Precision control under the effect of friction requires an effective compensation of friction. Since friction has a complex and highly nonlinear behaviour, it is generally insufficient to represent the friction in a dynamic control system only with a linear viscous model, which is mostly valid in high-velocity motions. Especially when the control system moves near zero velocity regions or changes the direction of motion, an accurate modelling of friction including the lowvelocity dynamic behaviour is a prerequisite to obtain a more complete and realistic dynamic model of the system. Furthermore, the parameters of the friction model should be identified as accurate as possible in order to attain a satisfactory performance. Therefore, the parameters of the friction should be estimated regarding the working conditions. The estimated friction force can then be used to improve the controlled performance of the dynamic system under consideration. In this thesis, the modelling, identification and compensation of friction in a rotary mechanical system are studied. The effectiveness of the existing friction models in the literature are investigated / namely the classical Coulomb with viscous friction model, the Stribeck friction model, the LuGre friction model, and the Generalized Maxwell-Slip (GMS) friction model. All friction models are applied to the system together with the same linear, proportional with derivative (PD)-type and proportional with integral and derivative (PID)-type feedback control actions for the sake of being faithful in comparison. The accuracy of the friction compensation methods is examined separately for both the low-velocity and high-velocity motions of the system. The precision of friction estimation is also shown in the case of using both the desired velocity and measured velocity as an input to the friction models. These control studies are verified in simulation environment and the corresponding results are given. Furthermore, an experimental set-up is designed and manufactured as a case study. The parameters of the aforementioned friction models are identified and the control laws with different friction models are applied to the system in order to demonstrate the compensation capabilities of the models. The results of the experiments are evaluated by comparing them among each other and with the simulation results.

The word piezo in greek means \to compress". Piezoelectric sensors work on the principle of direct piezoelectric effect, where a mechanical input generates a corresponding electric charge. The advantages of these sensors are wide fre-quency range of operation, high stiffness and small size. The main limitation of a piezoelectric sensor is that it cannot be used in measurements that are truly static. When a piezoelectric sensor is subjected to a static force, a fixed amount of charge is developed which would eventually decay at a rate dependent on the external impedance of the sensor circuitry. Operating sensors at resonance have been one of the methods to overcome the limitation of using piezoelectric sensors for static measurements. However, since both actuation and sensing are done by the same piezoelectric element, this results in a cross-talk of input and output signals. The drawback of using single piezoelectric element for actuation and sensing is overcome in this work by using two identical elements|one for actuation and one for sensing. The operating frequency is about 10 % of the natural frequency of the sensor, thus enabling to operate the sensor in non resonant mode. Since the actuation and sensing mechanisms are separated, static measurement can be carried out. The output signal from the sensing element is monitored by a Lock-in amplifier which works on the principle of phase sensitive detection. The advantage of this sensor design is high sensitivity along with narrow band detection. It can be shown that the voltage output of the sensor Vout / a1 + m(b1 + b2F + b3K) + c1F + d1K, where m and K are the external mass and interaction stiffness, respectively, F is the force acting on it. By maintaining any two of these three quantities constant, the remaining one can be measured without any difficulty. The non resonant mode of operation makes it possible to explore the potential of this sensor in investigating mechanics of solid-liquid (viscous), solid-solid (inelastic) and solid-tissue(viscoelastic) interactions. High sensitivity, wide range of measurement (1 g{1 g) and high resolutio(0.1 g) of the non resonant mass sensor makes it possible to use it in measure-ment of very small masses of the order 1 g. Typically, resonant sensors such as quartz crystal microbalance (QCM) are used for mass measurements at that range. However, since the performance of resonant sensors is controlled by damp-ing, a phenomenon known as `missing mass effect' arises. Operating a sensor in non resonant mode (stiffness controlled mode) is a way to overcome this problem, especially when the mass is viscous and/or viscoelastic in nature. Drosophila fly, egg and larvae are the viscoelastic masses that are measured using this non res-onant sensor. Evaporating sessile drops of water and Cetyl trimethylammonium bromide (CTAB) surfactant solution from nominally flat surfaces are monitored to characterize the sensor for viscous mass measurement. Evaporation rate per unit surface area remains more or less constant, during the initial stages of evap-oration. When the surfactant concentration is varied, evaporation rate per unit surface area is highest for solutions around critical miscelle concentration (CMC). A study is carried out to understand the effect of concentrations on spreading of ink over inkjet printing paper. It is found that the spreading is least around CMC, since spreading is dependent on the rate of evaporation. The non resonant piezoelectric sensor which has high stiffness and quick re-sponse is also capable of measuring very small frictional forces. This sensor is configured to work as an inertial slider. Friction measurement at micro scales is important for designing microsystems such as stick-slip actuators. At such length scales, experiments have to performed at low loads and high excitation frequencies. The support stiffness of such systems should be high and the force of friction generated during slipping, when displacements are smaller than the contact radius, are of the order of few N. The displacement during slipping (S) is dependent on the amplitude of the input voltage to the actuation element. The frictional force measured during slipping by the sensor element indicates that the co-efficient of friction ( ) is independent of the sliding velocity. The developed non resonant sensor in this work under small amplitude exci-tation, can measure force gradient (i.e. stiffness). The total force generated when a needle is inserted into a viscoelastic material is a sum of force due to stiffness of the material, friction and the cutting force at the tip. The force due to stiffness is dominant when the needle is bending the tissue before the puncture occurs. Use of the non resonant sensor in tandem with strain gauge force sensor enables distinguishing the three components of the total force. The slope of the force-displacement (F -d) curve during the initial stages of needle penetration into the viscoelastic material, before puncture, is indicative of the stiffness of the mate-rial. The peak force measured during penetration is higher for needles with larger diameters and lower insertion velocities. The viscoelastic response (relaxation) of the material remains independent of the insertion velocity, for a given thickness of the material and a constant needle diameter. In summary, the sensor designed and developed in this work operates in stiffness controlled mode to eliminate the `missing mass effect' encountered dur-ing resonant mode of operation, has been clearly highlighted. Mass, force and stiffness measurements are possible over a wide range just by varying the ampli-tude of the input signal to the actuator element. The advantages such as high stiffness, small size and high response makes it advantageous to carry out in-situ micro scale studies in scanning electron microscopy (SEM) and transmission electron microscopy (TEM).

