In modern wireless communication systems, new modulation types are introduced in order to support more users by considering spectral efficiency. These new signals are ensitive to nonlinearity when they have high peak to average ratio. The main part in the system that causes nonlinearity is the power amplifier. For power amplifiers, between linearity and efficiency, there is a trade-off. However, by using predistortion techniques, both linearity and efficiency can be obtained. In this thesis, various predistortion methods are explained and memory polynomial digital predistortion is studied because of its great advantages. The results are obtained by simulations through MATLAB and experiments. An open loop test bench is built up with real amplifier. During experimental procedure, as input two tone signal, 8psk modulated signal and pi/2 bpsk modulated signal are used. Predistortion with memory and memoryless predistortion performances are compared and superiority of the predistortion with memory is shown. Predistortion performance with respect to memory depth and polynomial order is also studied. Moreover, predistortion model range is investigated through evaluation of performance by applying predistorter function estimated at a specific bandwidth and power to other signals having different bandwidth and power. Besides these works, the details of predistortion algorithm and the problems that can be countered in practice are explained.

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The accurate description of fluid flow through porous media allows an engineer to properly analyze past behavior and predict future reservoir performance. In particular, appropriate mathematical models which describe fluid flow through porous media can be applied to well test and production data analysis. Such applications result in estimating important reservoir properties such as formation permeability, skin-factor, reservoir size, etc. "Real gas" flow problems (i.e., problems where the gas properties are specifically taken as implicit functions of pressure, temperature, and composition) are particularly challenging because the diffusivity equation for the "real gas" flow case is strongly non-linear. Whereas different methods exist which allow us to approximate the solution of the real gas diffusivity equation, all of these approximate methods have limitations. Whether in terms of limited applicability (say a specific pressure range), or due to the relative complexity (e.g., iterative character of the solution), each of the existing approximate solutions does have disadvantages. The purpose of this work is to provide a solution mechanism for the case of timedependent real gas flow which contains as few "limitations" as possible. In this work, we provide an approach which combines the so-called average pressure approximation, a convolution for the right-hand-side non-linearity, and the Laplace transformation (original concept was put forth by Mireles and Blasingame). Mireles and Blasingame used a similar scheme to solve the real gas flow problem conditioned by the constant rate inner boundary condition. In this work we provide solution schemes to solve the constant pressure inner boundary condition problem. Our new semi-analytical solution was developed and implemented in the form of a direct (non-iterative) numerical procedure and successfully verified against numerical simulation. Our work shows that while the validity of this approach does have its own assumptions (in particular, referencing the right-hand-side non-linearity to average reservoir pressure (similar to Mireles and Blasingame)), these assumptions are proved to be much less restrictive than those required by existing methods of solution for this problem. We believe that the accuracy of the proposed solution makes ituniversally applicable for gas reservoir engineering. This suggestion is based on the fact that no pseudotime formulation is used. We note that there are pseudotime implementations for this problem, but we also note that pseudotime requires a priori knowledge of the pressure distribution in the reservoir or iteration on gas-in-place. Our new approach has no such restrictions. In order to determine limits of validity of the proposed approach (i.e., the limitations imposed by the underlining assumptions), we discuss the nature of the average pressure approximation (which is the basis for this work). And, in order to prove the universal applicability of this approach, we have also applied this methodology to resolve the time-dependent inner boundary condition for real gas flow in reservoirs.

The underlying principles of how the nervous system selects specific muscle activation pattern, among many that produce the same movement, remain unknown. Experimental studies suggest that the nervous system may use fixed groups of muscles, referred to as muscle synergies, to produce functional motor outputs relevant to the task. In contrast, predictions from biomechanical models suggest that minimizing muscular effort may be the criteria how a muscle coordination pattern is organized for muscle synergies. However, both experimental and modeling evidence shows that stability, as well as energetic efficiency, also needs to be considered. Based on the hypothesis that the nervous system uses functionally stable muscle activation pattern for a muscle synergy, we investigated the stability of muscle patterns using a neuromechanical model of the cat hindlimb. Five unique muscle patterns that generate each of the five experimentally-identified muscle synergy force vectors at the endpoint were found using a minimum-effort criterion. We subjected the model to various perturbed conditions and evaluated functional stability of each of the five minimum-effort muscle synergies using a set of empirical criteria derived from experimental observations. Results show that minimum-effort muscle synergies can be functionally stable or unstable, suggesting that minimum-effort criterion is not always sufficient to predict physiologically relevant postural muscle synergies. Also, linearized system characteristics can robustly predict the behavior exhibited by fully dynamic and nonlinear biomechanical simulations. We conclude that functional stability, which assesses stability of a biomechanical system in a physiological context, must be considered when choosing a muscle activation pattern for a given motor task.

