Model and control of tendon actuated robots

The use of tendons for the transmission of the forces and the movements in robotic devices has been investigated from several researchers all over the world. The interest in this kind of actuation modality is based on the possibility of optimizing the position of the actuators with respect to the moving part of the robot, in the reduced weight, high reliability, simplicity in the mechanic design and, finally, in the reduced cost of the resulting kinematic chain. After a brief discussion about the benefits that the use of tendons can introduce in the motion control of a robotic device, the design and control aspects of the UB Hand 3 anthropomorphic robotic hand are presented. In particular, the tendon-sheaths transmission system adopted in the UB Hand 3 is analyzed and the problem of force control and friction compensation is taken into account. The implementation of a tendon based antagonistic actuated robotic arm is then investigated. With this kind of actuation modality, and by using transmission elements with nonlinear force/compression characteristic, it is possible to achieve simultaneous stiffness and position control, improving in this way the safety of the device during the operation in unknown environments and in the case of interaction with other robots or with humans. The problem of modeling and control of this type of robotic devices is then considered and the stability analysis of proposed controller is reported. At the end, some tools for the realtime simulation of dynamic systems are presented. This realtime simulation environment has been developed with the aim of improving the reliability of the realtime control applications both for rapid prototyping of controllers and as teaching tools for the automatic control courses.

Nonlinear/electromagnetic co-simulation of microwaves and millimeter-waves links

The Ph.D. thesis describes the simulations of different microwave links from the transmitter to the receiver intermediate-frequency ports, by means of a rigorous circuit-level nonlinear analysis approach coupled with the electromagnetic characterization of the transmitter and receiver front ends. This includes a full electromagnetic computation of the radiated far field which is used to establish the connection between transmitter and receiver. Digitally modulated radio-frequency drive is treated by a modulation-oriented harmonic-balance method based on Krylov-subspace model-order reduction to allow the handling of large-size front ends. Different examples of links have been presented: an End-to-End link simulated by making use of an artificial neural network model; the latter allows a fast computation of the link itself when driven by long sequences of the order of millions of samples. In this way a meaningful evaluation of such link performance aspects as the bit error rate becomes possible at the circuit level. Subsequently, a work focused on the co-simulation an entire link including a realistic simulation of the radio channel has been presented. The channel has been characterized by means of a deterministic approach, such as Ray Tracing technique. Then, a 2x2 multiple-input multiple-output antenna link has been simulated; in this work near-field and far-field coupling between radiating elements, as well as the environment factors, has been rigorously taken into account. Finally, within the scope to simulate an entire ultra-wideband link, the transmitting side of an ultrawideband link has been designed, and an interesting Front-End co-design technique application has been setup.

Electrothermal characterization and nonlinear modelling of GaN transistors for telecommunication circuit design

This thesis starts showing the main characteristics and application fields of the AlGaN/GaN HEMT technology, focusing on reliability aspects essentially due to the presence of low frequency dispersive phenomena which limit in several ways the microwave performance of this kind of devices. Based on an equivalent voltage approach, a new low frequency device model is presented where the dynamic nonlinearity of the trapping effect is taken into account for the first time allowing considerable improvements in the prediction of very important quantities for the design of power amplifier such as power added efficiency, dissipated power and internal device temperature. An innovative and low-cost measurement setup for the characterization of the device under low-frequency large-amplitude sinusoidal excitation is also presented. This setup allows the identification of the new low frequency model through suitable procedures explained in detail. In this thesis a new non-invasive empirical method for compact electrothermal modeling and thermal resistance extraction is also described. The new contribution of the proposed approach concerns the non linear dependence of the channel temperature on the dissipated power. This is very important for GaN devices since they are capable of operating at relatively high temperatures with high power densities and the dependence of the thermal resistance on the temperature is quite relevant. Finally a novel method for the device thermal simulation is investigated: based on the analytical solution of the tree-dimensional heat equation, a Visual Basic program has been developed to estimate, in real time, the temperature distribution on the hottest surface of planar multilayer structures. The developed solver is particularly useful for peak temperature estimation at the design stage when critical decisions about circuit design and packaging have to be made. It facilitates the layout optimization and reliability improvement, allowing the correct choice of the device geometry and configuration to achieve the best possible thermal performance.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.

Nonlinear Observers for Sensorless Control of Permanent Magnet Synchronous Motors

In this thesis, the industrial application of control a Permanent Magnet Synchronous Motor in a sensorless configuration has been faced, and in particular the task of estimating the unknown “parameters” necessary for the application of standard motor control algorithms. In literature several techniques have been proposed to cope with this task, among them the technique based on model-based nonlinear observer has been followed. The hypothesis of neglecting the mechanical dynamics from the motor model has been applied due to practical and physical considerations, therefore only the electromagnetic dynamics has been used for the observers design. First observer proposed is based on stator currents and Stator Flux dynamics described in a generic rotating reference frame. Stator flux dynamics are known apart their initial conditions which are estimated, with speed that is also unknown, through the use of the Adaptive Theory. The second observer proposed is based on stator currents and Rotor Flux dynamics described in a self-aligning reference frame. Rotor flux dynamics are described in the stationary reference frame exploiting polar coordinates instead of classical Cartesian coordinates, by means the estimation of amplitude and speed of the rotor flux. The stability proof is derived in a Singular Perturbation Framework, which allows for the use the current estimation errors as a measure of rotor flux estimation errors. The stability properties has been derived using a specific theory for systems with time scale separation, which guarantees a semi-global practical stability. For the two observer ideal simulations and real simulations have been performed to prove the effectiveness of the observers proposed, real simulations on which the effects of the Inverter nonlinearities have been introduced, showing the already known problems of the model-based observers for low speed applications.

