Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Rigid body dynamics and Kalman filtering

X-ray computed log tomography has always been applied for qualitative reconstructions. In most cases, a series of consecutive slices of the timber are scanned to estimate the 3D image reconstruction of the entire log. However, the unexpected movement of the timber under study influences the quality of image reconstruction since the position and orientation of some scanned slices can be incorrectly estimated. In addition, the reconstruction time remains a significant challenge for practical applications. The present study investigates the possibility to employ modern physics engines for the problem of estimating the position of a moving rigid body and its scanned slices which are subject to X-ray computed tomography. The current work includes implementations of the extended Kalman filter and an algebraic reconstruction method for fan-bean computer tomography. In addition, modern techniques such as NVidia PhysX and CUDA are used in current study. As the result, it is numerically shown that it is possible to apply the extended Kalman filter together with a real-time physics engine, known as PhysX, in order to determine the position of a moving object. It is shown that the position of the rigid body can be determined based only on reconstructions of its slices. However, the simulation of the body movement sometimes is subject to an error during Kalman filter employment as PhysX is not always able to continue simulating the movement properly because of incorrect state estimation.

Dynamic analysis of belt-drives using the absolute nodal coordinate formulation

Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

Experimental insights into deformation dynamics and intermittency in rapid granular shear flows

This work concerns the experimental study of rapid granular shear flows in annular Couette geometry. The flow is induced by continuous driving of the horizontal plate at the top of the granular bed in an annulus. The compressive pressure, driving torque, instantaneous bed height and rotational speed of the shearing plate are measured. Moreover, local stress fluctuations are measured in a medium made of steel spheres 2 and 3 mm in diameter. Both monodisperse packing and bidisperse packing are investigated to reveal the influence of size diversity in intermittent features of granular materials. Experiments are conducted in an annulus that can contain up to 15 kg of spherical steel balls. The shearing granular medium takes place via the rotation of the upper plate which compresses the material loaded inside the annulus. Fluctuations of compressive force are locally measured at the bottom of the annulus using a piezoelectric sensor. Rapid shear flow experiments are pursued at different compressive forces and shear rates and the sensitivity of fluctuations are then investigated by different means through monodisperse and bidisperse packings. Another important feature of rapid granular shear flows is the formation of ordered structures upon shearing. It requires a certain range for the amount of granular material (uniform size distribution) loaded in the system in order to obtain stable flows. This is studied more deeply in this thesis. The results of the current work bring some new insights into deformation dynamics and intermittency in rapid granular shear flows. The experimental apparatus is modified in comparison to earlier investigations. The measurements produce data for various quantities continuously sampled from the start of shearing to the end. Static failure and dynamic shearing ofa granular medium is investigated. The results of this work revealed some important features of failure dynamics and structure formation in the system. Furthermore, some computer simulations are performed in a 2D annulus to examine the nature of kinetic energy dissipation. It is found that turbulent flow models can statistically represent rapid granular flows with high accuracy. In addition to academic outcomes and scientific publications our results have a number of technological applications associated with grinding, mining and massive grain storages.

Real-Time Simulation of Mobile and Industrial Machines Using the Multibody Simulation Approach

This thesis introduces a real-time simulation environment based on the multibody simulation approach. The environment consists of components that are used in conventional product development, including computer aided drawing, visualization, dynamic simulation and finite element software architecture, data transfer and haptics. These components are combined to perform as a coupled system on one platform. The environment is used to simulate mobile and industrial machines at different stages of a product life time. Consequently, the demands of the simulated scenarios vary. In this thesis, a real-time simulation environment based on the multibody approach is used to study a reel mechanism of a paper machine and a gantry crane. These case systems are used to demonstrate the usability of the real-time simulation environment for fault detection purposes and in the context of a training simulator. In order to describe the dynamical performance of a mobile or industrial machine, the nonlinear equations of motion must be defined. In this thesis, the dynamical behaviour of machines is modelled using the multibody simulation approach. A multibody system may consist of rigid and flexible bodies which are joined using kinematic joint constraints while force components are used to describe the actuators. The strength of multibody dynamics relies upon its ability to describe nonlinearities arising from wearing of the components, friction, large rotations or contact forces in a systematic manner. For this reason, the interfaces between subsystems such as mechanics, hydraulics and control systems of the mechatronic machine can be defined and analyzed in a straightforward manner.

