Dissertations / Theses on the topic 'Time delayed feedback control (TDFC)'

Rotary Cranes (Tower Cranes) are common industrial structures that are used in building construction, factories, and harbors. These cranes are usually operated manually. With the size of these cranes becoming larger and the motion expected to be faster, the process of controlling them became dicult without using automatic control methods. In general, the movement of cranes has no prescribed path. Cranes have to be run under dierent operating conditions, which makes closed-loop control preferable. In this work, two types of controllers are studied: fuzzy logic and time-delayed position feedback controllers. The fuzzy logic controller is introduced first with the idea of split-horizon; that is, to use some fuzzy engines for tracking position and others for damping load oscillations. Then the time-delayed position feedback method is applied. Finally, an attempt to combine these two controllers into a hybrid controller is introduced. Computer simulations are used to verify the performance of these controllers. An experimental setup was built on which the time-delayed position feedback controller was tested. The results showed good performance.
Master of Science

Ship-mounted cranes are used to transfer cargo from large container ships to smaller lighters when deep-water ports are not available. The wave-induced motion of the crane ship produces large pendulations of hoisted cargo and causes operations to be suspended. In this work, we show that in boom type ship-mounted cranes, it is possible to reduce these pendulations significantly by controlling the slew and luff angles of the boom. Such a control can be achieved with the heavy equipment that is already part of the crane so that retrofitting existing cranes would require a small effort. Moreover, the control is superimposed on the commands of the operator transparently. The successful control strategy is based on delayed-position feedback of the cargo motion in-plane and out-of-plane of the boom and crane tower. Its effectiveness is demonstrated with a fully nonlinear three-dimensional computer simulation and with an experiment on a 1/24 scale model of a T-ACS (The Auxiliary Crane Ship) crane mounted on a platform moving with three degrees of freedom to simulate the ship roll, pitch, and heave motions of the crane ship. The results demonstrate that the pendulations can be significantly reduced, and therefore the range of sea conditions in which cargo-transfer operations could take place can be greatly expanded. Furthermore, the control strategy is applied experimentally to a scaled model of a tower crane. The effectiveness of the controller is demonstrated for both rotary and gantry modes of operation of the crane. This work was supported by the Office of Naval Research under Contract #N00014-96-1-1123.
Ph. D.

The main problem evaluated in this manuscript is the stabilization of periodic orbits of non-linear dynamical systems by use of feedback control. The goal of the control methods proposed in this work is to achieve a stable periodic oscillation. These control methods are applied to systems that present unstable periodic orbits in the state space, and the latter are the orbits to be stabilized.The methods proposed here are such that the resulting stable oscillation is obtained with low control effort, and the control signal is designed to converge to zero when the trajectory tends to the stabilized orbit. Local stability of the periodic orbits is analyzed by studying the stability of some linear time-periodic systems, using the Floquet stability theory. These linear systems are obtained by linearizing the trajectories in the vicinity of the periodic orbits.The control methods used for stabilization of periodic orbits here are the proportional feedback control, the delayed feedback control and the prediction-based feedback control. These methods are applied to discrete and continuous-time systems with the necessary modifications. The main contributions of the thesis are related to these methods, proposing an alternative control gain design, a new control law and related results.

The main objective of this work is to design robust, fast, and practical controllers for gantry and tower cranes. The controllers are designed to transfer the load from point to point as fast as possible and, at the same time, the load swing is kept small during the transfer process and completely vanishes at the load destination. Moreover, variations of the system parameters, such as the cable length and the load weight, are also included. Practical considerations, such as the control action power, and the maximum acceleration and velocity, are taken into account. In addition, friction effects are included in the design using a friction-compensation technique. The designed controllers are based on two approaches. In the first approach, a gain-scheduling feedback controller is designed to move the load from point to point within one oscillation cycle without inducing large swings. The settling time of the system is taken to be equal to the period of oscillation of the load. This criterion enables calculation of the controller feedback gains for varying load weight and cable length. The position references for this controller are step functions. Moreover, the position and swing controllers are treated in a unified way. In the second approach, the transfer process and the swing control are separated in the controller design. This approach requires designing two controllers independently: an anti-swing controller and a tracking controller. The objective of the anti-swing controller is to reduce the load swing. The tracking controller is responsible for making the trolley follow a reference position trajectory. We use a PD-controller for tracking, while the anti-swing controller is designed using three different methods: (a) a classical PD controller, (b) two controllers based on a delayed-feedback technique, and (c) a fuzzy logic controller that maps the delayed-feedback controller performance. To validate the designed controllers, an experimental setup was built. Although the designed controllers work perfectly in the computer simulations, the experimental results are unacceptable due to the high friction in the system. This friction deteriorates the system response by introducing time delay, high steady-state error in the trolley and tower positions, and high residual load swings. To overcome friction in the tower-crane model, we estimate the friction, then we apply an opposite control action to cancel it. To estimate the friction force, we assume a mathematical model and estimate the model coefficients using an off-line identification technique using the method of least squares. With friction compensation, the experimental results are in good agreement with the computer simulations. The gain-scheduling controllers transfer the load smoothly without inducing an overshoot in the trolley position. Moreover, the load can be transferred in a time near to the optimal time with small swing angles during the transfer process. With full-state feedback, the crane can reach any position in the working environment without exceeding the system power capability by controlling the forward gain in the feedback loop. For large distances, we have to decrease this gain, which in turn slows the transfer process. Therefore, this approach is more suitable for short distances. The tracking-anti-swing control approach is usually associated with overshoots in the translational and rotational motions. These overshoots increase with an increase in the maximum acceleration of the trajectories . The transfer time is longer than that obtained with the first approach. However, the crane can follow any trajectory, which makes the controller cope with obstacles in the working environment. Also, we do not need to recalculate the feedback gains for each transfer distance as in the gain-scheduling feedback controller.
Ph. D.

