During the last decades, virtual environments have become very popular and are largely used in many domains as, for example, prototyping, trainings for different devices, assistance in completing difficult tasks, etc. The interaction with the virtual reality, as well as the feedback force, is assured by haptic interfaces. Generally, such systems are affected by communication and processing time-delays, resulting in a deterioration of performances. In this thesis, a complete study of the existing methods, as well as theoretical tools and new solutions, are proposed for the haptic framework. First, a comparative study, based on the experimental results obtained on a 1-dof haptic system, highlights the advantages and drawbacks of the most common control algorithms ported from teleoperation to haptics. Next, the theoretical tools needed in analyzing the stability of the delayed systems in different situations, as well as the physical limitations of the experimental platforms considered, are examined. Besides the standard case of constant time-delays, uncertainties are also considered and modeled by different types of distributions (uniform, normal and gamma distribution with gap). In the sequel, for overcoming the drawback of time-delays, two new approaches are proposed. First, the use of Smith predictor-based control is addressed and a specific solution for haptic systems is developed and discussed. The main idea is to introduce into the Smith predictor the environmental forces by using the additional information from the virtual reality regarding the distances between the controlled virtual object and other objects in the scene. To overcome the loss of performances induced by using a fixed gain in the controllers for all situations (free or restricted motions), the second approach proposes a gain-scheduling Proportional Derivative control strategy depending on the distance until a possible collision. Both approaches are experimentally validated on a 3-dof haptic platform, under different scenarios elaborated gradually from simple situations - free and restricted motion, contacts with moving objects, to more complex situations - virtual box with fixed or moving sides.

This thesis addresses the H∞ analysis and control of continuous commensurate time-delay systems by frequential methods. First, the asymptotic behavior of the chains of poles are studied, and the conditions of stability for neutral systems with poles approaching the imaginary axis are given. The same analysis is done for fractional systems. In the sequel, a numerical method able to locate all the stability windows as well as the unstable root-locus for classical and fractional system is given. We conclude the analysis part by providing the stability crossing curves of a class of distributed delay system. Starting the synthesis part, we design PID controllers for unstable fractional systems using a small-gain theorem approach. Finally, using the Rekasius substitution, we construct a linear time invariant comparison system that allows us to get information about stability and H∞-norm for classical time-delay systems. Using this approach it is possible to design state and output feedback controllers, as well as linear filters for this class of systems.

In this thesis an adaptive backstepping control scheme is proposed for a class of multi-input perturbed systems with time-varying delays to solve regulation problems. The systems to be controlled contain n blocks¡¦ dynamic equations, hence n-1 virtual input controllers are designed from the first block to the (n-1)th block, and the backstepping controller is designed from the last block. In addition, adaptive mechanisms are embedded in each virtual input controllers and proposed controller, so that the least upper bounds of perturbations are not required to be known beforehand. Furthermore, the dynamic equations of the systems to be controlled need not satisfy strict-feedback form, and the upper bounds of the time delays as well as their derivatives need not to be known in advance either. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme.

M. Tech. Electrical Engineering. / Attempts to find computational efficient ways to identify and extract gunshot impulses from signals. Areas of study include Generalised Cross Correlation (GCC), sidelobe minimisation utilising Least Square (LS) techniques as well as training algorithms using a Reproducing Kernel Hilbert Space (RKHS) approach. It also incorporates Support Vector Machines (SVM) to train a network to recognise gunshot impulses. By combining these individual research areas more optimal solutions are obtainable.

No description available.

Thesis (M.Eng.(Control Engineering))--University of Pretoria, 2008. / Summary in English. Includes bibliographical references.