Novel Robot Solutions for Carrying out Field Joint Welding and Machining in the Assembly of the Vacuum Vessel of ITER

It is necessary to use highly specialized robots in ITER (International Thermonuclear Experimental Reactor) both in the manufacturing and maintenance of the reactor due to a demanding environment. The sectors of the ITER vacuum vessel (VV) require more stringent tolerances than normally expected for the size of the structure involved. VV consists of nine sectors that are to be welded together. The vacuum vessel has a toroidal chamber structure. The task of the designed robot is to carry the welding apparatus along a path with a stringent tolerance during the assembly operation. In addition to the initial vacuum vessel assembly, after a limited running period, sectors need to be replaced for repair. Mechanisms with closed-loop kinematic chains are used in the design of robots in this work. One version is a purely parallel manipulator and another is a hybrid manipulator where the parallel and serial structures are combined. Traditional industrial robots that generally have the links actuated in series are inherently not very rigid and have poor dynamic performance in high speed and high dynamic loading conditions. Compared with open chain manipulators, parallel manipulators have high stiffness, high accuracy and a high force/torque capacity in a reduced workspace. Parallel manipulators have a mechanical architecture where all of the links are connected to the base and to the end-effector of the robot. The purpose of this thesis is to develop special parallel robots for the assembly, machining and repairing of the VV of the ITER. The process of the assembly and machining of the vacuum vessel needs a special robot. By studying the structure of the vacuum vessel, two novel parallel robots were designed and built; they have six and ten degrees of freedom driven by hydraulic cylinders and electrical servo motors. Kinematic models for the proposed robots were defined and two prototypes built. Experiments for machine cutting and laser welding with the 6-DOF robot were carried out. It was demonstrated that the parallel robots are capable of holding all necessary machining tools and welding end-effectors in all positions accurately and stably inside the vacuum vessel sector. The kinematic models appeared to be complex especially in the case of the 10-DOF robot because of its redundant structure. Multibody dynamics simulations were carried out, ensuring sufficient stiffness during the robot motion. The entire design and testing processes of the robots appeared to be complex tasks due to the high specialization of the manufacturing technology needed in the ITER reactor, while the results demonstrate the applicability of the proposed solutions quite well. The results offer not only devices but also a methodology for the assembly and repair of ITER by means of parallel robots.

Non-Markovian Dynamics in Continuous Variable Quantum Systems

The present manuscript represents the completion of a research path carried forward during my doctoral studies in the University of Turku. It contains information regarding my scientific contribution to the field of open quantum systems, accomplished in collaboration with other scientists. The main subject investigated in the thesis is the non-Markovian dynamics of open quantum systems with focus on continuous variable quantum channels, e.g. quantum Brownian motion models. Non-Markovianity is here interpreted as a manifestation of the existence of a flow of information exchanged by the system and environment during the dynamical evolution. While in Markovian systems the flow is unidirectional, i.e. from the system to the environment, in non-Markovian systems there are time windows in which the flow is reversed and the quantum state of the system may regain coherence and correlations previously lost. Signatures of a non-Markovian behavior have been studied in connection with the dynamics of quantum correlations like entanglement or quantum discord. Moreover, in the attempt to recognisee non-Markovianity as a resource for quantum technologies, it is proposed, for the first time, to consider its effects in practical quantum key distribution protocols. It has been proven that security of coherent state protocols can be enhanced using non-Markovian properties of the transmission channels. The thesis is divided in two parts: in the first part I introduce the reader to the world of continuous variable open quantum systems and non-Markovian dynamics. The second part instead consists of a collection of five publications inherent to the topic.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Determining vehicle drivetrain dynamics using system identification

Target of this book is to propose an approach for modelling drivetrain dynamics in order to design further a vibration control system of a hybrid bus. In this thesis two approaches are examined and compared. First model is obtained by theoretical means: drivetrain is represented as a system of rotating masses, which motion is described with differential equations. Second model is obtained using system identification method: mathematical description of the dynamic behavior of a system is formed based on measured input (torque) and output (speed) data. Then two models are compared and an optimal approach is suggested.

