Stabilization of nonlinear systems with uncontrollablelinearization

The problem of local stabilization of nonlinear control systems with linearizations that contain uncontrollable modes on the imaginary axis is considered. A methodology of designing a stabilizing control is investigated. It involves the following steps: (1) reduction of the stability problem to the stability of the center manifold system, (2) simplification of the vector field on the center manifold using the theory of normal forms, and (3) finding conditions under which the simplified vector field is asymptotically stable. Three cases of degeneracies in the linearized system are treated, and sufficient conditions for the existence of stabilizing controls are given in each case. A theorem is presented regarding the robustness of the above control strategies     

Feedback linearization in the presence of uncertainties

After a brief review of feedback linearization, several approaches to the problem of parametric uncertainty are outlined, and the adaptive approach to both SISO and MIMO plants is discussed in detail. Based on experience with adaptive control of linear plants, two parameter update laws are chosen for nonlinear plants according to their relative degrees. The simpler of the two adaptive laws is applicable to plants with relative degree one. For plants with higher relative degree the adaptive scheme is more complex, but a simple update law can still be employed in the special case when the state diffeomorphism, required for linearization, does not depend on uncertain parameters. The simpler adaptive scheme is shown to be robust with respect to unmodelled dynamics.     

Fatigue crack growth rates and fracture toughness of rapidly solidified Al-8.5 pct Fe-1.2 pct V-1.7 pct Si alloys

The room-temperature fatigue crack growth rates (FCGR) and fracture toughness were evaluated for different crack plane orientations of an Al-8.5 Pct Fe-1.2 Pct V-1.7 Pct Si alloy produced by planar flow casting (PFC) and atomized melt deposition (AMD) processes. For the alloy produced by the PFC process, properties were determined in six different orientations, including the short transverse directions S-T and S-L. Diffusion bonding and adhesive bonding methods were used to prepare specimens for determining FCGR and fracture toughness in the short transverse direction. Interparticle boundaries control fracture properties in the alloy produced by PFC. Fracture toughness of the PFC alloy varies from 13.4 MPa√m to 30.8 MPa√m, depending on the orientation of the crack plane relative to the interparticle boundaries. Fatigue crack growth resistance and fracture toughness are greater in the L-T, L-S, and T-S directions than in the T-L, S-T, and S-L orientations. The alloy produced by AMD does not exhibit anisotropy in fracture toughness and fatigue crack growth resistance in the as-deposited condition or in the extruded condition. The fracture toughness varies from 17.2 MPa√m to 18.5 MPa√m for the as-deposited condition and from 19.8 MPa√m to 21.0 MPa√m for the extruded condition. Fracture properties are controlled by intrinsic factors in the alloy produced by AMD. Fatigue crack growth rates of the AMD alloy are comparable to those of the PFC alloy in the L-T orientation. The crack propagation modes were studied by optical metallographic examination of crack-microstructure interactions and scanning electron microscopy of the fracture surfaces.     

Creep-fatigue life prediction of in situ composite solders

Eutectic tin-lead solder alloys subjected to cyclic loading at room temperature experience creep-fatigue interactions due to high homologous temperature. Intermetallic reinforcements of Ni₃Sn₄ and Cu₆Sn₅ are incorporated into eutectic tin-lead alloy by rapid solidification processes to formin situ composite solders. In this study, thein situ composite solders were subjected to combined creep and fatigue deformation at room temperature. Under cyclic deformation, the dominant damage mechanism ofin situ composite solders is proposed to be growth of cavities. A constrained cavity growth model is applied to predict creep-fatigue life by taking into account the tensile loading component as well as the compressive loading component when reversed processes can occur. An algorithm to calculate cavity growth in each fatigue cycle is used to predict the number of fatigue cycles to failure, based on a critical cavity size of failure. Calculated lives are compared to experimental data under several fatigue histories, which include fully reversed stress-controlled fatigue, zero-tension stress-controlled fatigue, stress-controlled fatigue with tension hold time, fully reversed strain-controlled fatigue, and zero-tension straincontrolled fatigue. The model predicts the creep-fatigue lives within a factor of 2 with the incorporation of an appropriate compressive healing factor in most cases. Discrepancy between calculated lives and experimental results is discussed. This article is based on a presentation made in the symposium entitled “Creep and Fatigue in Metal Matrix Composites” at the 1994 TMS/ASM Spring meeting, held February 28–March 3, 1994, in San Francisco, California, under the auspices of the joint TMS-SMD/ASM-MSD Composite Materials Committee.     

Numerical solution of the stability of hydromagnetic couette flow with hall currents

In the present problem, we have studied numerically the effects of Hall currents and the magnetic Prandtl number $\text{P}{}_{\mathrm{m}}$ on the stability of hydromagnetie Couette flow. In obtaining a numerical solution of the problem by Runge-Kutta-Merson method (here after will be called as RKM method), we have used the approximate solution found by modified Galerkin method as the starting solution. The accuracy of the method is tested by comparing the numerical solution with the exact solution of Chandrasekhar [1]. It is found that even though Hall currents are destabilizing for small and large $\text{P}{}_{\mathrm{m}}$, they tend to stabilize for certain intermediate values.     

Determination of velocity and pressure distribution at the core inlet of pressurized water reactors

The velocity and pressure distributions at the inlet, or bottom face, of the core for various PWR geometries have been determined theoretically. The results show that the maldistribution at the core inlet is significant and that the peak normal velocity is approximately 2.6 times the centerline velocity. When normalized using the downcomer inner radius and the core exit velocity, the maldistribution of velocity entering the core is approximately the same for all geometries, with the velocity peaking at approximately the same radial distance (0.9r₁) from the centerline of the reactor. These results are based on negligible pressure drop through the core flow channels.     

Moisture losses from perishable commodities: recent research and developments

Moisture loss from stored perishable commodities has been a subject considerable research interest in recent years, both from the standpoint of improved design of refrigerated storages and measurement of transpiration coefficients. This Paper presents a review of recent literature on the subject.     

Asymptotic unbounded root loci--Formulas and computation

We study the asymptotic behavior of the dosed loop eigenvalues (root loci) of a strictly proper linear time-invariant control system as loop gain goes toinfty. The formulas are stated in terms of the eigenvalues of nested restricted linear maps of the formA(mod S_{2})|_{S_{1}}where S1and S2are subspaces of complementary dimension. Additional geometrical insight into the formulas is obtained by mechanizing the formulas using orthogonal projections. Our method and formulas are useful in other asymptotic calculations as well, e.g., hierarchical multiple-time scales aggregation of Markov chains with some infrequent transitions.