This thesis investigates the nature of joint dividend-and-earnings signalling in announcements to the New Zealand Stock Exchange in the 1990s. Initially the Market Model is used to compute expected returns, and the abnormal returns derived from these are subjected to restricted least squares regressions to separate out a putative dividend signal from the concurrent earnings signal. But with the Market Model, the zero-value company returns associated with an absence of trading in thinly traded stocks are over-represented in returns distributions leading to problems of bias. New models are developed that explicitly exploit zero returns. The first alternative methodology entails friction modelling, which uses a maximum likelihood estimation procedure to find the relationship coefficients and the range of returns that should be considered as zero, and then proceeds to treat them as a separate category. The second alternative methodology is that of state asset models, which take a fresh new look at investor perceptions of the connection between movements in company returns and those of the concurrent underlying market. Zero-value company returns cease to be zero in value, where a state model is rotated, or alternatively they can be modelled as an extra state. All three methodologies furnish some evidence of dividend signalling; but this evidence is highly dependent on small changes within the given methodology.

[pt] A abstração matemática de um processo físico é essencial em problemas de engenharia, pois muitas vezes pode ser impraticável ou impossível realizar experimentos no sistema real. Além disso, modelos matemáticos são mais flexíveis que protótipos físicos, permitindo um rápido refinamento dos projetos do sistema para otimizar várias medidas de desempenho. As aplicações dos modelos podem ser divididas em quatro partes, a saber: projeto, estimativa, controle e monitoramento. Algumas aplicações específicas são i) simulações, ii) soft sensors, iii) avaliação de desempenho, iv) controle estatístico de qualidade e v) detecção e diagnóstico de falhas. Este trabalho visa então: i) desenvolver diferentes classes de modelos capazes de simular com precisão a variável de saída de um sistema, ii) avaliar a eficiência dos algoritmos de otimização utilizados na tarefa de estimação de parâmetros, iii) avaliar qual modelo de atrito é o mais adequado para descrever esse fenômeno em um sistema de posicionamento. Os resultados mostraram que o atrito no sistema de posicionamento apresenta comportamento não linear e assimétrico, já que alguns termos dos modelos de atrito relacionados às velocidades positiva e negativa são significativamente diferentes um do outro. O resultado final do processo de otimização que usou um algoritmo de busca local foi altamente dependente das condições iniciais e do número de parâmetros estimados, o que elevou o erro de simulação. Entretanto, melhores estimativas da variável de saída foram alcançadas quando essa abordagem foi combinada com outros modelos de diferentes classes. Através dessa última abordagem o erro relativo foi reduzido em mais de 20 porcento. As simulações realizadas com os parâmetros estimados pelos algoritmos evolucionários foram mais acuradas, eles foram capazes de reduzir o erro relativo em quase 30 porcento quando comparados com o algoritmo de busca local. Considerando o segundo estudo de caso, o otimizador baseado em árvores de decisão se mostrou igualmente eficaz se comparado aos algoritmos evolucionários. O erro relativo das simulações usando os parâmetros estimados por esses algoritmos foi inferior a 8 porcento. Além disso, a forma do atrito reconstruído na segunda junta do manipulador robótico através dos parâmetros estimados pelos algoritmos está de acordo com o esperado. / [en] The mathematical abstraction of a physical process is essential in engineering problems, as it can often be impractical or impossible to perform experiments on the real system. Besides, mathematical models are more flexible than physical prototypes, allowing for quick refinement of system designs to optimize various performance measures. The applications of the models can be divided into four parts, namely: design, estimation, control and monitoring. Some specific applications are i) simulations, ii) soft sensors, iii) performance evaluation, iv) statistical quality control and, v) fault detection and diagnosis. This work aims to: i) develop different classes of models capable of accurately simulating the output variable of a system, ii) evaluate the efficiency of optimization algorithms used in the parameter estimation task, iii) assess which friction model is the most appropriate to describe this phenomenon in a positioning system. The results showed that the friction in the positioning system presents a nonlinear and asymmetric behavior since some terms of the friction models related to the positive and negative velocities are significantly different from each other. The final result of the optimization process that used a local search algorithm was highly dependent on the initial conditions and the number of estimated parameters, which increased the simulation error. However, better estimates of the output variable were achieved when this approach was combined with other models of different classes. Through this last approach, the relative error was reduced by more than 20 percent. The simulations performed with the parameters estimated by the evolutionary algorithms were more accurate, they were able to reduce the relative error by almost 30 percent when compared with the local search algorithm. Considering the second case study, the decision tree-based optimizer proved to be equally effective compared to evolutionary algorithms. The relative error of the simulations using the parameters estimated by these algorithms was less than 8 percent. Besides, the shape of the friction reconstructed in the second joint of the robotic manipulator through the parameters estimated by the algorithms is in accordance with the expected.