Real-time simulation of multibody systems with applications for working mobile vehicles

This dissertation describes an approach for developing a real-time simulation for working mobile vehicles based on multibody modeling. The use of multibody modeling allows comprehensive description of the constrained motion of the mechanical systems involved and permits real-time solving of the equations of motion. By carefully selecting the multibody formulation method to be used, it is possible to increase the accuracy of the multibody model while at the same time solving equations of motion in real-time. In this study, a multibody procedure based on semi-recursive and augmented Lagrangian methods for real-time dynamic simulation application is studied in detail. In the semirecursive approach, a velocity transformation matrix is introduced to describe the dependent coordinates into relative (joint) coordinates, which reduces the size of the generalized coordinates. The augmented Lagrangian method is based on usage of global coordinates and, in that method, constraints are accounted using an iterative process. A multibody system can be modelled as either rigid or flexible bodies. When using flexible bodies, the system can be described using a floating frame of reference formulation. In this method, the deformation mode needed can be obtained from the finite element model. As the finite element model typically involves large number of degrees of freedom, reduced number of deformation modes can be obtained by employing model order reduction method such as Guyan reduction, Craig-Bampton method and Krylov subspace as shown in this study The constrained motion of the working mobile vehicles is actuated by the force from the hydraulic actuator. In this study, the hydraulic system is modeled using lumped fluid theory, in which the hydraulic circuit is divided into volumes. In this approach, the pressure wave propagation in the hoses and pipes is neglected. The contact modeling is divided into two stages: contact detection and contact response. Contact detection determines when and where the contact occurs, and contact response provides the force acting at the collision point. The friction between tire and ground is modelled using the LuGre friction model, which describes the frictional force between two surfaces. Typically, the equations of motion are solved in the full matrices format, where the sparsity of the matrices is not considered. Increasing the number of bodies and constraint equations leads to the system matrices becoming large and sparse in structure. To increase the computational efficiency, a technique for solution of sparse matrices is proposed in this dissertation and its implementation demonstrated. To assess the computing efficiency, augmented Lagrangian and semi-recursive methods are implemented employing a sparse matrix technique. From the numerical example, the results show that the proposed approach is applicable and produced appropriate results within the real-time period.

Multibody models for examination of touchdown bearing systems

Increased rotational speed brings many advantages to an electric motor. One of the benefits is that when the desired power is generated at increased rotational speed, the torque demanded from the rotor decreases linearly, and as a consequence, a motor of smaller size can be used. Using a rotor with high rotational speed in a system with mechanical bearings can, however, create undesirable vibrations, and therefore active magnetic bearings (AMBs) are often considered a good option for the main bearings, as the rotor then has no mechanical contact with other parts of the system but levitates on the magnetic forces. On the other hand, such systems can experience overloading or a sudden shutdown of the electrical system, whereupon the magnetic field becomes extinct, and as a result of rotor delevitation, mechanical contact occurs. To manage such nonstandard operations, AMB-systems require mechanical touchdown bearings with an oversized bore diameter. The need for touchdown bearings seems to be one of the barriers preventing greater adoption of AMB technology, because in the event of an uncontrolled touchdown, failure may occur, for example, in the bearing’s cage or balls, or in the rotor. This dissertation consists of two parts: First, touchdown bearing misalignment in the contact event is studied. It is found that misalignment increases the likelihood of a potentially damaging whirling motion of the rotor. A model for analysis of the stresses occurring in the rotor is proposed. In the studies of misalignment and stresses, a flexible rotor using a finite element approach is applied. Simplified models of cageless and caged bearings are used for the description of touchdown bearings. The results indicate that an increase in misalignment can have a direct influence on the bending and shear stresses occurring in the rotor during the contact event. Thus, it was concluded that analysis of stresses arising in the contact event is essential to guarantee appropriate system dimensioning for possible contact events with misaligned touchdown bearings. One of the conclusions drawn from the first part of the study is that knowledge of the forces affecting the balls and cage of the touchdown bearings can enable a more reliable estimation of the service life of the bearing. Therefore, the second part of the dissertation investigates the forces occurring in the cage and balls of touchdown bearings and introduces two detailed models of touchdown bearings in which all bearing parts are modelled as independent bodies. Two multibody-based two-dimensional models of touchdown bearings are introduced for dynamic analysis of the contact event. All parts of the bearings are modelled with geometrical surfaces, and the bodies interact with each other through elastic contact forces. To assist in identification of the forces affecting the balls and cage in the contact event, the first model describes a touchdown bearing without a cage, and the second model describes a touchdown bearing with a cage. The introduced models are compared with the simplified models used in the first part of the dissertation through parametric study. Damages to the rotor, cage and balls are some of the main reasons for failures of AMB-systems. The stresses in the rotor in the contact event are defined in this work. Furthermore, the forces affecting key bodies of the bearings, cage and balls can be studied using the models of touchdown bearings introduced in this dissertation. Knowledge obtained from the introduced models is valuable since it can enable an optimum structure for a rotor and touchdown bearings to be designed.