Model reduction techniques in flexible multibody dynamics with application to engine cranktrain simulation

The development of a multibody model of a motorbike engine cranktrain is presented in this work, with an emphasis on flexible component model reduction. A modelling methodology based upon the adoption of non-ideal joints at interface locations, and the inclusion of component flexibility, is developed: both are necessary tasks if one wants to capture dynamic effects which arise in lightweight, high-speed applications. With regard to the first topic, both a ball bearing model and a journal bearing model are implemented, in order to properly capture the dynamic effects of the main connections in the system: angular contact ball bearings are modelled according to a five-DOF nonlinear scheme in order to grasp the crankshaft main bearings behaviour, while an impedance-based hydrodynamic bearing model is implemented providing an enhanced operation prediction at the conrod big end locations. Concerning the second matter, flexible models of the crankshaft and the connecting rod are produced. The well-established Craig-Bampton reduction technique is adopted as a general framework to obtain reduced model representations which are suitable for the subsequent multibody analyses. A particular component mode selection procedure is implemented, based on the concept of Effective Interface Mass, allowing an assessment of the accuracy of the reduced models prior to the nonlinear simulation phase. In addition, a procedure to alleviate the effects of modal truncation, based on the Modal Truncation Augmentation approach, is developed. In order to assess the performances of the proposed modal reduction schemes, numerical tests are performed onto the crankshaft and the conrod models in both frequency and modal domains. A multibody model of the cranktrain is eventually assembled and simulated using a commercial software. Numerical results are presented, demonstrating the effectiveness of the implemented flexible model reduction techniques. The advantages over the conventional frequency-based truncation approach are discussed.

Robust Nonlinear Output Regulation by Identification Tools

The present thesis focuses on the problem of robust output regulation for minimum phase nonlinear systems by means of identification techniques. Given a controlled plant and an exosystem (an autonomous system that generates eventual references or disturbances), the control goal is to design a proper regulator able to process the only measure available, i.e the error/output variable, in order to make it asymptotically vanishing. In this context, such a regulator can be designed following the well known “internal model principle” that states how it is possible to achieve the regulation objective by embedding a replica of the exosystem model in the controller structure. The main problem shows up when the exosystem model is affected by parametric or structural uncertainties, in this case, it is not possible to reproduce the exact behavior of the exogenous system in the regulator and then, it is not possible to achieve the control goal. In this work, the idea is to find a solution to the problem trying to develop a general framework in which coexist both a standard regulator and an estimator able to guarantee (when possible) the best estimate of all uncertainties present in the exosystem in order to give “robustness” to the overall control loop.

Stochastic local volatility model for fx markets

Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Boundary condition identification of a bridge pier using experimental data and FEM modal updating

Over the past twenty years, new technologies have required an increasing use of mathematical models in order to understand better the structural behavior: finite element method is the one mostly used. However, the reliability of this method applied to different situations has to be tried each time. Since it is not possible to completely model the reality, different hypothesis must be done: these are the main problems of FE modeling. The following work deals with this problem and tries to figure out a way to identify some of the unknown main parameters of a structure. This main research focuses on a particular path of study and development, but the same concepts can be applied to other objects of research. The main purpose of this work is the identification of unknown boundary conditions of a bridge pier using the data acquired experimentally with field tests and a FEM modal updating process. This work doesn’t want to be new, neither innovative. A lot of work has been done during the past years on this main problem and many solutions have been shown and published. This thesis just want to rework some of the main aspects of the structural optimization process, using a real structure as fitting model.

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

Advantages and Applications of Transforming Empirical Model Input Space with Dimensional Models

Model-based calibration of steady-state engine operation is commonly performed with highly parameterized empirical models that are accurate but not very robust, particularly when predicting highly nonlinear responses such as diesel smoke emissions. To address this problem, and to boost the accuracy of more robust non-parametric methods to the same level, GT-Power was used to transform the empirical model input space into multiple input spaces that simplified the input-output relationship and improved the accuracy and robustness of smoke predictions made by three commonly used empirical modeling methods: Multivariate Regression, Neural Networks and the k-Nearest Neighbor method. The availability of multiple input spaces allowed the development of two committee techniques: a 'Simple Committee' technique that used averaged predictions from a set of 10 pre-selected input spaces chosen by the training data and the "Minimum Variance Committee" technique where the input spaces for each prediction were chosen on the basis of disagreement between the three modeling methods. This latter technique equalized the performance of the three modeling methods. The successively increasing improvements resulting from the use of a single best transformed input space (Best Combination Technique), Simple Committee Technique and Minimum Variance Committee Technique were verified with hypothesis testing. The transformed input spaces were also shown to improve outlier detection and to improve k-Nearest Neighbor performance when predicting dynamic emissions with steady-state training data. An unexpected finding was that the benefits of input space transformation were unaffected by changes in the hardware or the calibration of the underlying GT-Power model.

Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.