Dynamic security limits the power transfer capacity between regions and therefore has an economic impact. The power modulation control of high-voltage direct current (HVDC) links can improve the dynamic security of the power system. Having several HVDC links in a system creates the opportunity to coordinate such control, and coordination also ensures that negative interactions do not occur among the controllable devices. This thesis aims to increase dynamic security by coordinating HVDC links, as an alternative to decreasing the transfer capacity. This thesis contributes four control approaches for increasing the dynamic stability, based on feedforward control, adaptive control, optimal control, and exact-feedback linearization control. Depending on the available measurements, dynamic system model, and system topology, one of the developed methods can be applied. The wide-area measurement system provides the central controller with real-time data and sends control signals to the HVDC links. The feedforward controller applies rapid power dispatch, and the strategy used here is to link the N-1 criterion between two systems. The adaptive controller uses the modal analysis approach; based on forecasted load paths, the controller gains are adaptively adjusted to maximize the damping in the system. The optimal controller is designed based on an estimated reduced-order model; system identification develops the model based on the system response. The exact-feedback linearization approach uses a pre-feedback loop to cancel the nonlinearities; a stabilizing controller is designed for the remaining linear system. The conclusion is that coordinating the HVDC links improves the dynamic stability, which makes it possible to increase the transfer capacity. This conclusion is also supported by simulations of each control approach. / QC 20110302

Power Amplifiers (PAs) are the key building blocks of the emerging wireless radios systems. They dominate the power consumption and sources of distortion, especially when driven with modulated signals. Several approaches have been devised to characterize the nonlinearity of a PA. Among these approaches, dynamic amplitude (AM/AM) and phase (AM/PM) distortion characteristics are widely used to characterize the PA nonlinearity and its effects on the output signal in power, frequency or time domains, when driven with realistic modulated signals. The inherent nonlinear behaviour of PAs generally yield output signals with an unacceptable quality, an undesirable level of out-of-band emission, high Error Vector Magnitudes (EVMs) and low Adjacent Channel Power Ratios (ACPRs), which usually fail to meet the established performance standards. Traditionally, PAs are forced to operate deeply in their back-off region, far from their power capacity, in order to pass the mandatory spectrum mask (ACPR requirement) and to achieve acceptable EVM. Despite its simplicity, this solution is increasingly discarded, as it leads to cost and power inefficient radios. Alternatively, several linearization techniques, such as feedback, feed-forward and predistortion, have been devised to tackle PA nonlinearity and, consequently, improve the achievable the linearity versus power efficiency trade-off. Among these linearization techniques, the Digital Pre-Distortion (DPD) technique consists of incorporating an extra nonlinear function before the PA, in order to preprocess the input signal to the PA, so that the overall cascaded systems behave linearly. The overall linearity of the cascaded system (DPD plus PA) relies primarily on the ability of the DPD function to produce nonlinearities that are equal in magnitude and out-of-phase to those generated by the PA. Hence, a good understanding and accurate modeling of PA distortions is a crucial step in the construction of an adequate DPD function. This thesis explores DPD through techniques based on Artificial Neural Networks (ANNs). The choice of ANN as a modeling tool was motivated by its proven strength in modeling dynamic nonlinear systems. This thesis starts by providing a summary of the PA nonlinearity problem background, as well as an overview of the most well-known linearization techniques, with a special focus on DPD techniques. The thesis then discusses ANN structures and the learning parameters. Finally, a novel Two Hidden Layers ANN (2HLANN) model is suggested to predict the dynamic nonlinear behaviour of wideband PAs. An extensive validation of the 2HLANN model demonstrates its excellent modeling accuracy and linearization capability.

