Nonlinear control synthesis by convex optimization

A stability criterion for nonlinear systems, recently derived by the third author, can be viewed as a dual to Lyapunov's second theorem. The criterion is stated in terms of a function which can be interpreted as the stationary density of a substance that is generated all over the state-space and flows along the system trajectories toward the equilibrium. The new criterion has a remarkable convexity property, which in this note is used for controller synthesis via convex optimization. Recent numerical methods for verification of positivity of multivariate polynomials based on sum of squares decompositions are used.     

Modeling and sensitivity analysis of fire emissions in southern Africa during SAFARI 2000

This paper uses three recently generated southern African satellite burned area products for the month of September 2000 in a sensitivity study of regional biomass burning emissions for a number of trace gases and particulates. Differences in the extent and location of areas burned among products generated from Moderate Resolution Imaging Spectroradiometer (MODIS), Systeme Pour l'Observation de la Terre (SPOT-VEGETATION), and Along Track Scanning Radiometer (ATSR-2) data are significant and result in different emissions estimates for woodland and grassland land cover types. Due to the different emission profiles in woodlands and grasslands, favoring relatively more products of incomplete combustion in woodlands compared with products of complete combustion in grasslands in the late dry season, these changes are not proportional to the differences in the burned area amounts. The importance of accurate burned area information not just in terms of the total area but also in terms of its spatial distribution becomes apparent from our modeling results. This paper highlights the urgent need for satellite data producers to provide accuracy assessments associated with satellite-derived products. Preferably, these accuracy data will be spatially explicit, or defined in a way that can be applied in a spatially explicit modeling context, to enable emissions uncertainties to be defined with respect to different landscape units in support of greenhouse gas emissions reporting.     

Structured optimal and robust control with multiple criteria: a convex solution

In this paper, the design of controllers that incorporate structural and multiobjective performance requirements is considered. The control structures under study cover nested, chained, hierarchical, delayed interaction and communications, and symmetric systems. Such structures are strongly related to several modern-day and future applications including integrated flight propulsion systems, platoons of vehicles, micro-electro-mechanical systems, networked control, control of networks, production lines and chemical processes. It is shown that the system classes presented have the common feature that all stabilizing controllers can be characterized by convex constraints on the Youla-Kucera parameter. Using this feature, a solution to a general optimal performance problem that incorporates time domain and frequency domain constraints is obtained. A synthesis procedure is provided which at every step yields a feasible controller together with a measure of its performance with respect to the optimal. Convergence to the optimal performance is established. An example of a multinode network congestion control problem is provided that illustrates the effectiveness of the developed methodology.     

Mg AZ80/SiC composite bars fabricated by infiltration of porous ceramic preforms

Semi-industrial samples of Mg AZ80/SiC/50p composites (machined bars with o.d.=80 mm and length=150 mm, having a maximum 2 vol pct of retained porosity) were successfully fabricated by pressureless, low-pressure (under overpressure of about 0.3 MPa) and moderate-pressure (under overpressure of about 0.8 MPa) infiltration. Pressureless infiltration was completed in 24 hours under the flowing atmosphere of nitrogen, whereas the moderate and low-pressure infiltrations were performed under a static atmosphere of pressurized nitrogen for 7 and 0.5 hours, respectively. The composite samples obtained by all applied infiltration paths posessed a homogeneous microstructure and superior mechanical properties as compared to the nonreinforced matrix. Due to the improved productivity of composite fabrication in comparison with the other two infiltration paths investigated in this work, the moderate-pressure infiltration process was recognized as the most competitive.     

Cr-Mo solid solutions forced by high-energy ball milling

Mixtures of Cr and Mo elemental powders, with the nominal compositions Cr₂₅Mo₇₅, Cr₅₀Mo₅₀, and Cr₇₅Mo₂₅, are processed by high-energy ball milling at ambient temperature. Milling is observed to force the mixing of the immiscible bcc elements Cr and Mo into solid solutions. The lattice parameter of these solid solutions, measured by X-ray diffraction (XRD), displays the expected positive deviation from Vegard’s law. These deviations are compared to the ones predicted by Eshelby’s inclusion model for dilute alloys. The conventional Williamson-Hall approach is shown to fail to determine the grain size in as-milled samples, probably due to the high density of dislocations. Annealing at 700 °C for 10 hours under argon leads to a large reduction in structural defect density, without inducing any significant decomposition. The mixing measured in Cr-Mo is discussed in the broader context of the mechanical mixing forced by ball milling in moderately immiscible systems.     

