Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples. © 2011 The Author(s).published_or_final_versionSpringer Open Choice, 28 May 201

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

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

Robot Manipulators

Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Modeling cerebrocerebellar control in horizontal planar arm movements of humans and the monkey

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (leaves 215-236).In daily life, animals including humans make a wide repertoire of limb movements effortlessly without consciously thinking about joint trajectories or muscle contractions. These movements are the outcome of a series of processes and computations carried out by multiple subsystems within the central nervous system. In particular, the cerebrocerebellar system is central to motor control and has been modeled by many investigators. The bulk of cerebrocerebellar control involves both forward command and sensory feedback information inextricably combined. However, it is not yet clear how these types of signals are reflected in spiking activity in cerebellar cells in vivo. Segmentation of apparently continuous movements was first observed more than a century ago. Since then, submovements, which have been identified by non-smooth speed profiles, have been described in many types of movements. However, physiological origins of submovement have not been well understood. This thesis demonstrates that a currently proposed recurrent integrator PID (RIPID) cerebellar limb control model (Massaquoi 2006a) is consistent with average neural activity recorded in a monkey by developing the Recurrent Integrator-based Cerebellar Simple Spike (RICSS) model.(cont.) The RICSS formulation is consistent with known or plausible cerebrocerebellar and spinocerebellar neurocircuitry, including hypothetical classification of mossy fiber signals. The RICSS model accounts well for variety of cerebellar simple spike activity recorded from the monkey and outperforms any other existing models. The RIPID model is extended to include a simplified cortico-basal ganglionic loop to capture statistical characterization of intermittency observed in individual trials of the monkey. In order to extend the capability of the RIPID model to a larger workspace and faster movements, the model needs to be gainscheduled based on the local state information. A linear parameter varying (LPV) formulation, which shares a similar structure to that suggested by the RICSS model, is performed and its applicability was tested on human subjects performing double step tasks which requires rapid change in movement directions.by Kazutaka Takahashi.Ph.D

Robust stabilisation of multivariable systems: A super-optimisation approach

The work aims to derive extended robust stability results for the case of unstructured uncertainty models of multivariable systems. More specifically, throughout the thesis, additive and coprime unstructured perturbation models are considered. Refined robust stabilisation problems of MIMO systems are defined and maximally robust controllers are synthesised in a state-space form. Unstructured perturbations which destabilise the feedback system for every optimal (maximally robust) controller are identified on the boundary of the optimal ball, i.e. the set of all admissible perturbations with norm equal to the maximum robust stability radius. Boundary perturbations are termed "uniformly destabilising" if they destabilise the closed-loop system for every optimal controller and it is shown that they all share a common characteristic, i.e. a projection of magnitude equal to the maximal robust stability radius, along a fixed direction defined by a pair of maximising vectors (scaled Schmidt pair) of a Hankel operator related to the problem. By imposing a directionality constraint it is shown that it is possible to increase the robust stability radius in every other direction by a subset of all optimal controllers. In order to solve this problem, super-optimisation techniques are developed. Independently a natural extension of Hankel norm approximations, the so-called super­ optimisation problem is posed and solved explicitly for the case of one-block problems in a state-space setting. It is thus shown that a subset of all maximally robust controllers, namely the class of super-optimal controllers, stabilises all perturbed plants within an extended stability radius 11,*(b), subject to a directionality constraint. In addition, the work is related to robust stabilisation subject to structured perturbations. The notions of structured robust stabilisation problem, and structured set approximation are defined in connection with the maximised set of permissible perturbations. It is further shown that µ*(J) can serve as an upper bound the structured robust stabilisation problem. The effect of µ*(J) as an upper bound depends on the compatibility between the two structures, the true structure and the artificial structure of the extended permissible set. [Look inside the thesis' abstract for an exact version of formulas and equations

Time-frequency investigation of heart rate variability and cardiovascular system modeling of normal and chronic obstructive pulmonary disease (COPD) subjects

A study has been designed to add insight to some questions that have not been fully investigated in the heart rate variability field and the cardiovascular regulation system in normal and Chronic Obstructive Pulmonary Disease (COPD) subjects. It explores the correlations between heart rate variability and cardiovascular regulation, which interact through complex multiple feedback and control loops. This work examines the coupling between heart rate (HR), respiration (RESP), and blood pressure (BP) via closed-loop system identification techniques in order to noninvasively assess the underlying physiology. In the first part of the study, the applications of five different bilinear time-frequency representations are evaluated on modeled HRV test signals, actual electrocardiograms (ECG), BP and RESP signals. Each distribution: the short time Fourier transform (STFT), the smoothed pseudo Wigner-Ville (SPWVD), the ChoiWilliams (CWD), the Bom-Jordan-Cohen (BJC) and wavelet distribution (WL), has unique characteristics which is shown to affect the amount of smoothing and the generation of cross-terms. The CWD and the WL are chosen for further application because of overcoming the drawbacks of other distributions by providing higher resolution in time and frequency while suppressing interferences between the signal components. In the second part of the study, the Morlet, Meyer, Daubechies 4, Mexican Hat and Haar wavelets are used to investigate the heart rate and blood pressure variability from both COPD and normal subjects. The results of wavelet analysis give much more useful information than the Cohen\u27s class representations. Here we are able to quantitatively assess the parasympathetic (HF) and sympatho-vagal balance (LF:HF) changes as a function of time. As a result, COPD subjects breathe faster, have higher blood pressure variability and lower HRV. In the third part of the study, a special class of the exogenous autoregressive (ARX) model is developed as an analytical tool for uncovering the hidden autonomic control processes. Non-parametric relationships between the input and outputs of the ARX model resulting in transfer function estimations of the noise filters and the input filter were used as mechanistic cardiovascular models that have shown to have predictive capabilities for the underlying autonomic nervous system activity of COPD patients. Transfer functions of COPD cardiovascular models have similar DC gains but show a larger lag in phase as compared to the models of normal subjects. Finally, a method of severity classification is presented. This method combines the techniques of principal component analysis (PCA) and cluster analysis (CA) and has been shown to separate the COPD from the normal population with 100% accuracy. It can also classify the COPD population into at risk , mild , moderate and severe stages with 100%, 90%, 88% and 100% accuracy respectively. As a result, cluster and principal component analysis can be used to separate COPD and normal subjects and can be used successfully in COPD severity classification