Fluid power technology has been widely used in industrial practice; however, its energy efficiency became a big concern in the recent years. Much progress has been made to improve fluid power energy efficiency from many aspects. Among these approaches, using a valve-less system to replace a traditional valve-controlled system showed eminent energy reduction. This thesis studies the valve-less solution-pump displacement controlled actuators- from the view of controls background. Singular perturbations have been applied to the fluid power to account for fluid stiffness; and a novel hydraulic circuit for single rod cylinder has been presented to increase the hydraulic circuit stabilities. Recursive Least Squares has been applied to account for measurement noise thus the parameters have fast convergence rate, square root algorithm has further applied to increase the controller's numerical stability and efficiency. It was showed that this technique is consistent with other techniques to increase controller's robustness. The developed algorithm is further extended to a hybrid adaptive control scheme to achieve desired trajectory tracking for general cases. A hardware test-bed using the invented hydraulic circuit was built up. The experimental results are presents and validated the proposed algorithms and the circuit itself. The end goal of this project is to develop control algorithms and hydraulic circuit suitable for industrial practice.

Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to be highly oscillatory if it contains a fast solution that varies regularly about a slow solution. As for multibody systems, stiff force elements and contacts between bodies can make a system highly oscillatory. Standard explicit numerical integration methods should take a very small step size to satisfy the absolute stability condition for all eigenvalues of the system and the computational cost is dictated by the fast solution. In this research, a new hybrid integration scheme is proposed, in which the local linearization method is combined with a conventional integration method such as the fourth-order Runge-Kutta. In this approach, the system is partitioned into fast and slow subsystems. Then, the two subsystems are transformed into a reduced and a boundary-layer system using the singular perturbation theory. The reduced system is solved by the fourth-order Runge-Kutta method while the boundary-layer system is solved by the local linearization method. This new hybrid scheme can handle the coupling between the fast and the slow subsystems efficiently. Unlike other multi-rate or multi-method schemes, extrapolation or interpolation process is not required to deal with the coupling between subsystems. Most of the coupling effect can be accounted for by the reduced (or quasi-steady-state) system while the minor transient effect is taken into consideration by averaging. In this research, the absolute stability region for this hybrid scheme is derived and it is shown that the absolute stability region is almost independent of the fast variables. Thus, the selection of the step size is not dictated by the fast solution when a highly oscillatory system is solved, in turn, the computational efficiency can be improved. The advantage of the proposed hybrid scheme is validated through several dynamic simulations of a vehicle system including a flexible tire model. The results reveal that the hybrid scheme can reduce the computation time of the vehicle dynamic simulation significantly while attaining comparable accuracy.

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In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable two-dimensional invariant manifold in transition zone, on which there is also a one-dimensional stable invariant manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the action-action-angle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the BZ reaction.

Orientadores: Helena Judith Nussenzveig Lopes, Milton da Costa Lopes Filho / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-21T02:48:33Z (GMT). No. of bitstreams: 1 Silva_LuizAlbertoViana_D.pdf: 1535000 bytes, checksum: dc971611cbda75b2a6dd72a0bd80d05f (MD5) Previous issue date: 2012 / Resumo: Um problema clássico em aberto é determinar se, em domínios com fronteira, soluções das equações de Navier-Stokes convergem, em um sentido apropriado, a uma solução das equações de Euler quando a viscosidade do fluido tende a zero. Baseados nesta importante questão, Kelliher, Lopes Filho e Nussenzveig Lopes examinaram, em [21], o comportamento de escoamentos com viscosidade pequena em domínios limitados com fronteira afastada, e descreveram condições precisas para que o escoamento limite fosse regido pelas equações de Euler no espaço todo. O presente trabalho é uma continuação natural do artigo mencionado, pois analisamos a dinâmica de escoamentos tridimensionais incompressíveis com viscosidade pequena em torno de obstáculos distantes. Mais precisamente, apresentamos uma estimativa fina que indica um comportamento assintótico para famílias de soluções das equações de Navier-Stokes em termos da viscosidade do escoamento e da localização do obstáculo, e contrastamos a referida estimativa com aquela demonstrada no contexto dos escoamentos em domínios limitados / Abstract: It is a classical open problem to determine if the vanishing viscosity limit can be established in the presence of boundaries. Based on this important issue, Kelliher, Lopes Filho and Nussenzveig Lopes studied in [21] the behavior of viscous incompresible flow in an expanding bounded domain when the viscosity is very small. To be more precise, these three authors described conditions under which the limiting flow satisfies the full space Euler equations. The present work is natural continuation of the aforementioned research since we consider 3D incompressible viscous flows around a distant obstacle along with the vanishing viscosity limit. Specificly, we obtain such a polynomial decay which shows an asymptotic behavior of families of 3D incompressible viscous flows, in the exterior of a single smooth obstacle, in terms of both the obstacle position and the small viscosity. Our approach allows us to compare our rate of convergence to that ones proved in [21] / Doutorado / Matematica / Doutor em Matemática

In this thesis, we study two stochastic reaction diffusion models - the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching the boundary of a properly embedded open set, termed the reaction region (or more generally some fixed lower dimensional sub-manifold). The Doi model uses reaction potentials, supported in the reaction region, whereby two molecules react with a fixed probability per unit time, λ, upon entering the reaction region. The problem considered is that of obtaining estimates for convergence rates, in λ, of the Doi model to the Smoluchowski model. This problem fits into the theory of singular perturbation or optimization, depending on which reactive boundary conditions one considers, and we solve it - at least for the bimolecular reaction with one stationary target.

To contribute to the design of next-generation high performance and low emission combustion devices, this study provides a series of high fidelity numerical simulations of turbulent premixed combustion and autoignition with different clean fuels. The first part of the thesis consists of the direct numerical simulations (DNS) of the lean hydrogen-air turbulent premixed flames at a wide range of Karlovitz number (Ka) conditions up to Ka = 1,126. Turbulence-chemistry interaction is discussed in terms of statistical analysis of the turbulent flame speed and flame structure. Global and local flame speed are separately studied through the fuel consumption speed and displacement speed of the flame front, respectively, and the results are compared with the reference laminar flames as well as similar studies in the literature. The global flame structure is assessed via cross-sectional and conditional averages, and modeling implication is further discussed. Detailed analysis of the local flame structure along the positive and negative curvature is also conducted, providing an understanding of the different behavior of local heat release response. Finally, as the modeling perspectives for Reynolds-averaged Navier-Stokes (RANS) and large eddy simulations (LES), the mean quantities of major species, intermediate species, density, the reaction rate of the progress variable, and heat release rate are assessed in the context of the probability density function (PDF). The second part of the thesis consists of applications of the advanced mathematical tool called the computational singular perturbation (CSP). A skeletal chemical mechanism is developed using the CSP algorithm for the autoignition of methanol and dimethyl ether blends, and the ignition delay time and laminar flame speed are validated for a wide range of mixture conditions. A series of autoignition simulations are carried out in the canonical counter flow mixing layer using the developed skeletal mechanism, and detailed analyses of the autoignition for the methanol and dimethyl ether blends at a wide range of strain rate conditions are provided using the CSP diagnostics tools for a wide range of chemical and fluid combinations.

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