It is sometimes necessary to transfer cargo from a large ship to a smaller ship at sea. Specially designed craneships are used for this task, however the wave-induced motions of the ship can cause large pendulations of cargo being hoisted by a ship-mounted crane. This makes cargo transfer in rough seas extremely dangerous and therefore transfer operations normally cease when sea state 3 is reached. If the cargo pendulations could be reduced in higher sea states, transfer operations would be possible. By controlling the boom luff angle, one can reduce the cargo pendulations in the plane of the boom significantly. A two-dimensional pendulum with a rigid massless cable and massive point load is used to model the system. A control law using time-delayed position feedback is developed and the system is simulated on a computer using the full nonlinear equations of motion. A three-degree-of-freedom ship-motion simulation platform, capable of simulating heave, pitch, and roll motions, was built. The computer simulation results were experimentally verified by mounting a 1/24th scale model of a T-ACS crane on the ship-motion simulation platform.
Master of Science

Diplomová práce pojednává o teorii chaotických dynamických systémů, speciálně se pak zabývá Rösslerovým systémem. Kromě standardních výpočtů spojených s bifurkační analýzou se práce zaměřuje na problém stabilizace, konkrétně na stabilizaci rovnovážných bodů. Ke stabilizaci je využita základní metoda zpětnovazebního řízení s časovým zpožděním. Významnou část práce tvoří zavedení a implementace obecné metody pro hledání vhodné volby parametrů vedoucí k úspěšné stabiliaci. Dalším diskutovaným tématem je možnost synchronizace dvou Rösslerových systémů pomocí různých synchronizačních schémat.

