimation: augmented state observer (ASO); sliding mode control (SMC); sliding mode fault estimation via Sliding Mode Observer (SMO); linear parameter-varying (LPV) control; two-level distributed control with learning coordination

Fault Tolerant Flight Control of Unmanned Aerial Vehicles

Safety, reliability and acceptable level of performance of dynamic control systems are the major keys in all control systems especially in safety-critical control systems. A controller should be capable of handling noises and uncertainties imposed to the controlled process. A fault-tolerant controller should be able to control a system with guaranteed stability and good or acceptable performance not only in normal operation conditions but also in the presence of partial faults or total failures that can be occurred in the components of the system. When a fault occurs in a system, it suddenly starts to behave in an unanticipated manner. Thereby, a fault-tolerant controller should be designed for being able to handle the fault and guarantee system stability and acceptable performance in the presence of faults/damages. This shows the importance and necessity of Fault-Tolerant Control (FTC) to safety-critical and even nowadays for some new and non-safety-critical systems. During recent years, Unmanned Aerial Vehicles (UAVs) have proved to play a significant role in military and civil applications. The success of UAVs in different missions guarantees the growing number of UAVs to be considerable in future. Reliability of UAVs and their components against faults and failures is one of the most important objectives for safety-critical systems including manned airplanes and UAVs. The reliability importance of UAVs is implied in the acknowledgement of the Office of the Secretary of Defense in the UAV Roadmap 2005-2030 by stating that, ”Improving UA [unmanned aircraft] reliability is the single most immediate and long-reaching need to ensure their success”. This statement gives a wide future scenery of safety, reliability and Fault-Tolerant Flight Control (FTFC) systems of UAVs. The main objective of this thesis is to investigate and compare some aspects of fault tolerant flight control techniques such as performance, robustness and capability of handling the faults and failures during the flight of UAVs. Several control techniques have been developed and tested on two main platforms at Concordia University for fault-tolerant control techniques development, implementation and flight test purposes: quadrotor and fixedwing UAVs. The FTC techniques developed are: Gain-Scheduled Proportional-Integral-Derivative (GS-PID), Control Allocation and Re-allocation (CA/RA), Model Reference Adaptive Control (MRAC), and finally the Linear Parameter Varying (LPV) control as an alternative and theoretically more comprehensive gain scheduling based control technique. The LPV technique is used to control the quadrotor helicopter for fault-free conditions. Also a GS-PID controller is used as a fault-tolerant controller and implemented on a fixedwing UAV in the presence of a stuck rudder failure case

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance