Integral sliding mode fault tolerant control allocation for a class of affine nonlinear system

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.This paper develops novel fault tolerant integral sliding mode control allocation schemes for a class of over-actuated affine nonlinear system. The proposed schemes rely on an existing baseline controller and the objective is to retain the nominal (fault-free) closed-loop performance in the face of actuator faults/failures by effectively utilizing actuator redundancy. The online control allocation reroutes the control effort to the healthy actuators using knowledge of the actuator effectiveness level estimates. One of the proposed schemes is tested in simulation using a well known high fidelity model of a large civil transport aircraft (B747) from the literature. Good simulation results show the efficacy of the scheme

Aircraft loss-of-control prevention and recovery: a hybrid control strategy

The Complexity of modern commercial and military aircrafts has necessitated better protection and recovery systems. With the tremendous advances in computer technology, control theory and better mathematical models, a number of issues (Prevention, Recon guration, Recovery, Operation near critical points, ... etc) moderately addressed in the past have regained interest in the aeronautical industry.Flight envelope is essential in all ying aerospace vehicles. Typically, ying the vehicle means remaining within the ight envelope at all times. Operation outside the normal ight regime is usually subject to failure of components (Actuators, Engines, Deection Surfaces) , pilots's mistakes, maneuverability near critical points and environmental conditions(crosswinds...) and in general characterized as Loss-Of-Control (LOC) because the aircraft no longer responds to pilot's inputs as expected.For the purpose of this work,(LOC) in aircraft is de ned as the departure from the safe set (controlled flight) recognized as the maximum controllable (reachable) set in the initial ight envelope. The LOC can be reached either through failure, unintended maneuvers, evolution near irregular points and disturbances. A coordinated strategy is investigated and designed to ensure that the aircraft can maneuver safely in their constraint domain and can also recover from abnormal regime. The procedure involves the computation of the largest controllable (reachable) set (Safe set) contained in the initial prescribed envelope. The problem is posed as a reachability problem using Hamilton-Jacobi Partial Di erential Equation(HJ - PDE) where a cost function is set to be minimized along trajectory departing from the given set. Prevention is then obtained by computing the controller which would allow the flight vehicle to remain in the maximum controlled set in a multi-objective set up. Then the recovery procedure is illustrated with a two - point boundary value problem. Once illustrate, a set of control strategies is designed for recovery purpose ranging from nonlinear smooth regulators with Hamilton Jacobi-Bellman (HJB) formulation to the switching controllers with High Order Sliding Mode Controllers (HOSMC). A coordinated strategy known as a high level supervisor is then implemented using the multi-models concept where models operate in specified safe regions of the state space.Ph.D., Mechanical Engineering and Mechanics -- Drexel University, 201

A Human Driver Model for Autonomous Lane Changing in Highways: Predictive Fuzzy Markov Game Driving Strategy

This study presents an integrated hybrid solution to mandatory lane changing problem to deal with accident avoidance by choosing a safe gap in highway driving. To manage this, a comprehensive treatment to a lane change active safety design is proposed from dynamics, control, and decision making aspects. My effort first goes on driver behaviors and relating human reasoning of threat in driving for modeling a decision making strategy. It consists of two main parts; threat assessment in traffic participants, (TV s) states, and decision making. The first part utilizes an complementary threat assessment of TV s, relative to the subject vehicle, SV , by evaluating the traffic quantities. Then I propose a decision strategy, which is based on Markov decision processes (MDPs) that abstract the traffic environment with a set of actions, transition probabilities, and corresponding utility rewards. Further, the interactions of the TV s are employed to set up a real traffic condition by using game theoretic approach. The question to be addressed here is that how an autonomous vehicle optimally interacts with the surrounding vehicles for a gap selection so that more effective performance of the overall traffic flow can be captured. Finding a safe gap is performed via maximizing an objective function among several candidates. A future prediction engine thus is embedded in the design, which simulates and seeks for a solution such that the objective function is maximized at each time step over a horizon. The combined system therefore forms a predictive fuzzy Markov game (FMG) since it is to perform a predictive interactive driving strategy to avoid accidents for a given traffic environment. I show the effect of interactions in decision making process by proposing both cooperative and non-cooperative Markov game strategies for enhanced traffic safety and mobility. This level is called the higher level controller. I further focus on generating a driver controller to complement the automated car’s safe driving. To compute this, model predictive controller (MPC) is utilized. The success of the combined decision process and trajectory generation is evaluated with a set of different traffic scenarios in dSPACE virtual driving environment. Next, I consider designing an active front steering (AFS) and direct yaw moment control (DYC) as the lower level controller that performs a lane change task with enhanced handling performance in the presence of varying front and rear cornering stiffnesses. I propose a new control scheme that integrates active front steering and the direct yaw moment control to enhance the vehicle handling and stability. I obtain the nonlinear tire forces with Pacejka model, and convert the nonlinear tire stiffnesses to parameter space to design a linear parameter varying controller (LPV) for combined AFS and DYC to perform a commanded lane change task. Further, the nonlinear vehicle lateral dynamics is modeled with Takagi-Sugeno (T-S) framework. A state-feedback fuzzy H∞ controller is designed for both stability and tracking reference. Simulation study confirms that the performance of the proposed methods is quite satisfactory

Nondeterministic hybrid dynamical systems

This thesis is concerned with the analysis, control and identification of hybrid dynamical systems. The main focus is on a particular class of hybrid systems consisting of linear subsystems. The discrete dynamic, i.e., the change between subsystems, is unknown or nondeterministic and cannot be influenced, i.e. controlled, directly. However changes in the discrete dynamic can be detected immediately, such that the current dynamic (subsystem) is known. In order to motivate the study of hybrid systems and show the merits of hybrid control theory, an example is given. It is shown that real world systems like Anti Locking Brakes (ABS) are naturally modelled by such a class of linear hybrids systems. It is shown that purely continuous feedback is not suitable since it cannot achieve maximum braking performance. A hybrid control strategy, which overcomes this problem, is presented. For this class of linear hybrid system with unknown discrete dynamic, a framework for robust control is established. The analysis methodology developed gives a robustness radius such that the stability under parameter variations can be analysed. The controller synthesis procedure is illustrated in a practical example where the control for an active suspension of a car is designed. Optimal control for this class of hybrid system is introduced. It is shows how a control law is obtained which minimises a quadratic performance index. The synthesis procedure is stated in terms of a convex optimisation problem using linear matrix inequalities (LMI). The solution of the LMI not only returns the controller but also the performance bound. Since the proposed controller structures require knowledge of the continuous state, an observer design is proposed. It is shown that the estimation error converges quadratically while minimising the covariance of the estimation error. This is similar to the Kalman filter for discrete or continuous time systems. Further, we show that the synthesis of the observer can be cast into an LMI, which conveniently solves the synthesis problem

Robust explicit model predictive control for hybrid linear systems with parameter uncertainties

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments

Control Methods for High-Speed Supercavitating Vehicles

Supercavitation is an emerging technology that enables underwater vehicles to reach un- precedented speed. With proper design of cavitator attached to the vehicle nose, the vehicle body is surrounded by water vapor cavity, eliminating skin friction drag. This technology offers unprecedented drag reduction, though poses problems for vehicle design. The gas bubble surrounding the hull introduces highly coupled dynamic behavior, representing a challenge for the control designer. Development of stable, controllable supercavitating vehi- cles requires solution for several open problems. This dissertation addresses the problem of control oriented modeling, stability augmentation, and reference tracking using parameter dependent control techniques for supercavitating vehicles.\ud The thesis is divided into three parts. A nonlinear dynamical model capturing the most important properties of the vehicle motion is developed from a control design perspective. The model includes memory effects associated with the time evolution of the cavity and uses lookup tables to determine forces.\ud To aid understanding the cavity-vehicle interaction, a longitudinal control scenario is developed for a simplified longitudinal dynamical model with guaranteed properties. Sig- nificant insight is gained on planing behavior and operating envelope using constrained control inputs.\ud Extending the longitudinal control problem, a linear parameter varying model of the coupled motion is developed to provide a platform for parameter dependent control syn- thesis. The mathematical model is scheduled with aerodynamic angles, uses steady-state approximation of the cavity, leading to uncertainty in the governing equations. Two Linear Parameter Varying (LPV) controllers are synthesized for the angle rate tracking problem, taking uncertainty into account. One uses traditional decoupled loops for pitch-, roll- and yaw-rate tracking. Ignoring the cross coupling, leads to more tractable subproblems . A controller, taking advantage of the coupling, is also presented in the thesis. The complexity of the coupled dynamics prohibits the synthesis of the controller as a single entity. Sev- eral LPV controllers synthesized for smaller overlapping regions of the parameter space are blended together, providing a single controller for the full flight envelope. Time-domain simulations of different vehicle-controller configurations, implemented on high-fidelity sim- ulations, provide insight into the capabilities of the supercavitating vehicle