Ce travail a pour objet l’étude des techniques rapides pour calculer l’état cyclique établi des problèmes d’évolution en mécanique non-linéaire avec des conditions de périodicité en espace-temps. Un exemple typique est le roulage stationnaire d’un pneu présentant des sculptures périodiques, où l’état en chaque point est le même que l’état observé au point correspondant de la sculpture suivante une période en temps auparavant.L’application de solveurs directs pour la solution de tels problèmes est impossible car ils exigent l’inversion des matrices gigantesques. Pour résoudre ce genre de problèmes, les logiciels de calcul utilisés dans l’industrie recherchent une telle solution cyclique comme la limite asymptotique d’un problème à valeur initiale avec des données initiales arbitraires. Cependant, quand le temps de relaxation du problème physique est élevé, la vitesse de convergence vers le cycle limite peut devenir trop lente. Comme on ne s’intéresse pas à la solution transitoire et que seul importe d’avoir un accès rapide au cycle limite, le développement des méthodes qui accélèrent la convergence vers le cycle limite sont d’un grand intérêt. Ce travail développe, étudie et compare deux techniques d’analyse et de calcul rapide de la solution périodique en espace-temps.La première est la méthode de Newton-Krylov, qui considère l’état initial comme l’inconnue du problème à calculer à partir de la condition de périodicité. Le problème résultant est résolu par l’algorithme de Newton-Raphson. Comme le Jacobien associé ne s’exprime pas explicitement mais uniquement implicitement à travers son action par multiplication, il est nécessaire d’introduire des solveurs itératifs de type Krylov. Par réutilisation optimale de l’information obtenue sur le Jacobien pendant le calcul du résidu, la résolution du système linéaire par algorithme de Krylov devient très rapide et de faible coût par rapport au calcul de l’erreur de périodicité. Cette technique de calcul peut être vue comme une méthode de tir. Mais nous l’écrivons ici par changement de variables sous la forme d’une méthode de type observateur-contrôleur, qui corrige la solution transitoire après chaque cycle et accélère ainsi la convergence vers la limite cyclique.La deuxième méthode de calcul et d’analyse proposée dans ce travail met en œuvre une modification du problème d’évolution initial en y introduisant un terme de contrôle rétroactif, basé sur l’erreur de périodicité. Le contrôle rétroactif est un outil bien connu et puissant dans le cadre de la stabilisation des orbites périodiques instables des processus chaotiques. Dans le cadre de ce travail, il est appliqué à un système initialement stable pour accélérer la convergence vers la limite cyclique. De plus, le terme de contrôle inclut les décalages en temps ainsi qu’en espace, ce qui complique son analyse. L’enjeu est ici de construire l’opérateur de gain à appliquer à l’erreur de périodicité dans le terme de contrôle. Dans un cadre linéaire très général, après décomposition spectrale et introduction des fonctions de Lambert, nous pouvons analyser explicitement l’existence et la convergence de solutions en temps, et construire la forme optimale du gain qui assure la convergence la plus rapide vers la solution cyclique. L’efficacité de la méthode proposée croit avec le temps de relaxation du problème. L’algorithme est présenté sous la forme d’un schéma prédicteur-correcteur en temps, où l’étape de correction est explicite et de très faible coût numérique. Sous cette forme, le contrôle proposé a été adapté et testé sur des problèmes non-linéaires. Les deux méthodes ont été appliquées sur diverses applications académiques et comparées à la méthode asymptotique classique. Enfin, elles ont été intégrées et mises en œuvre dans le code industriel de Michelin pour application au roulage stationnaire d’un pneu complet avec sculptures périodiques en présence de forces de contact au sol en régime de frottement adhérant-glissant
This work is focused on fast techniques for computing the steady cyclic states of evolution problems in non-linear mechanics with space and time periodicity conditions. This kind of problems can be faced, for instance, in the beating heart modeling. Another example concerns the rolling of a tyre with periodic sculptures, where the cyclic state satisfies "rolling" periodicity condition, including shifts both in time and space. More precisely, the state at any point is the same that at the corresponding point observed at the next sculpture one time period ago.Direct solvers for such problems are not very convenient, since they require inversion of very large matrices. In industrial applications, in order to avoid this, such a cyclic solution is usually computed as an asymptotic limit of the associated initial value problem with arbitrary initial data. However, when the relaxation time is high, convergence to the limit cycle can be very slow. In such cases nonetheless, one is not interested in the transient solution, but only in a fast access to the limit cycle. Thus, developing methods accelerating convergence to this limit is of high interest. This work is devoted to study and comparison of two techniques for fast calculation of the space-time periodic solution.The first is the well-known Newton-Krylov shooting method, looking for the initial state, which provides the space-time periodic solution. It considers the space-time periodicity condition as a non-linear equation on the unknown initial state, which is solved using Newton-Raphson technique. Since the associated Jacobian can not be expressed explicitly, the method uses one of the matrix-free Krylov iterative solvers. Using information stored while computing the residual to solve the linear system makes its calculation time negligible with respect to the residual calculation time. On the one hand, the algorithm is a shooting method, on the other side, it can be considered as an observer-controller method, correcting the transient solution after each cycle and accelerating convergence to the space-time periodic state.The second method, considered in this work, is an observer-controller type modification of the standard evolution to the limit cycle by introducing a feedback control term, based on the periodicity error. The time-delayed feedback control is a well-known powerful tool widely used for stabilization of unstable periodic orbits in deterministic chaotic systems. In this work the time-delayed feedback technique is applied to an a priori stable system in order to accelerate its convergence to the limit cycle. Moreover, given the space-time periodicity, along with the time-delay, the feedback term includes also a shift in space. One must then construct the gain operator, applied to the periodicity error in the control term. Our main result is to propose and to construct the optimal form of the gain operator for a very general class of linear evolution problems, providing the fastest convergence to the cyclic solution. The associated control term can be mechanically interpreted.Efficiency of the method increases with the problem's relaxation time. The method is presented in a simple predictor-corrector form, where correction is explicit and numerically cheap. In this later form, the feedback control has been also adapted and tested for a nonlinear problem.The discussed methods have been studied using academic applications and they also have been implemented into the Michelin industrial code, applied to a full 3D tyre model with periodic sculpture in presence of slip-stick frictional contact with the soil, and then compared to the standard asymptotic convergence

碩士
國立高雄應用科技大學
電機工程系
97
The problem of designing decentralized state feedback controller for a class of complex uncertain time-delay systems is studied in this thesis. Based on the new Lyapunov-Krasovskii functional adopted in [14], and the lemmas in the litarature [4, 11], we offer an alternated design method. A less conservative delay- independent linear matrix inequality (LMI) criterion is obtained compared to the litarature. We also design a state feedback controller such that the closed -loop uncertain system is asymptotically stable and also guarantees an -norm bound constraint on the disturbance attenuation for all admissible uncertainties. At the end of each subsection, practical examples are given to illustrate the effectiveness of the proposed approach.