Backstepping PDE Design: A Convex Optimization Approach

Abstract\u2014Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sumof- Squares (SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs

A Hamilton-Jacobi setup for the static output feedback stabilization of nonlinear systems

Published versio

Sources of variation of the cattle secondary sex ratio

International audienc

Path-tracking of a tractor-trailer vehicle along rectilinear and circular paths: A Lyapunov-based approach

Published versio

A globally stable algorithm for the integration of high-index differential-algebraic systems

The problem of constraint stabilization and numerical integration for differential-algebraic systems is addressed using Lyapunov theory. It is observed that the application of stabilization methods which rely on a linear feedback mechanism to nonlinear systems may result in trajectories with finite escape time. To overcome this problem we propose a method based on a nonlinear stabilization mechanism which guarantees the global existence and convergence of the solutions. Discretization schemes, which preserve the properties of the method, are also presented. The results are illustrated by means of the numerical integration of a slider-crank mechanism

A globally stable convergent algorithm for the integration of constrained mechanical systems

In this paper the problem of simulation of con- strained mechanical systems is addressed. In modeling multi- body mechanical systems, the Lagrange formulation produces a redundant set of differential-algebraic equations, the integra- tion of which can lead to several difficulties, for example the drift of the “constraint violation”. One of the most popular approaches to alleviate this issue is the so-called Baumgarte’s method that relies on a linear feedback mechanism. This method can however lead to numerical instabilities when applied to nonlinear (mechanical) systems. The objective of this study is to propose a new method that ensures existence of solutions and makes the constraint manifold asymptotically attractive. The proposed technique is illustrated by means of a simple example

THERMODYNAMIC ORC CYCLE DESIGN OPTIMIZATION FOR MEDIUM-LOW TEMPERATURE ENERGY SOURCES

In the large spectrum of organic fluids suitable for Rankine cycles, a fluid that is already wellknown and available on industrial scale but currently excluded from this kind of application has been selected. This choice is due to the remarkable characteristics of the fluid, such as its high molecular weight, good thermal stability, non-flammability, and atoxicity. Compared to those fluids nowadays common in the ORC market, its thermodynamic properties and fluid dynamic behavior lead to a peculiar configuration of the cycle: • Supercritical cycle, when heat input is at medium-high temperature; • Massive regeneration, to obtain higher efficiency; • Low specific work of the turbine; • Relatively high volumetric expansion ratio and relatively low absolute inlet volumetric flow; Accordingly, an innovative cycle design has been developed, including a once-through Hairpin primary heat exchanger and a multi-stage radial outflow expander. This last innovative component has been designed to get the best performance with the chosen fluid: • The high inlet/outlet volumetric flow ratio is well combined with the change in cross section across the radius; • Compared to an axial turbine, the lower inlet volumetric flow is compensated by higher blades at the first stage. It is feasible thanks to the change in section available along the radius, so that there is no need for partial admission; • The prismatic blade leads to constant velocity diagrams across the blade span; • It minimizes tip leakages and disk friction losses, due to the single disk / multi-stage configuration; • The intrinsical limit of a radial outflow expander to develop high enthalpy drop is not relevant for this cycle, presenting itself a very low enthalpy drop. Moreover the tip speed is limited by the low speed of sound and consequently this kind of expander suits well with this cycle arrangement. The results of this study, conducted through thermodynamic simulations, CFD, stress analysis and economic optimization show an ORC system that reaches high efficiencies, comparable to those typical of existing system

Oxidative potential associated with urban aerosol deposited into the respiratory system and relevant elemental and ionic fraction contributions

Size-segregated aerosol measurements were carried out at an urban and at an industrial site. Soluble and insoluble fractions of elements and inorganic ions were determined. Oxidative potential (OP) was assessed on the soluble fraction of Particulate Matter (PM) by ascorbic acid (AA), dichlorofluorescein (DCFH) and dithiothreitol (DTT) assays. Size resolved elemental, ion and OP doses in the head (H), tracheobronchial (TB) and alveolar (Al) regions were estimated using the Multiple-Path Particle Dosimetry (MPPD) model. The total aerosol respiratory doses due to brake and soil resuspension emissions were higher at the urban than at the industrial site. On the contrary, the doses of anthropic combustion tracers were generally higher at the industrial site. In general, the insoluble fraction was more abundantly distributed in the coarse than in the fine mode and vice versa for the soluble fraction. Consequently, for the latter, the percent of the total respiratory dose deposited in TB and Al regions increased. Oxidative potential assay (OPAA) doses were distributed in the coarse region; therefore, their major contribution was in the H region. The contribution in the TB and Al regions increased for OPDTT and OPDCFH

Effect Of The Ambient Temperature On The Performance Of Small Size SCO2 Based Pulverized Coal Power Plants

The present work focuses on the analysis of a novel coal fired sCO2 power plant concept developed in the frame of sCO2-Flex H2020 EU funded project. Fossil fuel fired power plants are expected to improve their flexibility in the future energy scenario characterized by a large share of non-predictable and nondispatchable renewable energy sources. This upcoming context requires a new generation of coal fired power plants with a smaller size, a high flexibility and minor requirements for the installation site like no need of water consumption. Carbon dioxide in supercritical cycles is recognized to be a possible solution for this technology shift and could replace in the future common steam Rankine cycles. This paper focuses on the impact of ambient temperature variation on a small size coal fired sCO2 power plants equipped with a dry cooling heat rejection unit, with the aim of understanding the effect on plant operability and system performance. A dedicate tool is implemented for offdesign behavior assessment and different control strategies are investigated. Results show that without a proper design of the heat rejection unit a small increase of ambient temperature may drastically limit the maximum attainable power output of the plant. This penalizing effect is more pronounced in hot locations, but this issue can be limited by adopting a sufficient over-sizing of the cycle heat rejection unit (HRU) or wet-and-dry solutions