Commande par mode glissant de paliers magnétiques actifs économes en énergie : une approche sans modèle

Abstract : Over the past three decades, various fields have witnessed a successful application of active magnetic bearing (AMB) systems. Their favorable features include supporting high-speed rotation, low power consumption, and rotor dynamics control. Although their losses are much lower than roller bearings, these losses could limit the operation in some applications such as flywheel energy storage systems and vacuum applications. Many researchers focused their efforts on boosting magnetic bearings energy efficiency via minimizing currents supplied to electromagnetic coils either by a software solution or a hardware solution. According to a previous study, we adopt the hardware solution in this thesis. More specifically, we investigate developing an efficient and yet simple control scheme for regulating a permanent magnet-biased active magnetic bearing system. The control objective here is to suppress the rotor vibrations and reduce the corresponding control currents as possible throughout a wide operating range. Although adopting the hardware approach could achieve an energy-efficient AMB, employing an advanced control scheme could achieve a further reduction in power consumption. Many advanced control techniques have been proposed in the literature to achieve a satisfactory performance. However, the complexity of the majority of control schemes and the potential requirement of powerful platform could discourage their application in practice. The motivation behind this work is to improve the closed-loop performance without the need to do model identification and following the conventional procedure for developing a model-based controller. Here, we propose applying the hybridization concept to exploit the classical PID control and some nonlinear control tools such as first- and second-order sliding mode control, high gain observer, backstepping, and adaptive techniques to develop efficient and practical control schemes. All developed control schemes in this thesis are digitally implemented and validated on the eZdsp F2812 control board. Therefore, the applicability of the proposed model-free techniques for practical application is demonstrated. Furthermore, some of the proposed control schemes successfully achieve a good compromise between the objectives of rotor vibration attenuation and control currents minimization over a wide operating range.Résumé: Au cours des trois dernières décennies, divers domaines ont connu une application réussie des systèmes de paliers magnétiques actifs (PMA). Leurs caractéristiques favorables comprennent une capacité de rotation à grande vitesse, une faible consommation d'énergie, et le contrôle de la dynamique du rotor. Bien que leurs pertes soient beaucoup plus basses que les roulements à rouleaux, ces pertes pourraient limiter l'opération dans certaines applications telles que les systèmes de stockage d'énergie à volant d'inertie et les applications sous vide. De nombreux chercheurs ont concentré leurs efforts sur le renforcement de l'efficacité énergétique des paliers magnétiques par la minimisation des courants fournis aux bobines électromagnétiques soit par une solution logicielle, soit par une solution matérielle. Selon une étude précédente, nous adoptons la solution matérielle dans cette thèse. Plus précisément, nous étudions le développement d'un système de contrôle efficace et simple pour réguler un système de palier magnétique actif à aimant permanent polarisé. L'objectif de contrôle ici est de supprimer les vibrations du rotor et de réduire les courants de commande correspondants autant que possible tout au long d'une large plage de fonctionnement. Bien que l'adoption de l'approche matérielle pourrait atteindre un PMA économe en énergie, un système de contrôle avancé pourrait parvenir à une réduction supplémentaire de la consommation d'énergie. De nombreuses techniques de contrôle avancées ont été proposées dans la littérature pour obtenir une performance satisfaisante. Cependant, la complexité de la majorité des systèmes de contrôle et l'exigence potentielle d’une plate-forme puissante pourrait décourager leur application dans la pratique. La motivation derrière ce travail est d'améliorer les performances en boucle fermée, sans la nécessité de procéder à l'identification du modèle et en suivant la procédure classique pour développer un contrôleur basé sur un modèle. Ici, nous proposons l'application du concept d'hybridation pour exploiter le contrôle PID classique et certains outils de contrôle non linéaires tels que contrôle par mode glissement du premier et du second ordre, observateur à grand gain, backstepping et techniques adaptatives pour développer des systèmes de contrôle efficaces et pratiques. Tous les systèmes de contrôle développés dans cette thèse sont numériquement mis en oeuvre et évaluées sur la carte de contrôle eZdsp F2812. Par conséquent, l'applicabilité des techniques de modèle libre proposé pour l'application pratique est démontrée. En outre, certains des régimes de contrôle proposés ont réalisé avec succès un bon compromis entre les objectifs au rotor d’atténuation des vibrations et la minimisation des courants de commande sur une grande plage de fonctionnement