Models, modelling and control design play important parts in automatic control. The contributions in this thesis concern topics in all three of these concepts. The poles are of fundamental importance when analyzing the behaviour of a system, and pole placement is an intuitive and natural approach for control design. A novel parameterization for state feedback gains for pole placement in the linear multiple input case is presented and analyzed. It is shown that when the open and closed loop poles are disjunct, every state feedback gain can be parameterized. Other properties are also investigated. Hammerstein models have a static non-linearity on the input. A method for exact compensation of such non-linearities, combined with introduction of integral action, is presented. Instead of inversion of the non-linearity the method utilizes differentiation, which in many cases is simpler. A partial differential equation (PDE) can be regarded as an infinite order model. Many model based control design techniques, like linear quadratic Gaussian control (LQG), require finite order models. Active damping of vibrations in a viscoelastic beam, modelled as a PDE, is considered. The beam is actuated by piezoelectric elements and its movements are measured by strain gauges. LQG design is used, for which different finite order models, approximating the PDE model, are constructed. The so obtained controllers are evaluated on the original PDE model. Minimization of the measured strain yields a satisfactory performance, but minimization of transversal deflection does not. The effect of the model accuracy of the finite order model approximations is also investigated. It turns out that a model with higher accuracy in a specified frequency interval gives controllers with better performance. The wave equation is another PDE. A PDE model, with one spatial dimension, is established. It describes wave propagation in a tube perforated with helical slots. The model describes waves of both extensional and torsional type, as well as the coupling between the two wave types. Experimental data are used for estimation of model parameters, and for assessment of the proposed model in two different cases. The model is found adequate when certain geometrical assumptions are valid.

We consider the problem of local linearization of power series defined over complete valued fields. The complex field case has been studied since the end of the nineteenth century, and renders a delicate number theoretical problem of small divisors related to diophantine approximation. Since a work of Herman and Yoccoz in 1981, there has been an increasing interest in generalizations to other valued fields like p-adic fields and various function fields. We present some new results in this domain of research. In particular, for fields of prime characteristic, the problem leads to a combinatorial problem of seemingly great complexity, albeit of another nature than in the complex field case. In cases for which linearization is possible, we estimate the size of linearization discs and prove existence of periodic points on the boundary. We also prove that transitivity and ergodicity is preserved under the linearization. In particular, transitivity and ergodicity on a sphere inside a non-Archimedean linearization disc is possible only for fields of p-adic numbers.

Feedforward is known to be one of the best methods for power amplifier linearization due to its superior linearization performance and broadband stable operation. However feedforward systems have relatively poor power efficiency and are complicated due to the presence of two nonlinear amplifiers and the requirements of amplitude, phase and delay matching within two different loops. In this thesis stochastic characterization of a simple feedforward system with autocorrelation analysis has been presented for Code Division Multiple Access (CDMA) applications taking the amplitude and delay mismatches into consideration. It has been assumed that, the input signal can be represented as Gaussian noise, main and error amplifiers can be modeled with third order AM/AM nonlinearities and there exists no phase mismatch within the loops. Hence closed form expressions, which relate the main channel and distorted adjacent channel power at any point in the feedforward circuitry to the system parameters, have been obtained. Consequently, a mathematical handy tool is achieved towards specifying the circuit parameters rapidly for optimum linearity performance and efficiency. The developed analytical model has been verified by Radio Frequency (RF) and system simulations. An alternative approach towards modeling feedforward systems for arbitrary signals has also been brought into consideration and has been verified with system simulations.

Characterization of nonlinear systems is a challenging task as the output can not be expressed simply in terms of input signal. Therefore, a universal analysis method is essential to simplify this procedure. Modeling of the input signal is a crucial part of such analysis. In this thesis, multi-tone representation is employed to model arbitrary, stochastically not well-defined input signals and thereafter characterize nonlinear systems. In order to verify the validity of multitone representation, multi-tone modeling concept is primarily applied to real life amplifier characterization in single amplifier configuration. This experiment demonstrated potential of multi-tone modeling concept in nonlinear system characterization and encouraged application of the concept to analysis of feedforward linearizers, which are complicated systems due to the presence of two nonlinear amplifiers and the requirement of strict amplitude, phase and delay matching within two loops of the circuit. It has been assumed that main and error amplifiers can be modeled with third order AM/AM nonlinearities and there exists no delay mismatch within the loops. Hence, closed form expressions relating the main and adjacent channel power at the output of the feedforward system to the system parameters are obtained. The developed model is verified by RF and system simulations. As a result, a mathematical handy tool to specify circuit parameters rapidly for optimum linearity performance and efficiency is achieved.