Second-order stresses and strains in heterogeneous steels: Self-consistent modeling and X-ray diffraction analysis

Theoretical and experimetal methods have been developed to characterize the effect of mechanical loading on the mesoscopic and macroscopic mechanical state of polycrystalline materials. Ferritic and austenitic single-phase materials were first analyzed, then phase interaction was studied in a multiductile phase material (austeno-ferritic duplex steel) and a natural reinforced composite (pearlitic steel). The theoretical method is based on the self-consistent approach in which elastic and plastic characteristics of the phases have been applied through the micromechanical behavior of single-crystal-using slip systems and microscopic hardening. The effects of a crystallographic texture and phase interaction during loading and after unloading were studied. The elastic and plastic anisotropy of the grains having the same crystallographic orientation were assessed by diffraction strain analysis. The simulation was compared with the experiments performed using the X-ray diffraction technique. In the considered duplex and pearlitic steels, it was observed that the ferrite stress state is much lower than the austenite and cementite ones. The results of diffraction strain distribution have showed the pertinence of the models and give valuable information, for example, for the yield stress and the hardening parameters of each phase in a two-phase material.     

Effect of broaching on high-temperature fatigue behavior in notched specimens of INCONEL 718

Notches were machined in specimens of INCONEL 718 by a broaching process, where differing broaching runs led to differing extents of subsurface deformation and surface roughness. Fatigue tests were carried out at 600 °C with a trapezoidal loading waveform at 0.25 Hz. The broaching process that led to the more severe subsurface deformation (but lower surface roughness) showed the worst fatigue performance. Analysis of total strain amplitude in the notch root with the aid of an elastoplastic finite-element (FE) model showed that the work hardening related to the subsurface deformation caused by the different broaching can account for the difference in fatigue lives. Differences in initiation and growth behavior were seen for the two broached finishes as well as for broached and subsequently polished samples. These differences are discussed in terms of a change in crack growth initiation and growth mechanisms due to the presence of the work-hardened layer.     

Cyclic oxidation response of multiphase niobium-based alloys

Cyclic oxidation tests were performed on multiphase Nb-based alloys containing silicide, Laves, and Nb solid solution phases. In particular, the oxidation resistance of six alloys with various compositions (Nb, Ti, Hf, Cr, Ge, and Si) and microstructures was characterized by thermal cycling from ambient temperature to a peak temperature that ranges from 900 °C to 1400 °C. Weight change data were obtained and the corresponding spalled oxides were collected and identified by X-ray diffraction. The results indicated that Nb-based alloys formed a mixture of CrNbO₄, Nb₂O₅, and Nb₂O₅ · TiO₂, with possibly small amounts of SiO₂ or GeO₂. The oxidation resistance was improved when CrNbO₄ formed instead of Nb₂O₅ and Nb₂O₅ · TiO₂. These results were used to assess the influence of microstructure and composition on the oxidation resistance of multiphase Nb-based alloys.     

Micromechanical approach to damage mechanics of composite materials with fabric tensors

The purpose of this study is to apply continuum damage mechanics – introduced through the concept of fabric tensors – to composite materials within the framework of the theory of elasticity. A directional data model of damage mechanics for composite materials will be developed using fabric tensors. The introduction of fabric tensors into the analysis of damage of composite materials will allow for an enhanced and better understood physical meaning of damage. The micromechanical approach will be used here to relate the damage effect through fabric tensors to the behavior of composite materials. In this approach, damage mechanics is introduced separately to the constituents of the composite material through different constituents’ damage effect tensors. The damaged properties of the composite system as a whole can then be obtained by proper homogenization of the damaged properties of the constituents.

The derivation of a generalized formulation of damage evolution will be shown here in a mathematically consistent manner that is based on sound thermodynamic principles. Numerical examples will be presented to show applicability. In addition, damage evolution for the one-dimensional tension case is also illustrated.