Advances in gain-scheduling and fault tolerant control techniques

This thesis presents some contributions to the state-of-the-art of the fields of gain-scheduling and fault tolerant control (FTC). In the area of gain-scheduling, the connections between the linear parameter varying (LPV) and Takagi-Sugeno (TS) paradigms are analyzed, showing that the methods for the automated generation of models by nonlinear embedding and by sector nonlinearity, developed for one class of systems, can be easily extended to deal with the other class. Then, two measures, based on the notions of overboundedness and region of attraction estimates, are proposed in order to compare different models and choose which one can be considered the best one. Later, the problem of designing state-feedback controllers for LPV systems has been considered, providing two main contributions. First, robust LPV controllers that can guarantee some desired performances when applied to uncertain LPV systems are designed, by using a double-layer polytopic description that takes into account both the variability due to the varying parameter vector and the uncertainty. Then, the idea of designing the controller in such a way that the required performances are scheduled by the varying parameters is explored, which provides an elegant way to vary online the behavior of the closed-loop system. In both cases, the problem reduces to finding a solution to a finite number of linear matrix inequalities (LMIs), which can be done efficiently using the available solvers. In the area of fault tolerant control, the thesis first shows that the aforementioned double-layer polytopic framework can be used for FTC, in such a way that different strategies (passive, active and hybrid) are obtained depending on the amount of available information. Later, an FTC strategy for LPV systems that involves a reconfigured reference model and virtual actuators is developed. It is shown that by including the saturations in the reference model equations, it is possible to design a model reference FTC system that automatically retunes the reference states whenever the system is affected by saturation nonlinearities. In this way, a graceful performance degradation in presence of actuator saturations is incorporated in an elegant way. Finally, the problem of FTC of unstable LPV systems subject to actuator saturations is considered. In this case, the design of the virtual actuator is performed in such a way that the convergence of the state trajectory to zero is assured despite the saturations and the appearance of faults. Also, it is shown that it is possible to obtain some guarantees about the tolerated delay between the fault occurrence and its isolation, and that the nominal controller can be designed so as to maximize the tolerated delay.Aquesta tesi presenta diverses contribucions a l'estat de l'art del control per planificació del guany i del control tolerant a fallades (FTC). Pel que fa al control per planificació del guany, s'analitzen les connexions entre els paradigmes dels sistemes lineals a paràmetres variants en el temps (LPV) i de Takagi-Sugeno (TS). Es demostra que els mètodes per a la generació automàtica de models mitjançant encastament no lineal i mitjançant no linealitat sectorial, desenvolupats per una classe de sistemes, es poden estendre fàcilment per fer-los servir amb l'altra classe. Es proposen dues mesures basades en les nocions de sobrefitació i d'estimació de la regió d'atracció, per tal de comparar diferents models i triar quin d'ells pot ser considerat el millor. Després, es considera el problema de dissenyar controladors per realimentació d'estat per a sistemes LPV, proporcionant dues contribucions principals. En primer lloc, fent servir una descripció amb doble capa politòpica que té en compte tant la variabilitat deguda al vector de paràmetres variants i la deguda a la incertesa, es dissenyen controladors LPV robustos que puguin garantir unes especificacions desitjades quan s'apliquen a sistemes LPV incerts. En segon lloc, s'explora la idea de dissenyar el controlador de tal manera que les especificacions requerides siguin programades pels paràmetres variants. Això proporciona una manera elegant de variar en línia el comportament del sistema en llaç tancat. En tots dos casos, el problema es redueix a trobar una solució d'un nombre finit de desigualtats matricials lineals (LMIs), que es poden resoldre fent servir algorismes numèrics disponibles i molt eficients. En l'àrea del control tolerant a fallades, primerament la tesi mostra que la descripció amb doble capa politòpica abans esmentada es pot utilitzar per fer FTC, de tal manera que, en funció de la quantitat d'informació disponible, s'obtenen diferents estratègies (passiva, activa i híbrida). Després, es desenvolupa una estratègia de FTC per a sistemes LPV que fa servir un model de referència reconfigurat combinat amb la tècnica d'actuadors virtuals. Es mostra que mitjançant la inclusió de les saturacions en les equacions del model de referència, és possible dissenyar un sistema de control tolerant a fallades que resintonitza automàticament els estats de referència cada vegada que el sistema es veu afectat per les no linealitats de la saturació en els actuadors. D'aquesta manera s'incorpora una degradació elegant de les especificacions en presència de saturacions d'actuadors. Finalment, es considera el problema de FTC per sistemes LPV inestables afectats per saturacions d'actuadors. En aquest cas, es porta a terme el disseny de l'actuador virtual de tal manera que la convergència a zero de la trajectòria d'estat està assegurada tot i les saturacions i l'aparició de fallades. A més, es mostra que és possible obtenir garanties sobre el retard tolerat entre l'aparició d'una fallada i el seu aïllament, i que el controlador nominal es pot dissenyar maximitzant el retard tolerat