This thesis proposes novel methods for identification and control of multivariable systems including multiple delays and describes their application to control of general anesthesia administration. First, an identification method for multivariable systems whose input and output paths have different time delays is presented. Second, a state predictor for multivariable systems whose input and output paths have different time delays is proposed. Third, the state predictor is used for constructing a state-predictive servo control system for controlled processes whose output paths have different time delays. A robust stability analysis method of the state-predictive servo control system is also examined. Furthermore, based on results of these theoretical studies, control systems for use in general anesthesia administration are developed. First, an identification method for multivariable systems whose input and output paths have different time delays is proposed. This method comprises two steps. In the first step, the delay lengths are estimated from the impulse response matrix identified from input and output (I/O) sequences using a subspace identification algorithm. In the second step, I/O sequences of a delay-free part are constructed from the original sequences and the delay estimates, and the system matrices of the delay-free part are identified. The proposed method is numerically stable and efficient. Moreover, it requires no complex optimization to obtain the delay estimates, nor does it require an assumption about the structure of the system matrices. Second, a state predictor is proposed for multivariable systems whose input and output paths have different time delays. The predictor consists of a full-order observer and a prediction mechanism. The former estimates a vector consisting of past states from the output. The latter predicts the current state from the estimated vector. The prediction error converges to zero at an arbitrary rate, which can be determined using pole assignment method, etc. In the proposed predictor, the interval length of the finite interval integration fed to the observer is shorter than that of an existing delay-compensating observer. Consequently, the proposed predictor is more numerically accurate than the delay-compensating observer. Using the proposed state predictor, a design method of a state-predictive servo controller is described for multivariable systems whose output paths have different time delays. Furthermore, a sufficient stability condition of the state-predictive servo control system against parameter mismatches is derived. Using a characteristic equation of the perturbed closed-loop system, a stability margin can be given on a plane whose axes correspond to the magnitudes of the mismatches on system matrices and on delay lengths. In the remainder of this thesis, development of anesthesia control systems is described to illustrate an application of the theoretical results described above. First, a hypnosis control system is presented. This system administers an intravenous hypnotic drug to regulate an electroencephalogram-derived index reflecting the patient’s hypnosis. The system comprises three functions: i) a model predictive controller that can take into account effects of time delay adequately, ii) an estimation function of individual parameters, and iii) a risk-control function for preventing undesirable states such as drug over-infusion or intra-operative arousal. Results of 79 clinical trials show that the system can reduce the total amount of drug infusion and maintain hypnosis more accurately than an anesthesiologist’s manual adjustment. Second, a simultaneous control system of hypnosis and muscle relaxation is described. For development of this system, a multivariable model of hypnosis and muscle relaxation is identified using the method proposed in this thesis. Then a state-predictive servo control system is designed for controlling hypnosis and muscle relaxation. Finally, the control system’s performance is evaluated through simulation. The resultant simultaneous control system satisfies the performance specifications of settling time, disturbance rejection ability, and a robust stability range. Although this system is not fully developed, the procedure of constructing this control system demonstrates the effectiveness of the proposed methods: the identification method for systems whose input and output paths have different time delays and the design and stability analysis methods of the state-predictive servo control system. / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13820号 / 工博第2924号 / 新制||工||1432(附属図書館) / 26036 / UT51-2008-C736 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 小林 哲生, 教授 萩原 朋道, 准教授 古谷 栄光 / 学位規則第4条第1項該当

Este trabalho tem por objetivo apresentar uma nova forma de analisar as redes de sincronismo de fase mutuamente conectadas. Estas redes são formadas por Phase-Locked Loops digitais ou DPLLs. O sinal gerado por cada DPLL é enviado a todos os demais dispositivos, formando a rede mutuamente conectada. Parte-se do pressuposto de que as ligações entre os dispositivos são dotadas de atrasos, o que dificulta o tratamento do problema. No entanto, é apresentado aqui um método para análise das malhas de sincronismo via discretização do modelo de tempo contínuo, objetivando dirimir essa dificuldade, já que atrasos são facilmente representados em modelos de tempo discreto. Para tanto, o modelo da rede no espaço de estados é equacionado a partir da rede. Esse modelo no espaço de estados é, então, discretizado e, enfim, pode-se determinar o estado síncrono da rede incluindo a freqüência de sincronismo e analisar sua estabilidade. Como se poderá constatar, escolhendo um período de amostragem adequado, pode-se representar o comportamento das redes de sincronismo com modelos discretos, obtendo elevado grau de precisão. / This work introduces a new method for studying a mutually-delayed-connected network of Digital Phase-Locked Loops DPLLs. The signal generated by a DPLL in the network is sent to all other devices in this same network. Because of delayed signals, it is difficult to treat this problem. So, its shown here a method for analyzing the networks via discretization of continuous time delay model in order to deal with this issue easily, considering that delays are naturally represented in discrete time models. First of all, a continuous state space model is obtained from mutually-connected network. Then, this model is discretized and, finally, the synchronous state can be determined and the stability can be analyzed. As shown below, choosing a proper time sample, the behavior of mutually-delayed-connected networks can be approximately represented by a discrete time model.