Robust fault tolerant control of induction motor system

Research into fault tolerant control (FTC, a set of techniques that are developed to increase plant availability and reduce the risk of safety hazards) for induction motors is motivated by practical concerns including the need for enhanced reliability, improved maintenance operations and reduced cost. Its aim is to prevent that simple faults develop into serious failure. Although, the subject of induction motor control is well known, the main topics in the literature are concerned with scalar and vector control and structural stability. However, induction machines experience various fault scenarios and to meet the above requirements FTC strategies based on existing or more advanced control methods become desirable. Some earlier studies on FTC have addressed particular problems of 3-phase sensor current/voltage FTC, torque FTC, etc. However, the development of these methods lacks a more general understanding of the overall problem of FTC for an induction motor based on a true fault classification of possible fault types.In order to develop a more general approach to FTC for induction motors, i.e. not just designing specific control approaches for individual induction motor fault scenarios, this thesis has carried out a systematic research on induction motor systems considering the various faults that can typically be present, having either “additive” fault or “multiplicative” effects on the system dynamics, according to whether the faults are sensor or actuator (additive fault) types or component or motor faults (multiplicative fault) types.To achieve the required objectives, an active approach to FTC is used, making use of fault estimation (FE, an approach that determine the magnitude of a fault signal online) and fault compensation. This approach of FTC/FE considers an integration of the electrical and mechanical dynamics, initially using adaptive and/or sliding mode observers, Linear Parameter Varying (LPV, in which nonlinear systems are locally decomposed into several linear systems scheduled by varying parameters) and then using back-stepping control combined with observer/estimation methods for handling certain forms of nonlinearity.In conclusion, the thesis proposed an integrated research of induction motor FTC/FE with the consideration of different types of faults and different types of uncertainties, and validated the approaches through simulations and experiments