Des systèmes avec des coefficients dépendant du retard ont été rencontrés dans diverses applications de la science et de l'ingénierie. Malgré la littérature abondante sur les systèmes de temporisation, il y a peu de résultats concernant l'analyse de stabilité des systèmes avec des coefficients dépendant du retard. Cette thèse est consacrée à l'analyse de stabilité de cette classe de systèmes.Les méthodes d'analyse de la stabilité sont développées à partir de l'équation caractéristique correspondante suivant une approche généralisée tau-décomposition. Étant donné un intervalle d'intérêt de retard, nous sommes capables d'identifier toutes les valeurs de retard critique contenues dans cet intervalle pour lesquelles l'équation caractéristique admet des racines sur l'axe imaginaire du plan complexe. Le critère de direction de croisement des racines sont proposées pour déterminer si ces racines caractéristique se déplacent vers le plan complexe demi-gauche ou demi-droite lorsque le paramètre de retard passe par ces valeurs de retard critique. Le nombre de racines caractéristiques instables pour un retard donné peut ainsi être déterminé. Notre analyse comprend les systèmes avec un seul retard ou des retards proportionnés sous certaines hypothèses. Le critère de direction de croisement des racines développés dans cette thèse peut être appliqués aux multiple racines caractéristiques, ou aux racines caractéristiques dont la position paramétrée par le retard est tangent à l'axe imaginaire. En tant qu'application, il est démontré que les systèmes avec des coefficients dépendant du retard peuvent provenir de schémas de contrôle qui utilisent une sortie retardée pour approcher ses dérivés pour la stabilisation. Les méthodes d'analyse de stabilité développées dans cette thèse sont adaptées et appliquées pour trouver les intervalles de retard qui atteignent un taux de convergence demandé du système en boucle fermée. / Systems with delay-dependent coefficients have been encountered in various applications of science and engineering. However, general and systematic stability analysis is rarely reported in the rich literature on time-delay systems. This thesis is committed to the stability analysis of such class of systems.Stability analysis methods are developed based on the corresponding characteristic equation following a generalized tau-decomposition approach. Given a delay interval of interest, we are able to identify all the critical delay values contained in this interval for which the characteristic equation admits roots on the imaginary axis of the complex plane. Various root crossing direction criteria are proposed to determine whether these characteristic roots move toward the left or the right half complex plane as the delay parameter sweeps through these critical delay values. The number of unstable characteristic roots for any given delay can thus be determined. Our analysis covers systems with a single delay or commensurate delays under certain assumptions. The root crossing direction criteria developed in this thesis can be applied to characteristic roots with multiplicity, or characteristic roots whose locus parametrized by the delay is tangent to the imaginary axis. As an application, it is demonstrated that systems with delay-dependent coefficients can arise from control schemes that use delayed output to approximate its derivatives for stabilization. The stability analysis methods developed in this thesis are tailored and applied to find the delay intervals that achieve a demanded convergence rate of the closed-loop system.

Les méthodologies de l'automatique ont joué au cours des dernières décennies un ´r^ole essentiel au sein de nombreux secteurs technologiques avancées. Cependant, de nombreuse questions restent ouvertes. Parmi celles-ci, celles concernant la stabilité et la stabilisation de systèmes non linéaires sont d'intérêt primordial. Afin de stabilizer un système (physique ou non), il est nécessaire de capter et interpreter en temps réel les informations hétérogènes caractérisant son fonctionnement afin intervenir efficacement. Actuellement ces informations ne sont pas captées en temps continu, mais de façon synchrone ou asynchrone et ceci est valable aussi pour les actuateurs. De façon très naturelle, on définit donc un système hybride, caractérisé par des dynamiques à la fois discrètes et continues. Dans ce contexte, cette thèse est orientée au développement de nouvelles méthodologies pour la stabilisation de systèmes échantillonnés non linéaires en se focalisant sur la stabilisation de formes cascades qui se retrouvent dans de nombreuse situations concretes. Pour cela, on étudiera l'effet de l'échantillonnage sur les propriétés de la dynamique continue et l'on proposera des méthodologies pour la conception de lois de commande qui ne requièrent pas d'assumptions supplémentaires au cas continu.Enfin, on étudiera l'effet de l'échantillonnage sur des systèmes présentant de retards sur les entrées. On développera des lois de commande stabilisantes exploitant la structure en cascade induite par l'échantillonnage. Des exemples académiques illustreront les calcules des solutions et leur performances tout au long du manuscript. / Over the last decades the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model.Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system. Academic examples will illustrate the computational aspects together with their performances throughout the whole manuscript.